diff --git a/gradle/wrapper/gradle-wrapper.properties b/gradle/wrapper/gradle-wrapper.properties
index e411586a54a..48c0a02ca41 100644
--- a/gradle/wrapper/gradle-wrapper.properties
+++ b/gradle/wrapper/gradle-wrapper.properties
@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-8.4-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-8.7-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelMerger.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelMerger.java
index da7e85f8a9e..313b188cb4f 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelMerger.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelMerger.java
@@ -7,7 +7,6 @@
 import java.util.Arrays;
 import java.util.List;
 
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.FormulaTermLabel;
 import de.uka.ilkd.key.logic.label.TermLabel;
@@ -22,8 +21,8 @@ public class FormulaTermLabelMerger implements TermLabelMerger {
      * {@inheritDoc}
      */
     @Override
-    public boolean mergeLabels(SequentFormula existingSF, Term existingTerm,
-            TermLabel existingLabel, SequentFormula rejectedSF, Term rejectedTerm,
+    public boolean mergeLabels(Term existingSF, Term existingTerm,
+            TermLabel existingLabel, Term rejectedSF, Term rejectedTerm,
             TermLabel rejectedLabel, List<TermLabel> mergedLabels) {
         if (existingLabel != null) {
             FormulaTermLabel fExisting = (FormulaTermLabel) existingLabel;
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelRefactoring.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelRefactoring.java
index f55f6111dcc..ed1005355a9 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelRefactoring.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelRefactoring.java
@@ -84,9 +84,9 @@ public class FormulaTermLabelRefactoring implements TermLabelRefactoring {
 
     /**
      * Key used in {@link TermLabelState} by the {@link FormulaTermLabelUpdate} to indicate that a
-     * refactoring of specified {@link SequentFormula}s ({@link RefactoringScope#SEQUENT}) is
+     * refactoring of specified {@link Term}s ({@link RefactoringScope#SEQUENT}) is
      * required, which will be performed by
-     * {@link #refactorSequentFormulas(TermLabelState, Services, Term, LabelCollection)}.
+     * {@link #refactorTerms(TermLabelState, Services, Term, LabelCollection)}.
      * <p>
      * This is for instance required if the assumes clause of a rule has a {@link FormulaTermLabel}
      * but the application does not have it. Example rules are:
@@ -95,7 +95,7 @@ public class FormulaTermLabelRefactoring implements TermLabelRefactoring {
      * </ul>
      */
     private static final String SEQUENT_FORMULA_REFACTORING_REQUIRED =
-        "sequentFormulaRefactoringRequired";
+        "TermRefactoringRequired";
 
     /**
      * {@inheritDoc}
@@ -118,7 +118,7 @@ public RefactoringScope defineRefactoringScope(TermLabelState state, Services se
             return RefactoringScope.APPLICATION_CHILDREN_AND_GRANDCHILDREN_SUBTREE_AND_PARENTS;
         } else if (isUpdateRefactoringRequired(state)) {
             return RefactoringScope.APPLICATION_BELOW_UPDATES;
-        } else if (containsSequentFormulasToRefactor(state)) {
+        } else if (containsTermsToRefactor(state)) {
             return RefactoringScope.SEQUENT;
         } else if (SyntacticalReplaceVisitor.SUBSTITUTION_WITH_LABELS_HINT.equals(hint)) {
             return RefactoringScope.APPLICATION_BELOW_UPDATES;
@@ -152,8 +152,8 @@ public void refactorLabels(TermLabelState state, Services services,
             refactorInCaseOfNewIdRequired(state, goal, term, services, labels);
         } else if (isUpdateRefactoringRequired(state)) {
             refactorBelowUpdates(applicationPosInOccurrence, term, labels);
-        } else if (containsSequentFormulasToRefactor(state)) {
-            refactorSequentFormulas(state, services, term, labels);
+        } else if (containsTermsToRefactor(state)) {
+            refactorTerms(state, services, term, labels);
         } else if (SyntacticalReplaceVisitor.SUBSTITUTION_WITH_LABELS_HINT.equals(hint)) {
             refactorSubstitution(term, tacletTerm, labels);
         }
@@ -238,7 +238,7 @@ private void refactorBelowUpdates(PosInOccurrence applicationPosInOccurrence, Te
     }
 
     /**
-     * Refactors the specified {@link SequentFormula}s.
+     * Refactors the specified {@link Term}s.
      *
      * @param state The {@link TermLabelState} of the current rule application.
      * @param services The {@link Services} used by the {@link Proof} on which a {@link Rule} is
@@ -246,10 +246,12 @@ private void refactorBelowUpdates(PosInOccurrence applicationPosInOccurrence, Te
      * @param term The {@link Term} which is now refactored.
      * @param labels The new labels the {@link Term} will have after the refactoring.
      */
-    private void refactorSequentFormulas(TermLabelState state, Services services, final Term term,
+    private void refactorTerms(TermLabelState state, Services services, final Term term,
             LabelCollection labels) {
-        Set<SequentFormula> sequentFormulas = getSequentFormulasToRefactor(state);
-        if (CollectionUtil.search(sequentFormulas, element -> element.formula() == term) != null) {
+        Set<Term> Terms = getTermsToRefactor(state);
+        if (CollectionUtil.search(Terms, element -> {
+            return element == term;
+        }) != null) {
             FormulaTermLabel termLabel = (FormulaTermLabel) term.getLabel(FormulaTermLabel.NAME);
             if (termLabel != null) {
                 labels.remove(termLabel);
@@ -373,45 +375,45 @@ public static void setParentRefactoringRequired(TermLabelState state, boolean re
     }
 
     /**
-     * Checks if {@link SequentFormula}s to refactor are specified.
+     * Checks if {@link Term}s to refactor are specified.
      *
      * @param state The {@link TermLabelState} to read from.
-     * @return {@code true} at least one {@link SequentFormula} needs to be refactored,
+     * @return {@code true} at least one {@link Term} needs to be refactored,
      *         {@code false} refactoring is not required.
      */
-    public static boolean containsSequentFormulasToRefactor(TermLabelState state) {
+    public static boolean containsTermsToRefactor(TermLabelState state) {
         Map<Object, Object> labelState = state.getLabelState(FormulaTermLabel.NAME);
         @SuppressWarnings("unchecked")
-        Set<SequentFormula> sfSet =
-            (Set<SequentFormula>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
+        Set<Term> sfSet =
+            (Set<Term>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
         return sfSet != null && !sfSet.isEmpty();
     }
 
     /**
-     * Returns the {@link SequentFormula}s to refactor.
+     * Returns the {@link Term}s to refactor.
      *
      * @param state The {@link TermLabelState} to read from.
-     * @return The {@link SequentFormula}s to refactor.
+     * @return The {@link Term}s to refactor.
      */
-    public static Set<SequentFormula> getSequentFormulasToRefactor(TermLabelState state) {
+    public static Set<Term> getTermsToRefactor(TermLabelState state) {
         Map<Object, Object> labelState = state.getLabelState(FormulaTermLabel.NAME);
         @SuppressWarnings("unchecked")
-        Set<SequentFormula> sfSet =
-            (Set<SequentFormula>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
+        Set<Term> sfSet =
+            (Set<Term>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
         return sfSet;
     }
 
     /**
-     * Adds the given {@link SequentFormula} for refactoring purpose.
+     * Adds the given {@link Term} for refactoring purpose.
      *
      * @param state The {@link TermLabelState} to modify.
-     * @param sf The {@link SequentFormula} to add.
+     * @param sf The {@link Term} to add.
      */
-    public static void addSequentFormulaToRefactor(TermLabelState state, SequentFormula sf) {
+    public static void addTermToRefactor(TermLabelState state, Term sf) {
         Map<Object, Object> labelState = state.getLabelState(FormulaTermLabel.NAME);
         @SuppressWarnings("unchecked")
-        Set<SequentFormula> sfSet =
-            (Set<SequentFormula>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
+        Set<Term> sfSet =
+            (Set<Term>) labelState.get(SEQUENT_FORMULA_REFACTORING_REQUIRED);
         if (sfSet == null) {
             sfSet = new LinkedHashSet<>();
             labelState.put(SEQUENT_FORMULA_REFACTORING_REQUIRED, sfSet);
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelUpdate.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelUpdate.java
index 2ae4dbc912d..ac55939d736 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelUpdate.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/FormulaTermLabelUpdate.java
@@ -72,11 +72,12 @@ public void updateLabels(TermLabelState state, Services services,
         }
         if (ruleApp instanceof TacletApp ta) {
             if (ta.ifInstsComplete() && ta.ifFormulaInstantiations() != null) {
-                Map<SequentFormula, FormulaTermLabel> ifLabels =
+                Map<Term, FormulaTermLabel> ifLabels =
                     new LinkedHashMap<>();
                 for (IfFormulaInstantiation ifInst : ta.ifFormulaInstantiations()) {
+                    final Term assumesFml = ifInst.getConstrainedFormula();
                     FormulaTermLabel ifLabel = StayOnFormulaTermLabelPolicy.searchFormulaTermLabel(
-                        ifInst.getConstrainedFormula().formula().getLabels());
+                        assumesFml.getLabels());
                     if (ifLabel != null) {
                         ifLabels.put(ifInst.getConstrainedFormula(), ifLabel);
                     }
@@ -85,14 +86,14 @@ public void updateLabels(TermLabelState state, Services services,
                     if (TruthValueTracingUtil.isLogicOperator(newTerm.op(), newTerm.subs())
                     // || TruthValueEvaluationUtil.isPredicate(newTermOp)
                     ) {
-                        for (Entry<SequentFormula, FormulaTermLabel> ifEntry : ifLabels
+                        for (Entry<Term, FormulaTermLabel> ifEntry : ifLabels
                                 .entrySet()) {
                             FormulaTermLabel ifLabel = ifEntry.getValue();
                             int labelSubID = FormulaTermLabel.newLabelSubID(services, ifLabel);
                             FormulaTermLabel newLabel = new FormulaTermLabel(ifLabel.getMajorId(),
                                 labelSubID, Collections.singletonList(ifLabel.getId()));
                             labels.add(newLabel);
-                            FormulaTermLabelRefactoring.addSequentFormulaToRefactor(state,
+                            FormulaTermLabelRefactoring.addTermToRefactor(state,
                                 ifEntry.getKey());
                         }
                     }
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/StayOnFormulaTermLabelPolicy.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/StayOnFormulaTermLabelPolicy.java
index 7d2ea52c692..98360e9fe59 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/StayOnFormulaTermLabelPolicy.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/rule/label/StayOnFormulaTermLabelPolicy.java
@@ -69,8 +69,8 @@ public TermLabel keepLabel(TermLabelState state, Services services,
                         originalLabelIds.add(mostImportantLabel.getId());
                     }
                 }
-                if (tacletHint.getSequentFormula() != null) {
-                    if (!TruthValueTracingUtil.isPredicate(tacletHint.getSequentFormula())) {
+                if (tacletHint.getTerm() != null) {
+                    if (!TruthValueTracingUtil.isPredicate(tacletHint.getTerm())) {
                         newLabelIdRequired = true;
                     }
                 } else if (tacletHint.getTerm() != null) {
@@ -164,10 +164,6 @@ public static FormulaTermLabel searchFormulaTermLabel(ImmutableArray<TermLabel>
      * @return {@code true} is top level, {@code false} is not top level.
      */
     protected boolean isTopLevel(TacletLabelHint tacletHint, Term tacletTerm) {
-        if (TacletOperation.REPLACE_TERM.equals(tacletHint.getTacletOperation())) {
-            return tacletHint.getTerm() == tacletTerm;
-        } else {
-            return tacletHint.getSequentFormula().formula() == tacletTerm;
-        }
+        return tacletHint.getTerm() == tacletTerm;
     }
 }
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/AbstractUpdateExtractor.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/AbstractUpdateExtractor.java
index e04c2be2a75..830214147aa 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/AbstractUpdateExtractor.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/AbstractUpdateExtractor.java
@@ -152,8 +152,8 @@ protected Set<Term> computeInitialObjectsToIgnore(boolean ignoreExceptionVariabl
             // Add initial updates which are used as backup of the heap and method arguments. They
             // are not part of the source code and should be ignored.
             Sequent sequent = getRoot().sequent();
-            for (SequentFormula sf : sequent.succedent()) {
-                Term term = sf.formula();
+            for (Term sf : sequent.succedent()) {
+                Term term = sf;
                 if (Junctor.IMP.equals(term.op())) {
                     fillInitialObjectsToIgnoreRecursively(term.sub(1), result);
                 }
@@ -434,9 +434,9 @@ protected boolean hasFreeVariables(Term term) {
     protected Set<ExtractLocationParameter> extractLocationsFromSequent(Sequent sequent,
             Set<Term> objectsToIgnore) throws ProofInputException {
         Set<ExtractLocationParameter> result = new LinkedHashSet<>();
-        for (SequentFormula sf : sequent) {
+        for (Term sf : sequent) {
             result.addAll(extractLocationsFromTerm(
-                OriginTermLabel.removeOriginLabels(sf.formula(), getServices()), objectsToIgnore));
+                OriginTermLabel.removeOriginLabels(sf, getServices()), objectsToIgnore));
         }
         return result;
     }
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicExecutionTreeBuilder.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicExecutionTreeBuilder.java
index 35e6ea1b81d..2f96a4927a4 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicExecutionTreeBuilder.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicExecutionTreeBuilder.java
@@ -249,8 +249,8 @@ public SymbolicExecutionTreeBuilder(Proof proof, boolean mergeBranchConditions,
     protected void initMethodCallStack(final Node root, Services services) {
         // Find all modalities in the succedent
         final List<Term> modalityTerms = new LinkedList<>();
-        for (SequentFormula sequentFormula : root.sequent().succedent()) {
-            sequentFormula.formula().execPreOrder(new DefaultVisitor() {
+        for (Term succFml : root.sequent().succedent()) {
+            succFml.execPreOrder(new DefaultVisitor() {
                 @Override
                 public void visit(Term visited) {
                     if (visited.op() instanceof Modality
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicLayoutExtractor.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicLayoutExtractor.java
index 7d849a0530f..8cd7cd1c19b 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicLayoutExtractor.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/SymbolicLayoutExtractor.java
@@ -309,7 +309,7 @@ protected ImmutableList<Term> extractInitialUpdates() {
         Sequent sequent = getRoot().sequent();
         assert sequent.antecedent().isEmpty();
         assert sequent.succedent().size() == 1;
-        Term sf = sequent.succedent().get(0).formula();
+        final Term sf = sequent.succedent().get(0);
         assert sf.op() == Junctor.IMP;
         Term modality = sf.sub(1);
         return TermBuilder.goBelowUpdates2(modality).first;
@@ -680,9 +680,9 @@ protected Set<ExtractLocationParameter> updateLocationsAccordingtoEquivalentClas
     protected Set<Term> collectObjectsFromSequent(Sequent sequent, Set<Term> objectsToIgnore)
             throws ProofInputException {
         Set<Term> result = new LinkedHashSet<>();
-        for (SequentFormula sf : sequent) {
+        for (Term sf : sequent) {
             if (SymbolicExecutionUtil.checkSkolemEquality(sf) == 0) {
-                result.addAll(collectSymbolicObjectsFromTerm(sf.formula(), objectsToIgnore));
+                result.addAll(collectSymbolicObjectsFromTerm(sf, objectsToIgnore));
             }
         }
         return result;
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/TruthValueTracingUtil.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/TruthValueTracingUtil.java
index d4a12b894c9..bafe6a9a052 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/TruthValueTracingUtil.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/TruthValueTracingUtil.java
@@ -16,7 +16,6 @@
 import de.uka.ilkd.key.logic.DefaultVisitor;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.label.FormulaTermLabel;
@@ -59,16 +58,6 @@ public final class TruthValueTracingUtil {
     private TruthValueTracingUtil() {
     }
 
-    /**
-     * Checks if the given {@link SequentFormula} is a predicate.
-     *
-     * @param sequentFormula The {@link SequentFormula} to check.
-     * @return {@code true} is predicate, {@code false} is something else.
-     */
-    public static boolean isPredicate(SequentFormula sequentFormula) {
-        return sequentFormula != null && isPredicate(sequentFormula.formula());
-    }
-
     /**
      * Checks if the given {@link Term} is a predicate.
      *
@@ -342,8 +331,8 @@ private static List<LabelOccurrence> findInvolvedLabels(
             if (tacletApp.ifInstsComplete() && tacletApp.ifFormulaInstantiations() != null) {
                 for (IfFormulaInstantiation ifInst : tacletApp.ifFormulaInstantiations()) {
                     assert ifInst instanceof IfFormulaInstSeq;
-                    Term term = ifInst.getConstrainedFormula().formula();
-                    TermLabel label = term.getLabel(termLabelName);
+                    final Term assumesFml = ifInst.getConstrainedFormula();
+                    TermLabel label = assumesFml.getLabel(termLabelName);
                     if (label instanceof FormulaTermLabel) {
                         result.add(new LabelOccurrence((FormulaTermLabel) label,
                             ((IfFormulaInstSeq) ifInst).inAntec()));
@@ -451,7 +440,7 @@ private static void updatePredicateResultBasedOnNewMinorIdsOSS(
             parentPio.subTerm().execPreOrder(new DefaultVisitor() {
                 @Override
                 public void visit(Term visited) {
-                    checkForNewMinorIdsOSS(childPio.sequentFormula(), visited, termLabelName,
+                    checkForNewMinorIdsOSS(childPio.sequentLevelFormula(), visited, termLabelName,
                         parentPio, tb, results);
                 }
             });
@@ -459,7 +448,7 @@ public void visit(Term visited) {
             PosInOccurrence currentPio = parentPio;
             while (!currentPio.isTopLevel()) {
                 currentPio = currentPio.up();
-                checkForNewMinorIdsOSS(childPio.sequentFormula(), currentPio.subTerm(),
+                checkForNewMinorIdsOSS(childPio.sequentLevelFormula(), currentPio.subTerm(),
                     termLabelName, parentPio, tb, results);
             }
         }
@@ -468,7 +457,7 @@ public void visit(Term visited) {
     /**
      * Checks if new minor IDs are available in case of {@link OneStepSimplifier} usage.
      *
-     * @param onlyChangedChildSF The only changed {@link SequentFormula} in the child {@link Node}.
+     * @param onlyChangedChildSF The only changed {@link Term} in the child {@link Node}.
      * @param term The {@link Term} contained in the child {@link Node} to check.
      * @param termLabelName The name of the {@link TermLabel} which is added to predicates.
      * @param parentPio The {@link PosInOccurrence} of the applied rule of the parent {@link Node}.
@@ -476,7 +465,7 @@ public void visit(Term visited) {
      * @param results The {@link Map} with all available {@link MultiEvaluationResult}s.
      */
     private static void checkForNewMinorIdsOSS(
-            SequentFormula onlyChangedChildSF, Term term,
+            Term onlyChangedChildSF, Term term,
             Name termLabelName, PosInOccurrence parentPio, TermBuilder tb,
             Map<String, MultiEvaluationResult> results) {
         TermLabel label = term.getLabel(termLabelName);
@@ -492,7 +481,7 @@ private static void checkForNewMinorIdsOSS(
     /**
      * Checks if new minor IDs are available in case of {@link OneStepSimplifier} usage.
      *
-     * @param onlyChangedChildSF The only changed {@link SequentFormula} in the child {@link Node}.
+     * @param onlyChangedChildSF The only changed {@link Term} in the child {@link Node}.
      * @param label The {@link FormulaTermLabel} of interest.
      * @param antecedentRuleApplication {@code true} rule applied on antecedent, {@code false} rule
      *        applied on succedent.
@@ -500,7 +489,7 @@ private static void checkForNewMinorIdsOSS(
      * @return The computed instruction {@link Term} or {@code null} if not available.
      */
     private static Term checkForNewMinorIdsOSS(
-            SequentFormula onlyChangedChildSF,
+            Term onlyChangedChildSF,
             FormulaTermLabel label, boolean antecedentRuleApplication, TermBuilder tb) {
         // Search replacements
         List<Term> antecedentReplacements = new LinkedList<>();
@@ -553,7 +542,7 @@ public void visit(Term visited) {
                 if (parentRuleApp instanceof TacletApp ta) {
                     if (ta.ifInstsComplete() && ta.ifFormulaInstantiations() != null) {
                         for (IfFormulaInstantiation ifInst : ta.ifFormulaInstantiations()) {
-                            checkForNewMinorIds(childNode, ifInst.getConstrainedFormula().formula(),
+                            checkForNewMinorIds(childNode, ifInst.getConstrainedFormula(),
                                 termLabelName, parentPio, tb, results);
                         }
                     }
@@ -601,10 +590,10 @@ private static Term checkForNewMinorIds(
         // Search replacements
         List<Term> antecedentReplacements = new LinkedList<>();
         List<Term> succedentReplacements = new LinkedList<>();
-        for (SequentFormula sf : childNode.sequent().antecedent()) {
+        for (Term sf : childNode.sequent().antecedent()) {
             listLabelReplacements(sf, label.name(), label.getId(), antecedentReplacements);
         }
-        for (SequentFormula sf : childNode.sequent().succedent()) {
+        for (Term sf : childNode.sequent().succedent()) {
             listLabelReplacements(sf, label.name(), label.getId(), succedentReplacements);
         }
         // Compute term
@@ -613,17 +602,17 @@ private static Term checkForNewMinorIds(
     }
 
     /**
-     * Lists all label replacements in the given {@link SequentFormula}.
+     * Lists all label replacements in the given {@link Term}.
      *
-     * @param sf The {@link SequentFormula} to analyze.
+     * @param sf The {@link Term} to analyze.
      * @param labelName The name of the {@link TermLabel} which is added to predicates.
      * @param labelId The label ID of interest.
      * @param resultToFill The result {@link List} to fill.
      */
     private static void listLabelReplacements(
-            final SequentFormula sf, final Name labelName,
+            final Term sf, final Name labelName,
             final String labelId, final List<Term> resultToFill) {
-        sf.formula().execPreOrder(new DefaultVisitor() {
+        sf.execPreOrder(new DefaultVisitor() {
             @Override
             public boolean visitSubtree(Term visited) {
                 return !hasLabelOfInterest(visited);
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/AbstractExecutionMethodReturn.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/AbstractExecutionMethodReturn.java
index d74bfb41cd4..b757d6c6f08 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/AbstractExecutionMethodReturn.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/AbstractExecutionMethodReturn.java
@@ -9,7 +9,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.SourceElement;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
 import de.uka.ilkd.key.proof.Node;
@@ -180,11 +179,11 @@ protected IExecutionVariable[] lazyComputeCallStateVariables() throws ProofInput
         assert proofNode.childrenCount() == 1;
         PosInOccurrence originalPIO = methodCall.getModalityPIO();
         int index = originalPIO.isInAntec()
-                ? proofNode.sequent().antecedent().indexOf(originalPIO.sequentFormula())
-                : proofNode.sequent().succedent().indexOf(originalPIO.sequentFormula());
+                ? proofNode.sequent().antecedent().indexOf(originalPIO.sequentLevelFormula())
+                : proofNode.sequent().succedent().indexOf(originalPIO.sequentLevelFormula());
         // Search relevant position in child node
         Node childNode = proofNode.child(0);
-        SequentFormula nodeSF =
+        Term nodeSF =
             originalPIO.isInAntec() ? childNode.sequent().antecedent().get(index)
                     : childNode.sequent().succedent().get(index);
         PosInOccurrence modalityPIO =
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/ExecutionAuxiliaryContract.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/ExecutionAuxiliaryContract.java
index 293a231f50f..2e06327f513 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/ExecutionAuxiliaryContract.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/model/impl/ExecutionAuxiliaryContract.java
@@ -88,7 +88,7 @@ protected String lazyComputeName() throws ProofInputException {
         assert "Usage".equals(usageNode.getNodeInfo().getBranchLabel())
                 : "Block Contract Rule has changed.";
         Term usagePrecondition = usageNode.sequent().antecedent()
-                .get(usageNode.sequent().antecedent().size() - 1).formula();
+                .get(usageNode.sequent().antecedent().size() - 1);
         // Find remembrance heaps and local variables
         while (applicationTerm.op() == UpdateApplication.UPDATE_APPLICATION) {
             assert applicationTerm.sub(0) == usagePrecondition.sub(0)
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/AbstractSideProofRule.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/AbstractSideProofRule.java
index b4f25f305e1..b3f5c71b399 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/AbstractSideProofRule.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/AbstractSideProofRule.java
@@ -14,7 +14,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.PosInTerm;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.JFunction;
 import de.uka.ilkd.key.proof.Goal;
@@ -103,12 +102,12 @@ protected List<Triple<Term, Set<Term>, Node>> computeResultsAndConditions(Servic
      *
      * @param pio The {@link PosInOccurrence} which defines the {@link Term} to replace.
      * @param newTerm The new {@link Term}.
-     * @return The created {@link SequentFormula} in which the {@link Term} is replaced.
+     * @return The created {@link Term} in which the {@link Term} is replaced.
      */
-    protected static SequentFormula replace(PosInOccurrence pio, Term newTerm, Services services) {
+    protected static Term replace(PosInOccurrence pio, Term newTerm, Services services) {
         // Iterate along the PosInOccurrence and collect the parents and indices
         Deque<Pair<Integer, Term>> indexAndParents = new LinkedList<>();
-        Term root = pio.sequentFormula().formula();
+        Term root = pio.sequentLevelFormula();
         final PosInTerm pit = pio.posInTerm();
         for (int i = 0, sz = pit.depth(); i < sz; i++) {
             int next = pit.getIndexAt(i);
@@ -124,7 +123,7 @@ protected static SequentFormula replace(PosInOccurrence pio, Term newTerm, Servi
             root = services.getTermFactory().createTerm(parent.op(), newSubs, parent.boundVars(),
                 parent.getLabels());
         }
-        return new SequentFormula(root);
+        return root;
     }
 
     /**
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/ModalitySideProofRule.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/ModalitySideProofRule.java
index 6c1fc13fb94..cef7f53abd2 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/ModalitySideProofRule.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/ModalitySideProofRule.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -39,7 +38,7 @@
  * A {@link BuiltInRule} which evaluates a modality in a side proof.
  * </p>
  * <p>
- * This rule is applicable on top level terms ({@link SequentFormula}) of the form.
+ * This rule is applicable on top level terms ({@link Term}) of the form.
  * <ul>
  * <li>{@code {...}\[...\](<something> = <var>)} or</li>
  * <li>{@code {...}\<...\>(<something> = <var>)} or</li>
@@ -49,8 +48,8 @@
  * The leading updates are optional and any {@link Modality} is supported.
  * </p>
  * <p>
- * The original {@link SequentFormula} which contains the equality is always removed in the
- * following {@link Goal}. For each possible result value is a {@link SequentFormula} added to the
+ * The original {@link Term} which contains the equality is always removed in the
+ * following {@link Goal}. For each possible result value is a {@link Term} added to the
  * {@link Sequent} of the form:
  * <ul>
  * <li>Antecedent: {@code <resultCondition> -> <something> = <result>} or</li>
@@ -169,7 +168,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                     .cloneProofEnvironmentWithOwnOneStepSimplifier(goal.proof(), true);
             final Services sideProofServices = sideProofEnv.getServicesForEnvironment();
             Sequent sequentToProve = SymbolicExecutionSideProofUtil
-                    .computeGeneralSequentToProve(goal.sequent(), pio.sequentFormula());
+                    .computeGeneralSequentToProve(goal.sequent(), pio.sequentLevelFormula());
             JFunction newPredicate = createResultFunction(sideProofServices, varTerm.sort());
             final TermBuilder tb = sideProofServices.getTermBuilder();
             Term newTerm = tb.func(newPredicate, varTerm);
@@ -178,7 +177,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                 modalityTerm.getLabels());
             Term newModalityWithUpdatesTerm = tb.applySequential(updates, newModalityTerm);
             sequentToProve = sequentToProve
-                    .addFormula(new SequentFormula(newModalityWithUpdatesTerm), false, false)
+                    .addFormula(newModalityWithUpdatesTerm, false, false)
                     .sequent();
             // Compute results and their conditions
             List<Triple<Term, Set<Term>, Node>> conditionsAndResultsMap =
@@ -207,12 +206,12 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                 }
                 Term newImplication = tb.imp(newCondition, modalityTerm.sub(0).sub(1));
                 Term newImplicationWithUpdates = tb.applySequential(updates, newImplication);
-                resultGoal.addFormula(new SequentFormula(newImplicationWithUpdates),
+                resultGoal.addFormula(newImplicationWithUpdates,
                     pio.isInAntec(), false);
             } else {
                 // Add result directly as new top level formula
                 for (Term result : resultTerms) {
-                    resultGoal.addFormula(new SequentFormula(result), pio.isInAntec(), false);
+                    resultGoal.addFormula(result, pio.isInAntec(), false);
                 }
             }
             return goals;
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/QuerySideProofRule.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/QuerySideProofRule.java
index 2f00a4a8941..1ec20e96789 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/QuerySideProofRule.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/rule/QuerySideProofRule.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.logic.PIOPathIterator;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -45,12 +44,12 @@
  * </ul>
  * </p>
  * <p>
- * The original {@link SequentFormula} which contains the equality is always removed in the
+ * The original {@link Term} which contains the equality is always removed in the
  * following {@link Goal}. How the result of the query computed in the side proof is represented
  * depends on the occurrence of the equality:
  * <ol>
  * <li><b>top level {@code <something> = <query>} or {@code <query> = <something>}</b><br>
- * For each possible result value is a {@link SequentFormula} added to the {@link Sequent} of the
+ * For each possible result value is a {@link Term} added to the {@link Sequent} of the
  * form:
  * <ul>
  * <li>Antecedent: {@code <resultCondition> -> <something> = <result>} or</li>
@@ -62,7 +61,7 @@
  * <li><b>right side of an implication on top level
  * {@code <queryCondition> -> <something> = <query>} or
  * {@code <queryCondition> -> <query> = <something>}</b><br>
- * For each possible result value is a {@link SequentFormula} added to the {@link Sequent} of the
+ * For each possible result value is a {@link Term} added to the {@link Sequent} of the
  * form:
  * <ul>
  * <li>Antecedent: {@code
@@ -93,9 +92,9 @@
  * </li>
  * <li><b>everywhere else {@code ...(<something> = <query>)...} or
  * {@code ...(<query> = <something>)...}</b><br>
- * In the original {@link SequentFormula} is the {@code <query>} replaced by a new constant function
+ * In the original {@link Term} is the {@code <query>} replaced by a new constant function
  * named {@code QueryResult} and added to the antecedent/succedent in which it was contained before.
- * For each possible result value is an additional {@link SequentFormula} added to the
+ * For each possible result value is an additional {@link Term} added to the
  * <b>antecedent</b> of the form:
  * <ul>
  * <li>{@code <resultCondition> -> QueryResult = <result>} or</li>
@@ -196,7 +195,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
             // Extract required Terms from goal
             PosInOccurrence pio = ruleApp.posInOccurrence();
             Sequent goalSequent = goal.sequent();
-            SequentFormula equalitySF = pio.sequentFormula();
+            Term equalitySF = pio.sequentLevelFormula();
             Term equalityTerm = pio.subTerm();
             Term queryTerm;
             Term varTerm;
@@ -211,9 +210,10 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                 varFirst = false;
             }
             Term queryConditionTerm = null;
-            if (equalitySF.formula().op() == Junctor.IMP
-                    && equalitySF.formula().sub(1) == equalityTerm) {
-                queryConditionTerm = equalitySF.formula().sub(0);
+            if (equalitySF.op() == Junctor.IMP) {
+                if (equalitySF.sub(1) == equalityTerm) {
+                    queryConditionTerm = equalitySF.sub(0);
+                }
             }
             // Compute sequent for side proof to compute query in.
             // New OneStepSimplifier is required because it has an internal state and the default
@@ -226,7 +226,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
             JFunction newPredicate = createResultFunction(sideProofServices, queryTerm.sort());
             Term newTerm = sideProofServices.getTermBuilder().func(newPredicate, queryTerm);
             sequentToProve =
-                sequentToProve.addFormula(new SequentFormula(newTerm), false, false).sequent();
+                sequentToProve.addFormula(newTerm, false, false).sequent();
             // Compute results and their conditions
             List<Triple<Term, Set<Term>, Node>> conditionsAndResultsMap =
                 computeResultsAndConditions(services, goal, sideProofEnv, sequentToProve,
@@ -246,7 +246,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                     if (queryConditionTerm != null) {
                         resultTerm = tb.imp(queryConditionTerm, resultTerm);
                     }
-                    resultGoal.addFormula(new SequentFormula(resultTerm), pio.isInAntec(), false);
+                    resultGoal.addFormula(resultTerm, pio.isInAntec(), false);
                 }
             } else {
                 JFunction resultFunction = createResultConstant(services, varTerm.sort());
@@ -261,7 +261,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence pos, TermServices services) {
                     Term resultTerm = tb.imp(conditionTerm,
                         varFirst ? tb.equals(resultFunctionTerm, conditionsAndResult.first)
                                 : tb.equals(conditionsAndResult.first, resultFunctionTerm));
-                    resultGoal.addFormula(new SequentFormula(resultTerm), true, false);
+                    resultGoal.addFormula(resultTerm, true, false);
                 }
             }
             return goals;
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/slicing/AbstractSlicer.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/slicing/AbstractSlicer.java
index 56ead50dddb..d875fafffd6 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/slicing/AbstractSlicer.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/slicing/AbstractSlicer.java
@@ -69,7 +69,7 @@ public ImmutableArray<Node> slice(Node seedNode, ReferencePrefix seedLocation,
             ImmutableList<ISymbolicEquivalenceClass> sec) throws ProofInputException {
         // Solve this reference
         PosInOccurrence pio = seedNode.getAppliedRuleApp().posInOccurrence();
-        Term topLevel = pio.sequentFormula().formula();
+        Term topLevel = pio.sequentLevelFormula();
         Term modalityTerm = TermBuilder.goBelowUpdates(topLevel);
         Services services = seedNode.proof().getServices();
         ExecutionContext ec =
@@ -209,7 +209,7 @@ public ReferencePrefix getThisReference() {
      */
     protected SequentInfo analyzeSequent(Node node, ImmutableList<ISymbolicEquivalenceClass> sec) {
         PosInOccurrence pio = node.getAppliedRuleApp().posInOccurrence();
-        Term topLevel = pio.sequentFormula().formula();
+        Term topLevel = pio.sequentLevelFormula();
         Pair<ImmutableList<Term>, Term> pair = TermBuilder.goBelowUpdates2(topLevel);
         Term modalityTerm = pair.second;
         SymbolicExecutionTermLabel label =
@@ -283,14 +283,14 @@ protected void analyzeEquivalenceClasses(Services services,
      */
     protected void analyzeSequent(Services services, Sequent sequent,
             Map<Location, SortedSet<Location>> aliases, ReferencePrefix thisReference) {
-        for (SequentFormula sf : sequent.antecedent()) {
-            Term term = sf.formula();
+        for (Term sf : sequent.antecedent()) {
+            Term term = sf;
             if (Equality.EQUALS == term.op()) {
                 analyzeEquality(services, term, aliases, thisReference);
             }
         }
-        for (SequentFormula sf : sequent.succedent()) {
-            Term term = sf.formula();
+        for (Term sf : sequent.succedent()) {
+            Term term = sf;
             if (Junctor.NOT == term.op()) {
                 Term negatedTerm = term.sub(0);
                 if (Equality.EQUALS == negatedTerm.op()) {
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsFeature.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsFeature.java
index b82c837cd0c..20904e34173 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsFeature.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsFeature.java
@@ -7,7 +7,6 @@
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.Equality;
 import de.uka.ilkd.key.logic.op.Junctor;
@@ -27,7 +26,7 @@
  * <p>
  * This means the cut is only applied if the cut formula is not an equality or if it is not a
  * negated formula or if the (negated) equality is not contained as top term
- * ({@link SequentFormula}) in the {@link Sequent} ignoring the order of the equality children.
+ * ({@link Term}) in the {@link Sequent} ignoring the order of the equality children.
  * </p>
  *
  * @author Martin Hentschel
@@ -49,9 +48,9 @@ protected boolean filter(RuleApp app, PosInOccurrence pos, Goal goal, MutableSta
                 Term cutFormulaC0 = cutFormula.sub(0);
                 Term cutFormulaC1 = cutFormula.sub(1);
                 boolean contains = false;
-                Iterator<SequentFormula> iter = goal.sequent().iterator();
+                Iterator<Term> iter = goal.sequent().iterator();
                 while (!contains && iter.hasNext()) {
-                    Term formula = iter.next().formula();
+                    Term formula = iter.next();
                     if (formula.op() == Junctor.NOT) {
                         formula = formula.sub(0);
                     }
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsTermGenerator.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsTermGenerator.java
index db00d1469bf..b06a9f7f4a8 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsTermGenerator.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/CutHeapObjectsTermGenerator.java
@@ -12,7 +12,6 @@
 import de.uka.ilkd.key.logic.DefaultVisitor;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.JFunction;
 import de.uka.ilkd.key.proof.Goal;
@@ -38,13 +37,13 @@ public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
         // Compute collect terms of sequent formulas
         Sequent sequent = goal.sequent();
         Set<Term> topTerms = new LinkedHashSet<>();
-        for (SequentFormula sf : sequent) {
-            topTerms.add(sf.formula());
+        for (Term sf : sequent) {
+            topTerms.add(sf);
         }
         // Compute equality terms
         HeapLDT heapLDT = goal.node().proof().getServices().getTypeConverter().getHeapLDT();
         Set<Term> equalityTerms = new LinkedHashSet<>();
-        for (SequentFormula sf : sequent) {
+        for (Term sf : sequent) {
             collectEqualityTerms(sf, equalityTerms, topTerms, heapLDT,
                 goal.node().proof().getServices());
         }
@@ -52,19 +51,19 @@ public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
     }
 
     /**
-     * Computes all possible equality terms between objects in the given {@link SequentFormula}.
+     * Computes all possible equality terms between objects in the given {@link Term}.
      *
-     * @param sf The {@link SequentFormula} to work with.
+     * @param sf The {@link Term} to work with.
      * @param equalityTerms The result {@link Set} with the equality {@link Term}s to fill.
      * @param topTerms The terms of all sequent formulas
      * @param heapLDT The {@link HeapLDT} to use.
      * @param services TODO
      */
-    protected void collectEqualityTerms(SequentFormula sf, Set<Term> equalityTerms,
+    protected void collectEqualityTerms(Term sf, Set<Term> equalityTerms,
             Set<Term> topTerms, HeapLDT heapLDT, Services services) {
         // Collect objects (target of store operations on heap)
         Set<Term> storeLocations = new LinkedHashSet<>();
-        collectStoreLocations(sf.formula(), storeLocations, heapLDT);
+        collectStoreLocations(sf, storeLocations, heapLDT);
         // Check if equality checks are possible
         if (storeLocations.size() >= 2) {
             // Generate all possible equality checks
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/SimplifyTermStrategy.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/SimplifyTermStrategy.java
index a6594e4e05b..ceeb80aa40f 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/SimplifyTermStrategy.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/SimplifyTermStrategy.java
@@ -60,7 +60,7 @@ protected Feature setupApprovalF() {
                     TacletApp ta = (TacletApp) app;
                     if (ta.ifFormulaInstantiations() != null) {
                         for (IfFormulaInstantiation ifi : ta.ifFormulaInstantiations()) {
-                            if (ifi.getConstrainedFormula().formula()
+                            if (ifi.getConstrainedFormula()
                                     .containsLabel(SymbolicExecutionUtil.RESULT_LABEL)) {
                                 hasLabel = true;
                             }
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/breakpoint/AbstractConditionalBreakpoint.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/breakpoint/AbstractConditionalBreakpoint.java
index c6084f2b8fb..d997436ad8e 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/breakpoint/AbstractConditionalBreakpoint.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/strategy/breakpoint/AbstractConditionalBreakpoint.java
@@ -32,6 +32,7 @@
 import de.uka.ilkd.key.symbolic_execution.util.SymbolicExecutionSideProofUtil;
 import de.uka.ilkd.key.symbolic_execution.util.SymbolicExecutionUtil;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
 
@@ -76,7 +77,7 @@ public abstract class AbstractConditionalBreakpoint extends AbstractHitCountBrea
      * A {@link Map} mapping from relevant variables for the condition to their runtime equivalent
      * in KeY
      */
-    private Map<SVSubstitute, SVSubstitute> variableNamingMap;
+    private Map<SyntaxElement, SyntaxElement> variableNamingMap;
 
     /**
      * The list of parameter variables of the method that contains the associated breakpoint
@@ -162,14 +163,14 @@ private void putValuesFromGlobalVars(ProgramVariable varForCondition, Node node,
      *
      * @return the cloned map
      */
-    private Map<SVSubstitute, SVSubstitute> getOldMap() {
-        Map<SVSubstitute, SVSubstitute> oldMap = new HashMap<>();
-        for (Entry<SVSubstitute, SVSubstitute> svSubstituteSVSubstituteEntry : getVariableNamingMap()
+    private Map<SyntaxElement, SyntaxElement> getOldMap() {
+        Map<SyntaxElement, SyntaxElement> oldMap = new HashMap<>();
+        for (Entry<SyntaxElement, SyntaxElement> svSubstituteSVSubstituteEntry : getVariableNamingMap()
                 .entrySet()) {
             Entry<?, ?> oldEntry = svSubstituteSVSubstituteEntry;
-            if (oldEntry.getKey() instanceof SVSubstitute
-                    && oldEntry.getValue() instanceof SVSubstitute) {
-                oldMap.put((SVSubstitute) oldEntry.getKey(), (SVSubstitute) oldEntry.getValue());
+            if (oldEntry.getKey() instanceof SyntaxElement
+                    && oldEntry.getValue() instanceof SyntaxElement) {
+                oldMap.put((SyntaxElement) oldEntry.getKey(), (SyntaxElement) oldEntry.getValue());
             }
         }
         return oldMap;
@@ -200,7 +201,7 @@ private void freeVariablesAfterReturn(Node node, RuleApp ruleApp, boolean inScop
      * @param oldMap the oldMap variableNamings
      */
     private void putValuesFromRenamings(ProgramVariable varForCondition, Node node, boolean inScope,
-            Map<SVSubstitute, SVSubstitute> oldMap, RuleApp ruleApp) {
+            Map<SyntaxElement, SyntaxElement> oldMap, RuleApp ruleApp) {
         // look for renamings KeY did
         boolean found = false;
         // get current renaming tables
@@ -215,7 +216,7 @@ private void putValuesFromRenamings(ProgramVariable varForCondition, Node node,
                         .getHashMap().entrySet()) {
                     Entry<?, ?> entry = value;
                     if (entry.getKey() instanceof LocationVariable
-                            && entry.getValue() instanceof SVSubstitute) {
+                            && entry.getValue() instanceof SyntaxElement) {
                         if ((VariableNamer.getBasename(((LocationVariable) entry.getKey()).name()))
                                 .equals(varForCondition.name())
                                 && ((LocationVariable) entry.getKey()).name().toString()
@@ -229,7 +230,7 @@ private void putValuesFromRenamings(ProgramVariable varForCondition, Node node,
                             // add new value
                             toKeep.add((LocationVariable) entry.getValue());
                             getVariableNamingMap().put(varForCondition,
-                                (SVSubstitute) entry.getValue());
+                                (SyntaxElement) entry.getValue());
                             found = true;
                             break;
                         } else if (inScope && ((LocationVariable) entry.getKey()).name()
@@ -242,7 +243,7 @@ private void putValuesFromRenamings(ProgramVariable varForCondition, Node node,
                             // add new value
                             toKeep.add((LocationVariable) entry.getValue());
                             getVariableNamingMap().put(varForCondition,
-                                (SVSubstitute) entry.getValue());
+                                (SyntaxElement) entry.getValue());
                             found = true;
                             break;
                         }
@@ -263,7 +264,7 @@ private void putValuesFromRenamings(ProgramVariable varForCondition, Node node,
     protected void refreshVarMaps(RuleApp ruleApp, Node node) {
         boolean inScope = isInScope(node);
         // collect old values
-        Map<SVSubstitute, SVSubstitute> oldMap = getOldMap();
+        Map<SyntaxElement, SyntaxElement> oldMap = getOldMap();
         // put values into map which have to be replaced
         for (ProgramVariable varForCondition : getVarsForCondition()) {
             // put global variables only done when a variable is instantiated by
@@ -498,14 +499,14 @@ public Set<LocationVariable> getToKeep() {
     /**
      * @return the variableNamingMap
      */
-    public Map<SVSubstitute, SVSubstitute> getVariableNamingMap() {
+    public Map<SyntaxElement, SyntaxElement> getVariableNamingMap() {
         return variableNamingMap;
     }
 
     /**
      * @param variableNamingMap the variableNamingMap to set
      */
-    public void setVariableNamingMap(Map<SVSubstitute, SVSubstitute> variableNamingMap) {
+    public void setVariableNamingMap(Map<SyntaxElement, SyntaxElement> variableNamingMap) {
         this.variableNamingMap = variableNamingMap;
     }
 
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionSideProofUtil.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionSideProofUtil.java
index 766547c958c..bafc9353346 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionSideProofUtil.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionSideProofUtil.java
@@ -57,24 +57,24 @@ private SymbolicExecutionSideProofUtil() {
 
     /**
      * Computes a general {@link Sequent} to prove in a side proof which contains all
-     * {@link SequentFormula} of the original {@link Sequent} except the given current
-     * {@link SequentFormula} and those which contains modalities and queries.
+     * {@link Term} of the original {@link Sequent} except the given current
+     * {@link Term} and those which contains modalities and queries.
      *
      * @param goalSequent The original {@link Sequent} of the current {@link Goal}.
-     * @param currentSF The {@link SequentFormula} to ignore.
+     * @param currentSF The {@link Term} to ignore.
      * @return The general initial {@link Sequent}.
      */
     public static Sequent computeGeneralSequentToProve(Sequent goalSequent,
-            SequentFormula currentSF) {
+            Term currentSF) {
         Sequent sequentToProve = Sequent.EMPTY_SEQUENT;
-        for (SequentFormula sf : goalSequent.antecedent()) {
+        for (Term sf : goalSequent.antecedent()) {
             if (sf != currentSF) {
                 if (!containsModalityOrQuery(sf)) {
                     sequentToProve = sequentToProve.addFormula(sf, true, false).sequent();
                 }
             }
         }
-        for (SequentFormula sf : goalSequent.succedent()) {
+        for (Term sf : goalSequent.succedent()) {
             if (sf != currentSF) {
                 if (!containsModalityOrQuery(sf)) {
                     sequentToProve = sequentToProve.addFormula(sf, false, false).sequent();
@@ -121,16 +121,16 @@ public static List<Pair<Term, Node>> computeResults(Services services, Proof pro
                 }
                 Sequent sequent = resultGoal.sequent();
                 List<Term> results = new LinkedList<>();
-                for (SequentFormula sf : sequent.antecedent()) {
-                    if (sf.formula().containsLabel(label)) {
-                        Term result = sf.formula();
+                for (Term sf : sequent.antecedent()) {
+                    if (sf.containsLabel(label)) {
+                        Term result = sf;
                         result = services.getTermBuilder().not(result);
                         results.add(result);
                     }
                 }
-                for (SequentFormula sf : sequent.succedent()) {
-                    if (sf.formula().containsLabel(label)) {
-                        Term result = sf.formula();
+                for (Term sf : sequent.succedent()) {
+                    if (sf.containsLabel(label)) {
+                        Term result = sf;
                         results.add(result);
                     }
                 }
@@ -189,12 +189,12 @@ public static List<Triple<Term, Set<Term>, Node>> computeResultsAndConditions(Se
                     throw new IllegalStateException("Not all applicable rules are applied.");
                 }
                 Sequent sequent = resultGoal.sequent();
-                boolean newPredicateIsSequentFormula = isOperatorASequentFormula(sequent, operator);
+                boolean newPredicateIsTerm = isOperatorATerm(sequent, operator);
                 Set<Term> resultConditions = new LinkedHashSet<>();
                 Term result = null;
-                for (SequentFormula sf : sequent.antecedent()) {
-                    if (newPredicateIsSequentFormula) {
-                        if (Operator.opEquals(sf.formula().op(), operator)) {
+                for (Term sf : sequent.antecedent()) {
+                    if (newPredicateIsTerm) {
+                        if (Operator.opEquals(sf.op(), operator)) {
                             throw new IllegalStateException(
                                 "Result predicate found in antecedent.");
                         } else {
@@ -208,19 +208,19 @@ public static List<Triple<Term, Set<Term>, Node>> computeResultsAndConditions(Se
                     }
                     if (!isIrrelevantCondition(services, sequentToProve,
                         relevantThingsInSequentToProve, sf)) {
-                        if (resultConditions.add(sf.formula()) && addNamesToServices) {
-                            addNewNamesToNamespace(services, sf.formula());
+                        if (resultConditions.add(sf) && addNamesToServices) {
+                            addNewNamesToNamespace(services, sf);
                         }
                     }
                 }
-                for (SequentFormula sf : sequent.succedent()) {
-                    if (newPredicateIsSequentFormula) {
-                        if (Operator.opEquals(sf.formula().op(), operator)) {
+                for (Term sf : sequent.succedent()) {
+                    if (newPredicateIsTerm) {
+                        if (Operator.opEquals(sf.op(), operator)) {
                             if (result != null) {
                                 throw new IllegalStateException(
                                     "Result predicate found multiple times in succedent.");
                             }
-                            result = sf.formula().sub(0);
+                            result = sf.sub(0);
                         }
                     } else {
                         Term constructedResult = constructResultIfContained(services, sf, operator);
@@ -235,9 +235,9 @@ public static List<Triple<Term, Set<Term>, Node>> computeResultsAndConditions(Se
                     if (result == null) {
                         if (!isIrrelevantCondition(services, sequentToProve,
                             relevantThingsInSequentToProve, sf)) {
-                            if (resultConditions.add(services.getTermBuilder().not(sf.formula()))
+                            if (resultConditions.add(services.getTermBuilder().not(sf))
                                     && addNamesToServices) {
-                                addNewNamesToNamespace(services, sf.formula());
+                                addNewNamesToNamespace(services, sf);
                             }
                         }
                     }
@@ -254,11 +254,6 @@ public static List<Triple<Term, Set<Term>, Node>> computeResultsAndConditions(Se
         }
     }
 
-    private static Term constructResultIfContained(Services services, SequentFormula sf,
-            Operator operator) {
-        return constructResultIfContained(services, sf.formula(), operator);
-    }
-
     private static Term constructResultIfContained(Services services, Term term,
             Operator operator) {
         if (Operator.opEquals(term.op(), operator)) {
@@ -287,9 +282,11 @@ private static Term constructResultIfContained(Services services, Term term,
         }
     }
 
-    private static boolean isOperatorASequentFormula(Sequent sequent, final Operator operator) {
+    private static boolean isOperatorATerm(Sequent sequent, final Operator operator) {
         return CollectionUtil.search(sequent,
-            element -> Operator.opEquals(element.formula().op(), operator)) != null;
+            element -> {
+                return Operator.opEquals(element.op(), operator);
+            }) != null;
     }
 
     /**
@@ -315,17 +312,6 @@ public void visit(Term visited) {
         });
     }
 
-    /**
-     * Checks if the given {@link SequentFormula} contains a modality or query.
-     *
-     * @param sf The {@link SequentFormula} to check.
-     * @return {@code true} contains at least one modality or query, {@code false} contains no
-     *         modalities and no queries.
-     */
-    public static boolean containsModalityOrQuery(SequentFormula sf) {
-        return containsModalityOrQuery(sf.formula());
-    }
-
     /**
      * Checks if the given {@link Term} contains a modality or query.
      *
@@ -384,8 +370,8 @@ public boolean isContainsModalityOrQuery() {
     public static Set<Operator> extractRelevantThings(final Services services,
             Sequent sequentToProve) {
         final Set<Operator> result = new HashSet<>();
-        for (SequentFormula sf : sequentToProve) {
-            sf.formula().execPreOrder(new DefaultVisitor() {
+        for (Term sf : sequentToProve) {
+            sf.execPreOrder(new DefaultVisitor() {
                 @Override
                 public void visit(Term visited) {
                     if (isRelevantThing(services, visited)) {
@@ -426,29 +412,29 @@ private static boolean isRelevantThing(Services services, Term term) {
     }
 
     /**
-     * Checks if the given {@link SequentFormula} is a relevant condition.
+     * Checks if the given {@link Term} is a relevant condition.
      *
      * @param services The {@link Services} to use.
      * @param initialSequent The initial {@link Sequent} of the side proof.
      * @param relevantThingsInSequentToProve The relevant things found in the initial
      *        {@link Sequent}.
-     * @param sf The {@link SequentFormula} to check.
-     * @return {@code true} {@link SequentFormula} is relevant condition, {@code false}
-     *         {@link SequentFormula} is not a relevant condition.
+     * @param sf The {@link Term} to check.
+     * @return {@code true} {@link Term} is relevant condition, {@code false}
+     *         {@link Term} is not a relevant condition.
      */
     public static boolean isIrrelevantCondition(Services services, Sequent initialSequent,
-            Set<Operator> relevantThingsInSequentToProve, SequentFormula sf) {
+            Set<Operator> relevantThingsInSequentToProve, Term sf) {
         return initialSequent.antecedent().contains(sf) || initialSequent.succedent().contains(sf)
                 || containsModalityOrQuery(sf) // isInOrOfAntecedent(initialSequent, sf) ||
                 || containsIrrelevantThings(services, sf, relevantThingsInSequentToProve);
     }
 
-    // public static boolean isInOrOfAntecedent(Sequent initialSequent, SequentFormula sf) {
+    // public static boolean isInOrOfAntecedent(Sequent initialSequent, Term sf) {
     // Term term = sf.formula();
     // boolean result = false;
-    // Iterator<SequentFormula> iter = initialSequent.antecedent().iterator();
+    // Iterator<Term> iter = initialSequent.antecedent().iterator();
     // while (!result && iter.hasNext()) {
-    // SequentFormula next = iter.next();
+    // Term next = iter.next();
     // if (isInOr(next.formula(), term)) {
     // result = true;
     // }
@@ -471,26 +457,26 @@ public static boolean isIrrelevantCondition(Services services, Sequent initialSe
     // }
 
     /**
-     * Checks if the given {@link SequentFormula} contains irrelevant things (things which are not
+     * Checks if the given {@link Term} contains irrelevant things (things which are not
      * contained in the relevantThingsToProve and are no Java types)
      *
      * @param services The {@link Services} to use.
-     * @param sf The {@link SequentFormula} to check.
+     * @param sf The {@link Term} to check.
      * @param relevantThings The relevant things.
-     * @return {@code true} The {@link SequentFormula} contains irrelevant things, {@code false} the
-     *         {@link SequentFormula} contains no irrelevant things.
+     * @return {@code true} The {@link Term} contains irrelevant things, {@code false} the
+     *         {@link Term} contains no irrelevant things.
      */
-    public static boolean containsIrrelevantThings(Services services, SequentFormula sf,
+    public static boolean containsIrrelevantThings(Services services, Term sf,
             Set<Operator> relevantThings) {
         ContainsIrrelevantThingsVisitor visitor =
             new ContainsIrrelevantThingsVisitor(services, relevantThings);
-        sf.formula().execPostOrder(visitor);
+        sf.execPostOrder(visitor);
         return visitor.isContainsIrrelevantThings();
     }
 
     /**
      * Utility class used by
-     * {@link #containsIrrelevantThings(Services, SequentFormula, Set)}.
+     * {@link #containsIrrelevantThings(Services, Term, Set)}.
      *
      * @author Martin Hentschel
      */
@@ -540,8 +526,8 @@ public void visit(Term visited) {
         /**
          * Returns the result.
          *
-         * @return The {@link SequentFormula} contains irrelevant things, {@code false} the
-         *         {@link SequentFormula} contains no irrelevant things.
+         * @return The {@link Term} contains irrelevant things, {@code false} the
+         *         {@link Term} contains no irrelevant things.
          */
         public boolean isContainsIrrelevantThings() {
             return containsIrrelevantThings;
@@ -699,13 +685,13 @@ public static Term extractOperatorTerm(Goal goal, final Operator operator) {
     public static Term extractOperatorTerm(Node node, final Operator operator) {
         assert node != null;
         // Search formula with the given operator in sequent (or in some cases below the updates)
-        SequentFormula sf = CollectionUtil.search(node.sequent(), element -> {
-            Term term = element.formula();
+        Term sf = CollectionUtil.search(node.sequent(), element -> {
+            Term term = element;
             term = TermBuilder.goBelowUpdates(term);
             return Objects.equals(term.op(), operator);
         });
         if (sf != null) {
-            Term term = sf.formula();
+            Term term = sf;
             term = TermBuilder.goBelowUpdates(term);
             return term;
         } else {
diff --git a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionUtil.java b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionUtil.java
index 785b03e3d80..55e8831a48c 100644
--- a/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionUtil.java
+++ b/key.core.symbolic_execution/src/main/java/de/uka/ilkd/key/symbolic_execution/util/SymbolicExecutionUtil.java
@@ -189,7 +189,7 @@ public static Term simplify(InitConfig initConfig, Proof parentProof, Term term)
                 .cloneProofEnvironmentWithOwnOneStepSimplifier(initConfig, true);
         // Create Sequent to prove
         Sequent sequentToProve =
-            Sequent.EMPTY_SEQUENT.addFormula(new SequentFormula(term), false, true).sequent();
+            Sequent.EMPTY_SEQUENT.addFormula(term, false, true).sequent();
         // Return created Sequent and the used predicate to identify the value interested in.
         ApplyStrategyInfo info = SymbolicExecutionSideProofUtil.startSideProof(parentProof,
             sideProofEnv, sequentToProve);
@@ -245,8 +245,8 @@ public static Term sequentToImplication(Sequent sequent, Services services) {
     public static ImmutableList<Term> listSemisequentTerms(Semisequent semisequent) {
         ImmutableList<Term> terms = ImmutableSLList.nil();
         if (semisequent != null) {
-            for (SequentFormula sf : semisequent) {
-                terms = terms.append(sf.formula());
+            for (Term sf : semisequent) {
+                terms = terms.append(sf);
             }
         }
         return terms;
@@ -487,7 +487,7 @@ public static SiteProofVariableValueInput createExtractReturnVariableValueSequen
         Term modalityTerm = services.getTermBuilder().dia(newJavaBlock, newTerm);
         // Get the updates from the return node which includes the value interested in.
         Term originalModifiedFormula =
-            methodReturnNode.getAppliedRuleApp().posInOccurrence().sequentFormula().formula();
+            methodReturnNode.getAppliedRuleApp().posInOccurrence().sequentLevelFormula();
         ImmutableList<Term> originalUpdates =
             TermBuilder.goBelowUpdates2(originalModifiedFormula).first;
         // Create Sequent to prove with new succedent.
@@ -668,16 +668,16 @@ public static IExecutionConstraint[] createExecutionConstraints(IExecutionNode<?
             List<IExecutionConstraint> constraints = new LinkedList<>();
             Node proofNode = node.getProofNode();
             Sequent sequent = proofNode.sequent();
-            for (SequentFormula sf : sequent.antecedent()) {
-                if (!containsSymbolicExecutionLabel(sf.formula())) {
+            for (Term sf : sequent.antecedent()) {
+                if (!containsSymbolicExecutionLabel(sf)) {
                     constraints.add(new ExecutionConstraint(node.getSettings(), proofNode,
-                        node.getModalityPIO(), sf.formula()));
+                        node.getModalityPIO(), sf));
                 }
             }
-            for (SequentFormula sf : sequent.succedent()) {
-                if (!containsSymbolicExecutionLabel(sf.formula())) {
+            for (Term sf : sequent.succedent()) {
+                if (!containsSymbolicExecutionLabel(sf)) {
                     constraints.add(new ExecutionConstraint(node.getSettings(), proofNode,
-                        node.getModalityPIO(), tb.not(sf.formula())));
+                        node.getModalityPIO(), tb.not(sf)));
                 }
             }
             return constraints.toArray(new IExecutionConstraint[0]);
@@ -820,11 +820,11 @@ public static List<IProgramVariable> collectAllElementaryUpdateTerms(Node node)
         if (node != null) {
             Services services = node.proof().getServices();
             List<IProgramVariable> result = new LinkedList<>();
-            for (SequentFormula sf : node.sequent().antecedent()) {
-                internalCollectAllElementaryUpdateTerms(services, result, sf.formula());
+            for (Term sf : node.sequent().antecedent()) {
+                internalCollectAllElementaryUpdateTerms(services, result, sf);
             }
-            for (SequentFormula sf : node.sequent().succedent()) {
-                internalCollectAllElementaryUpdateTerms(services, result, sf.formula());
+            for (Term sf : node.sequent().succedent()) {
+                internalCollectAllElementaryUpdateTerms(services, result, sf);
             }
             return result;
         } else {
@@ -1339,8 +1339,8 @@ public static PosInOccurrence findModalityWithMaxSymbolicExecutionLabelId(
         if (semisequent != null) {
             int maxId = Integer.MIN_VALUE;
             PosInOccurrence maxPio = null;
-            for (SequentFormula sf : semisequent) {
-                PosInTerm current = findModalityWithMaxSymbolicExecutionLabelId(sf.formula());
+            for (Term sf : semisequent) {
+                PosInTerm current = findModalityWithMaxSymbolicExecutionLabelId(sf);
                 if (current != null) {
                     PosInOccurrence pio = new PosInOccurrence(sf, current, inAntec);
                     SymbolicExecutionTermLabel label = getSymbolicExecutionLabel(pio.subTerm());
@@ -1424,8 +1424,8 @@ public static PosInOccurrence findModalityWithMinSymbolicExecutionLabelId(
         if (semisequent != null) {
             int maxId = Integer.MIN_VALUE;
             PosInOccurrence minPio = null;
-            for (SequentFormula sf : semisequent) {
-                PosInTerm current = findModalityWithMinSymbolicExecutionLabelId(sf.formula());
+            for (Term sf : semisequent) {
+                PosInTerm current = findModalityWithMinSymbolicExecutionLabelId(sf);
                 if (current != null) {
                     PosInOccurrence pio = new PosInOccurrence(sf, current, inAntec);
                     SymbolicExecutionTermLabel label = getSymbolicExecutionLabel(pio.subTerm());
@@ -2085,8 +2085,8 @@ else if (rightTerm.op() == Junctor.IMP
     public static ContractPostOrExcPostExceptionVariableResult searchContractPostOrExcPostExceptionVariable(
             Node node, Services services) throws ProofInputException {
         Semisequent antecedent = node.sequent().antecedent();
-        SequentFormula sf = antecedent.get(antecedent.size() - 1);
-        Term workingTerm = sf.formula();
+        Term sf = antecedent.get(antecedent.size() - 1);
+        Term workingTerm = sf;
         Pair<ImmutableList<Term>, Term> updatesAndTerm = TermBuilder.goBelowUpdates2(workingTerm);
         workingTerm = updatesAndTerm.second;
         if (workingTerm.op() != Junctor.AND) {
@@ -2257,7 +2257,7 @@ private static Term computeLoopInvariantBuiltInRuleAppBranchCondition(Node paren
             Services services = parent.proof().getServices();
             Node useNode = parent.child(2);
             Semisequent antecedent = useNode.sequent().antecedent();
-            Term invTerm = antecedent.get(antecedent.size() - 1).formula();
+            Term invTerm = antecedent.get(antecedent.size() - 1);
             // Extract loop condition from child
             Term loopConditionModalityTerm =
                 posInOccurrenceInOtherNode(parent, app.posInOccurrence(), node);
@@ -2371,7 +2371,7 @@ private static Term computeBlockContractBuiltInRuleAppBranchCondition(Node paren
             // Compute invariant (last antecedent formula of the use branch)
             Services services = parent.proof().getServices();
             Semisequent antecedent = node.sequent().antecedent();
-            Term condition = antecedent.get(antecedent.size() - 1).formula();
+            Term condition = antecedent.get(antecedent.size() - 1);
             if (simplify) {
                 // New OneStepSimplifier is required because it has an internal state and the
                 // default instance can't be used parallel.
@@ -2469,7 +2469,7 @@ public static PosInOccurrence posInOccurrenceToOtherSequent(Sequent original,
             PosInOccurrence pio, Sequent toApplyTo) {
         if (original != null && pio != null && toApplyTo != null) {
             // Search index of formula in original sequent
-            SequentFormula originalSF = pio.sequentFormula();
+            Term originalSF = pio.sequentLevelFormula();
             boolean antecendet = pio.isInAntec();
             int index;
             if (antecendet) {
@@ -2478,7 +2478,7 @@ public static PosInOccurrence posInOccurrenceToOtherSequent(Sequent original,
                 index = original.succedent().indexOf(originalSF);
             }
             if (index >= 0) {
-                final SequentFormula toApplyToSF =
+                final Term toApplyToSF =
                     (antecendet ? toApplyTo.antecedent() : toApplyTo.succedent()).get(index);
                 return new PosInOccurrence(toApplyToSF, pio.posInTerm(), antecendet);
             } else {
@@ -2535,8 +2535,8 @@ private static Term computeTacletAppBranchCondition(Node parent, Node node, bool
                 // Remove replace part of symbolic execution rules
                 if (NodeInfo.isSymbolicExecution(app.taclet())) {
                     Sequent sequent = (Sequent) goalTemplate.replaceWithExpressionAsObject();
-                    for (SequentFormula sf : sequent.antecedent()) {
-                        Term replaceTerm = instantiateTerm(node, sf.formula(), app, services);
+                    for (Term sf : sequent.antecedent()) {
+                        Term replaceTerm = instantiateTerm(node, sf, app, services);
                         replaceTerm = services.getTermBuilder().applyUpdatePairsSequential(
                             app.instantiations().getUpdateContext(), replaceTerm);
                         Term originalTerm = findReplacement(node.sequent().antecedent(),
@@ -2544,8 +2544,8 @@ private static Term computeTacletAppBranchCondition(Node parent, Node node, bool
                         assert originalTerm != null;
                         newAntecedents = newAntecedents.removeFirst(originalTerm);
                     }
-                    for (SequentFormula sf : sequent.succedent()) {
-                        Term replaceTerm = instantiateTerm(node, sf.formula(), app, services);
+                    for (Term sf : sequent.succedent()) {
+                        Term replaceTerm = instantiateTerm(node, sf, app, services);
                         replaceTerm = services.getTermBuilder().applyUpdatePairsSequential(
                             app.instantiations().getUpdateContext(), replaceTerm);
                         Term originalTerm = findReplacement(node.sequent().succedent(),
@@ -2637,7 +2637,7 @@ private static Term computeTacletAppBranchCondition(Node parent, Node node, bool
     }
 
     /**
-     * Lists the {@link Term}s of all new {@link SequentFormula} in the child {@link Semisequent}.
+     * Lists the {@link Term}s of all new {@link Term} in the child {@link Semisequent}.
      *
      * @param parent The parent {@link Semisequent}.
      * @param child The child {@link Semisequent}.
@@ -2645,14 +2645,14 @@ private static Term computeTacletAppBranchCondition(Node parent, Node node, bool
      */
     private static ImmutableList<Term> listNewSemisequentTerms(Semisequent parent,
             Semisequent child) {
-        Set<SequentFormula> parentSFs = new HashSet<>();
-        for (SequentFormula sf : parent) {
+        Set<Term> parentSFs = new HashSet<>();
+        for (Term sf : parent) {
             parentSFs.add(sf);
         }
         ImmutableList<Term> result = ImmutableSLList.nil();
-        for (SequentFormula sf : child) {
+        for (Term sf : child) {
             if (!parentSFs.contains(sf)) {
-                result = result.append(sf.formula());
+                result = result.append(sf);
             }
         }
         return result;
@@ -2669,9 +2669,15 @@ private static ImmutableList<Term> listNewSemisequentTerms(Semisequent parent,
      */
     private static Term findReplacement(Semisequent semisequent,
             final PosInOccurrence posInOccurrence, final Term replaceTerm) {
-        SequentFormula sf = CollectionUtil.search(semisequent,
-            element -> checkReplaceTerm(element.formula(), posInOccurrence, replaceTerm));
-        return sf != null ? sf.formula() : null;
+        Term sf = CollectionUtil.search(semisequent,
+            element -> {
+                return checkReplaceTerm(element, posInOccurrence, replaceTerm);
+            });
+        if (sf != null) {
+            return sf;
+        } else {
+            return null;
+        }
     }
 
     /**
@@ -2931,7 +2937,7 @@ public static Sequent createSequentToProveWithNewSuccedent(Node node, PosInOccur
             if (node.proof().root() == node) {
                 originalUpdates = computeRootElementaryUpdates(node);
             } else {
-                Term originalModifiedFormula = pio.sequentFormula().formula();
+                Term originalModifiedFormula = pio.sequentLevelFormula();
                 originalUpdates = TermBuilder.goBelowUpdates2(originalModifiedFormula).first;
             }
             // Create new sequent
@@ -2952,8 +2958,8 @@ public static Sequent createSequentToProveWithNewSuccedent(Node node, PosInOccur
     public static ImmutableList<Term> computeRootElementaryUpdates(Node root) {
         ImmutableList<Term> result = ImmutableSLList.nil();
         Sequent sequent = root.sequent();
-        for (SequentFormula sf : sequent.succedent()) {
-            Term term = sf.formula();
+        for (Term sf : sequent.succedent()) {
+            Term term = sf;
             if (Junctor.IMP.equals(term.op())) {
                 result = result.prepend(collectElementaryUpdates(term.sub(1)));
             }
@@ -3031,7 +3037,7 @@ public static Sequent createSequentToProveWithNewSuccedent(Node node, PosInOccur
         // were not modified by the applied rule
         Sequent originalSequentWithoutMethodFrame =
             SymbolicExecutionSideProofUtil.computeGeneralSequentToProve(node.sequent(),
-                pio != null ? pio.sequentFormula() : null);
+                pio != null ? pio.sequentLevelFormula() : null);
         Set<Term> skolemTerms = newSuccedentToProve != null
                 ? collectSkolemConstants(originalSequentWithoutMethodFrame, newSuccedentToProve)
                 : collectSkolemConstants(originalSequentWithoutMethodFrame, tb.parallel(updates));
@@ -3045,13 +3051,13 @@ public static Sequent createSequentToProveWithNewSuccedent(Node node, PosInOccur
             newSuccedentToProve =
                 addLabelRecursiveToNonSkolem(factory, newSuccedentToProve, RESULT_LABEL);
         }
-        Sequent sequentToProve = newSuccedentToProve != null
-                ? originalSequentWithoutMethodFrame
-                        .addFormula(new SequentFormula(newSuccedentToProve), false, true).sequent()
+        Sequent sequentToProve;
+        sequentToProve = newSuccedentToProve != null ? originalSequentWithoutMethodFrame
+                .addFormula(newSuccedentToProve, false, true).sequent()
                 : originalSequentWithoutMethodFrame;
         if (additionalAntecedent != null) {
             sequentToProve = sequentToProve
-                    .addFormula(new SequentFormula(additionalAntecedent), true, false).sequent();
+                    .addFormula(additionalAntecedent, true, false).sequent();
         }
         return sequentToProve;
     }
@@ -3067,10 +3073,10 @@ public static Sequent createSequentToProveWithNewSuccedent(Node node, PosInOccur
     private static Sequent labelSkolemConstants(
             Sequent sequent, Set<Term> constantsToLabel,
             TermFactory factory) {
-        for (SequentFormula sf : sequent.antecedent()) {
+        for (Term sf : sequent.antecedent()) {
             int skolemEquality = checkSkolemEquality(sf);
             if (skolemEquality == -1) {
-                Term equality = sf.formula();
+                Term equality = sf;
                 if (constantsToLabel.contains(equality.sub(0))) {
                     Term definition =
                         addLabelRecursiveToNonSkolem(factory, equality.sub(1), RESULT_LABEL);
@@ -3082,11 +3088,11 @@ private static Sequent labelSkolemConstants(
                     Term newEquality =
                         factory.createTerm(equality.op(), new ImmutableArray<>(newSubs),
                             equality.boundVars(), equality.getLabels());
-                    sequent = sequent.changeFormula(new SequentFormula(newEquality),
+                    sequent = sequent.changeFormula(newEquality,
                         new PosInOccurrence(sf, PosInTerm.getTopLevel(), true)).sequent();
                 }
             } else if (skolemEquality == 1) {
-                Term equality = sf.formula();
+                Term equality = sf;
                 if (constantsToLabel.contains(equality.sub(1))) {
                     Term definition =
                         addLabelRecursiveToNonSkolem(factory, equality.sub(0), RESULT_LABEL);
@@ -3098,7 +3104,7 @@ private static Sequent labelSkolemConstants(
                     Term newEquality =
                         factory.createTerm(equality.op(), new ImmutableArray<>(newSubs),
                             equality.boundVars(), equality.getLabels());
-                    sequent = sequent.changeFormula(new SequentFormula(newEquality),
+                    sequent = sequent.changeFormula(newEquality,
                         new PosInOccurrence(sf, PosInTerm.getTopLevel(), true)).sequent();
                 }
             }
@@ -3225,7 +3231,7 @@ public static boolean isSkolemConstant(Term term) {
     }
 
     /**
-     * Removes all {@link SequentFormula}s with a skolem equality from the given {@link Sequent} if
+     * Removes all {@link Term}s with a skolem equality from the given {@link Sequent} if
      * the skolem {@link Term} is not contained in the given {@link Collection}.
      *
      * @param sequent The {@link Sequent} to modify.
@@ -3236,10 +3242,10 @@ public static boolean isSkolemConstant(Term term) {
     private static Sequent removeAllUnusedSkolemEqualities(Sequent sequent,
             Collection<Term> skolemConstants) {
         Sequent result = sequent;
-        for (SequentFormula sf : sequent.antecedent()) {
+        for (Term sf : sequent.antecedent()) {
             result = removeAllUnusedSkolemEqualities(result, sf, true, skolemConstants);
         }
-        for (SequentFormula sf : sequent.succedent()) {
+        for (Term sf : sequent.succedent()) {
             result = removeAllUnusedSkolemEqualities(result, sf, false, skolemConstants);
         }
         return result;
@@ -3247,17 +3253,17 @@ private static Sequent removeAllUnusedSkolemEqualities(Sequent sequent,
 
     /**
      * Helper method of {@link #removeAllUnusedSkolemEqualities(Sequent, Collection)} which removes
-     * the given {@link SequentFormula} if required.
+     * the given {@link Term} if required.
      *
      * @param sequent The {@link Sequent} to modify.
-     * @param sf The {@link SequentFormula} to remove if its skolem {@link Term} is not listed.
+     * @param sf The {@link Term} to remove if its skolem {@link Term} is not listed.
      * @param antecedent {@code true} antecedent, {@code false} succedent.
      * @param skolemConstants The allowed skolem {@link Term}s.
-     * @return The modified {@link Sequent} in which the {@link SequentFormula} might be removed.
+     * @return The modified {@link Sequent} in which the {@link Term} might be removed.
      */
-    private static Sequent removeAllUnusedSkolemEqualities(Sequent sequent, SequentFormula sf,
+    private static Sequent removeAllUnusedSkolemEqualities(Sequent sequent, Term sf,
             boolean antecedent, Collection<Term> skolemConstants) {
-        Term term = sf.formula();
+        Term term = sf;
         boolean remove = false;
         if (term.op() == Equality.EQUALS) {
             if (isSkolemConstant(term.sub(0))) {
@@ -3276,17 +3282,6 @@ private static Sequent removeAllUnusedSkolemEqualities(Sequent sequent, SequentF
         }
     }
 
-    /**
-     * Checks if the given {@link SequentFormula} is a skolem equality.
-     *
-     * @param sf The {@link SequentFormula} to check.
-     * @return {@code -1} left side of skolem equality, {@code 0} no skolem equality, {@code 1}
-     *         right side of skolem equality.
-     */
-    public static int checkSkolemEquality(SequentFormula sf) {
-        return checkSkolemEquality(sf.formula());
-    }
-
     /**
      * Checks if the given {@link Term} is a skolem equality.
      *
@@ -3427,8 +3422,8 @@ public static Term replaceSkolemConstants(Sequent sequent, Term term, Services s
     private static List<Term> findSkolemReplacements(Sequent sequent, Term skolemConstant,
             Term skolemEquality) {
         List<Term> result = new LinkedList<>();
-        for (SequentFormula sf : sequent) {
-            Term term = sf.formula();
+        for (Term sf : sequent) {
+            Term term = sf;
             if (term != skolemEquality) {
                 int skolemCheck = checkSkolemEquality(term);
                 if (skolemCheck == -1) {
@@ -4111,10 +4106,12 @@ public static boolean lazyComputeIsMainBranchVerified(Node node) {
                     Node leaf = leafsIter.next();
                     if (!leaf.isClosed()) {
                         final Term toSearch = predicate;
-                        SequentFormula topLevelPredicate = CollectionUtil
+                        Term topLevelPredicate = CollectionUtil
                                 .search(leaf.sequent().succedent(),
-                                    element -> Operator.opEquals(toSearch.op(),
-                                        element.formula().op()));
+                                    element -> {
+                                        return Operator.opEquals(toSearch.op(),
+                                            element.op());
+                                    });
                         if (topLevelPredicate == null) {
                             verified = false;
                         }
@@ -4151,9 +4148,11 @@ public static boolean lazyComputeIsAdditionalBranchVerified(Node node) {
                         for (Term term : additinalPredicates) {
                             additinalOperatos.add(term.op());
                         }
-                        SequentFormula topLevelPredicate =
+                        Term topLevelPredicate =
                             CollectionUtil.search(leaf.sequent().succedent(),
-                                element -> additinalOperatos.contains(element.formula().op()));
+                                element -> {
+                                    return additinalOperatos.contains(element.op());
+                                });
                         if (topLevelPredicate == null) {
                             verified = false;
                         }
@@ -4199,8 +4198,8 @@ public static Sort lazyComputeExceptionSort(Node node, IProgramVariable exceptio
             // Search final value of the exceptional variable which is used to check if the verified
             // program terminates normally
             ImmutableArray<Term> value = null;
-            for (SequentFormula f : node.sequent().succedent()) {
-                Pair<ImmutableList<Term>, Term> updates = TermBuilder.goBelowUpdates2(f.formula());
+            for (Term f : node.sequent().succedent()) {
+                Pair<ImmutableList<Term>, Term> updates = TermBuilder.goBelowUpdates2(f);
                 Iterator<Term> iter = updates.first.iterator();
                 while (value == null && iter.hasNext()) {
                     value = extractValueFromUpdate(iter.next(), exceptionVariable);
diff --git a/key.core.symbolic_execution/src/test/java/de/uka/ilkd/key/symbolic_execution/testcase/AbstractSymbolicExecutionTestCase.java b/key.core.symbolic_execution/src/test/java/de/uka/ilkd/key/symbolic_execution/testcase/AbstractSymbolicExecutionTestCase.java
index 95c6da8fe33..2b0a9703bd7 100644
--- a/key.core.symbolic_execution/src/test/java/de/uka/ilkd/key/symbolic_execution/testcase/AbstractSymbolicExecutionTestCase.java
+++ b/key.core.symbolic_execution/src/test/java/de/uka/ilkd/key/symbolic_execution/testcase/AbstractSymbolicExecutionTestCase.java
@@ -1638,7 +1638,7 @@ protected String getTryContent(Proof proof) {
         Node node = proof.root();
         Sequent sequent = node.sequent();
         assertEquals(1, sequent.succedent().size());
-        Term succedent = sequent.succedent().get(0).formula();
+        Term succedent = sequent.succedent().get(0);
         assertEquals(2, succedent.arity());
         Term updateApplication = succedent.subs().get(1);
         assertEquals(2, updateApplication.arity());
diff --git a/key.core.testgen/src/main/java/de/uka/ilkd/key/smt/testgen/AbstractTestGenerator.java b/key.core.testgen/src/main/java/de/uka/ilkd/key/smt/testgen/AbstractTestGenerator.java
index 2fbfc7b1ce4..7ee2a1cf76a 100644
--- a/key.core.testgen/src/main/java/de/uka/ilkd/key/smt/testgen/AbstractTestGenerator.java
+++ b/key.core.testgen/src/main/java/de/uka/ilkd/key/smt/testgen/AbstractTestGenerator.java
@@ -11,7 +11,6 @@
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
 import de.uka.ilkd.key.macros.ProofMacroFinishedInfo;
@@ -283,19 +282,19 @@ private Proof createProofForTestingNoDuplicate(Node node, List<Proof> otherProof
         final Sequent oldSequent = node.sequent();
         Sequent newSequent =
             Sequent.createSequent(Semisequent.EMPTY_SEMISEQUENT, Semisequent.EMPTY_SEMISEQUENT);
-        Iterator<SequentFormula> it = oldSequent.antecedent().iterator();
+        Iterator<Term> it = oldSequent.antecedent().iterator();
         while (it.hasNext()) {
-            final SequentFormula sf = it.next();
+            final Term sf = it.next();
             // Allow updates modailities in the antecedent
-            if (hasModalities(sf.formula(), false)) {
+            if (hasModalities(sf, false)) {
                 continue;
             }
             newSequent = newSequent.addFormula(sf, true, false).sequent();
         }
         it = oldSequent.succedent().iterator();
         while (it.hasNext()) {
-            final SequentFormula sf = it.next();
-            if (hasModalities(sf.formula(), removePostCondition)) {
+            final Term sf = it.next();
+            if (hasModalities(sf, removePostCondition)) {
                 continue;
             }
             newSequent = newSequent.addFormula(sf, false, false).sequent();
diff --git a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ModelGenerator.java b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ModelGenerator.java
index 0b66418b71b..1d1d4deaf7d 100644
--- a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ModelGenerator.java
+++ b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ModelGenerator.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Namespace;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.op.IProgramVariable;
@@ -149,7 +148,7 @@ private boolean addModelToTerm(Model m) {
 
         if (!tmodel.equals(tb.tt())) {
             Term notTerm = tb.not(tmodel);
-            SequentFormula sf = new SequentFormula(notTerm);
+            Term sf = notTerm;
             goal.addFormula(sf, true, true);
             return true;
         }
@@ -175,14 +174,14 @@ public Term sequentToTerm(Sequent s) {
 
         final TermBuilder tb = services.getTermBuilder();
         ante = ante.append(tb.tt());
-        for (SequentFormula f : s.antecedent()) {
-            ante = ante.append(f.formula());
+        for (Term f : s.antecedent()) {
+            ante = ante.append(f);
         }
 
         ImmutableList<Term> succ = ImmutableSLList.nil();
         succ = succ.append(tb.ff());
-        for (SequentFormula f : s.succedent()) {
-            succ = succ.append(f.formula());
+        for (Term f : s.succedent()) {
+            succ = succ.append(f);
         }
 
         return tb.imp(tb.and(ante), tb.or(succ));
diff --git a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ProofInfo.java b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ProofInfo.java
index ed33123fa61..33c304467e5 100644
--- a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ProofInfo.java
+++ b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/ProofInfo.java
@@ -146,7 +146,7 @@ private boolean isFalseConstant(Operator o) {
     }
 
     public Term getPO() {
-        return proof.root().sequent().succedent().get(0).formula();
+        return proof.root().sequent().succedent().get(0);
     }
 
 
diff --git a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/TestCaseGenerator.java b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/TestCaseGenerator.java
index 3b0112a4f05..a4e35640e88 100644
--- a/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/TestCaseGenerator.java
+++ b/key.core.testgen/src/main/java/de/uka/ilkd/key/testgen/TestCaseGenerator.java
@@ -14,7 +14,6 @@
 import de.uka.ilkd.key.java.declaration.ParameterDeclaration;
 import de.uka.ilkd.key.java.declaration.VariableSpecification;
 import de.uka.ilkd.key.ldt.HeapLDT;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.*;
 import de.uka.ilkd.key.proof.Node;
@@ -602,17 +601,15 @@ protected String inferSort(Map<String, Sort> typeInfMap, String progVar) {
 
     protected Map<String, Sort> generateTypeInferenceMap(Node n) {
         HashMap<String, Sort> typeInfMap = new HashMap<>();
-        for (SequentFormula sequentFormula : n.sequent()) {
-            Term t = sequentFormula.formula();
-            generateTypeInferenceMapHelper(t, typeInfMap);
+        for (Term seqFml : n.sequent()) {
+            generateTypeInferenceMapHelper(seqFml, typeInfMap);
         }
         return typeInfMap;
     }
 
     private void generateTypeInferenceMapHelper(Term t, Map<String, Sort> map) {
         Operator op = t.op();
-        if (op instanceof ProgramVariable) {
-            ProgramVariable pv = (ProgramVariable) t.op();
+        if (op instanceof ProgramVariable pv) {
             final String name = pv.name().toString();
             if (map.containsKey(name)) {
                 if (map.get(name) != pv.sort()) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/api/Matcher.java b/key.core/src/main/java/de/uka/ilkd/key/api/Matcher.java
index 9105d67b4f4..196733d7d10 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/api/Matcher.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/api/Matcher.java
@@ -7,7 +7,7 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.nparser.KeyAst;
 import de.uka.ilkd.key.nparser.KeyIO;
@@ -85,9 +85,9 @@ public List<VariableAssignments> matchPattern(String pattern, Sequent currentSeq
             ImmutableArray<IfFormulaInstantiation> succCand =
                 IfFormulaInstSeq.createList(currentSeq, false, copyServices);
 
-            SequentFormula[] patternArray = new SequentFormula[patternSeq.size()];
+            Term[] patternArray = new Term[patternSeq.size()];
             int i = 0;
-            for (SequentFormula fm : patternSeq) {
+            for (Term fm : patternSeq) {
                 patternArray[i++] = fm;
             }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/api/SearchNode.java b/key.core/src/main/java/de/uka/ilkd/key/api/SearchNode.java
index bf08e9862ac..973f983a845 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/api/SearchNode.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/api/SearchNode.java
@@ -3,7 +3,6 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.api;
 
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
@@ -12,13 +11,13 @@
  * Created by sarah on 5/2/17.
  */
 public final class SearchNode {
-    private final SequentFormula[] pattern;
+    private final Term[] pattern;
     private final int pos;
     private final int succAntPos;
     private final MatchConditions mc;
 
 
-    public SearchNode(SequentFormula[] pattern, int succAntPos) {
+    public SearchNode(Term[] pattern, int succAntPos) {
         this.pattern = pattern;
         this.pos = 0;
         this.succAntPos = succAntPos;
@@ -38,7 +37,7 @@ public boolean isAntecedent() {
     }
 
     public Term getPatternTerm() {
-        return pattern[pos].formula();
+        return pattern[pos];
     }
 
     public boolean isFinished() {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletAssumesModel.java b/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletAssumesModel.java
index f4d6ba8618a..e7216887766 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletAssumesModel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletAssumesModel.java
@@ -9,7 +9,6 @@
 import de.uka.ilkd.key.java.Position;
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.NamespaceSet;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.OriginTermLabel.NodeOrigin;
 import de.uka.ilkd.key.logic.label.OriginTermLabel.SpecType;
@@ -41,7 +40,7 @@ public String toString(Services services) {
         }
 
         @Override
-        public SequentFormula getConstrainedFormula() {
+        public Term getConstrainedFormula() {
             return null;
         }
     };
@@ -127,7 +126,7 @@ public IfFormulaInstantiation getSelection(int pos)
                 new NodeOrigin(SpecType.USER_INTERACTION,
                     app.rule().displayName(), goal.node().serialNr()));
 
-            return new IfFormulaInstDirect(new SequentFormula(term));
+            return new IfFormulaInstDirect(term);
         } catch (RecognitionException e) {
             throw new SVInstantiationParserException(manualInput,
                 Position.fromOneZeroBased(pos, e.charPositionInLine),
diff --git a/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletInstantiationModel.java b/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletInstantiationModel.java
index 9948b481af2..756cfe4bcfc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletInstantiationModel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/control/instantiation_model/TacletInstantiationModel.java
@@ -125,14 +125,14 @@ private void initIfChoiceModels() {
             ImmutableArray<IfFormulaInstantiation> succCand =
                 IfFormulaInstSeq.createList(seq, false, services);
 
-            Iterator<SequentFormula> it = ifseq.iterator();
+            Iterator<Term> it = ifseq.iterator();
             Term ifFma;
             MatchConditions matchCond = app.matchConditions();
 
             ifChoiceModel = new TacletAssumesModel[size];
 
             for (int i = 0; i < size; i++) {
-                ifFma = it.next().formula();
+                ifFma = it.next();
                 ifChoiceModel[i] =
                     new TacletAssumesModel(
                         ifFma, taclet().getMatcher().matchIf((i < asize ? antecCand : succCand),
diff --git a/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/AbstractFinishAuxiliaryComputationMacro.java b/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/AbstractFinishAuxiliaryComputationMacro.java
index f0afb84aea8..648f9a76e3e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/AbstractFinishAuxiliaryComputationMacro.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/AbstractFinishAuxiliaryComputationMacro.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Namespace;
 import de.uka.ilkd.key.logic.NamespaceSet;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermFactory;
@@ -120,11 +119,11 @@ private static Term buildFormulaFromGoal(Goal symbExecGoal) {
         final TermBuilder tb = symbExecGoal.proof().getServices().getTermBuilder();
         final TermFactory tf = symbExecGoal.proof().getServices().getTermFactory();
         Term result = tb.tt();
-        for (final SequentFormula f : symbExecGoal.sequent().antecedent()) {
-            result = tb.and(result, f.formula());
+        for (final Term f : symbExecGoal.sequent().antecedent()) {
+            result = tb.and(result, f);
         }
-        for (final SequentFormula f : symbExecGoal.sequent().succedent()) {
-            result = tb.and(result, tb.not(f.formula()));
+        for (final Term f : symbExecGoal.sequent().succedent()) {
+            result = tb.and(result, tb.not(f));
         }
         result = TermLabelManager.removeIrrelevantLabels(result, tf);
         return result;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/SelfcompositionStateExpansionMacro.java b/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/SelfcompositionStateExpansionMacro.java
index 18daf7aa846..c514cba0579 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/SelfcompositionStateExpansionMacro.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/informationflow/macros/SelfcompositionStateExpansionMacro.java
@@ -70,8 +70,9 @@ protected Strategy createStrategy(Proof proof, PosInOccurrence posInOcc) {
     protected boolean ruleApplicationInContextAllowed(RuleApp ruleApp, PosInOccurrence pio,
             Goal goal) {
         String ruleName = ruleApp.rule().name().toString();
-        return !"andLeft".equals(ruleName)
-                || !(pio.sequentFormula().formula().op() instanceof UpdateApplication);
+        if (!"andLeft".equals(ruleName))
+            return true;
+        return !(pio.sequentLevelFormula().op() instanceof UpdateApplication);
     }
 
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/informationflow/proof/InfFlowProof.java b/key.core/src/main/java/de/uka/ilkd/key/informationflow/proof/InfFlowProof.java
index cf2f9226bbe..f2827c91b52 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/informationflow/proof/InfFlowProof.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/informationflow/proof/InfFlowProof.java
@@ -5,7 +5,6 @@
 
 import de.uka.ilkd.key.informationflow.po.InfFlowProofSymbols;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.BuiltInRuleIndex;
 import de.uka.ilkd.key.proof.Proof;
@@ -98,11 +97,11 @@ public void addGoalTemplates(Taclet t) {
         ImmutableList<TacletGoalTemplate> temps = t.goalTemplates();
         assert temps != null;
         for (TacletGoalTemplate tgt : temps) {
-            for (SequentFormula sf : tgt.sequent().antecedent().asList()) {
-                addLabeledTotalTerm(sf.formula());
+            for (Term sf : tgt.sequent().antecedent().asList()) {
+                addLabeledTotalTerm(sf);
             }
-            for (SequentFormula sf : tgt.sequent().succedent().asList()) {
-                addLabeledTotalTerm(sf.formula());
+            for (Term sf : tgt.sequent().succedent().asList()) {
+                addLabeledTotalTerm(sf);
             }
         }
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/executor/InfFlowContractAppTacletExecutor.java b/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/executor/InfFlowContractAppTacletExecutor.java
index a3a7fa718f6..a32bab1b947 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/executor/InfFlowContractAppTacletExecutor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/executor/InfFlowContractAppTacletExecutor.java
@@ -43,12 +43,13 @@ protected void addToAntec(Semisequent semi, TermLabelState termLabelState,
             TacletLabelHint labelHint, SequentChangeInfo currentSequent, PosInOccurrence pos,
             PosInOccurrence applicationPosInOccurrence, MatchConditions matchCond, Goal goal,
             RuleApp tacletApp, Services services) {
-        final ImmutableList<SequentFormula> replacements = instantiateSemisequent(semi,
+        final ImmutableList<Term> replacements = instantiateSemisequent(semi,
             termLabelState, labelHint, pos, matchCond, goal, tacletApp, services);
         assert replacements.size() == 1
                 : "information flow taclets must have " + "exactly one add!";
+        final Term replacement = replacements.iterator().next();
         updateStrategyInfo(services.getProof().openEnabledGoals().head(),
-            replacements.iterator().next().formula());
+            replacement);
         super.addToAntec(semi, termLabelState, labelHint, currentSequent, pos,
             applicationPosInOccurrence, matchCond, goal, tacletApp, services);
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/tacletbuilder/AbstractInfFlowContractAppTacletBuilder.java b/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/tacletbuilder/AbstractInfFlowContractAppTacletBuilder.java
index 474082a360b..82694a57efd 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/tacletbuilder/AbstractInfFlowContractAppTacletBuilder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/informationflow/rule/tacletbuilder/AbstractInfFlowContractAppTacletBuilder.java
@@ -247,9 +247,9 @@ private Taclet genInfFlowContractApplTaclet(Goal goal, ProofObligationVars appDa
 
         // create sequents
         Sequent assumesSeq =
-            Sequent.createAnteSequent(new Semisequent(new SequentFormula(schemaAssumes)));
+            Sequent.createAnteSequent(new Semisequent(schemaAssumes));
         Sequent replaceWithSeq =
-            Sequent.createAnteSequent(new Semisequent(new SequentFormula(replaceWithTerm)));
+            Sequent.createAnteSequent(new Semisequent(replaceWithTerm));
 
         // create taclet
         InfFlowContractAppRewriteTacletBuilder tacletBuilder =
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/Comment.java b/key.core/src/main/java/de/uka/ilkd/key/java/Comment.java
index 0d556acb369..60221fca8fe 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/Comment.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/Comment.java
@@ -5,6 +5,8 @@
 
 import de.uka.ilkd.key.java.visitor.Visitor;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Comment element of Java source code.
  */
@@ -71,4 +73,14 @@ public boolean equals(Object o) {
         }
         return (getText().equals(cmp.getText()));
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("Comment has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/NonTerminalProgramElement.java b/key.core/src/main/java/de/uka/ilkd/key/java/NonTerminalProgramElement.java
index ca20a719d4d..1865f6e964c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/NonTerminalProgramElement.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/NonTerminalProgramElement.java
@@ -3,6 +3,8 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.java;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Non terminal program element. taken from COMPOST and changed to achieve an immutable structure
  */
@@ -25,4 +27,8 @@ public interface NonTerminalProgramElement extends ProgramElement {
      */
     ProgramElement getChildAt(int index);
 
+    @Override
+    default SyntaxElement getChild(int n) {
+        return getChildAt(n);
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/SourceElement.java b/key.core/src/main/java/de/uka/ilkd/key/java/SourceElement.java
index 046d51538cb..206efd7fb8e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/SourceElement.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/SourceElement.java
@@ -4,7 +4,8 @@
 package de.uka.ilkd.key.java;
 
 import de.uka.ilkd.key.java.visitor.Visitor;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
+
+import org.key_project.logic.SyntaxElement;
 
 /**
  * A source element is a piece of syntax. It does not necessarily have a semantics, at least none
@@ -12,7 +13,7 @@
  * to achieve an immutable structure
  */
 
-public interface SourceElement extends SVSubstitute {
+public interface SourceElement extends SyntaxElement {
 
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/TerminalProgramElement.java b/key.core/src/main/java/de/uka/ilkd/key/java/TerminalProgramElement.java
index 902e791ace6..e6fdc309f71 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/TerminalProgramElement.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/TerminalProgramElement.java
@@ -3,9 +3,12 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.java;
 
+import org.key_project.logic.TerminalSyntaxElement;
+
 /**
  * Terminal program element. taken from COMPOST and changed to achieve an immutable structure
  */
 
-public interface TerminalProgramElement extends ProgramElement {
+public interface TerminalProgramElement extends ProgramElement, TerminalSyntaxElement {
+
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/declaration/MethodDeclaration.java b/key.core/src/main/java/de/uka/ilkd/key/java/declaration/MethodDeclaration.java
index 04346acf3a7..fc59c65e880 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/declaration/MethodDeclaration.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/declaration/MethodDeclaration.java
@@ -163,7 +163,7 @@ public SourceElement getFirstElement() {
 
     @Override
     public SourceElement getLastElement() {
-        return getChildAt(getChildCount() - 1).getLastElement();
+        return getChildAt(this.getChildCount() - 1).getLastElement();
     }
 
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/declaration/Modifier.java b/key.core/src/main/java/de/uka/ilkd/key/java/declaration/Modifier.java
index 357d417d3ca..b8fd1e2d410 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/declaration/Modifier.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/declaration/Modifier.java
@@ -4,16 +4,16 @@
 package de.uka.ilkd.key.java.declaration;
 
 import de.uka.ilkd.key.java.JavaProgramElement;
-import de.uka.ilkd.key.java.TerminalProgramElement;
 import de.uka.ilkd.key.java.visitor.Visitor;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.ExtList;
 
 /**
  * Modifier. taken from COMPOST and changed to achieve an immutable structure
  */
 
-public abstract class Modifier extends JavaProgramElement implements TerminalProgramElement {
+public abstract class Modifier extends JavaProgramElement {
 
     /**
      * Modifier.
@@ -56,4 +56,14 @@ public String getText() {
     public void visit(Visitor v) {
         v.performActionOnModifier(this);
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(getClass() + " " + this + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/Instanceof.java b/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/Instanceof.java
index 284c254db72..d53c134154e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/Instanceof.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/Instanceof.java
@@ -31,13 +31,13 @@ public class Instanceof extends TypeOperator {
 
     public Instanceof(ExtList children) {
         super(children);
-        assert getChildCount() == 2 : "not 2 children but " + getChildCount();
+        assert this.getChildCount() == 2 : "not 2 children but " + this.getChildCount();
     }
 
 
     public Instanceof(Expression unaryChild, TypeReference typeref) {
         super(unaryChild, typeref);
-        assert getChildCount() == 2 : "not 2 children but " + getChildCount();
+        assert this.getChildCount() == 2 : "not 2 children but " + this.getChildCount();
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/New.java b/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/New.java
index bc7027d5498..6d041245c71 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/New.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/expression/operator/New.java
@@ -99,7 +99,7 @@ public SourceElement getFirstElementIncludingBlocks() {
 
     @Override
     public SourceElement getLastElement() {
-        return getChildAt(getChildCount() - 1).getLastElement();
+        return getChildAt(this.getChildCount() - 1).getLastElement();
     }
 
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/statement/IForUpdates.java b/key.core/src/main/java/de/uka/ilkd/key/java/statement/IForUpdates.java
index a532522aa5e..75d499d1cdf 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/statement/IForUpdates.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/statement/IForUpdates.java
@@ -7,7 +7,7 @@
 
 import org.key_project.util.collection.ImmutableArray;
 
-public interface IForUpdates extends de.uka.ilkd.key.java.TerminalProgramElement {
+public interface IForUpdates extends de.uka.ilkd.key.java.NonTerminalProgramElement {
 
     int size();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/statement/ILoopInit.java b/key.core/src/main/java/de/uka/ilkd/key/java/statement/ILoopInit.java
index c8528112d4d..ee0bc657b95 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/statement/ILoopInit.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/statement/ILoopInit.java
@@ -4,11 +4,11 @@
 package de.uka.ilkd.key.java.statement;
 
 import de.uka.ilkd.key.java.LoopInitializer;
-import de.uka.ilkd.key.java.TerminalProgramElement;
+import de.uka.ilkd.key.java.NonTerminalProgramElement;
 
 import org.key_project.util.collection.ImmutableArray;
 
-public interface ILoopInit extends TerminalProgramElement {
+public interface ILoopInit extends NonTerminalProgramElement {
 
     int size();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/statement/LoopScopeBlock.java b/key.core/src/main/java/de/uka/ilkd/key/java/statement/LoopScopeBlock.java
index 90b373e1438..60d71b65f31 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/statement/LoopScopeBlock.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/statement/LoopScopeBlock.java
@@ -107,7 +107,7 @@ public ImmutableArray<ProgramPrefix> getPrefixElements() {
     @Override
     public PosInProgram getFirstActiveChildPos() {
         return getStatementCount() == 0 ? PosInProgram.TOP
-                : PosInProgram.TOP.down(getChildCount() - 1).down(0);
+                : PosInProgram.TOP.down(this.getChildCount() - 1).down(0);
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/statement/MethodFrame.java b/key.core/src/main/java/de/uka/ilkd/key/java/statement/MethodFrame.java
index ede5682ff23..105e3ab446a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/statement/MethodFrame.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/statement/MethodFrame.java
@@ -53,7 +53,8 @@ public MethodFrame(IProgramVariable resultVar, IExecutionContext execContext,
         this.execContext = execContext;
 
         firstActiveChildPos =
-            body.isEmpty() ? PosInProgram.TOP : PosInProgram.TOP.down(getChildCount() - 1).down(0);
+            body.isEmpty() ? PosInProgram.TOP
+                    : PosInProgram.TOP.down(getChildCount() - 1).down(0);
 
         Debug.assertTrue(execContext != null, "methodframe: executioncontext missing");
         Debug.assertTrue(body != null, "methodframe: body missing");
@@ -78,7 +79,8 @@ public MethodFrame(IProgramVariable resultVar, IExecutionContext execContext,
         this.execContext = execContext;
 
         firstActiveChildPos =
-            body.isEmpty() ? PosInProgram.TOP : PosInProgram.TOP.down(getChildCount() - 1).down(0);
+            body.isEmpty() ? PosInProgram.TOP
+                    : PosInProgram.TOP.down(getChildCount() - 1).down(0);
 
 
         Debug.assertTrue(execContext != null, "methodframe: executioncontext missing");
diff --git a/key.core/src/main/java/de/uka/ilkd/key/java/statement/Try.java b/key.core/src/main/java/de/uka/ilkd/key/java/statement/Try.java
index 9011234e233..02386a7c6e9 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/java/statement/Try.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/java/statement/Try.java
@@ -137,7 +137,7 @@ public SourceElement getFirstElement() {
 
 
     public SourceElement getLastElement() {
-        return getChildAt(getChildCount() - 1).getLastElement();
+        return getChildAt(this.getChildCount() - 1).getLastElement();
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/BoundVarsVisitor.java b/key.core/src/main/java/de/uka/ilkd/key/logic/BoundVarsVisitor.java
index da51f6c54f6..76f5407d600 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/BoundVarsVisitor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/BoundVarsVisitor.java
@@ -40,8 +40,8 @@ public void visit(Term visited) {
      * visits a sequent
      */
     public void visit(Sequent visited) {
-        for (SequentFormula cf : visited) {
-            visit(cf.formula());
+        for (Term cf : visited) {
+            visit(cf);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/FormulaChangeInfo.java b/key.core/src/main/java/de/uka/ilkd/key/logic/FormulaChangeInfo.java
index a01138a9dfb..e7c72d25703 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/FormulaChangeInfo.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/FormulaChangeInfo.java
@@ -10,10 +10,10 @@
  * @param newFormula             modified formula
  * @see SequentChangeInfo
  */
-public record FormulaChangeInfo(PosInOccurrence positionOfModification, SequentFormula newFormula) {
+public record FormulaChangeInfo(PosInOccurrence positionOfModification, Term newFormula) {
 
-    public SequentFormula getOriginalFormula() {
-        return positionOfModification().sequentFormula();
+    public Term getOriginalFormula() {
+        return positionOfModification().sequentLevelFormula();
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/JavaBlock.java b/key.core/src/main/java/de/uka/ilkd/key/logic/JavaBlock.java
index b7d72e26382..9f18163e5e7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/JavaBlock.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/JavaBlock.java
@@ -8,6 +8,7 @@
 import de.uka.ilkd.key.pp.PrettyPrinter;
 
 import org.key_project.logic.Program;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.EqualsModProofIrrelevancy;
 
 import org.slf4j.Logger;
@@ -128,4 +129,18 @@ public int hashCodeModProofIrrelevancy() {
         }
         return hashCode;
     }
+
+    @Override
+    public int getChildCount() {
+        if (prg == null || this == EMPTY_JAVABLOCK)
+            return 0;
+        return 1;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        if (n == 0)
+            return prg;
+        throw new IndexOutOfBoundsException("JavaBlock " + this + " has only one child");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/PosInOccurrence.java b/key.core/src/main/java/de/uka/ilkd/key/logic/PosInOccurrence.java
index 0674d8b557b..03c6dd859e0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/PosInOccurrence.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/PosInOccurrence.java
@@ -3,9 +3,11 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.logic;
 
+import java.util.Objects;
+
 /**
- * This class describes a position in an occurrence of a term. A SequentFormula and a PosInTerm
- * determine an object of this class exactly.
+ * This class describes the position of an occurrence of a term within a formula.
+ * The top level formula and a {@link PosInTerm} which describes the exact occurrence.
  */
 public final class PosInOccurrence {
 
@@ -17,7 +19,7 @@ public static PosInOccurrence findInSequent(Sequent seq, int formulaNumber, PosI
     /**
      * the constrained formula the pos in occurrence describes
      */
-    private final SequentFormula sequentFormula;
+    private final Term sequentLevelFormula;
 
     // saves 8 bytes (due to alignment issues) per instance if we use a
     // short here instead of an int
@@ -28,7 +30,7 @@ public static PosInOccurrence findInSequent(Sequent seq, int formulaNumber, PosI
      */
     private final boolean inAntec;
 
-    /** the position in sequentFormula.formula() */
+    /** the position in sequentLevelFormula */
     private final PosInTerm posInTerm;
 
     /**
@@ -36,20 +38,20 @@ public static PosInOccurrence findInSequent(Sequent seq, int formulaNumber, PosI
      */
     private volatile Term subTermCache = null;
 
-    public PosInOccurrence(SequentFormula sequentFormula, PosInTerm posInTerm, boolean inAntec) {
+    public PosInOccurrence(Term sequentLevelFormula, PosInTerm posInTerm, boolean inAntec) {
         assert posInTerm != null;
-        assert sequentFormula != null;
+        assert sequentLevelFormula != null;
         this.inAntec = inAntec;
-        this.sequentFormula = sequentFormula;
+        this.sequentLevelFormula = sequentLevelFormula;
         this.posInTerm = posInTerm;
-        this.hashCode = (short) (sequentFormula.hashCode() * 13 + posInTerm.hashCode());
+        this.hashCode = (short) Objects.hash(sequentLevelFormula, inAntec, posInTerm);
     }
 
     /**
-     * returns the SequentFormula that determines the occurrence of this PosInOccurrence
+     * returns the Term that determines the occurrence of this PosInOccurrence
      */
-    public SequentFormula sequentFormula() {
-        return sequentFormula;
+    public Term sequentLevelFormula() {
+        return sequentLevelFormula;
     }
 
     /**
@@ -66,7 +68,7 @@ public int depth() {
      * {@link de.uka.ilkd.key.logic.PosInTerm}.
      */
     public PosInOccurrence down(int i) {
-        return new PosInOccurrence(sequentFormula, posInTerm.down(i), inAntec);
+        return new PosInOccurrence(sequentLevelFormula, posInTerm.down(i), inAntec);
     }
 
     /**
@@ -78,7 +80,7 @@ public boolean eqEquals(Object obj) {
             return false;
         }
 
-        if (!sequentFormula.equals(cmp.sequentFormula)) {
+        if (!sequentLevelFormula.equals(cmp.sequentLevelFormula)) {
             return false;
         }
 
@@ -100,7 +102,7 @@ public boolean equals(Object obj) {
 
         // NB: the class <code>NonDuplicateAppFeature</code> depends on the usage
         // of <code>!=</code> in this condition
-        if (sequentFormula() != cmp.sequentFormula()) {
+        if (sequentLevelFormula() != cmp.sequentLevelFormula()) {
             return false;
         }
 
@@ -139,7 +141,7 @@ public boolean isTopLevel() {
 
     /**
      * List all subterms between the root and the position this objects points to; the first term is
-     * the whole term <code>constrainedFormula().formula()</code>, the last one
+     * the whole sequent level <code>formula</code>, the last one
      * <code>subTerm()</code>
      *
      * @return an iterator that walks from the root of the term to the position this
@@ -151,10 +153,9 @@ public PIOPathIterator iterator() {
 
     /**
      * The usage of this method is strongly discouraged, use {@link PosInOccurrence#iterator}
-     * instead. describes the exact occurrence of the referred term inside
-     * {@link SequentFormula#formula()}
+     * instead. describes the exact occurrence of the referred term
      *
-     * @return the position in the formula of the SequentFormula of this PosInOccurrence.
+     * @return the position of the occurrence within the sequent level formula.
      */
     public PosInTerm posInTerm() {
         return posInTerm;
@@ -169,9 +170,9 @@ public PosInTerm posInTerm() {
      *         <code>constrainedFormula()</code>. It is not tested whether this position exists
      *         within <code>p_newFormula</code>
      */
-    public PosInOccurrence replaceConstrainedFormula(SequentFormula p_newFormula) {
+    public PosInOccurrence replaceConstrainedFormula(Term p_newFormula) {
         assert p_newFormula != null;
-        if (p_newFormula == sequentFormula) {
+        if (p_newFormula == sequentLevelFormula) {
             return this;
         }
         return new PosInOccurrence(p_newFormula, posInTerm, inAntec);
@@ -182,7 +183,7 @@ public PosInOccurrence replaceConstrainedFormula(SequentFormula p_newFormula) {
      */
     public Term subTerm() {
         if (subTermCache == null) {
-            subTermCache = posInTerm.getSubTerm(sequentFormula.formula());
+            subTermCache = posInTerm.getSubTerm(sequentLevelFormula);
         }
         return subTermCache;
     }
@@ -194,13 +195,13 @@ public PosInOccurrence topLevel() {
         if (isTopLevel()) {
             return this;
         }
-        return new PosInOccurrence(sequentFormula, PosInTerm.getTopLevel(), inAntec);
+        return new PosInOccurrence(sequentLevelFormula, PosInTerm.getTopLevel(), inAntec);
     }
 
 
     /** toString */
     public String toString() {
-        return "Term " + posInTerm() + " of " + sequentFormula();
+        return "Term " + posInTerm() + " of " + sequentLevelFormula();
     }
 
 
@@ -211,7 +212,7 @@ public String toString() {
     public PosInOccurrence up() {
         assert !isTopLevel() : "not possible to go up from top level position";
 
-        return new PosInOccurrence(sequentFormula, posInTerm.up(), inAntec);
+        return new PosInOccurrence(sequentLevelFormula, posInTerm.up(), inAntec);
 
     }
 
@@ -244,7 +245,7 @@ public PosInOccurrence getPosInOccurrence() {
             // <code>next()</code> faster
 
             final PosInOccurrence pio;
-            pio = new PosInOccurrence(sequentFormula, posInTerm.firstN(count - 1), inAntec);
+            pio = new PosInOccurrence(sequentLevelFormula, posInTerm.firstN(count - 1), inAntec);
 
 
             return pio;
@@ -271,7 +272,7 @@ public int next() {
             int res;
 
             if (currentSubTerm == null) {
-                currentSubTerm = sequentFormula.formula();
+                currentSubTerm = sequentLevelFormula;
             } else {
                 currentSubTerm = currentSubTerm.sub(child);
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/ProgramConstruct.java b/key.core/src/main/java/de/uka/ilkd/key/logic/ProgramConstruct.java
index 70bd980e18b..8b68b44f4dc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/ProgramConstruct.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/ProgramConstruct.java
@@ -18,6 +18,8 @@
 import de.uka.ilkd.key.logic.op.IProgramMethod;
 import de.uka.ilkd.key.logic.op.IProgramVariable;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * A type that implement this interface can be used in all java programs instead of an expression or
  * statement. For example class SchemaVariable implements this interface to be able to stand for
@@ -26,4 +28,9 @@
 public interface ProgramConstruct extends Expression, Statement, ILoopInit, IForUpdates, IGuard,
         Label, TerminalProgramElement, ExpressionStatement, TypeReference, IProgramVariable,
         IProgramMethod, Branch, IExecutionContext, MethodName {
+    @Override
+    SyntaxElement getChild(int n);
+
+    @Override
+    int getChildCount();
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/Semisequent.java b/key.core/src/main/java/de/uka/ilkd/key/logic/Semisequent.java
index a8ce511c4fb..f858fe328cc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/Semisequent.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/Semisequent.java
@@ -18,12 +18,12 @@
  * future versions it can be enhanced to do other simplifications. A sequent and so a semisequent
  * has to be immutable.
  */
-public class Semisequent implements Iterable<SequentFormula> {
+public class Semisequent implements Iterable<Term> {
 
     /** the empty semisequent (using singleton pattern) */
     public static final Semisequent EMPTY_SEMISEQUENT = new Empty();
-    /** list with the {@link SequentFormula}s of the Semisequent */
-    private final ImmutableList<SequentFormula> seqList;
+    /** list with the {@link Term}s of the Semisequent */
+    private final ImmutableList<Term> seqList;
 
     /** used by inner class Empty */
     private Semisequent() {
@@ -37,7 +37,7 @@ private Semisequent() {
      *
      * @param seqList list of sequent formulas
      */
-    public Semisequent(ImmutableList<SequentFormula> seqList) {
+    public Semisequent(ImmutableList<Term> seqList) {
         assert !seqList.isEmpty();
         this.seqList = seqList;
     }
@@ -49,7 +49,7 @@ public Semisequent(ImmutableList<SequentFormula> seqList) {
      *
      * @param seqList list of sequent formulas
      */
-    public Semisequent(Collection<SequentFormula> seqList) {
+    public Semisequent(Collection<Term> seqList) {
         assert !seqList.isEmpty();
         this.seqList = ImmutableList.fromList(seqList);
     }
@@ -62,7 +62,7 @@ public Semisequent(Collection<SequentFormula> seqList) {
      *
      * @param seqList list of sequent formulas
      */
-    public static Semisequent create(Collection<SequentFormula> seqList) {
+    public static Semisequent create(Collection<Term> seqList) {
         if (seqList.isEmpty()) {
             return EMPTY_SEMISEQUENT;
         }
@@ -73,9 +73,9 @@ public static Semisequent create(Collection<SequentFormula> seqList) {
     /**
      * creates a new Semisequent with the Semisequent elements in seqList
      */
-    public Semisequent(SequentFormula seqFormula) {
+    public Semisequent(Term seqFormula) {
         assert seqFormula != null;
-        this.seqList = ImmutableSLList.<SequentFormula>nil().append(seqFormula);
+        this.seqList = ImmutableSLList.<Term>nil().append(seqFormula);
     }
 
 
@@ -84,23 +84,23 @@ public Semisequent(SequentFormula seqFormula) {
      * returning same semisequent if inserting would create redundancies
      *
      * @param idx int encoding the place the element has to be put
-     * @param sequentFormula {@link SequentFormula} to be inserted
+     * @param fml {@link Term} to be inserted
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insert(int idx, SequentFormula sequentFormula) {
-        return removeRedundance(idx, sequentFormula);
+    public SemisequentChangeInfo insert(int idx, Term fml) {
+        return removeRedundance(idx, fml);
     }
 
     /**
      * inserts the elements of the list at the specified index performing redundancy checks
      *
      * @param idx int encoding the place where the insertion starts
-     * @param insertionList IList<SequentFormula> to be inserted starting at idx
+     * @param insertionList IList<Term> to be inserted starting at idx
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insert(int idx, ImmutableList<SequentFormula> insertionList) {
+    public SemisequentChangeInfo insert(int idx, ImmutableList<Term> insertionList) {
         return removeRedundance(idx, insertionList);
     }
 
@@ -108,23 +108,23 @@ public SemisequentChangeInfo insert(int idx, ImmutableList<SequentFormula> inser
      * inserts element at index 0 performing redundancy checks, this may result in returning same
      * semisequent if inserting would create redundancies
      *
-     * @param sequentFormula SequentFormula to be inserted
+     * @param fml the Term to be inserted
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insertFirst(SequentFormula sequentFormula) {
-        return insert(0, sequentFormula);
+    public SemisequentChangeInfo insertFirst(Term fml) {
+        return insert(0, fml);
     }
 
     /**
      * inserts element at index 0 performing redundancy checks, this may result in returning same
      * semisequent if inserting would create redundancies
      *
-     * @param insertions IList<SequentFormula> to be inserted
+     * @param insertions IList<Term> to be inserted
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insertFirst(ImmutableList<SequentFormula> insertions) {
+    public SemisequentChangeInfo insertFirst(ImmutableList<Term> insertions) {
         return insert(0, insertions);
     }
 
@@ -132,23 +132,23 @@ public SemisequentChangeInfo insertFirst(ImmutableList<SequentFormula> insertion
      * inserts element at the end of the semisequent performing redundancy checks, this may result
      * in returning same semisequent if inserting would create redundancies
      *
-     * @param sequentFormula {@link SequentFormula} to be inserted
+     * @param fml {@link Term} to be inserted
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insertLast(SequentFormula sequentFormula) {
-        return insert(size(), sequentFormula);
+    public SemisequentChangeInfo insertLast(Term fml) {
+        return insert(size(), fml);
     }
 
     /**
      * inserts the formulas of the list at the end of the semisequent performing redundancy checks,
      * this may result in returning same semisequent if inserting would create redundancies
      *
-     * @param insertions the IList<SequentFormula> to be inserted
+     * @param insertions the IList<Term> to be inserted
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo insertLast(ImmutableList<SequentFormula> insertions) {
+    public SemisequentChangeInfo insertLast(ImmutableList<Term> insertions) {
         return insert(size(), insertions);
     }
 
@@ -163,21 +163,21 @@ public boolean isEmpty() {
 
 
     /**
-     * inserts new SequentFormula at index idx and removes duplicates, perform simplifications etc.
+     * inserts new fml at index idx and removes duplicates, perform simplifications etc.
      *
      * @param fci null if the formula to be added is new, otherwise an object telling which formula
-     *        is replaced with the new formula <code>sequentFormula</code>, and what are the
+     *        is replaced with the new formula <code>fml</code>, and what are the
      *        differences between the two formulas
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
     private SemisequentChangeInfo insertAndRemoveRedundancyHelper(int idx,
-            SequentFormula sequentFormula, SemisequentChangeInfo semiCI, FormulaChangeInfo fci) {
+            Term fml, SemisequentChangeInfo semiCI, FormulaChangeInfo fci) {
 
         // Search for equivalent formulas and weakest constraint
-        ImmutableList<SequentFormula> searchList = semiCI.getFormulaList();
-        final SequentFormula[] newSeqList = new SequentFormula[searchList.size()];
-        SequentFormula cf;
+        ImmutableList<Term> searchList = semiCI.getFormulaList();
+        final Term[] newSeqList = new Term[searchList.size()];
+        Term cf;
         int pos = -1;
 
         while (!searchList.isEmpty()) {
@@ -185,12 +185,13 @@ private SemisequentChangeInfo insertAndRemoveRedundancyHelper(int idx,
             cf = searchList.head();
             searchList = searchList.tail();
 
-            if (sequentFormula != null
-                    && cf.formula().equalsModProperty(sequentFormula.formula(),
-                        RENAMING_PROPERTY)) {
-                semiCI.rejectedFormula(sequentFormula);
-                return semiCI; // semisequent already contains formula
+            if (fml != null) {
+                if (cf.equalsModProperty(fml,
+                    RENAMING_PROPERTY)) {
+                    semiCI.rejectedFormula(fml);
+                    return semiCI; // semisequent already contains formula
 
+                }
             }
             newSeqList[pos] = cf;
         }
@@ -198,15 +199,15 @@ private SemisequentChangeInfo insertAndRemoveRedundancyHelper(int idx,
 
         // compose resulting formula list
         if (fci == null) {
-            semiCI.addedFormula(idx, sequentFormula);
+            semiCI.addedFormula(idx, fml);
         } else {
             semiCI.modifiedFormula(idx, fci);
         }
 
-        final ImmutableList<SequentFormula> orig = semiCI.getFormulaList();
+        final ImmutableList<Term> orig = semiCI.getFormulaList();
         pos = Math.min(idx, orig.size());
 
-        searchList = semiCI.getFormulaList().take(pos).prepend(sequentFormula);
+        searchList = semiCI.getFormulaList().take(pos).prepend(fml);
 
         while (pos > 0) {
             --pos;
@@ -223,23 +224,23 @@ private SemisequentChangeInfo insertAndRemoveRedundancyHelper(int idx,
      * . inserts new ConstrainedFormulas starting at index idx and removes duplicates, perform
      * simplifications etc.
      *
-     * @param sequentFormulasToBeInserted the {@link ImmutableList<SequentFormula>} to be inserted
+     * @param TermsToBeInserted the {@link ImmutableList<Term>} to be inserted
      *        at position idx
-     * @param idx an int that means insert sequentFormula at the idx-th position in the semisequent
+     * @param idx an int that means insert Term at the idx-th position in the semisequent
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
     private SemisequentChangeInfo insertAndRemoveRedundancy(int idx,
-            ImmutableList<SequentFormula> sequentFormulasToBeInserted, SemisequentChangeInfo sci) {
+            ImmutableList<Term> TermsToBeInserted, SemisequentChangeInfo sci) {
 
         int pos = idx;
-        ImmutableList<SequentFormula> oldFormulas = sci.getFormulaList();
+        ImmutableList<Term> oldFormulas = sci.getFormulaList();
 
-        while (!sequentFormulasToBeInserted.isEmpty()) {
-            final SequentFormula aSequentFormula = sequentFormulasToBeInserted.head();
-            sequentFormulasToBeInserted = sequentFormulasToBeInserted.tail();
+        while (!TermsToBeInserted.isEmpty()) {
+            final Term aTerm = TermsToBeInserted.head();
+            TermsToBeInserted = TermsToBeInserted.tail();
 
-            sci = insertAndRemoveRedundancyHelper(pos, aSequentFormula, sci, null);
+            sci = insertAndRemoveRedundancyHelper(pos, aTerm, sci, null);
 
             if (sci.getFormulaList() != oldFormulas) {
                 pos = sci.getIndex() + 1;
@@ -253,55 +254,55 @@ private SemisequentChangeInfo insertAndRemoveRedundancy(int idx,
      * . inserts new ConstrainedFormulas starting at index idx and removes duplicates, perform
      * simplifications etc.
      *
-     * @param sequentFormula the IList<SequentFormula> to be inserted at position idx
-     * @param idx an int that means insert sequentFormula at the idx-th position in the semisequent
+     * @param Term the IList<Term> to be inserted at position idx
+     * @param idx an int that means insert Term at the idx-th position in the semisequent
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
     private SemisequentChangeInfo removeRedundance(int idx,
-            ImmutableList<SequentFormula> sequentFormula) {
-        return insertAndRemoveRedundancy(idx, sequentFormula, new SemisequentChangeInfo(seqList));
+            ImmutableList<Term> Term) {
+        return insertAndRemoveRedundancy(idx, Term, new SemisequentChangeInfo(seqList));
     }
 
 
     /**
-     * . inserts new SequentFormula at index {@code idx} and removes duplicates, perform
+     * . inserts new fml at index {@code idx} and removes duplicates, perform
      * simplifications etc.
      *
-     * @param sequentFormula the SequentFormula to be inserted at position idx
-     * @param idx an int that means insert sequentFormula at the idx-th position in the semisequent
-     * @return new Semisequent with sequentFormula at index idx and removed redundancies
+     * @param fml the fml to be inserted at position idx
+     * @param idx an int that means insert fml at the idx-th position in the semisequent
+     * @return new Semisequent with fml at index idx and removed redundancies
      */
-    private SemisequentChangeInfo removeRedundance(int idx, SequentFormula sequentFormula) {
-        return insertAndRemoveRedundancyHelper(idx, sequentFormula,
+    private SemisequentChangeInfo removeRedundance(int idx, Term fml) {
+        return insertAndRemoveRedundancyHelper(idx, fml,
             new SemisequentChangeInfo(seqList), null);
     }
 
 
     /**
-     * replaces the element at place idx with sequentFormula
+     * replaces the element at place idx with fml
      *
      * @param pos the PosInOccurrence describing the position of and within the formula below which
-     *        the formula differs from the new formula <code>sequentFormula</code>
-     * @param sequentFormula the SequentFormula replacing the old element at index idx
+     *        the formula differs from the new formula <code>fml</code>
+     * @param fml the fml replacing the old element at index idx
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
-    public SemisequentChangeInfo replace(PosInOccurrence pos, SequentFormula sequentFormula) {
-        final int idx = indexOf(pos.sequentFormula());
-        final FormulaChangeInfo fci = new FormulaChangeInfo(pos, sequentFormula);
-        return insertAndRemoveRedundancyHelper(idx, sequentFormula, remove(idx), fci);
+    public SemisequentChangeInfo replace(PosInOccurrence pos, Term fml) {
+        final int idx = indexOf(pos.sequentLevelFormula());
+        final FormulaChangeInfo fci = new FormulaChangeInfo(pos, fml);
+        return insertAndRemoveRedundancyHelper(idx, fml, remove(idx), fci);
     }
 
     /**
-     * replaces the <tt>idx</tt>-th formula by <tt>sequentFormula</tt>
+     * replaces the <tt>idx</tt>-th formula by <tt>fml</tt>
      *
      * @param idx the int with the position of the formula to be replaced
-     * @param sequentFormula the SequentFormula replacing the formula at the given position
+     * @param fml the fml replacing the formula at the given position
      * @return a SemisequentChangeInfo containing the new sequent and a diff to the old one
      */
-    public SemisequentChangeInfo replace(int idx, SequentFormula sequentFormula) {
-        return insertAndRemoveRedundancyHelper(idx, sequentFormula, remove(idx), null);
+    public SemisequentChangeInfo replace(int idx, Term fml) {
+        return insertAndRemoveRedundancyHelper(idx, fml, remove(idx), null);
     }
 
     /**
@@ -309,14 +310,14 @@ public SemisequentChangeInfo replace(int idx, SequentFormula sequentFormula) {
      * of the list to the semisequent behind the replaced formula
      *
      * @param pos the formula to be replaced
-     * @param replacements the IList<SequentFormula> whose head replaces the element at index idx
+     * @param replacements the IList<Term> whose head replaces the element at index idx
      *        and the tail is added to the semisequent
      * @return a semi sequent change information object with the new semisequent and information
      *         which formulas have been added or removed
      */
     public SemisequentChangeInfo replace(PosInOccurrence pos,
-            ImmutableList<SequentFormula> replacements) {
-        final int idx = indexOf(pos.sequentFormula());
+            ImmutableList<Term> replacements) {
+        final int idx = indexOf(pos.sequentLevelFormula());
         return insertAndRemoveRedundancy(idx, replacements, remove(idx));
     }
 
@@ -327,7 +328,7 @@ public SemisequentChangeInfo replace(PosInOccurrence pos,
      * @param replacements the new formulas
      * @return change information including the resulting semisequent after the replacement
      */
-    public SemisequentChangeInfo replace(int idx, ImmutableList<SequentFormula> replacements) {
+    public SemisequentChangeInfo replace(int idx, ImmutableList<Term> replacements) {
         return insertAndRemoveRedundancy(idx, replacements, remove(idx));
     }
 
@@ -346,14 +347,14 @@ public int size() {
      */
     public SemisequentChangeInfo remove(int idx) {
 
-        ImmutableList<SequentFormula> newList = seqList;
+        ImmutableList<Term> newList = seqList;
         int index = 0;
 
         if (idx < 0 || idx >= size()) {
             return new SemisequentChangeInfo(seqList);
         }
 
-        final SequentFormula[] temp = new SequentFormula[idx];
+        final Term[] temp = new Term[idx];
 
         while (index < idx) {// go to idx
             temp[index] = newList.head();
@@ -362,7 +363,7 @@ public SemisequentChangeInfo remove(int idx) {
         }
 
         // remove the element that is at head of newList
-        final SequentFormula removedFormula = newList.head();
+        final Term removedFormula = newList.head();
         newList = newList.tail();
 
         for (int k = index - 1; k >= 0; k--) {
@@ -377,18 +378,18 @@ public SemisequentChangeInfo remove(int idx) {
     }
 
     /**
-     * returns the index of the given {@link SequentFormula} or {@code -1} if the sequent formula is
-     * not found. Equality of sequent formulas is checked sing the identy check (i.e.,
+     * returns the index of the given {@link Term} or {@code -1} if the sequent formula is
+     * not found. Identity (not equality) of sequent formulas is checked (i.e.,
      * <code>==</code>)
      *
-     * @param sequentFormula the {@link SequentFormula} to look for
-     * @return index of sequentFormula (-1 if not found)
+     * @param fml the {@link Term} to look for
+     * @return index of fml (-1 if not found)
      */
-    public int indexOf(SequentFormula sequentFormula) {
-        ImmutableList<SequentFormula> searchList = seqList;
+    public int indexOf(Term fml) {
+        ImmutableList<Term> searchList = seqList;
         int index = 0;
         while (!searchList.isEmpty()) {
-            if (searchList.head() == sequentFormula) {
+            if (searchList.head() == fml) {
                 return index;
             }
             searchList = searchList.tail();
@@ -401,53 +402,53 @@ public int indexOf(SequentFormula sequentFormula) {
      * gets the element at a specific index
      *
      * @param idx int representing the index of the element we want to have
-     * @return {@link SequentFormula} found at index idx
+     * @return {@link Term} found at index idx
      * @throws IndexOutOfBoundsException if idx is negative or greater or equal to
      *         {@link Sequent#size()}
      */
-    public SequentFormula get(int idx) {
+    public Term get(int idx) {
         if (idx < 0 || idx >= seqList.size()) {
             throw new IndexOutOfBoundsException();
         }
         return seqList.take(idx).head();
     }
 
-    /** @return the first {@link SequentFormula} of this Semisequent */
-    public SequentFormula getFirst() {
+    /** @return the first {@link Term} of this Semisequent */
+    public Term getFirst() {
         return seqList.head();
     }
 
     /**
-     * checks if the {@link SequentFormula} occurs in this Semisequent (identity check)
+     * checks if the {@link Term} occurs in this Semisequent (identity check)
      *
-     * @param sequentFormula the {@link SequentFormula} to look for
-     * @return true iff. sequentFormula has been found in this Semisequent
+     * @param fml the {@link Term} to look for
+     * @return true iff. fml has been found in this Semisequent
      */
-    public boolean contains(SequentFormula sequentFormula) {
-        return indexOf(sequentFormula) != -1;
+    public boolean contains(Term fml) {
+        return indexOf(fml) != -1;
     }
 
     /**
-     * checks if a {@link SequentFormula} is in this Semisequent (equality check)
+     * checks if a {@link Term} is in this Semisequent (equality check)
      *
-     * @param sequentFormula the {@link SequentFormula} to look for
-     * @return true iff. sequentFormula has been found in this Semisequent
+     * @param fml the {@link Term} to look for
+     * @return true iff. fml has been found in this Semisequent
      */
-    public boolean containsEqual(SequentFormula sequentFormula) {
-        return seqList.contains(sequentFormula);
+    public boolean containsEqual(Term fml) {
+        return seqList.contains(fml);
     }
 
     /**
      * returns iterator about the elements of the sequent
      *
-     * @return Iterator<SequentFormula>
+     * @return Iterator<Term>
      */
     @Override
-    public Iterator<SequentFormula> iterator() {
+    public Iterator<Term> iterator() {
         return seqList.iterator();
     }
 
-    public ImmutableList<SequentFormula> asList() {
+    public ImmutableList<Term> asList() {
         return seqList;
     }
 
@@ -459,21 +460,17 @@ public boolean equals(Object o) {
         return seqList.equals(((Semisequent) o).seqList);
     }
 
-
     @Override
     public int hashCode() {
         return seqList.hashCode();
     }
 
-
     /** @return String representation of this Semisequent */
     @Override
     public String toString() {
         return seqList.toString();
     }
 
-
-
     // inner class used to represent an empty semisequent
     private static class Empty extends Semisequent {
 
@@ -485,40 +482,40 @@ private Empty() {
          * inserts the element always at index 0 ignores the first argument
          *
          * @param idx int encoding the place the element has to be put
-         * @param sequentFormula {@link SequentFormula} to be inserted
-         * @return semisequent change information object with new semisequent with sequentFormula at
+         * @param fml {@link Term} to be inserted
+         * @return semisequent change information object with new semisequent with fml at
          *         place idx
          */
         @Override
-        public SemisequentChangeInfo insert(int idx, SequentFormula sequentFormula) {
-            return insertFirst(sequentFormula);
+        public SemisequentChangeInfo insert(int idx, Term fml) {
+            return insertFirst(fml);
         }
 
         /**
          * inserts the element at index 0
          *
-         * @param sequentFormula {@link SequentFormula} to be inserted
-         * @return semisequent change information object with new semisequent with sequentFormula at
+         * @param fml {@link Term} to be inserted
+         * @return semisequent change information object with new semisequent with Term at
          *         place idx
          */
         @Override
-        public SemisequentChangeInfo insertFirst(SequentFormula sequentFormula) {
+        public SemisequentChangeInfo insertFirst(Term fml) {
             final SemisequentChangeInfo sci = new SemisequentChangeInfo(
-                ImmutableSLList.<SequentFormula>nil().prepend(sequentFormula));
-            sci.addedFormula(0, sequentFormula);
+                ImmutableSLList.<Term>nil().prepend(fml));
+            sci.addedFormula(0, fml);
             return sci;
         }
 
         /**
          * inserts the element at the end of the semisequent
          *
-         * @param sequentFormula {@link SequentFormula} to be inserted
-         * @return semisequent change information object with new semisequent with sequentFormula at
+         * @param fml {@link Term} to be inserted
+         * @return semisequent change information object with new semisequent with fml at
          *         place idx
          */
         @Override
-        public SemisequentChangeInfo insertLast(SequentFormula sequentFormula) {
-            return insertFirst(sequentFormula);
+        public SemisequentChangeInfo insertLast(Term fml) {
+            return insertFirst(fml);
         }
 
 
@@ -533,16 +530,16 @@ public boolean isEmpty() {
         }
 
         /**
-         * replaces the element at place idx with sequentFormula
+         * replaces the element at place idx with Term
          *
          * @param idx an int specifying the index of the element that has to be replaced
-         * @param sequentFormula the {@link SequentFormula} replacing the old element at index idx
-         * @return semisequent change information object with new semisequent with sequentFormula at
+         * @param fml the {@link Term} replacing the old element at index idx
+         * @return semisequent change information object with new semisequent with Term at
          *         place idx
          */
         @Override
-        public SemisequentChangeInfo replace(int idx, SequentFormula sequentFormula) {
-            return insertFirst(sequentFormula);
+        public SemisequentChangeInfo replace(int idx, Term fml) {
+            return insertFirst(fml);
         }
 
         /** @return int counting the elements of this semisequent */
@@ -563,13 +560,13 @@ public SemisequentChangeInfo remove(int idx) {
         }
 
         /**
-         * returns index of a {@link SequentFormula}
+         * returns index of a {@link Term}
          *
-         * @param sequentFormula the {@link SequentFormula} the index want to be determined
-         * @return index of sequentFormula
+         * @param fml the {@link Term} the index want to be determined
+         * @return index of Term
          */
         @Override
-        public int indexOf(SequentFormula sequentFormula) {
+        public int indexOf(Term fml) {
             return -1;
         }
 
@@ -577,29 +574,29 @@ public int indexOf(SequentFormula sequentFormula) {
          * gets the element at a specific index
          *
          * @param idx int representing the index of the element we want to have
-         * @return {@link SequentFormula} found at index idx
+         * @return {@link Term} found at index idx
          */
         @Override
-        public SequentFormula get(int idx) {
+        public Term get(int idx) {
             return null;
         }
 
         /**
-         * @return the first SequentFormula of this Semisequent
+         * @return the first Term of this Semisequent
          */
         @Override
-        public SequentFormula getFirst() {
+        public Term getFirst() {
             return null;
         }
 
         /**
-         * checks if a {@link SequentFormula} is in this Semisequent
+         * checks if a {@link Term} is in this Semisequent
          *
-         * @param sequentFormula the {@link SequentFormula} to look for
-         * @return true iff. sequentFormula has been found in this Semisequent
+         * @param fml the {@link Term} to look for
+         * @return true iff. Term has been found in this Semisequent
          */
         @Override
-        public boolean contains(SequentFormula sequentFormula) {
+        public boolean contains(Term fml) {
             return false;
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/SemisequentChangeInfo.java b/key.core/src/main/java/de/uka/ilkd/key/logic/SemisequentChangeInfo.java
index fdb9d8e3aa5..cd9a937f74c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/SemisequentChangeInfo.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/SemisequentChangeInfo.java
@@ -13,18 +13,18 @@
 public class SemisequentChangeInfo {
 
     /** contains the added formulas to the semisequent */
-    private ImmutableList<SequentFormula> added = ImmutableSLList.nil();
+    private ImmutableList<Term> added = ImmutableSLList.nil();
     /** contains the removed formulas from the semisequent */
-    private ImmutableList<SequentFormula> removed = ImmutableSLList.nil();
+    private ImmutableList<Term> removed = ImmutableSLList.nil();
     /** contains the modified formulas from the semisequent */
     private ImmutableList<FormulaChangeInfo> modified = ImmutableSLList.nil();
     /** stores the redundance free formula list of the semisequent */
-    private ImmutableList<SequentFormula> modifiedSemisequent = ImmutableSLList.nil();
+    private ImmutableList<Term> modifiedSemisequent = ImmutableSLList.nil();
     /**
      * contains formulas that have been tried to add, but which have been rejected due to already
      * existing formulas in the sequent subsuming these formulas
      */
-    private ImmutableList<SequentFormula> rejected = ImmutableSLList.nil();
+    private ImmutableList<Term> rejected = ImmutableSLList.nil();
 
     /** */
     private int lastFormulaIndex = -1;
@@ -32,7 +32,7 @@ public class SemisequentChangeInfo {
     public SemisequentChangeInfo() {
     }
 
-    public SemisequentChangeInfo(ImmutableList<SequentFormula> formulas) {
+    public SemisequentChangeInfo(ImmutableList<Term> formulas) {
         this.modifiedSemisequent = formulas;
     }
 
@@ -60,21 +60,21 @@ public boolean hasChanged() {
      * sets the list of constrained formula containing all formulas of the semisequent after the
      * operation
      */
-    public void setFormulaList(ImmutableList<SequentFormula> list) {
+    public void setFormulaList(ImmutableList<Term> list) {
         modifiedSemisequent = list;
     }
 
     /**
      * returns the list of constrained formula of the new semisequent
      */
-    public ImmutableList<SequentFormula> getFormulaList() {
+    public ImmutableList<Term> getFormulaList() {
         return modifiedSemisequent;
     }
 
     /**
      * logs an added formula at position idx
      */
-    public void addedFormula(int idx, SequentFormula cf) {
+    public void addedFormula(int idx, Term cf) {
         added = added.prepend(cf);
         lastFormulaIndex = idx;
     }
@@ -85,7 +85,7 @@ public void addedFormula(int idx, SequentFormula cf) {
     public void modifiedFormula(int idx, FormulaChangeInfo fci) {
         // This information can overwrite older records about removed
         // formulas
-        removed = removed.removeAll(fci.positionOfModification().sequentFormula());
+        removed = removed.removeAll(fci.positionOfModification().sequentLevelFormula());
         modified = modified.prepend(fci);
         lastFormulaIndex = idx;
     }
@@ -93,18 +93,18 @@ public void modifiedFormula(int idx, FormulaChangeInfo fci) {
     /**
      * returns the list of all added constrained formulas
      *
-     * @return IList<SequentFormula> added to the semisequent
+     * @return IList<Term> added to the semisequent
      */
-    public ImmutableList<SequentFormula> addedFormulas() {
+    public ImmutableList<Term> addedFormulas() {
         return added;
     }
 
     /**
      * returns the list of all removed constrained formulas
      *
-     * @return IList<SequentFormula> removed from the semisequent
+     * @return IList<Term> removed from the semisequent
      */
-    public ImmutableList<SequentFormula> removedFormulas() {
+    public ImmutableList<Term> removedFormulas() {
         return removed;
     }
 
@@ -114,7 +114,7 @@ public ImmutableList<SequentFormula> removedFormulas() {
      *
      * @return list of formulas rejected due to redundancy
      */
-    public ImmutableList<SequentFormula> rejectedFormulas() {
+    public ImmutableList<Term> rejectedFormulas() {
         return this.rejected;
     }
 
@@ -123,16 +123,16 @@ public ImmutableList<SequentFormula> rejectedFormulas() {
      * adding formula <tt>f</tt> to the semisequent failed due to a redundance check. This means an
      * equal or stronger formula is already present in the semisequent
      *
-     * @param f the SequentFormula
+     * @param f the Term
      */
-    public void rejectedFormula(SequentFormula f) {
+    public void rejectedFormula(Term f) {
         this.rejected = this.rejected.append(f);
     }
 
     /**
      * returns the list of all modification positions
      *
-     * @return IList<SequentFormula> modified within the semisequent
+     * @return IList<Term> modified within the semisequent
      */
     public ImmutableList<FormulaChangeInfo> modifiedFormulas() {
         return modified;
@@ -141,7 +141,7 @@ public ImmutableList<FormulaChangeInfo> modifiedFormulas() {
     /**
      * logs an added formula at position idx
      */
-    public void removedFormula(int idx, SequentFormula cf) {
+    public void removedFormula(int idx, Term cf) {
         removed = removed.prepend(cf);
 
         lastFormulaIndex = (lastFormulaIndex == idx) ? -1
@@ -166,7 +166,7 @@ public void combine(SemisequentChangeInfo succ) {
             return;
         }
 
-        for (SequentFormula sf : succ.removed) {
+        for (Term sf : succ.removed) {
             predecessor.added = predecessor.added.removeAll(sf);
 
             boolean skip = false;
@@ -194,14 +194,14 @@ public void combine(SemisequentChangeInfo succ) {
             }
         }
 
-        for (SequentFormula sf : succ.added) {
+        for (Term sf : succ.added) {
             predecessor.removed = predecessor.removed.removeAll(sf);
             if (!predecessor.added.contains(sf)) {
                 predecessor.addedFormula(succ.lastFormulaIndex, sf);
             }
         }
 
-        for (SequentFormula sf : succ.rejected) {
+        for (Term sf : succ.rejected) {
             if (!predecessor.rejected.contains(sf)) {
                 predecessor.rejectedFormula(sf);
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/Sequent.java b/key.core/src/main/java/de/uka/ilkd/key/logic/Sequent.java
index a3b8424f2de..a931457f419 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/Sequent.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/Sequent.java
@@ -8,7 +8,6 @@
 import java.util.Set;
 
 import de.uka.ilkd.key.logic.label.TermLabel;
-import de.uka.ilkd.key.logic.op.QuantifiableVariable;
 
 import org.key_project.logic.Name;
 import org.key_project.util.collection.ImmutableList;
@@ -23,7 +22,7 @@
  * {@link Sequent#createSuccSequent} or by inserting formulas directly into
  * {@link Sequent#EMPTY_SEQUENT}.
  */
-public class Sequent implements Iterable<SequentFormula> {
+public class Sequent implements Iterable<Term> {
 
     public static final Sequent EMPTY_SEQUENT = NILSequent.INSTANCE;
 
@@ -95,7 +94,7 @@ private Sequent(Semisequent antecedent, Semisequent succedent) {
      * first the formulas are inserted at the beginning or end of the ante-/succedent.
      * (NOTICE:Sequent determines index using identy (==) not equality.)
      *
-     * @param cf the SequentFormula to be added
+     * @param cf the Term to be added
      * @param antec boolean selecting the correct semisequent where to insert the formulas. If set
      *        to true, the antecedent is taken otherwise the succedent.
      * @param first boolean if true the formula is added at the beginning of the ante-/succedent,
@@ -103,7 +102,7 @@ private Sequent(Semisequent antecedent, Semisequent succedent) {
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo addFormula(SequentFormula cf, boolean antec, boolean first) {
+    public SequentChangeInfo addFormula(Term cf, boolean antec, boolean first) {
 
         final Semisequent seq = antec ? antecedent : succedent;
 
@@ -117,15 +116,15 @@ public SequentChangeInfo addFormula(SequentFormula cf, boolean antec, boolean fi
      * adds a formula to the sequent at the given position. (NOTICE:Sequent determines index using
      * identy (==) not equality.)
      *
-     * @param cf a SequentFormula to be added
+     * @param cf a Term to be added
      * @param p a PosInOccurrence describes position in the sequent
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo addFormula(SequentFormula cf, PosInOccurrence p) {
+    public SequentChangeInfo addFormula(Term cf, PosInOccurrence p) {
         final Semisequent seq = getSemisequent(p);
 
-        final SemisequentChangeInfo semiCI = seq.insert(seq.indexOf(p.sequentFormula()), cf);
+        final SemisequentChangeInfo semiCI = seq.insert(seq.indexOf(p.sequentLevelFormula()), cf);
 
         return SequentChangeInfo.createSequentChangeInfo(p.isInAntec(), semiCI,
             composeSequent(p.isInAntec(), semiCI.semisequent()), this);
@@ -136,7 +135,7 @@ public SequentChangeInfo addFormula(SequentFormula cf, PosInOccurrence p) {
      * of first the formulas are inserted at the beginning or end of the ante-/succedent.
      * (NOTICE:Sequent determines index using identity (==) not equality.)
      *
-     * @param insertions the IList<SequentFormula> to be added
+     * @param insertions the IList<Term> to be added
      * @param antec boolean selecting the correct semisequent where to insert the formulas. If set
      *        to true, the antecedent is taken otherwise the succedent.
      * @param first boolean if true the formulas are added at the beginning of the ante-/succedent,
@@ -144,7 +143,7 @@ public SequentChangeInfo addFormula(SequentFormula cf, PosInOccurrence p) {
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo addFormula(ImmutableList<SequentFormula> insertions, boolean antec,
+    public SequentChangeInfo addFormula(ImmutableList<Term> insertions, boolean antec,
             boolean first) {
 
         final Semisequent seq = antec ? antecedent : succedent;
@@ -160,17 +159,17 @@ public SequentChangeInfo addFormula(ImmutableList<SequentFormula> insertions, bo
      * adds the formulas of list insertions to the sequent starting at position p. (NOTICE:Sequent
      * determines index using identy (==) not equality.)
      *
-     * @param insertions a IList<SequentFormula> with the formulas to be added
+     * @param insertions a IList<Term> with the formulas to be added
      * @param p the PosInOccurrence describing the position where to insert the formulas
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo addFormula(ImmutableList<SequentFormula> insertions,
+    public SequentChangeInfo addFormula(ImmutableList<Term> insertions,
             PosInOccurrence p) {
         final Semisequent seq = getSemisequent(p);
 
         final SemisequentChangeInfo semiCI =
-            seq.insert(seq.indexOf(p.sequentFormula()), insertions);
+            seq.insert(seq.indexOf(p.sequentLevelFormula()), insertions);
 
         return SequentChangeInfo.createSequentChangeInfo(p.isInAntec(), semiCI,
             composeSequent(p.isInAntec(), semiCI.semisequent()), this);
@@ -184,7 +183,7 @@ public SequentChangeInfo addFormula(ImmutableList<SequentFormula> insertions,
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo replaceFormula(int formulaNr, SequentFormula replacement) {
+    public SequentChangeInfo replaceFormula(int formulaNr, Term replacement) {
         checkFormulaIndex(formulaNr);
         formulaNr--;
         boolean inAntec = formulaNr < antecedent.size();
@@ -207,12 +206,12 @@ public Semisequent antecedent() {
      * replaces the formula at the given position with another one (NOTICE:Sequent determines index
      * using identity (==) not equality.)
      *
-     * @param newCF the SequentFormula replacing the old one
+     * @param newCF the Term replacing the old one
      * @param p a PosInOccurrence describes position in the sequent
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo changeFormula(SequentFormula newCF, PosInOccurrence p) {
+    public SequentChangeInfo changeFormula(Term newCF, PosInOccurrence p) {
         final SemisequentChangeInfo semiCI = getSemisequent(p).replace(p, newCF);
 
         return SequentChangeInfo.createSequentChangeInfo(p.isInAntec(), semiCI,
@@ -224,13 +223,13 @@ public SequentChangeInfo changeFormula(SequentFormula newCF, PosInOccurrence p)
      * list elements to the sequent (NOTICE:Sequent determines index using identity (==) not
      * equality.)
      *
-     * @param replacements the IList<SequentFormula> whose head replaces the formula at position p
+     * @param replacements the IList<Term> whose head replaces the formula at position p
      *        and adds the rest of the list behind the changed formula
      * @param p a PosInOccurrence describing the position of the formula to be replaced
      * @return a SequentChangeInfo which contains the new sequent and information which formulas
      *         have been added or removed
      */
-    public SequentChangeInfo changeFormula(ImmutableList<SequentFormula> replacements,
+    public SequentChangeInfo changeFormula(ImmutableList<Term> replacements,
             PosInOccurrence p) {
 
         final SemisequentChangeInfo semiCI = getSemisequent(p).replace(p, replacements);
@@ -292,9 +291,9 @@ public boolean equals(Object o) {
      * @return an integer strictly greater than zero for the position of the given sequent formula
      *         on the proof sequent.
      */
-    public int formulaNumberInSequent(boolean inAntec, SequentFormula cfma) {
+    public int formulaNumberInSequent(boolean inAntec, Term cfma) {
         int n = inAntec ? 0 : antecedent.size();
-        final Iterator<SequentFormula> formIter =
+        final Iterator<Term> formIter =
             inAntec ? antecedent.iterator() : succedent.iterator();
         while (formIter.hasNext()) {
             n++;
@@ -315,7 +314,7 @@ public int formulaNumberInSequent(boolean inAntec, SequentFormula cfma) {
      */
     public int formulaNumberInSequent(PosInOccurrence pio) {
         var inAntec = pio.isInAntec();
-        var formula = pio.sequentFormula();
+        var formula = pio.sequentLevelFormula();
         return formulaNumberInSequent(inAntec, formula);
     }
 
@@ -326,7 +325,7 @@ public int formulaNumberInSequent(PosInOccurrence pio) {
      * @param formulaNumber formula number
      * @return the sequent formula at that position
      */
-    public SequentFormula getFormulabyNr(int formulaNumber) {
+    public Term getFormulabyNr(int formulaNumber) {
         checkFormulaIndex(formulaNumber);
         if (formulaNumber <= antecedent.size()) {
             return antecedent.get(formulaNumber - 1);
@@ -335,7 +334,7 @@ public SequentFormula getFormulabyNr(int formulaNumber) {
     }
 
     /**
-     * returns the semisequent in which the SequentFormula described by PosInOccurrence p lies
+     * returns the semisequent in which the Term described by PosInOccurrence p lies
      */
     private Semisequent getSemisequent(PosInOccurrence p) {
         return p.isInAntec() ? antecedent() : succedent();
@@ -352,7 +351,7 @@ public int hashCode() {
      * @return iterator about all ConstrainedFormulae of the sequent
      */
     @Override
-    public Iterator<SequentFormula> iterator() {
+    public Iterator<Term> iterator() {
         return new SequentIterator(antecedent(), succedent());
     }
 
@@ -376,7 +375,7 @@ public boolean numberInAntec(int formulaNumber) {
     public SequentChangeInfo removeFormula(PosInOccurrence p) {
         final Semisequent seq = getSemisequent(p);
 
-        final SemisequentChangeInfo semiCI = seq.remove(seq.indexOf(p.sequentFormula()));
+        final SemisequentChangeInfo semiCI = seq.remove(seq.indexOf(p.sequentLevelFormula()));
 
         return SequentChangeInfo.createSequentChangeInfo(p.isInAntec(),
             semiCI, composeSequent(p.isInAntec(), semiCI.semisequent()), this);
@@ -406,23 +405,6 @@ public String toString() {
         return antecedent().toString() + "==>" + succedent().toString();
     }
 
-    /**
-     * returns true iff the given variable is bound in a formula of a SequentFormula in this
-     * sequent.
-     *
-     * @param v the bound variable to search for
-     */
-    public boolean varIsBound(QuantifiableVariable v) {
-        for (SequentFormula sequentFormula : this) {
-            final BoundVarsVisitor bvv = new BoundVarsVisitor();
-            sequentFormula.formula().execPostOrder(bvv);
-            if (bvv.getBoundVariables().contains(v)) {
-                return true;
-            }
-        }
-        return false;
-    }
-
     private static final class NILSequent extends Sequent {
         private static final NILSequent INSTANCE = new NILSequent();
 
@@ -435,27 +417,22 @@ public boolean isEmpty() {
         }
 
         @Override
-        public Iterator<SequentFormula> iterator() {
-            return ImmutableSLList.<SequentFormula>nil().iterator();
-        }
-
-        @Override
-        public boolean varIsBound(QuantifiableVariable v) {
-            return false;
+        public Iterator<Term> iterator() {
+            return ImmutableSLList.<Term>nil().iterator();
         }
 
     }
 
-    static class SequentIterator implements Iterator<SequentFormula> {
+    static class SequentIterator implements Iterator<Term> {
 
         /**
          * The iterator over the ancedent of the proof sequent.
          */
-        private final Iterator<SequentFormula> anteIt;
+        private final Iterator<Term> anteIt;
         /**
          * The iterator over the succedent of the proof sequent.
          */
-        private final Iterator<SequentFormula> succIt;
+        private final Iterator<Term> succIt;
 
         /**
          * Constructs a new iterator over a proof sequent.
@@ -474,7 +451,7 @@ public boolean hasNext() {
         }
 
         @Override
-        public SequentFormula next() {
+        public Term next() {
             if (anteIt.hasNext()) {
                 return anteIt.next();
             }
@@ -514,8 +491,8 @@ private static Set<Name> getLabelsForTermRecursively(Term term) {
      */
     public Set<Name> getOccuringTermLabels() {
         final Set<Name> result = new HashSet<>();
-        for (final SequentFormula sf : this) {
-            result.addAll(getLabelsForTermRecursively(sf.formula()));
+        for (final Term sf : this) {
+            result.addAll(getLabelsForTermRecursively(sf));
         }
         return result;
     }
@@ -526,16 +503,16 @@ public Set<Name> getOccuringTermLabels() {
      * @param form the given formula
      * @return true if this sequent contains the given formula
      */
-    public boolean contains(SequentFormula form) {
+    public boolean contains(Term form) {
         return antecedent.contains(form) || succedent.contains(form);
     }
 
     /**
-     * Returns a list containing every {@link SequentFormula} in this sequent.
+     * Returns a list containing every {@link Term} in this sequent.
      *
-     * @return a list containing every {@link SequentFormula} in this sequent.
+     * @return a list containing every {@link Term} in this sequent.
      */
-    public ImmutableList<SequentFormula> asList() {
+    public ImmutableList<Term> asList() {
         return antecedent.asList().append(succedent.asList());
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/SequentChangeInfo.java b/key.core/src/main/java/de/uka/ilkd/key/logic/SequentChangeInfo.java
index 9253b647ada..c1f9bcf163e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/SequentChangeInfo.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/SequentChangeInfo.java
@@ -148,7 +148,7 @@ public SemisequentChangeInfo getSemisequentChangeInfo(boolean antec) {
      *        antecedent; false means succedent)
      * @return list of formulas added to the selected semisequent
      */
-    public ImmutableList<SequentFormula> addedFormulas(boolean antec) {
+    public ImmutableList<Term> addedFormulas(boolean antec) {
         return antec
                 ? (antecedent != null ? antecedent.addedFormulas() : ImmutableSLList.nil())
                 : (succedent != null ? succedent.addedFormulas() : ImmutableSLList.nil());
@@ -160,9 +160,9 @@ public ImmutableList<SequentFormula> addedFormulas(boolean antec) {
      *
      * @return list of formulas added to sequent
      */
-    public ImmutableList<SequentFormula> addedFormulas() {
-        final ImmutableList<SequentFormula> addedFormulasAntec = addedFormulas(true);
-        final ImmutableList<SequentFormula> addedFormulasSucc = addedFormulas(false);
+    public ImmutableList<Term> addedFormulas() {
+        final ImmutableList<Term> addedFormulasAntec = addedFormulas(true);
+        final ImmutableList<Term> addedFormulasSucc = addedFormulas(false);
 
         return concatenateHelper(addedFormulasAntec, addedFormulasSucc);
 
@@ -177,7 +177,7 @@ public ImmutableList<SequentFormula> addedFormulas() {
      *        antecedent; false means succedent)
      * @return list of formulas removed from the selected semisequent
      */
-    public ImmutableList<SequentFormula> removedFormulas(boolean antec) {
+    public ImmutableList<Term> removedFormulas(boolean antec) {
         return antec
                 ? (antecedent != null ? antecedent.removedFormulas() : ImmutableSLList.nil())
                 : (succedent != null ? succedent.removedFormulas() : ImmutableSLList.nil());
@@ -189,9 +189,9 @@ public ImmutableList<SequentFormula> removedFormulas(boolean antec) {
      *
      * @return list of formulas removed from the sequent
      */
-    public ImmutableList<SequentFormula> removedFormulas() {
-        final ImmutableList<SequentFormula> removedFormulasAntec = removedFormulas(true);
-        final ImmutableList<SequentFormula> removedFormulasSucc = removedFormulas(false);
+    public ImmutableList<Term> removedFormulas() {
+        final ImmutableList<Term> removedFormulasAntec = removedFormulas(true);
+        final ImmutableList<Term> removedFormulasSucc = removedFormulas(false);
 
         return concatenateHelper(removedFormulasAntec, removedFormulasSucc);
     }
@@ -231,7 +231,7 @@ public ImmutableList<FormulaChangeInfo> modifiedFormulas() {
      *        antecedent; false means succedent)
      * @return list of formulas rejected when trying to add to the selected semisequent
      */
-    public ImmutableList<SequentFormula> rejectedFormulas(boolean antec) {
+    public ImmutableList<Term> rejectedFormulas(boolean antec) {
         return antec
                 ? (antecedent != null ? antecedent.rejectedFormulas() : ImmutableSLList.nil())
                 : (succedent != null ? succedent.rejectedFormulas() : ImmutableSLList.nil());
@@ -242,9 +242,9 @@ public ImmutableList<SequentFormula> rejectedFormulas(boolean antec) {
      *
      * @return list of rejected formulas
      */
-    public ImmutableList<SequentFormula> rejectedFormulas() {
-        final ImmutableList<SequentFormula> rejectedFormulasAntec = rejectedFormulas(true);
-        final ImmutableList<SequentFormula> rejectedFormulasSucc = rejectedFormulas(false);
+    public ImmutableList<Term> rejectedFormulas() {
+        final ImmutableList<Term> rejectedFormulasAntec = rejectedFormulas(true);
+        final ImmutableList<Term> rejectedFormulasSucc = rejectedFormulas(false);
 
         return concatenateHelper(rejectedFormulasAntec, rejectedFormulasSucc);
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/SequentFormula.java b/key.core/src/main/java/de/uka/ilkd/key/logic/SequentFormula.java
deleted file mode 100644
index 38325df369f..00000000000
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/SequentFormula.java
+++ /dev/null
@@ -1,90 +0,0 @@
-/* This file is part of KeY - https://key-project.org
- * KeY is licensed under the GNU General Public License Version 2
- * SPDX-License-Identifier: GPL-2.0-only */
-package de.uka.ilkd.key.logic;
-
-import de.uka.ilkd.key.ldt.JavaDLTheory;
-import de.uka.ilkd.key.logic.op.AbstractTermTransformer;
-
-import org.key_project.util.EqualsModProofIrrelevancy;
-
-import static de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY;
-
-
-/**
- * A sequent formula is a wrapper around a formula that occurs as top level formula in a sequent.
- * SequentFormula instances have to be unique in the sequent as they are used by PosInOccurrence to
- * determine the exact position. In earlier KeY versions this class was called ConstrainedFormula as
- * it was equipped with an additional constraints. It would be interesting to add more value to this
- * class by providing a way to add additional annotations or to cache local information about the
- * formula.
- */
-public class SequentFormula implements EqualsModProofIrrelevancy {
-
-    private final Term term;
-
-    /**
-     * Cached value for {@link #hashCode()}.
-     */
-    private final int hashCode;
-    /**
-     * Cached value for {@link #hashCodeModProofIrrelevancy()}.
-     */
-    private final int hashCode2;
-
-    /**
-     * creates a new SequentFormula
-     *
-     * @param term a Term of sort {@link JavaDLTheory#FORMULA}
-     */
-    public SequentFormula(Term term) {
-        if (term.sort() != JavaDLTheory.FORMULA
-                && term.sort() != AbstractTermTransformer.METASORT) {
-            throw new RuntimeException("A Term instead of a formula: " + term);
-        }
-        this.term = term;
-        this.hashCode = term.hashCode() * 13;
-        this.hashCode2 = term.hashCodeModProperty(PROOF_IRRELEVANCY_PROPERTY);
-    }
-
-    /** @return the stored Term */
-    public Term formula() {
-        return term;
-    }
-
-    /** equal if terms and constraints are equal */
-    public boolean equals(Object obj) {
-        if (this == obj) {
-            return true;
-        }
-        if (obj instanceof SequentFormula cmp) {
-            return term.equals(cmp.formula());
-        }
-        return false;
-    }
-
-    /** String representation */
-    public String toString() {
-        return term.toString();
-    }
-
-    public int hashCode() {
-        return hashCode;
-    }
-
-    @Override
-    public boolean equalsModProofIrrelevancy(Object obj) {
-        if (this == obj) {
-            return true;
-        }
-        if (obj instanceof SequentFormula cmp) {
-            return term.equalsModProperty(cmp.formula(), PROOF_IRRELEVANCY_PROPERTY);
-        }
-        return false;
-    }
-
-    @Override
-    public int hashCodeModProofIrrelevancy() {
-        return hashCode2;
-    }
-}
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/Term.java b/key.core/src/main/java/de/uka/ilkd/key/logic/Term.java
index 60c03e6fdae..95c7cd3e1df 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/Term.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/Term.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.logic.label.TermLabel;
 import de.uka.ilkd.key.logic.op.Operator;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 
 import org.key_project.logic.Name;
 import org.key_project.logic.Visitor;
@@ -43,7 +42,8 @@
  * supported: {@link Term#execPostOrder(Visitor)} and {@link Term#execPreOrder(Visitor)}.
  */
 public interface Term
-        extends SVSubstitute, Sorted, TermEqualsModProperty, org.key_project.logic.Term {
+        extends Sorted, TermEqualsModProperty, org.key_project.logic.Term {
+
     @Override
     Operator op();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/BlockContractValidityTermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/BlockContractValidityTermLabel.java
index c4181e3c988..f4cb02f511f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/BlockContractValidityTermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/BlockContractValidityTermLabel.java
@@ -40,7 +40,7 @@ public ProgramVariable exceptionVariable() {
      * {@inheritDoc}
      */
     @Override
-    public ProgramVariable getChild(int i) {
+    public ProgramVariable getTLChild(int i) {
         if (i == 0) {
             return exceptionVariable();
         }
@@ -51,7 +51,7 @@ public ProgramVariable getChild(int i) {
      * {@inheritDoc}
      */
     @Override
-    public int getChildCount() {
+    public int getTLChildCount() {
         return 1;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/FormulaTermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/FormulaTermLabel.java
index cde4271a90d..def77a6dd50 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/FormulaTermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/FormulaTermLabel.java
@@ -134,7 +134,7 @@ public String toString() {
      * {@inheritDoc}
      */
     @Override
-    public Object getChild(int i) {
+    public Object getTLChild(int i) {
         return switch (i) {
         case 0 -> getId();
         case 1 -> beforeIds;
@@ -146,7 +146,7 @@ public Object getChild(int i) {
      * {@inheritDoc}
      */
     @Override
-    public int getChildCount() {
+    public int getTLChildCount() {
         if (beforeIds != null) {
             return 2;
         } else {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/OriginTermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/OriginTermLabel.java
index 1e3edea26ed..ac11b3ee4aa 100755
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/OriginTermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/OriginTermLabel.java
@@ -57,7 +57,7 @@ public class OriginTermLabel implements TermLabel {
     public final static Name NAME = new Name("origin");
 
     /**
-     * @see #getChildCount()
+     * @see #getTLChildCount()
      */
     public final static int CHILD_COUNT = 2;
     public static final Sort[] EMPTY_SORTS = new Sort[0];
@@ -251,9 +251,9 @@ public static SequentChangeInfo removeOriginLabels(Sequent seq, Services service
         SequentChangeInfo changes = null;
 
         for (int i = 1; i <= seq.size(); ++i) {
-            SequentFormula oldFormula = seq.getFormulabyNr(i);
-            SequentFormula newFormula = new SequentFormula(
-                OriginTermLabel.removeOriginLabels(oldFormula.formula(), services));
+            Term oldFormula = seq.getFormulabyNr(i);
+            Term uAssumptions = OriginTermLabel.removeOriginLabels(oldFormula, services);
+            Term newFormula = uAssumptions;
             SequentChangeInfo change = seq.changeFormula(newFormula,
                 PosInOccurrence.findInSequent(seq, i, PosInTerm.getTopLevel()));
 
@@ -450,7 +450,7 @@ public Name name() {
     }
 
     @Override
-    public Object getChild(int i) {
+    public Object getTLChild(int i) {
         if (i == 0) {
             return origin;
         } else if (i == 1) {
@@ -461,7 +461,7 @@ public Object getChild(int i) {
     }
 
     @Override
-    public int getChildCount() {
+    public int getTLChildCount() {
         return CHILD_COUNT;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/ParameterlessTermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/ParameterlessTermLabel.java
index 850c5c1b3d5..596410ce3e8 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/ParameterlessTermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/ParameterlessTermLabel.java
@@ -139,7 +139,7 @@ public Name name() {
      * {@link IndexOutOfBoundsException}.
      */
     @Override
-    public Object getChild(int i) {
+    public Object getTLChild(int i) {
         throw new IndexOutOfBoundsException();
     }
 
@@ -150,7 +150,7 @@ public Object getChild(int i) {
      * Simple term labels have no parameters. This always returns 0.
      */
     @Override
-    public int getChildCount() {
+    public int getTLChildCount() {
         return 0;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/SymbolicExecutionTermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/SymbolicExecutionTermLabel.java
index 03659186d6a..6596ce2ba89 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/SymbolicExecutionTermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/SymbolicExecutionTermLabel.java
@@ -50,7 +50,7 @@ public String toString() {
      * {@inheritDoc}
      */
     @Override
-    public Object getChild(int i) {
+    public Object getTLChild(int i) {
         if (i == 0) {
             return id();
         }
@@ -61,7 +61,7 @@ public Object getChild(int i) {
      * {@inheritDoc}
      */
     @Override
-    public int getChildCount() {
+    public int getTLChildCount() {
         return 1;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabel.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabel.java
index b514fbd04d5..160615c9f3c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabel.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabel.java
@@ -5,7 +5,6 @@
 
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabelManager.TermLabelConfiguration;
 import de.uka.ilkd.key.logic.op.Modality;
@@ -20,6 +19,8 @@
 
 import org.key_project.logic.Name;
 import org.key_project.logic.Named;
+import org.key_project.logic.SyntaxElement;
+import org.key_project.logic.TerminalSyntaxElement;
 
 // spotless:off     // this protects the JavaDoc from automatic reformatting
 /**
@@ -34,8 +35,8 @@
  * without parameters class {@link ParameterlessTermLabel} can be used.
  * </p>
  * <p>
- * A term label can have parameters accessible via {@link #getChild(int)} and
- * {@link #getChildCount()}. Such parameters can be any {@link Object}. But keep in mind that it is
+ * A term label can have parameters accessible via {@link #getTLChild(int)} and
+ * {@link #getTLChildCount()}. Such parameters can be any {@link Object}. But keep in mind that it is
  * required to parse {@link String}s into {@link Term}s, e.g. if it is used in a Taclet definition
  * or if a cut rule is applied. For convenience parameters are always printed as {@link String}s
  * and have to be parsed individually into the required {@link Object} instances via a
@@ -55,14 +56,14 @@
  * </p>
  * <p>
  * Antecedent and succedent of a {@link Sequent} are sets. The equality check if a
- * {@link SequentFormula} is already contained ignores {@link TermLabel}s. To ensure that
+ * {@link Term} is already contained ignores {@link TermLabel}s. To ensure that
  * {@link TermLabel}s are not lost,
  * {@link TermLabelManager#mergeLabels(de.uka.ilkd.key.java.Services,
  *         de.uka.ilkd.key.logic.SequentChangeInfo)}
- * merges the labels of the existing {@link SequentFormula} with those of the rejected
- * {@link SequentFormula}. How this is done in detail is implemented by a {@link TermLabelMerger}.
+ * merges the labels of the existing {@link Term} with those of the rejected
+ * {@link Term}. How this is done in detail is implemented by a {@link TermLabelMerger}.
  * If no {@link TermLabelMerger} is available, the {@link TermLabel} of the rejected
- * {@link SequentFormula} are lost.
+ * {@link Term} are lost.
  * </p>
  * <p>
  * To implement a new {@link TermLabel} follow the following steps:
@@ -124,7 +125,7 @@
  *              which works on {@link RefactoringScope#SEQUENT} to freely add or remove
  *              {@link TermLabel}s on any {@link Term} of the {@link Sequent}.</li>
  *          <li>Implement a {@link TermLabelMerger} to ensure that {@link TermLabel}s are maintained
- *              in case of rejected {@link SequentFormula}s.</li>
+ *              in case of rejected {@link Term}s.</li>
  *       </ul>
  *    </li>
  *    <li>
@@ -150,7 +151,7 @@
  * @see TermLabelManager
  */
 // spotless:on
-public interface TermLabel extends Named {
+public interface TermLabel extends Named, SyntaxElement, /* TODO: Remove */ TerminalSyntaxElement {
 
     /**
      * Retrieves the i-th parameter object of this term label.
@@ -161,16 +162,16 @@ public interface TermLabel extends Named {
      * @param i the number of the parameter to retrieve ( {@code 0 <= i < getChildCount()})
      * @return the selected parameter
      * @throws IndexOutOfBoundsException if the given parameter number <tt>i</tt> is negative or
-     *         greater-or-equal the number of parameters returned by {@link #getChildCount()}
+     *         greater-or-equal the number of parameters returned by {@link #getTLChildCount()}
      */
-    Object getChild(int i);
+    Object getTLChild(int i);
 
     /**
      * Gets the number of parameters of this term label.
      *
      * @return the number of parameters (a non-negative number)
      */
-    int getChildCount();
+    int getTLChildCount();
 
     /**
      * Returns {@code true} iff this label is used in any way during the proof. E.g.,
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabelManager.java b/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabelManager.java
index 6ac56f95a64..4dc798830b8 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabelManager.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/label/TermLabelManager.java
@@ -50,7 +50,7 @@
  * <ul>
  * <li>{@link #refactorGoal(TermLabelState, Services, PosInOccurrence, Rule, Goal, Object, Term)}:
  * The full sequent</li>
- * <li>{@link #refactorSequentFormula(TermLabelState, Services, Term, PosInOccurrence, Rule, Goal, Object, Term)}
+ * <li>{@link #refactorTerm(TermLabelState, Services, Term, PosInOccurrence, Rule, Goal, Object, Term)}
  * : The sequent formula which contains the application term on which the rule is applied</li>
  * <li>{@link #refactorTerm(TermLabelState, Services, PosInOccurrence, Term, Rule, Goal, Object, Term)}
  * : The current term.</li>
@@ -955,8 +955,8 @@ protected void performUpdater(TermLabelState state, Services services,
     }
 
     /**
-     * Refactors all labels on the {@link PosInOccurrence} in the given {@link Term} of a
-     * {@link SequentFormula}.
+     * Refactors all labels on the {@link PosInOccurrence} in the given {@link Term} representing a
+     * sequent level formula
      *
      * @param state The {@link TermLabelState} of the current rule application.
      * @param services The {@link Services} used by the {@link Proof} on which a {@link Rule} is
@@ -970,21 +970,21 @@ protected void performUpdater(TermLabelState state, Services services,
      * @param tacletTerm The optional taclet {@link Term}.
      * @return The updated application {@link Term}.
      */
-    public static Term refactorSequentFormula(TermLabelState state, Services services,
-            Term sequentFormula, PosInOccurrence applicationPosInOccurrence, Rule rule, Goal goal,
+    public static Term refactorTerm(TermLabelState state, Services services,
+            Term seqLevelFml, PosInOccurrence applicationPosInOccurrence, Rule rule, Goal goal,
             Object hint, Term tacletTerm) {
         TermLabelManager manager = getTermLabelManager(services);
         if (manager != null) {
-            return manager.refactorSequentFormula(state, services, sequentFormula,
+            return manager.refactorTerm(state, services, seqLevelFml,
                 applicationPosInOccurrence, goal, hint, rule, tacletTerm);
         } else {
-            return sequentFormula;
+            return seqLevelFml;
         }
     }
 
     /**
-     * Refactors all labels on the {@link PosInOccurrence} in the given {@link Term} of a
-     * {@link SequentFormula}.
+     * Refactors all labels on the {@link PosInOccurrence} in the given {@link Term} representing
+     * a sequent level formula.
      *
      * @param state The {@link TermLabelState} of the current rule application.
      * @param services The {@link Services} used by the {@link Proof} on which a {@link Rule} is
@@ -998,11 +998,11 @@ public static Term refactorSequentFormula(TermLabelState state, Services service
      * @param tacletTerm The optional taclet {@link Term}.
      * @return The updated application {@link Term}.
      */
-    public Term refactorSequentFormula(TermLabelState state, Services services, Term sequentFormula,
+    public Term refactorTerm(TermLabelState state, Services services, Term seqLevelFml,
             PosInOccurrence applicationPosInOccurrence, Goal goal, Object hint, Rule rule,
             Term tacletTerm) {
         final PosInTerm pos = applicationPosInOccurrence.posInTerm();
-        final Term oldTerm = pos.getSubTerm(sequentFormula);
+        final Term oldTerm = pos.getSubTerm(seqLevelFml);
         // Compute active refactorings
         RefactoringsContainer refactorings = computeRefactorings(state, services,
             applicationPosInOccurrence, oldTerm, rule, goal, hint, tacletTerm);
@@ -1020,7 +1020,7 @@ public Term refactorSequentFormula(TermLabelState state, Services services, Term
                 refactorings.childAndGrandchildRefactoringsAndParents(), services,
                 applicationPosInOccurrence, oldTerm, rule, goal, hint, tacletTerm);
         } else {
-            return sequentFormula;
+            return seqLevelFml;
         }
     }
 
@@ -1159,12 +1159,12 @@ public void refactorGoal(TermLabelState state, Services services,
             Term root = replaceTerm(state, applicationPosInOccurrence, newApplicationTerm, tf,
                 refactorings.childAndGrandchildRefactoringsAndParents(), services,
                 applicationPosInOccurrence, newApplicationTerm, rule, goal, hint, tacletTerm);
-            goal.changeFormula(new SequentFormula(root), applicationPosInOccurrence.topLevel());
+            goal.changeFormula(root, applicationPosInOccurrence.topLevel());
         } else if (!refactorings.childAndGrandchildRefactoringsAndParents().isEmpty()) {
             Term root = replaceTerm(state, applicationPosInOccurrence, applicationTerm, tf,
                 refactorings.childAndGrandchildRefactoringsAndParents(), services,
                 applicationPosInOccurrence, newApplicationTerm, rule, goal, hint, tacletTerm);
-            goal.changeFormula(new SequentFormula(root), applicationPosInOccurrence.topLevel());
+            goal.changeFormula(root, applicationPosInOccurrence.topLevel());
         }
         // Do sequent refactoring if required
         if (!refactorings.sequentRefactorings().isEmpty() && goal != null) {
@@ -1669,13 +1669,13 @@ protected void refactorSemisequent(TermLabelState state, Services services,
             Object hint, Term tacletTerm, Semisequent semisequent, boolean inAntec,
             Set<TermLabelRefactoring> activeRefactorings) {
         if (!activeRefactorings.isEmpty()) {
-            for (SequentFormula sfa : semisequent) {
+            for (Term sfa : semisequent) {
                 Term updatedTerm =
                     refactorLabelsRecursive(state, services, applicationPosInOccurrence,
-                        applicationTerm, rule, goal, hint, tacletTerm, sfa.formula(),
+                        applicationTerm, rule, goal, hint, tacletTerm, sfa,
                         activeRefactorings);
-                if (!sfa.formula().equals(updatedTerm)) {
-                    goal.changeFormula(new SequentFormula(updatedTerm),
+                if (!sfa.equals(updatedTerm)) {
+                    goal.changeFormula(updatedTerm,
                         new PosInOccurrence(sfa, PosInTerm.getTopLevel(), inAntec));
                 }
             }
@@ -1962,11 +1962,11 @@ public static TermLabel findInnerMostParentLabel(PosInOccurrence pio, Name termL
     }
 
     /**
-     * Merges the {@link TermLabel}s of the rejected {@link SequentFormula}s into the resulting
+     * Merges the {@link TermLabel}s of the rejected {@link Term}s into the resulting
      * {@link Sequent}.
      *
      * @param currentSequent The {@link SequentChangeInfo} which lists the rejected
-     *        {@link SequentFormula}s.
+     *        {@link Term}s.
      * @param services The {@link Services} to use.
      */
     public static void mergeLabels(SequentChangeInfo currentSequent, Services services) {
@@ -1977,47 +1977,49 @@ public static void mergeLabels(SequentChangeInfo currentSequent, Services servic
     }
 
     /**
-     * Merges the {@link TermLabel}s of the rejected {@link SequentFormula}s into the resulting
+     * Merges the {@link TermLabel}s of the rejected {@link Term}s into the resulting
      * {@link Sequent}.
      *
      * @param services The {@link Services} to use.
      * @param currentSequent The {@link SequentChangeInfo} which lists the rejected
-     *        {@link SequentFormula}s.
+     *        {@link Term}s.
      */
     public void mergeLabels(Services services, SequentChangeInfo currentSequent) {
-        for (SequentFormula rejectedSF : currentSequent.getSemisequentChangeInfo(true)
+        for (Term rejectedSF : currentSequent.getSemisequentChangeInfo(true)
                 .rejectedFormulas()) {
             mergeLabels(currentSequent, services, rejectedSF, true);
         }
-        for (final SequentFormula rejectedSF : currentSequent.getSemisequentChangeInfo(false)
+        for (final Term rejectedSF : currentSequent.getSemisequentChangeInfo(false)
                 .rejectedFormulas()) {
             mergeLabels(currentSequent, services, rejectedSF, false);
         }
     }
 
     /**
-     * Merges the {@link TermLabel}s of the given {@link SequentFormula} into the resulting
+     * Merges the {@link TermLabel}s of the given {@link Term} into the resulting
      * {@link Sequent}.
      *
      * @param currentSequent The {@link SequentChangeInfo} which lists the rejected
-     *        {@link SequentFormula}s.
+     *        {@link Term}s.
      * @param services The {@link Services} to use.
-     * @param rejectedSF The rejected {@link SequentFormula} to work with.
-     * @param inAntecedent {@code true} rejected {@link SequentFormula} is in antecedent,
+     * @param rejectedSF The rejected {@link Term} to work with.
+     * @param inAntecedent {@code true} rejected {@link Term} is in antecedent,
      *        {@code false} it is in succedent.
      */
     protected void mergeLabels(SequentChangeInfo currentSequent, Services services,
-            SequentFormula rejectedSF, boolean inAntecedent) {
-        final Term rejectedTerm = rejectedSF.formula();
+            Term rejectedSF, boolean inAntecedent) {
+        final Term rejectedTerm = rejectedSF;
         if (rejectedTerm.hasLabels()) {
-            // Search existing SequentFormula
+            // Search existing Term
             Semisequent s = currentSequent.getSemisequentChangeInfo(inAntecedent).semisequent();
-            SequentFormula existingSF = CollectionUtil.search(s,
-                element -> element.formula().equalsModProperty(rejectedTerm,
-                    RENAMING_PROPERTY));
+            Term existingSF = CollectionUtil.search(s,
+                element -> {
+                    return element.equalsModProperty(rejectedTerm,
+                        RENAMING_PROPERTY);
+                });
             if (existingSF != null) {
                 // Create list of new labels
-                Term existingTerm = existingSF.formula();
+                Term existingTerm = existingSF;
                 List<TermLabel> mergedLabels = new LinkedList<>();
                 CollectionUtil.addAll(mergedLabels, existingTerm.getLabels());
                 boolean labelsChanged = false;
@@ -2039,7 +2041,7 @@ protected void mergeLabels(SequentChangeInfo currentSequent, Services services,
                         existingTerm.subs(), existingTerm.boundVars(),
                         new ImmutableArray<>(mergedLabels));
                     SequentChangeInfo sci =
-                        currentSequent.sequent().changeFormula(new SequentFormula(newTerm),
+                        currentSequent.sequent().changeFormula(newTerm,
                             new PosInOccurrence(existingSF, PosInTerm.getTopLevel(), inAntecedent));
                     currentSequent.combine(sci);
                 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ElementaryUpdate.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ElementaryUpdate.java
index 0837fda6089..c4ae30a8789 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ElementaryUpdate.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ElementaryUpdate.java
@@ -9,6 +9,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -58,4 +59,16 @@ public static ElementaryUpdate getInstance(UpdateableOperator lhs) {
     public UpdateableOperator lhs() {
         return lhs;
     }
+
+    @Override
+    public int getChildCount() {
+        return 1;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        if (n == 0)
+            return lhs;
+        throw new IndexOutOfBoundsException("Elementary updates only contain 1 child");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Equality.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Equality.java
index ecd4c878dfc..09fa71a855e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Equality.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Equality.java
@@ -6,6 +6,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -34,4 +35,14 @@ public final class Equality extends AbstractSortedOperator {
     private Equality(Name name, Sort targetSort) {
         super(name, new Sort[] { targetSort, targetSort }, JavaDLTheory.FORMULA, true);
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/FormulaSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/FormulaSV.java
index f93b960860e..270c2a92c89 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/FormulaSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/FormulaSV.java
@@ -7,12 +7,13 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 
 
 /**
  * A schema variable that is used as placeholder for formulas.
  */
-public final class FormulaSV extends OperatorSV {
+public final class FormulaSV extends OperatorSV implements TerminalSyntaxElement {
 
     /**
      * @param name the name of the SchemaVariable
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfExThenElse.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfExThenElse.java
index be40110ea40..c7f05ada203 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfExThenElse.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfExThenElse.java
@@ -6,6 +6,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.TermCreationException;
 import org.key_project.logic.op.AbstractOperator;
 import org.key_project.logic.sort.Sort;
@@ -44,4 +45,14 @@ public <T extends org.key_project.logic.Term> void validTopLevelException(T term
             throw new TermCreationException(this, term);
         }
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfThenElse.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfThenElse.java
index a7fe9097055..a77b49ec111 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfThenElse.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/IfThenElse.java
@@ -8,6 +8,7 @@
 import de.uka.ilkd.key.logic.sort.ProgramSVSort;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.TermCreationException;
 import org.key_project.logic.op.AbstractOperator;
 import org.key_project.logic.sort.Sort;
@@ -85,4 +86,14 @@ public <T extends org.key_project.logic.Term> void validTopLevelException(T term
             throw new TermCreationException(this, term);
         }
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Junctor.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Junctor.java
index e2b1162c6cc..42b78108d67 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Junctor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Junctor.java
@@ -6,6 +6,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -62,4 +63,14 @@ private static Sort[] createFormulaSortArray(int arity) {
     private Junctor(Name name, int arity) {
         super(name, createFormulaSortArray(arity), JavaDLTheory.FORMULA, true);
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("The Junctor operator " + name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/LogicVariable.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/LogicVariable.java
index d4e8aa5def9..fe94c1c3b01 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/LogicVariable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/LogicVariable.java
@@ -9,6 +9,7 @@
 
 import org.key_project.logic.Name;
 import org.key_project.logic.ParsableVariable;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 import org.key_project.util.EqualsModProofIrrelevancy;
 
@@ -43,4 +44,14 @@ public boolean equalsModProofIrrelevancy(Object obj) {
     public int hashCodeModProofIrrelevancy() {
         return Objects.hash(name(), sort());
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("Logic variable " + name() + " does not have children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Modality.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Modality.java
index 0510d66fc73..c9d4557970b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Modality.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Modality.java
@@ -125,7 +125,7 @@ public String toString() {
         return super.toString();
     }
 
-    public static class JavaModalityKind extends Kind implements SVSubstitute {
+    public static class JavaModalityKind extends Kind {
         private static final Map<String, JavaModalityKind> kinds = new HashMap<>();
         /**
          * The diamond operator of dynamic logic. A formula <alpha;>Phi can be read as after
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ObserverFunction.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ObserverFunction.java
index 95d0597ab6c..3edd92a4333 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ObserverFunction.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ObserverFunction.java
@@ -7,6 +7,7 @@
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.logic.ProgramElementName;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 import org.key_project.util.collection.ImmutableArray;
 
@@ -22,7 +23,7 @@
  */
 public class ObserverFunction extends JFunction implements IObserverFunction {
 
-    private final KeYJavaType container;
+    private final Qualifier<KeYJavaType> container;
     private final boolean isStatic;
     private final ImmutableArray<KeYJavaType> paramTypes;
     private final KeYJavaType type;
@@ -42,7 +43,7 @@ public ObserverFunction(String baseName, Sort sort, KeYJavaType type, Sort heapS
         assert type == null || type.getSort() == sort;
         assert container != null;
         this.type = type;
-        this.container = container;
+        this.container = Qualifier.create(container);
         this.isStatic = isStatic;
         this.paramTypes = paramTypes;
         this.heapCount = heapCount;
@@ -107,7 +108,7 @@ public final KeYJavaType getType() {
      */
     @Override
     public final KeYJavaType getContainerType() {
-        return container;
+        return container.getQualifier();
     }
 
 
@@ -169,4 +170,15 @@ public final ImmutableArray<KeYJavaType> getParamTypes() {
         return paramTypes;
     }
 
+    @Override
+    public int getChildCount() {
+        return 1;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        if (n == 0)
+            return container;
+        throw new IndexOutOfBoundsException("ObserverFunction " + name() + " has only one child");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Operator.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Operator.java
index e12cfc522c6..3647725e850 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Operator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Operator.java
@@ -13,7 +13,7 @@
  * etc. have to implement this interface.
  */
 public interface Operator
-        extends org.key_project.logic.op.Operator, SVSubstitute, EqualsModProofIrrelevancy {
+        extends org.key_project.logic.op.Operator, EqualsModProofIrrelevancy {
 
     /**
      * comparator to compare operators; for modalities only their kind is compared
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramSV.java
index 0a4733e4792..0d43f11b6e9 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramSV.java
@@ -22,6 +22,7 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 import org.key_project.util.collection.ImmutableList;
 
@@ -32,7 +33,8 @@
  * Objects of this class are schema variables matching program constructs within modal operators.
  * The particular construct being matched is determined by the ProgramSVSort of the schema variable.
  */
-public final class ProgramSV extends OperatorSV implements ProgramConstruct, UpdateableOperator {
+public final class ProgramSV extends OperatorSV
+        implements ProgramConstruct, UpdateableOperator, SyntaxElement {
     public static final Logger LOGGER = LoggerFactory.getLogger(ProgramSV.class);
 
     private static final ProgramList EMPTY_LIST_INSTANTIATION =
@@ -142,13 +144,18 @@ public Expression getExpressionAt(int index) {
     }
 
     @Override
-    public int getChildCount() {
-        return 0;
+    public ProgramElement getChildAt(int index) {
+        return this;
     }
 
     @Override
-    public ProgramElement getChildAt(int index) {
-        return this;
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("ProgramSV " + this + " has no children");
+    }
+
+    @Override
+    public int getChildCount() {
+        return 0;
     }
 
     @Override
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramVariable.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramVariable.java
index 40cb2da7762..67210bebe7f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramVariable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/ProgramVariable.java
@@ -16,6 +16,7 @@
 import de.uka.ilkd.key.rule.MatchConditions;
 
 import org.key_project.logic.ParsableVariable;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 import org.key_project.util.ExtList;
 
@@ -256,4 +257,15 @@ public MatchConditions match(SourceData source, MatchConditions matchCond) {
             return null;
         }
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(
+            "Program variable " + name() + " does not have children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Qualifier.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Qualifier.java
new file mode 100644
index 00000000000..2450b036d2e
--- /dev/null
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Qualifier.java
@@ -0,0 +1,31 @@
+/* This file is part of KeY - https://key-project.org
+ * KeY is licensed under the GNU General Public License Version 2
+ * SPDX-License-Identifier: GPL-2.0-only */
+package de.uka.ilkd.key.logic.op;
+
+import java.util.WeakHashMap;
+
+import org.key_project.logic.TerminalSyntaxElement;
+
+public class Qualifier<T> implements TerminalSyntaxElement {
+    private final T qualifier;
+
+    private static final WeakHashMap<Object, Qualifier<?>> INSTANCES = new WeakHashMap<>();
+
+    private Qualifier(T qualifier) {
+        this.qualifier = qualifier;
+    }
+
+    synchronized static <T> Qualifier<T> create(T qualifier) {
+        if (INSTANCES.containsKey(qualifier)) {
+            return (Qualifier<T>) INSTANCES.get(qualifier);
+        }
+        var q = new Qualifier<>(qualifier);
+        INSTANCES.put(qualifier, q);
+        return q;
+    }
+
+    public T getQualifier() {
+        return qualifier;
+    }
+}
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Quantifier.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Quantifier.java
index bbf777afbfd..e73cb2e17c6 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/Quantifier.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/Quantifier.java
@@ -6,6 +6,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 /**
@@ -36,4 +37,14 @@ private Quantifier(Name name) {
         super(name, new Sort[] { JavaDLTheory.FORMULA }, JavaDLTheory.FORMULA,
             new Boolean[] { true }, true);
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SVSubstitute.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SVSubstitute.java
deleted file mode 100644
index b7f183d6ed5..00000000000
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SVSubstitute.java
+++ /dev/null
@@ -1,12 +0,0 @@
-/* This file is part of KeY - https://key-project.org
- * KeY is licensed under the GNU General Public License Version 2
- * SPDX-License-Identifier: GPL-2.0-only */
-package de.uka.ilkd.key.logic.op;
-
-/**
- * JavaCardDL syntactical elements implement this interface if they can occur as instantiations of
- * schema variables.
- */
-public interface SVSubstitute {
-
-}
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SkolemTermSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SkolemTermSV.java
index 19bce65bc98..1cd550fa69d 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SkolemTermSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SkolemTermSV.java
@@ -7,6 +7,7 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 /**
@@ -14,7 +15,7 @@
  * variables have to be accompanied by a "NewDependingOn" varcond, although with the removal of the
  * meta variable mechanism, this would no longer really be necessary.
  */
-public final class SkolemTermSV extends OperatorSV {
+public final class SkolemTermSV extends OperatorSV implements TerminalSyntaxElement {
 
     /**
      * Creates a new schema variable that is used as placeholder for skolem terms.
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SortDependingFunction.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SortDependingFunction.java
index 4d0e486211a..bd675d35d89 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SortDependingFunction.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SortDependingFunction.java
@@ -12,6 +12,7 @@
 import de.uka.ilkd.key.logic.sort.ProgramSVSort;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 import org.key_project.util.collection.ImmutableArray;
 
@@ -29,7 +30,7 @@ public final class SortDependingFunction extends JFunction {
     private static final Logger LOGGER = LoggerFactory.getLogger(SortDependingFunction.class);
 
     private final SortDependingFunctionTemplate template;
-    private final Sort sortDependingOn;
+    private final Qualifier<Sort> sortDependingOn;
 
 
     // -------------------------------------------------------------------------
@@ -41,7 +42,7 @@ private SortDependingFunction(SortDependingFunctionTemplate template, Sort sortD
             instantiateResultSort(template, sortDependingOn),
             instantiateArgSorts(template, sortDependingOn), null, template.unique, false);
         this.template = template;
-        this.sortDependingOn = sortDependingOn;
+        this.sortDependingOn = Qualifier.create(sortDependingOn);
     }
 
 
@@ -168,7 +169,7 @@ && instantiateName(getKind(), sort).toString().contains("seqGet")
 
 
     public Sort getSortDependingOn() {
-        return sortDependingOn;
+        return sortDependingOn.getQualifier();
     }
 
 
@@ -188,4 +189,18 @@ public Name getKind() {
     private record SortDependingFunctionTemplate(GenericSort sortDependingOn, Name kind, Sort sort,
             ImmutableArray<Sort> argSorts, boolean unique) {
     }
+
+    @Override
+    public int getChildCount() {
+        return 1;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        if (n == 0) {
+            return sortDependingOn;
+        }
+        throw new IndexOutOfBoundsException(
+            "SortDependingFunction " + name() + " has only one child");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SubstOp.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SubstOp.java
index f993389d350..193fcc78e60 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/SubstOp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/SubstOp.java
@@ -7,6 +7,7 @@
 import de.uka.ilkd.key.logic.TermBuilder;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.TermCreationException;
 import org.key_project.logic.op.AbstractOperator;
 import org.key_project.logic.sort.Sort;
@@ -72,4 +73,15 @@ public <T extends org.key_project.logic.Term> void validTopLevelException(T term
     // Term res = cfSubst.apply(term.sub(1));
     // return res;
     // }
+
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("SubstOp " + name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermLabelSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermLabelSV.java
index 4662b1f17ad..fc1fb8526e3 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermLabelSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermLabelSV.java
@@ -8,11 +8,12 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 
 /**
  * A schema variable which matches term labels
  */
-public final class TermLabelSV extends OperatorSV implements SchemaVariable, TermLabel {
+public final class TermLabelSV extends OperatorSV implements TermLabel, TerminalSyntaxElement {
 
     TermLabelSV(Name name) {
         super(name, JavaDLTheory.TERMLABEL, true, false);
@@ -29,12 +30,12 @@ public String toString() {
     }
 
     @Override
-    public Object getChild(int i) {
-        throw new IndexOutOfBoundsException();
+    public int getTLChildCount() {
+        return 0;
     }
 
     @Override
-    public int getChildCount() {
-        return 0;
+    public Object getTLChild(int i) {
+        throw new IndexOutOfBoundsException();
     }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermSV.java
index b057d045105..15353a7aaea 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermSV.java
@@ -7,13 +7,14 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
 /**
  * A schema variable that is used as placeholder for terms.
  */
-public final class TermSV extends OperatorSV {
+public final class TermSV extends OperatorSV implements TerminalSyntaxElement {
 
     /**
      * @param name the name of the schema variable
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermTransformer.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermTransformer.java
index b722678fd3d..4ca7e30a52f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermTransformer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/TermTransformer.java
@@ -7,11 +7,14 @@
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.TerminalSyntaxElement;
+
 /**
  * TermTransformer perform complex term transformation which cannot be (efficiently or at all)
  * described by taclets.
  */
-public interface TermTransformer extends org.key_project.logic.op.SortedOperator, Operator {
+public interface TermTransformer extends org.key_project.logic.op.SortedOperator, Operator,
+        /* TODO: check */ TerminalSyntaxElement {
 
     /**
      * initiates term transformation of <tt>term</tt>. Note the top level operator of of parameter
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateApplication.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateApplication.java
index fb6ff4791b6..19c503cff67 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateApplication.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateApplication.java
@@ -7,6 +7,7 @@
 import de.uka.ilkd.key.logic.Term;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.TermCreationException;
 import org.key_project.logic.op.AbstractOperator;
 import org.key_project.logic.sort.Sort;
@@ -77,4 +78,14 @@ public static Term getTarget(Term t) {
         assert t.op() == UPDATE_APPLICATION;
         return t.sub(targetPos());
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("UpdateApplication has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateJunctor.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateJunctor.java
index 38b43150538..ca3586e9aa8 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateJunctor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateJunctor.java
@@ -6,6 +6,7 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -34,4 +35,14 @@ private static Sort[] createUpdateSortArray(int arity) {
     private UpdateJunctor(Name name, int arity) {
         super(name, createUpdateSortArray(arity), JavaDLTheory.UPDATE, false);
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("UpdateJunctor " + name() + " has no children");
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateSV.java
index 44b86cbd2c3..089f3b003e4 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/UpdateSV.java
@@ -7,12 +7,13 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 
 
 /**
  * A schema variable that is used as placeholder for updates.
  */
-public final class UpdateSV extends OperatorSV {
+public final class UpdateSV extends OperatorSV implements TerminalSyntaxElement {
 
 
     UpdateSV(Name name) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/op/VariableSV.java b/key.core/src/main/java/de/uka/ilkd/key/logic/op/VariableSV.java
index 1024cf7b45d..fcbec1e7937 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/op/VariableSV.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/op/VariableSV.java
@@ -6,12 +6,14 @@
 import de.uka.ilkd.key.util.pp.Layouter;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.TerminalSyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 /**
  * Schema variable that is instantiated with logical variables.
  */
-public final class VariableSV extends OperatorSV implements QuantifiableVariable {
+public final class VariableSV extends OperatorSV
+        implements QuantifiableVariable, TerminalSyntaxElement {
 
     /**
      * Creates a new SchemaVariable that is used as placeholder for bound(quantified) variables.
@@ -34,4 +36,6 @@ public void layout(Layouter<?> l) {
         l.print("\\schemaVar \\variables ").print(sort().name().toString()).print(" ")
                 .print(name().toString());
     }
+
+
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/logic/package-info.java b/key.core/src/main/java/de/uka/ilkd/key/logic/package-info.java
index 6b837c99a90..a30dfb3f8b4 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/logic/package-info.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/logic/package-info.java
@@ -24,7 +24,7 @@
  * {@link de.uka.ilkd.key.logic.Sequent}s consist of two {@link
  * de.uka.ilkd.key.logic.Semisequent}s which represent a
  * duplicate-free list of a {@link
- * de.uka.ilkd.key.logic.SequentFormula}s. The latter consist of
+ * de.uka.ilkd.key.logic.Term}s. The latter consist of
  * a {@link de.uka.ilkd.key.logic.Constraint} and a {@link
  * de.uka.ilkd.key.logic.Term} of a special sort {@link
  * de.uka.ilkd.key.logic.sort.Sort#FORMULA}.
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/AbstractBlastingMacro.java b/key.core/src/main/java/de/uka/ilkd/key/macros/AbstractBlastingMacro.java
index e225fca54bc..18c841493e0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/AbstractBlastingMacro.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/AbstractBlastingMacro.java
@@ -17,7 +17,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.SortCollector;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
@@ -68,14 +67,14 @@ protected void addInvariantFormula(Goal goal) {
 
         SortCollector sortCollector = new SortCollector();
 
-        for (SequentFormula sf : goal.sequent()) {
-            sf.formula().execPreOrder(sortCollector);
+        for (Term sf : goal.sequent()) {
+            sf.execPreOrder(sortCollector);
         }
 
         Set<Sort> sorts = sortCollector.getSorts();
         sorts.remove(nullSort);
-        List<SequentFormula> formulae = createFormulae(goal.proof().getServices(), sorts);
-        for (SequentFormula sf : formulae) {
+        List<Term> formulae = createFormulae(goal.proof().getServices(), sorts);
+        for (Term sf : formulae) {
             Sequent s = goal.sequent();
             Semisequent antecedent = s.antecedent();
             if (!antecedent.containsEqual(sf)) {
@@ -98,8 +97,8 @@ private boolean containsSubTypes(Sort s, Set<Sort> sorts) {
         return false;
     }
 
-    private List<SequentFormula> createFormulae(Services services, Set<Sort> sorts) {
-        List<SequentFormula> result = new LinkedList<>();
+    private List<Term> createFormulae(Services services, Set<Sort> sorts) {
+        List<Term> result = new LinkedList<>();
 
         JavaInfo info = services.getJavaInfo();
         SpecificationRepository spec = services.getSpecificationRepository();
@@ -132,7 +131,7 @@ private List<SequentFormula> createFormulae(Services services, Set<Sort> sorts)
         return result;
     }
 
-    private static void addFormulas(List<SequentFormula> result, KeYJavaType kjt, ClassAxiom c,
+    private static void addFormulas(List<Term> result, KeYJavaType kjt, ClassAxiom c,
             LogicVariable o, LogicVariable h, Services services) {
         TermBuilder tb = new TermBuilder(services.getTermFactory(), services);
         Term exactInstance = tb.exactInstance(kjt.getSort(), tb.var(o));
@@ -162,10 +161,10 @@ private static void addFormulas(List<SequentFormula> result, KeYJavaType kjt, Cl
                     exactInstanceEquiv = tb.all(h, tb.all(o, exactInstanceEquiv));
                     instanceImpl = tb.all(h, tb.all(o, instanceImpl));
 
-                    result.add(new SequentFormula(exactInstanceEquiv));
+                    result.add(exactInstanceEquiv);
 
                     if (!right.equals(tb.tt())) {
-                        result.add(new SequentFormula(instanceImpl));
+                        result.add(instanceImpl);
                     }
                 } else if (right.op().name().equals(inv.op().name())) {
 
@@ -176,21 +175,17 @@ private static void addFormulas(List<SequentFormula> result, KeYJavaType kjt, Cl
                     exactInstanceEquiv = tb.all(h, tb.all(o, exactInstanceEquiv));
                     instanceImpl = tb.all(h, tb.all(o, instanceImpl));
 
-                    result.add(new SequentFormula(exactInstanceEquiv));
+                    result.add(exactInstanceEquiv);
 
                     if (!left.equals(tb.tt())) {
-                        result.add(new SequentFormula(instanceImpl));
+                        result.add(instanceImpl);
                     }
 
                 } else {
-                    Term f = t;
-                    f = tb.all(h, tb.all(o, f));
-                    result.add(new SequentFormula(f));
+                    result.add(tb.all(h, tb.all(o, t)));
                 }
             } else {
-                Term f = t;
-                f = tb.all(h, tb.all(o, f));
-                result.add(new SequentFormula(f));
+                result.add(tb.all(h, tb.all(o, t)));
             }
         } catch (Exception e) {
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/FinishSymbolicExecutionUntilMergePointMacro.java b/key.core/src/main/java/de/uka/ilkd/key/macros/FinishSymbolicExecutionUntilMergePointMacro.java
index 59b6f499d5f..f9a5a8e94d7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/FinishSymbolicExecutionUntilMergePointMacro.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/FinishSymbolicExecutionUntilMergePointMacro.java
@@ -150,9 +150,9 @@ public void taskFinished(TaskFinishedInfo info) {
      * @return true iff the given succedent has one formula with a break point statement.
      */
     private boolean hasBreakPoint(Semisequent succedent) {
-        for (SequentFormula formula : succedent.asList()) {
+        for (Term formula : succedent.asList()) {
             if (blockElems.contains(JavaTools
-                    .getActiveStatement(MergeRuleUtils.getJavaBlockRecursive(formula.formula())))) {
+                    .getActiveStatement(MergeRuleUtils.getJavaBlockRecursive(formula)))) {
                 return true;
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/ModalityCache.java b/key.core/src/main/java/de/uka/ilkd/key/macros/ModalityCache.java
index b55b1137bc9..99dad89cc9c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/ModalityCache.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/ModalityCache.java
@@ -6,7 +6,6 @@
 import java.util.Map;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.ParameterlessTermLabel;
 import de.uka.ilkd.key.logic.op.Modality;
@@ -79,8 +78,8 @@ public boolean hasModality(Sequent sequent) {
         }
 
         var result = false;
-        for (SequentFormula sequentFormula : sequent) {
-            if (termHasModality(sequentFormula.formula())) {
+        for (Term fml : sequent) {
+            if (termHasModality(fml)) {
                 result = true;
                 break;
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/FocusCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/FocusCommand.java
index a27f4613191..2b83dd87ccb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/FocusCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/FocusCommand.java
@@ -73,23 +73,27 @@ private void hideAll(Sequent toKeep) throws ScriptException {
         assert goal != null : "not null by contract of the method";
 
         // The formulas to keep in the antecedent
-        ImmutableList<Term> keepAnte = toKeep.antecedent().asList().map(SequentFormula::formula);
-        ImmutableList<SequentFormula> ante = goal.sequent().antecedent().asList();
+        ImmutableList<Term> keepAnte = toKeep.antecedent().asList().map(term1 -> term1);
+        ImmutableList<Term> ante = goal.sequent().antecedent().asList();
 
-        for (SequentFormula seqFormula : ante) {
+        for (Term seqFormula : ante) {
             // This means "!keepAnte.contains(seqFormula.formula)" but with equality mod renaming!
             if (!keepAnte.exists(
-                it -> it.equalsModProperty(seqFormula.formula(), RENAMING_PROPERTY))) {
+                it -> {
+                    return it.equalsModProperty(seqFormula, RENAMING_PROPERTY);
+                })) {
                 Taclet tac = getHideTaclet("left");
                 makeTacletApp(goal, seqFormula, tac, true);
             }
         }
 
-        ImmutableList<Term> keepSucc = toKeep.succedent().asList().map(SequentFormula::formula);
-        ImmutableList<SequentFormula> succ = goal.sequent().succedent().asList();
-        for (SequentFormula seqFormula : succ) {
+        ImmutableList<Term> keepSucc = toKeep.succedent().asList().map(term -> term);
+        ImmutableList<Term> succ = goal.sequent().succedent().asList();
+        for (Term seqFormula : succ) {
             if (!keepSucc.exists(
-                it -> it.equalsModProperty(seqFormula.formula(), RENAMING_PROPERTY))) {
+                it -> {
+                    return it.equalsModProperty(seqFormula, RENAMING_PROPERTY);
+                })) {
                 Taclet tac = getHideTaclet("right");
                 makeTacletApp(goal, seqFormula, tac, false);
             }
@@ -110,7 +114,7 @@ private Taclet getHideTaclet(String pos) {
      * @param tac the taclet top apply (either hide_left or hide_right)
      * @param antec whether the formula is in the antecedent
      */
-    private void makeTacletApp(Goal g, SequentFormula toHide, Taclet tac, boolean antec) {
+    private void makeTacletApp(Goal g, Term toHide, Taclet tac, boolean antec) {
 
         // hide rules only applicable to top-level terms/sequent formulas
         PosInTerm pit = PosInTerm.getTopLevel();
@@ -126,7 +130,7 @@ private void makeTacletApp(Goal g, SequentFormula toHide, Taclet tac, boolean an
 
         TacletApp app =
             PosTacletApp.createPosTacletApp((FindTaclet) tac, inst, pio, proof.getServices());
-        app = app.addCheckedInstantiation(sv, toHide.formula(), proof.getServices(), true);
+        app = app.addCheckedInstantiation(sv, toHide, proof.getServices(), true);
         g.apply(app);
 
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/HideCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/HideCommand.java
index 85edd078c0b..f1458b91d73 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/HideCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/HideCommand.java
@@ -5,11 +5,7 @@
 
 import java.util.Map;
 
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.macros.scripts.meta.Option;
 import de.uka.ilkd.key.proof.Goal;
@@ -56,11 +52,11 @@ public void execute(Parameters args) throws ScriptException, InterruptedExceptio
 
         Taclet hideLeft =
             state.getProof().getEnv().getInitConfigForEnvironment().lookupActiveTaclet(HIDE_LEFT);
-        for (SequentFormula s : args.sequent.antecedent()) {
+        for (Term s : args.sequent.antecedent()) {
             TacletApp app = NoPosTacletApp.createNoPosTacletApp(hideLeft);
-            SequentFormula s2 = find(s, goal.sequent().antecedent());
+            Term s2 = find(s, goal.sequent().antecedent());
             SchemaVariable sv = app.uninstantiatedVars().iterator().next();
-            app = app.addCheckedInstantiation(sv, s2.formula(), service, true);
+            app = app.addCheckedInstantiation(sv, s2, service, true);
             app = app.setPosInOccurrence(new PosInOccurrence(s2, PosInTerm.getTopLevel(), true),
                 service);
             goal.apply(app);
@@ -68,20 +64,20 @@ public void execute(Parameters args) throws ScriptException, InterruptedExceptio
 
         Taclet hideRight =
             state.getProof().getEnv().getInitConfigForEnvironment().lookupActiveTaclet(HIDE_RIGHT);
-        for (SequentFormula s : args.sequent.succedent()) {
+        for (Term s : args.sequent.succedent()) {
             TacletApp app = NoPosTacletApp.createNoPosTacletApp(hideRight);
-            SequentFormula s2 = find(s, goal.sequent().succedent());
+            Term s2 = find(s, goal.sequent().succedent());
             SchemaVariable sv = app.uninstantiatedVars().iterator().next();
-            app = app.addCheckedInstantiation(sv, s2.formula(), service, true);
+            app = app.addCheckedInstantiation(sv, s2, service, true);
             app = app.setPosInOccurrence(new PosInOccurrence(s2, PosInTerm.getTopLevel(), false),
                 service);
             goal.apply(app);
         }
     }
 
-    private SequentFormula find(SequentFormula sf, Semisequent semiseq) throws ScriptException {
-        for (SequentFormula s : semiseq) {
-            if (s.formula().equalsModProperty(sf.formula(), TERM_LABELS_PROPERTY)) {
+    private Term find(Term sf, Semisequent semiseq) throws ScriptException {
+        for (Term s : semiseq) {
+            if (s.equalsModProperty(sf, TERM_LABELS_PROPERTY)) {
                 return s;
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/InstantiateCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/InstantiateCommand.java
index 41ee9436a12..0b676600f19 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/InstantiateCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/InstantiateCommand.java
@@ -109,19 +109,21 @@ private ImmutableList<TacletApp> findAllTacletApps(Parameters p, EngineState sta
         index.autoModeStopped();
 
         ImmutableList<TacletApp> allApps = ImmutableSLList.nil();
-        for (SequentFormula sf : g.node().sequent().antecedent()) {
-            if (p.formula != null
-                    && !sf.formula().equalsModProperty(p.formula, RENAMING_PROPERTY)) {
-                continue;
+        for (Term sf : g.node().sequent().antecedent()) {
+            if (p.formula != null) {
+                if (!sf.equalsModProperty(p.formula, RENAMING_PROPERTY)) {
+                    continue;
+                }
             }
             allApps = allApps.append(index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), true), services));
         }
 
-        for (SequentFormula sf : g.node().sequent().succedent()) {
-            if (p.formula != null
-                    && !sf.formula().equalsModProperty(p.formula, RENAMING_PROPERTY)) {
-                continue;
+        for (Term sf : g.node().sequent().succedent()) {
+            if (p.formula != null) {
+                if (!sf.equalsModProperty(p.formula, RENAMING_PROPERTY)) {
+                    continue;
+                }
             }
             allApps = allApps.append(index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), false), services));
@@ -149,8 +151,8 @@ private void computeFormula(Parameters params, Goal goal) throws ScriptException
         Node n = goal.node();
         Sequent seq = n.sequent();
         int occ = params.occ;
-        for (SequentFormula form : seq.antecedent().asList()) {
-            Term term = form.formula();
+        for (Term form : seq.antecedent().asList()) {
+            Term term = form;
             Term stripped = stripUpdates(term);
             if (stripped.op() == Quantifier.ALL) {
                 String varName = stripped.boundVars().get(0).name().toString();
@@ -164,8 +166,8 @@ private void computeFormula(Parameters params, Goal goal) throws ScriptException
             }
         }
 
-        for (SequentFormula form : seq.succedent().asList()) {
-            Term term = form.formula();
+        for (Term form : seq.succedent().asList()) {
+            Term term = form;
             Term stripped = stripUpdates(term);
             if (stripped.op() == Quantifier.EX) {
                 String varName = stripped.boundVars().get(0).name().toString();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/MacroCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/MacroCommand.java
index 2a431b1cad5..d0e5299907b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/MacroCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/MacroCommand.java
@@ -9,9 +9,7 @@
 
 import de.uka.ilkd.key.control.AbstractUserInterfaceControl;
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.Sequent;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.macros.ProofMacro;
 import de.uka.ilkd.key.macros.ProofMacroFinishedInfo;
 import de.uka.ilkd.key.macros.scripts.meta.Option;
@@ -129,8 +127,9 @@ public static PosInOccurrence extractMatchingPio(final Sequent sequent, final St
         boolean matched = false;
 
         for (int i = 1; i < sequent.size() + 1; i++) {
+            Term fml = sequent.getFormulabyNr(i);
             final boolean matchesRegex = formatTermString(
-                LogicPrinter.quickPrintTerm(sequent.getFormulabyNr(i).formula(), services))
+                LogicPrinter.quickPrintTerm(fml, services))
                         .matches(".*" + matchRegEx + ".*");
             if (matchesRegex) {
                 if (matched) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RewriteCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RewriteCommand.java
index 4c15504162b..2863889ee48 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RewriteCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RewriteCommand.java
@@ -111,21 +111,23 @@ private ImmutableList<TacletApp> findAllTacletApps(Parameters p, EngineState sta
 
         // filter taclets that are applicable on the given formula
         // filter taclets that are applicable on the given formula in the antecedent
-        for (SequentFormula sf : g.node().sequent().antecedent()) {
+        for (Term sf : g.node().sequent().antecedent()) {
 
-            if (p.formula != null
-                    && !sf.formula().equalsModProperty(p.formula, RENAMING_PROPERTY)) {
-                continue;
+            if (p.formula != null) {
+                if (!sf.equalsModProperty(p.formula, RENAMING_PROPERTY)) {
+                    continue;
+                }
             }
             allApps = allApps.append(index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), true), services));
         }
 
         // filter taclets that are applicable on the given formula in the succedent
-        for (SequentFormula sf : g.node().sequent().succedent()) {
-            if (p.formula != null
-                    && !sf.formula().equalsModProperty(p.formula, RENAMING_PROPERTY)) {
-                continue;
+        for (Term sf : g.node().sequent().succedent()) {
+            if (p.formula != null) {
+                if (!sf.equalsModProperty(p.formula, RENAMING_PROPERTY)) {
+                    continue;
+                }
             }
             allApps = allApps.append(index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), false), services));
@@ -159,7 +161,7 @@ private List<PosInOccurrence> findAndExecReplacement(Parameters p,
 
                             RewriteTaclet rw = (RewriteTaclet) pta.taclet();
                             if (pta.complete()) {
-                                SequentFormula rewriteResult = rw.getExecutor().getRewriteResult(
+                                Term rewriteResult = rw.getExecutor().getRewriteResult(
                                     goalold, null, goalold.proof().getServices(), pta);
 
                                 executeRewriteTaclet(p, pta, goalold, rewriteResult);
@@ -187,8 +189,8 @@ private List<PosInOccurrence> findAndExecReplacement(Parameters p,
      * @param rewriteResult
      */
     private void executeRewriteTaclet(Parameters p, PosTacletApp pta, Goal goalold,
-            SequentFormula rewriteResult) {
-        if (rewriteResult.formula().equals(p.replace)
+            Term rewriteResult) {
+        if (rewriteResult.equals(p.replace)
                 || getTermAtPos(rewriteResult, pta.posInOccurrence()).equals(p.replace)) {
             failposInOccs.remove(pta.posInOccurrence());
             succposInOccs.add(pta.posInOccurrence());
@@ -207,13 +209,13 @@ private void executeRewriteTaclet(Parameters p, PosTacletApp pta, Goal goalold,
      * @param pio PosInOccurrence of the to be returned term
      * @return term at pio
      */
-    public Term getTermAtPos(SequentFormula sf, PosInOccurrence pio) {
+    public Term getTermAtPos(Term sf, PosInOccurrence pio) {
         if (pio.isTopLevel()) {
-            return sf.formula();
+            return sf;
 
         } else {
             PosInTerm pit = pio.posInTerm();
-            return getSubTerm(sf.formula(), pit.iterator());
+            return getSubTerm(sf, pit.iterator());
         }
 
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RuleCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RuleCommand.java
index a107e4c8c96..b1d07c04693 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RuleCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/RuleCommand.java
@@ -254,7 +254,7 @@ private ImmutableList<IBuiltInRuleApp> findBuiltInRuleApps(Parameters p, EngineS
         final BuiltInRuleAppIndex index = g.ruleAppIndex().builtInRuleAppIndex();
 
         ImmutableList<IBuiltInRuleApp> allApps = ImmutableSLList.nil();
-        for (SequentFormula sf : g.node().sequent().antecedent()) {
+        for (Term sf : g.node().sequent().antecedent()) {
             if (!isFormulaSearchedFor(p, sf, services)) {
                 continue;
             }
@@ -263,7 +263,7 @@ private ImmutableList<IBuiltInRuleApp> findBuiltInRuleApps(Parameters p, EngineS
                 index.getBuiltInRule(g, new PosInOccurrence(sf, PosInTerm.getTopLevel(), true)));
         }
 
-        for (SequentFormula sf : g.node().sequent().succedent()) {
+        for (Term sf : g.node().sequent().succedent()) {
             if (!isFormulaSearchedFor(p, sf, services)) {
                 continue;
             }
@@ -285,7 +285,7 @@ private ImmutableList<TacletApp> findAllTacletApps(Parameters p, EngineState sta
         index.autoModeStopped();
 
         ImmutableList<TacletApp> allApps = ImmutableSLList.nil();
-        for (SequentFormula sf : g.node().sequent().antecedent()) {
+        for (Term sf : g.node().sequent().antecedent()) {
             if (!isFormulaSearchedFor(p, sf, services)) {
                 continue;
             }
@@ -294,7 +294,7 @@ private ImmutableList<TacletApp> findAllTacletApps(Parameters p, EngineState sta
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), true), services));
         }
 
-        for (SequentFormula sf : g.node().sequent().succedent()) {
+        for (Term sf : g.node().sequent().succedent()) {
             if (!isFormulaSearchedFor(p, sf, services)) {
                 continue;
             }
@@ -307,21 +307,21 @@ private ImmutableList<TacletApp> findAllTacletApps(Parameters p, EngineState sta
     }
 
     /**
-     * Returns true iff the given {@link SequentFormula} either matches the
+     * Returns true iff the given {@link Term} either matches the
      * {@link Parameters#formula} parameter or its String representation matches the
      * {@link Parameters#matches} regex. If both parameters are not supplied, always returns true.
      *
      * @param p The {@link Parameters} object.
-     * @param sf The {@link SequentFormula} to check.
+     * @param sf The {@link Term} to check.
      * @return true if <code>sf</code> matches.
      */
-    private boolean isFormulaSearchedFor(Parameters p, SequentFormula sf, Services services)
+    private boolean isFormulaSearchedFor(Parameters p, Term sf, Services services)
             throws ScriptException {
         final boolean satisfiesFormulaParameter =
-            p.formula != null && sf.formula().equalsModProperty(p.formula, RENAMING_PROPERTY);
+            p.formula != null && sf.equalsModProperty(p.formula, RENAMING_PROPERTY);
 
         final boolean satisfiesMatchesParameter = p.matches != null
-                && formatTermString(LogicPrinter.quickPrintTerm(sf.formula(), services))
+                && formatTermString(LogicPrinter.quickPrintTerm(sf, services))
                         .matches(".*" + p.matches + ".*");
 
         return (p.formula == null && p.matches == null) || satisfiesFormulaParameter
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/SelectCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/SelectCommand.java
index f43592bde92..e62b8222786 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/SelectCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/SelectCommand.java
@@ -11,7 +11,6 @@
 
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.macros.scripts.meta.Option;
 import de.uka.ilkd.key.proof.Goal;
@@ -134,8 +133,8 @@ private boolean contains(Sequent seq, Term formula) {
     }
 
     private boolean contains(Semisequent semiseq, Term formula) {
-        for (SequentFormula sf : semiseq.asList()) {
-            if (sf.formula().equalsModProperty(formula, RENAMING_PROPERTY)) {
+        for (Term sf : semiseq.asList()) {
+            if (sf.equalsModProperty(formula, RENAMING_PROPERTY)) {
                 return true;
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/UnhideCommand.java b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/UnhideCommand.java
index 1a1bfcf4055..4399ad0beba 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/UnhideCommand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/macros/scripts/UnhideCommand.java
@@ -59,10 +59,14 @@ public void execute(Parameters args) throws ScriptException, InterruptedExceptio
         Goal goal = state.getFirstOpenAutomaticGoal();
 
         Set<Term> antes = new HashSet<>();
-        args.sequent.antecedent().forEach(sf -> antes.add(sf.formula()));
+        args.sequent.antecedent().forEach(sf -> {
+            antes.add(sf);
+        });
 
         Set<Term> succs = new HashSet<>();
-        args.sequent.succedent().forEach(sf -> succs.add(sf.formula()));
+        args.sequent.succedent().forEach(sf -> {
+            succs.add(sf);
+        });
 
         RuleAppIndex index = goal.ruleAppIndex();
         ImmutableList<NoPosTacletApp> apps = index.getNoFindTaclet(FILTER, service);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ExpressionBuilder.java b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ExpressionBuilder.java
index 1d638f33534..dab8f44a1a1 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ExpressionBuilder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ExpressionBuilder.java
@@ -559,13 +559,13 @@ public Object visitTermorseq(KeYParser.TermorseqContext ctx) {
         if (head != null && ss != null) {
             // A sequent with only head in the antecedent.
             Semisequent ant = Semisequent.EMPTY_SEMISEQUENT;
-            ant = ant.insertFirst(new SequentFormula(head)).semisequent();
+            ant = ant.insertFirst(head).semisequent();
             return Sequent.createSequent(ant, ss);
         }
         if (head != null && s != null) {
             // A sequent. Prepend head to the antecedent.
             Semisequent newAnt = s.antecedent();
-            newAnt = newAnt.insertFirst(new SequentFormula(head)).semisequent();
+            newAnt = newAnt.insertFirst(head).semisequent();
             return Sequent.createSequent(newAnt, s.succedent());
         }
         if (ss != null) {
@@ -583,7 +583,7 @@ public Semisequent visitSemisequent(KeYParser.SemisequentContext ctx) {
         }
         Term head = accept(ctx.term());
         if (head != null) {
-            ss = ss.insertFirst(new SequentFormula(head)).semisequent();
+            ss = ss.insertFirst(head).semisequent();
         }
         return ss;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ProblemFinder.java b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ProblemFinder.java
index 02b4702e60d..dfbc3c110b1 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ProblemFinder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/ProblemFinder.java
@@ -104,7 +104,7 @@ public ProblemFinder(Services services, NamespaceSet nss) {
         if (obj instanceof Sequent s)
             return s;
         if (obj instanceof Term t)
-            return Sequent.createSuccSequent(new Semisequent(new SequentFormula(t)));
+            return Sequent.createSuccSequent(new Semisequent(t));
         return null;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/TacletPBuilder.java b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/TacletPBuilder.java
index 3e558815f71..05f0191628e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/TacletPBuilder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/nparser/builder/TacletPBuilder.java
@@ -151,7 +151,7 @@ public Taclet visitTaclet(KeYParser.TacletContext ctx) {
             }
             TacletBuilder<?> b = createTacletBuilderFor(null, RewriteTaclet.NONE, ctx);
             currentTBuilder.push(b);
-            SequentFormula sform = new SequentFormula(form);
+            Term sform = form;
             Semisequent semi = new Semisequent(sform);
             Sequent addSeq = Sequent.createAnteSequent(semi);
             ImmutableList<Taclet> noTaclets = ImmutableSLList.nil();
@@ -322,8 +322,9 @@ private TacletBuilder<? extends Taclet> createDeconstructorEQTaclet(
         var res = schemaVariables[argIndex];
 
         tacletBuilder.setFind(tb.func(function, tb.var(x)));
+        Term uAssumptions = tb.equals(tb.var(x), tb.func(consFn, args));
         tacletBuilder.setIfSequent(Sequent.createAnteSequent(
-            new Semisequent(new SequentFormula(tb.equals(tb.var(x), tb.func(consFn, args))))));
+            new Semisequent(uAssumptions)));
         tacletBuilder.addTacletGoalTemplate(new RewriteTacletGoalTemplate(tb.var(res)));
         tacletBuilder.setApplicationRestriction(RewriteTaclet.SAME_UPDATE_LEVEL);
 
@@ -350,7 +351,7 @@ private TacletBuilder<? extends Taclet> createInductionTaclet(
 
         var use = tb.all(qvar, tb.var(phi));
         var useCase = new TacletGoalTemplate(
-            Sequent.createAnteSequent(new Semisequent(new SequentFormula(use))),
+            Sequent.createAnteSequent(new Semisequent(use)),
             ImmutableSLList.nil());
         useCase.setName("Use case of " + ctx.name.getText());
         cases.add(useCase);
@@ -364,7 +365,7 @@ private TacletGoalTemplate createGoalDtConstructor(KeYParser.Datatype_constructo
             VariableSV qvar, Term var, Sort sort) {
         var constr = createQuantifiedFormula(it, qvar, var, sort);
         var goal = new TacletGoalTemplate(
-            Sequent.createSuccSequent(new Semisequent(new SequentFormula(constr))),
+            Sequent.createSuccSequent(new Semisequent(constr)),
             ImmutableSLList.nil());
         goal.setName(it.getText());
         return goal;
@@ -393,7 +394,7 @@ private RewriteTacletBuilder<RewriteTaclet> createAxiomTaclet(
         var axiom = tb.equals(find, tb.and(cases));
 
         var goal = new TacletGoalTemplate(
-            Sequent.createAnteSequent(new Semisequent(new SequentFormula(axiom))),
+            Sequent.createAnteSequent(new Semisequent(axiom)),
             ImmutableSLList.nil());
         tacletBuilder.addTacletGoalTemplate(goal);
 
@@ -474,8 +475,9 @@ private RewriteTacletBuilder<RewriteTaclet> createConstructorSplit(
             for (int i = 0; i < args.length; i++) {
                 args[i] = variables.get(context.argName.get(i).getText());
             }
+            Term uAssumptions = tb.equals(tb.var(phi), tb.func(func, args));
             Semisequent antec =
-                new Semisequent(new SequentFormula(tb.equals(tb.var(phi), tb.func(func, args))));
+                new Semisequent(uAssumptions);
             Sequent addedSeq = Sequent.createAnteSequent(antec);
             TacletGoalTemplate goal = new TacletGoalTemplate(addedSeq, ImmutableSLList.nil());
             goal.setName("#var = " + context.name.getText());
@@ -757,14 +759,14 @@ public ImmutableList<Taclet> visitTacletlist(KeYParser.TacletlistContext ctx) {
             if (findSeq.isEmpty()) {
                 return new NoFindTacletBuilder();
             } else if (findSeq.antecedent().size() == 1 && findSeq.succedent().isEmpty()) {
-                Term findFma = findSeq.antecedent().get(0).formula();
+                Term findFma = findSeq.antecedent().get(0);
                 AntecTacletBuilder b = new AntecTacletBuilder();
                 b.setFind(findFma);
                 b.setIgnoreTopLevelUpdates(
                     (applicationRestriction & RewriteTaclet.IN_SEQUENT_STATE) == 0);
                 return b;
             } else if (findSeq.antecedent().isEmpty() && findSeq.succedent().size() == 1) {
-                Term findFma = findSeq.succedent().get(0).formula();
+                Term findFma = findSeq.succedent().get(0);
                 SuccTacletBuilder b = new SuccTacletBuilder();
                 b.setFind(findFma);
                 b.setIgnoreTopLevelUpdates(
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/HideSequentPrintFilter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/HideSequentPrintFilter.java
index cf6c0156476..1e5667184c7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/HideSequentPrintFilter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/HideSequentPrintFilter.java
@@ -7,7 +7,7 @@
 import java.util.regex.Matcher;
 import java.util.regex.Pattern;
 
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.pp.IdentitySequentPrintFilter.IdentityFilterEntry;
 
 import org.key_project.util.collection.ImmutableSLList;
@@ -32,7 +32,7 @@ public HideSequentPrintFilter(SequentViewLogicPrinter lp, boolean regex) {
 
     @Override
     protected void filterSequent() {
-        Iterator<SequentFormula> it;
+        Iterator<Term> it;
 
         if (antec != null) {
             // Result has already been computed. No need to recompute.
@@ -53,7 +53,7 @@ protected void filterSequent() {
         antec = ImmutableSLList.nil();
         it = originalSequent.antecedent().iterator();
         while (it.hasNext()) {
-            SequentFormula sf = it.next();
+            Term sf = it.next();
             lp.reset();
             lp.printConstrainedFormula(sf);
             String formString = lp.result();
@@ -66,7 +66,7 @@ protected void filterSequent() {
         succ = ImmutableSLList.nil();
         it = originalSequent.succedent().iterator();
         while (it.hasNext()) {
-            SequentFormula sf = it.next();
+            Term sf = it.next();
             lp.reset();
             lp.printConstrainedFormula(sf);
             String formString = lp.result();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/IdentitySequentPrintFilter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/IdentitySequentPrintFilter.java
index ae73d537ebb..6230c2ea20b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/IdentitySequentPrintFilter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/IdentitySequentPrintFilter.java
@@ -3,7 +3,7 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.pp;
 
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 
 import org.key_project.util.collection.ImmutableList;
 
@@ -24,11 +24,11 @@ protected void filterSequent() {
 
     /**
      *
-     * @param sequentFormula the formula to filter
+     * @param fml the formula to filter
      * @return the FilterEntry from the formula
      */
-    protected SequentPrintFilterEntry filterFormula(SequentFormula sequentFormula) {
-        return new IdentityFilterEntry(sequentFormula);
+    protected SequentPrintFilterEntry filterFormula(Term fml) {
+        return new IdentityFilterEntry(fml);
     }
 
     /**
@@ -60,14 +60,14 @@ public static class IdentityFilterEntry implements SequentPrintFilterEntry {
         /**
          * the original Formula being filtered
          */
-        final SequentFormula originalFormula;
+        final Term originalFormula;
 
         /**
          * constructor
          *
          * @param originalFormula the original formula to be filtered
          */
-        IdentityFilterEntry(SequentFormula originalFormula) {
+        IdentityFilterEntry(Term originalFormula) {
             this.originalFormula = originalFormula;
         }
 
@@ -76,7 +76,7 @@ public static class IdentityFilterEntry implements SequentPrintFilterEntry {
          *
          * @return the original formula
          */
-        public SequentFormula getFilteredFormula() {
+        public Term getFilteredFormula() {
             return originalFormula;
         }
 
@@ -85,7 +85,7 @@ public SequentFormula getFilteredFormula() {
          *
          * @return the original formula
          */
-        public SequentFormula getOriginalFormula() {
+        public Term getOriginalFormula() {
             return originalFormula;
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/InitialPositionTable.java b/key.core/src/main/java/de/uka/ilkd/key/pp/InitialPositionTable.java
index 33a568bcc7b..854726f7709 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/InitialPositionTable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/InitialPositionTable.java
@@ -5,7 +5,7 @@
 
 import de.uka.ilkd.key.logic.IntIterator;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
@@ -13,7 +13,7 @@
 /**
  * An InitialPositionTable is a PositionTable that describes the beginning of the element/subelement
  * relationship. Thus, an InitialPositionTable describes the information on where the
- * {@link SequentFormula}e of a sequent are located. It is the root of the tree of PositionTables
+ * {@link Term}e of a sequent are located. It is the root of the tree of PositionTables
  * and may be asked for a PosInSequent for a given index position and a given Sequent.
  *
  * <p>
@@ -80,7 +80,7 @@ private PosInSequent getTopPIS(ImmutableList<Integer> posList, SequentPrintFilte
 
     /**
      * Returns the path for a given PosInOccurrence. This is built up from the initial 0, the number
-     * of the SequentFormula in the sequent, the position in the constrained formula, and possibly
+     * of the Term in the sequent, the position in the constrained formula, and possibly
      * inside a Metavariable instantiation.
      *
      * @param pio the given PosInOccurrence
@@ -90,7 +90,7 @@ private PosInSequent getTopPIS(ImmutableList<Integer> posList, SequentPrintFilte
     public ImmutableList<Integer> pathForPosition(PosInOccurrence pio, SequentPrintFilter filter) {
         ImmutableList<Integer> p = ImmutableSLList.nil();
         p = prependPathInFormula(p, pio);
-        int index = indexOfCfma(pio.sequentFormula(), filter);
+        int index = indexOfCfma(pio.sequentLevelFormula(), filter);
         if (index == -1) {
             return null;
         }
@@ -116,7 +116,7 @@ private ImmutableList<Integer> prependPathInFormula(ImmutableList<Integer> p,
      * @param filter the current filter
      * @return the index of the given formula in the sequent as printed
      */
-    private int indexOfCfma(SequentFormula cfma, SequentPrintFilter filter) {
+    private int indexOfCfma(Term cfma, SequentPrintFilter filter) {
         ImmutableList<SequentPrintFilterEntry> list =
             filter.getFilteredAntec().append(filter.getFilteredSucc());
         int k;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/LogicPrinter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/LogicPrinter.java
index 409c6dd32cd..0ab328fcaf8 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/LogicPrinter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/LogicPrinter.java
@@ -751,8 +751,8 @@ public void printSemisequent(ImmutableList<SequentPrintFilterEntry> formulas) {
      *
      * @param cfma the constrained formula to be printed
      */
-    public void printConstrainedFormula(SequentFormula cfma) {
-        printTerm(cfma.formula());
+    public void printConstrainedFormula(Term cfma) {
+        printTerm(cfma);
     }
 
     /**
@@ -816,11 +816,11 @@ void printLabels(Term t, String left, String right) {
                 afterFirst = true;
             }
             layouter.print(l.name().toString());
-            if (l.getChildCount() > 0) {
+            if (l.getTLChildCount() > 0) {
                 layouter.print("(").beginC();
-                for (int i = 0; i < l.getChildCount(); i++) {
-                    layouter.print("\"" + l.getChild(i).toString() + "\"");
-                    if (i < l.getChildCount() - 1) {
+                for (int i = 0; i < l.getTLChildCount(); i++) {
+                    layouter.print("\"" + l.getTLChild(i).toString() + "\"");
+                    if (i < l.getTLChildCount() - 1) {
                         layouter.print(",").ind(1, 2);
                     }
                 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/PosInSequent.java b/key.core/src/main/java/de/uka/ilkd/key/pp/PosInSequent.java
index ce8f82b1e2a..93a17a13cc6 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/PosInSequent.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/PosInSequent.java
@@ -31,11 +31,11 @@ public static PosInSequent createSequentPos() {
     }
 
     /**
-     * creates a PosInSequent that points to a SequentFormula described by a PosInOccurrence.
-     * Additionally a boolean indicates whether the the whole SequentFormula or just the formula is
+     * creates a PosInSequent that points to a Term described by a PosInOccurrence.
+     * Additionally a boolean indicates whether the the whole Term or just the formula is
      * meant.
      *
-     * @param posInOcc the PositionInOccurrence describing the SequentFormula and maybe a subterm of
+     * @param posInOcc the PositionInOccurrence describing the Term and maybe a subterm of
      *        its formula.
      */
     public static PosInSequent createCfmaPos(PosInOccurrence posInOcc) {
@@ -92,7 +92,7 @@ public Range getFirstJavaStatementRange() {
 
 
     /**
-     * returns the PosInOccurrence if the PosInSequent marks a SequentFormula or parts of it, null
+     * returns the PosInOccurrence if the PosInSequent marks a Term or parts of it, null
      * otherwise.
      */
     public PosInOccurrence getPosInOccurrence() {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/PositionTable.java b/key.core/src/main/java/de/uka/ilkd/key/pp/PositionTable.java
index 1ffebb4e6d7..1ba59a1e63e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/PositionTable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/PositionTable.java
@@ -5,7 +5,7 @@
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
@@ -44,7 +44,7 @@ public class PositionTable {
     private final int rows;
 
     /**
-     * creates a new PositionTable with the number of subterms (or number of SequentFormula in a
+     * creates a new PositionTable with the number of subterms (or number of Term in a
      * Semisequent, or the number of Semisequents in a Sequent, etc.)
      *
      * @param rows the number of direct sub-elements in the term whose position information is
@@ -243,7 +243,7 @@ protected PosInSequent getSequentPIS(ImmutableList<Integer> posList,
 
         // This can raise a NPE sporadically. (MU 19)
         // This raises an NPE repeatably (JS/MU 21) #1650
-        SequentFormula cfma = filterEntry.getOriginalFormula();
+        Term cfma = filterEntry.getOriginalFormula();
 
         PosInOccurrence currentPos = new PosInOccurrence(cfma, PosInTerm.getTopLevel(),
             filter.getOriginalSequent().antecedent().contains(cfma));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/RegroupSequentPrintFilter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/RegroupSequentPrintFilter.java
index b2ec7475952..85ad34827a4 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/RegroupSequentPrintFilter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/RegroupSequentPrintFilter.java
@@ -7,7 +7,7 @@
 import java.util.regex.Matcher;
 import java.util.regex.Pattern;
 
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.pp.IdentitySequentPrintFilter.IdentityFilterEntry;
 
 import org.key_project.util.collection.ImmutableSLList;
@@ -33,7 +33,7 @@ public RegroupSequentPrintFilter(SequentViewLogicPrinter lp, boolean regex) {
     @Override
     protected void filterSequent() {
 
-        Iterator<SequentFormula> it;
+        Iterator<Term> it;
 
         if (searchString == null || searchString.length() < 3) {
             filterIdentity();
@@ -48,7 +48,7 @@ protected void filterSequent() {
         antec = ImmutableSLList.nil();
         it = originalSequent.antecedent().iterator();
         while (it.hasNext()) {
-            SequentFormula sf = it.next();
+            Term sf = it.next();
             lp.reset();
             lp.printConstrainedFormula(sf);
             String formString = lp.result();
@@ -63,7 +63,7 @@ protected void filterSequent() {
         succ = ImmutableSLList.nil();
         it = originalSequent.succedent().iterator();
         while (it.hasNext()) {
-            SequentFormula sf = it.next();
+            Term sf = it.next();
             lp.reset();
             lp.printConstrainedFormula(sf);
             String formString = lp.result();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilter.java
index 0018fe2a215..4d54c77793a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilter.java
@@ -6,7 +6,7 @@
 import java.util.Iterator;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.pp.IdentitySequentPrintFilter.IdentityFilterEntry;
 
 import org.key_project.util.collection.ImmutableList;
@@ -83,7 +83,7 @@ public ImmutableList<SequentPrintFilterEntry> getFilteredSucc() {
      */
     protected void filterIdentity() {
         antec = ImmutableSLList.nil();
-        Iterator<SequentFormula> it = originalSequent.antecedent().iterator();
+        Iterator<Term> it = originalSequent.antecedent().iterator();
         while (it.hasNext()) {
             antec = antec.append(new IdentityFilterEntry(it.next()));
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilterEntry.java b/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilterEntry.java
index dd1e2b42fad..91129b4dc5f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilterEntry.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/SequentPrintFilterEntry.java
@@ -3,7 +3,7 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.pp;
 
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 
 
 /**
@@ -15,11 +15,11 @@ public interface SequentPrintFilterEntry {
     /**
      * Formula to display
      */
-    SequentFormula getFilteredFormula();
+    Term getFilteredFormula();
 
     /**
      * Original formula from sequent
      */
-    SequentFormula getOriginalFormula();
+    Term getOriginalFormula();
 
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/pp/ShowSelectedSequentPrintFilter.java b/key.core/src/main/java/de/uka/ilkd/key/pp/ShowSelectedSequentPrintFilter.java
index 9ac6e9acc4b..ac229e5c847 100755
--- a/key.core/src/main/java/de/uka/ilkd/key/pp/ShowSelectedSequentPrintFilter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/pp/ShowSelectedSequentPrintFilter.java
@@ -4,7 +4,7 @@
 package de.uka.ilkd.key.pp;
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
@@ -65,25 +65,26 @@ public static final class Entry implements SequentPrintFilterEntry {
         /**
          * The filtered formula, i.e., the formula at {@code pos}.
          */
-        private final SequentFormula filtered;
+        private final Term filtered;
 
         /**
          * The origin formula, i.e., the formula at {@code pos.getTopLevel()}.
          */
-        private final SequentFormula original;
+        private final Term original;
 
         private Entry(PosInOccurrence pos) {
-            filtered = new SequentFormula(pos.subTerm());
-            original = pos.sequentFormula();
+            Term uAssumptions = pos.subTerm();
+            filtered = uAssumptions;
+            original = pos.sequentLevelFormula();
         }
 
         @Override
-        public SequentFormula getFilteredFormula() {
+        public Term getFilteredFormula() {
             return filtered;
         }
 
         @Override
-        public SequentFormula getOriginalFormula() {
+        public Term getOriginalFormula() {
             return original;
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/BuiltInRuleAppIndex.java b/key.core/src/main/java/de/uka/ilkd/key/proof/BuiltInRuleAppIndex.java
index 350d9f0d849..4b65c4f88f9 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/BuiltInRuleAppIndex.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/BuiltInRuleAppIndex.java
@@ -87,13 +87,13 @@ private void scanSimplificationRule(ImmutableList<BuiltInRule> rules, Goal goal,
         final Node node = goal.node();
         final Sequent seq = node.sequent();
 
-        for (final SequentFormula sf : (antec ? seq.antecedent() : seq.succedent())) {
+        for (final Term sf : (antec ? seq.antecedent() : seq.succedent())) {
             scanSimplificationRule(rules, goal, antec, sf, listener);
         }
     }
 
     private void scanSimplificationRule(ImmutableList<BuiltInRule> rules, Goal goal, boolean antec,
-            SequentFormula cfma, NewRuleListener listener) {
+            Term cfma, NewRuleListener listener) {
         final PosInOccurrence pos = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), antec);
         ImmutableList<BuiltInRule> subrules = ImmutableSLList.nil();
         while (!rules.isEmpty()) {
@@ -145,9 +145,9 @@ public void sequentChanged(Goal goal, SequentChangeInfo sci, NewRuleListener lis
 
     private void scanAddedFormulas(Goal goal, boolean antec, SequentChangeInfo sci,
             NewRuleListener listener) {
-        ImmutableList<SequentFormula> cfmas = sci.addedFormulas(antec);
+        ImmutableList<Term> cfmas = sci.addedFormulas(antec);
         while (!cfmas.isEmpty()) {
-            final SequentFormula cfma = cfmas.head();
+            final Term cfma = cfmas.head();
             scanSimplificationRule(index.rules(), goal, antec, cfma, listener);
             cfmas = cfmas.tail();
         }
@@ -160,7 +160,7 @@ private void scanModifiedFormulas(Goal goal, boolean antec, SequentChangeInfo sc
 
         while (!fcis.isEmpty()) {
             final FormulaChangeInfo fci = fcis.head();
-            final SequentFormula cfma = fci.newFormula();
+            final Term cfma = fci.newFormula();
             scanSimplificationRule(index.rules(), goal, antec, cfma, listener);
             fcis = fcis.tail();
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/FormulaTagManager.java b/key.core/src/main/java/de/uka/ilkd/key/proof/FormulaTagManager.java
index b71df3fa24a..415d2d1869c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/FormulaTagManager.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/FormulaTagManager.java
@@ -102,7 +102,7 @@ private void updateTags(SequentChangeInfo sci, boolean p_antec, Goal p_goal) {
     }
 
     private void addTags(SequentChangeInfo sci, boolean p_antec, Goal p_goal) {
-        for (SequentFormula constrainedFormula : sci.addedFormulas(p_antec)) {
+        for (Term constrainedFormula : sci.addedFormulas(p_antec)) {
             final PosInOccurrence pio =
                 new PosInOccurrence(constrainedFormula, PosInTerm.getTopLevel(), p_antec);
             createNewTag(pio, p_goal);
@@ -110,7 +110,7 @@ private void addTags(SequentChangeInfo sci, boolean p_antec, Goal p_goal) {
     }
 
     private void removeTags(SequentChangeInfo sci, boolean p_antec, Goal p_goal) {
-        for (SequentFormula constrainedFormula : sci.removedFormulas(p_antec)) {
+        for (Term constrainedFormula : sci.removedFormulas(p_antec)) {
             final PosInOccurrence pio =
                 new PosInOccurrence(constrainedFormula, PosInTerm.getTopLevel(), p_antec);
             removeTag(pio);
@@ -148,7 +148,7 @@ private void createNewTags(Goal p_goal, boolean p_antec) {
         final Sequent seq = p_goal.sequent();
         final Semisequent ss = p_antec ? seq.antecedent() : seq.succedent();
 
-        for (SequentFormula s : ss) {
+        for (Term s : ss) {
             final PosInOccurrence pio = new PosInOccurrence(s, PosInTerm.getTopLevel(), p_antec);
             createNewTag(pio, p_goal);
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/Goal.java b/key.core/src/main/java/de/uka/ilkd/key/proof/Goal.java
index 9885acd6145..48e08240c3b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/Goal.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/Goal.java
@@ -379,10 +379,10 @@ public void setSequent(SequentChangeInfo sci) {
      * adds a formula to the sequent before the given position and informs the rule application
      * index about this change
      *
-     * @param cf the SequentFormula to be added
+     * @param cf the Term to be added
      * @param p PosInOccurrence encodes the position
      */
-    public void addFormula(SequentFormula cf, PosInOccurrence p) {
+    public void addFormula(Term cf, PosInOccurrence p) {
         setSequent(sequent().addFormula(cf, p));
     }
 
@@ -390,12 +390,12 @@ public void addFormula(SequentFormula cf, PosInOccurrence p) {
      * adds a formula to the antecedent or succedent of a sequent. Either at its front or back and
      * informs the rule application index about this change
      *
-     * @param cf the SequentFormula to be added
-     * @param inAntec boolean true(false) if SequentFormula has to be added to antecedent
+     * @param cf the Term to be added
+     * @param inAntec boolean true(false) if Term has to be added to antecedent
      *        (succedent)
      * @param first boolean true if at the front, if false then cf is added at the back
      */
-    public void addFormula(SequentFormula cf, boolean inAntec, boolean first) {
+    public void addFormula(Term cf, boolean inAntec, boolean first) {
         setSequent(sequent().addFormula(cf, inAntec, first));
     }
 
@@ -403,10 +403,10 @@ public void addFormula(SequentFormula cf, boolean inAntec, boolean first) {
      * replaces a formula at the given position and informs the rule application index about this
      * change
      *
-     * @param cf the SequentFormula replacing the old one
+     * @param cf the Term replacing the old one
      * @param p the PosInOccurrence encoding the position
      */
-    public void changeFormula(SequentFormula cf, PosInOccurrence p) {
+    public void changeFormula(Term cf, PosInOccurrence p) {
         setSequent(sequent().changeFormula(cf, p));
     }
 
@@ -607,10 +607,10 @@ public ImmutableList<Goal> apply(final RuleApp ruleApp) {
          * caught.
          */
         NamespaceSet originalNamespaces = getLocalNamespaces();
-        Services overlayServices = proof.getServices().getOverlay(originalNamespaces);
         final ImmutableList<Goal> goalList;
         var time = System.nanoTime();
         try {
+            Services overlayServices = proof.getServices().getOverlay(originalNamespaces);
             goalList = ruleApp.execute(this, overlayServices);
         } finally {
             PERF_APP_EXECUTE.getAndAdd(System.nanoTime() - time);
@@ -702,12 +702,12 @@ public void makeLocalNamespacesFrom(NamespaceSet ns) {
     public List<RuleApp> getAllBuiltInRuleApps() {
         final BuiltInRuleAppIndex index = ruleAppIndex().builtInRuleAppIndex();
         LinkedList<RuleApp> ruleApps = new LinkedList<>();
-        for (SequentFormula sf : node().sequent().antecedent()) {
+        for (Term sf : node().sequent().antecedent()) {
             ImmutableList<IBuiltInRuleApp> t =
                 index.getBuiltInRule(this, new PosInOccurrence(sf, PosInTerm.getTopLevel(), true));
             t.forEach(ruleApps::add);
         }
-        for (SequentFormula sf : node().sequent().succedent()) {
+        for (Term sf : node().sequent().succedent()) {
             ImmutableList<IBuiltInRuleApp> t =
                 index.getBuiltInRule(this, new PosInOccurrence(sf, PosInTerm.getTopLevel(), false));
             t.forEach(ruleApps::add);
@@ -725,13 +725,13 @@ protected boolean filter(Taclet taclet) {
                 return true;
             }
         };
-        for (SequentFormula sf : node().sequent().antecedent()) {
+        for (Term sf : node().sequent().antecedent()) {
             ImmutableList<TacletApp> tacletAppAtAndBelow = index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), true), services);
             tacletAppAtAndBelow.forEach(allApps::add);
         }
 
-        for (SequentFormula sf : node().sequent().succedent()) {
+        for (Term sf : node().sequent().succedent()) {
             ImmutableList<TacletApp> tacletAppAtAndBelow = index.getTacletAppAtAndBelow(filter,
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), false), services);
             tacletAppAtAndBelow.forEach(allApps::add);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/OpReplacer.java b/key.core/src/main/java/de/uka/ilkd/key/proof/OpReplacer.java
index 55a54a489f3..a50e7a424b1 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/OpReplacer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/OpReplacer.java
@@ -10,9 +10,9 @@
 import de.uka.ilkd.key.logic.TermFactory;
 import de.uka.ilkd.key.logic.op.Operator;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.util.InfFlowSpec;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.DefaultImmutableSet;
 import org.key_project.util.collection.ImmutableArray;
 import org.key_project.util.collection.ImmutableList;
@@ -36,7 +36,7 @@ public class OpReplacer {
     /**
      * The replacement map.
      */
-    private final ReplacementMap<? extends SVSubstitute, ? extends SVSubstitute> map;
+    private final ReplacementMap<? extends SyntaxElement, ? extends SyntaxElement> map;
 
     /**
      * <p>
@@ -53,7 +53,7 @@ public class OpReplacer {
      *        with
      * @param tf a term factory.
      */
-    public OpReplacer(Map<? extends SVSubstitute, ? extends SVSubstitute> map, TermFactory tf) {
+    public OpReplacer(Map<? extends SyntaxElement, ? extends SyntaxElement> map, TermFactory tf) {
         this(map, tf, null);
     }
 
@@ -65,12 +65,12 @@ public OpReplacer(Map<? extends SVSubstitute, ? extends SVSubstitute> map, TermF
      * @param tf a term factory.
      * @param proof the currently loaded proof
      */
-    public OpReplacer(Map<? extends SVSubstitute, ? extends SVSubstitute> map, TermFactory tf,
+    public OpReplacer(Map<? extends SyntaxElement, ? extends SyntaxElement> map, TermFactory tf,
             Proof proof) {
         assert map != null;
 
         this.map = map instanceof ReplacementMap
-                ? (ReplacementMap<? extends SVSubstitute, ? extends SVSubstitute>) map
+                ? (ReplacementMap<? extends SyntaxElement, ? extends SyntaxElement>) map
                 : ReplacementMap.create(tf, proof, map);
 
         this.tf = tf;
@@ -234,7 +234,7 @@ public Term replace(Term term) {
             return newTerm;
         }
 
-        for (SVSubstitute svs : map.keySet()) {
+        for (SyntaxElement svs : map.keySet()) {
             if (term.equalsModProperty(svs, TERM_LABELS_PROPERTY)) {
                 return (Term) map.get(svs);
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/ProgVarReplacer.java b/key.core/src/main/java/de/uka/ilkd/key/proof/ProgVarReplacer.java
index 730707056a3..bbf6a42dad3 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/ProgVarReplacer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/ProgVarReplacer.java
@@ -144,9 +144,8 @@ public SVInstantiations replace(SVInstantiations insts) {
                     result = result.replace(sv, newA, services);
                 }
             } else if (ie instanceof TermInstantiation) {
-                Term t = (Term) inst;
-                Term newT = replace(t);
-                if (newT != t) {
+                Term newT = replace((Term) inst);
+                if (newT != inst) {
                     result = result.replace(sv, newT, services);
                 }
             } else {
@@ -183,11 +182,11 @@ public SemisequentChangeInfo replace(Semisequent s) {
         SemisequentChangeInfo result = new SemisequentChangeInfo();
         result.setFormulaList(s.asList());
 
-        final Iterator<SequentFormula> it = s.iterator();
+        final Iterator<Term> it = s.iterator();
 
         for (int formulaNumber = 0; it.hasNext(); formulaNumber++) {
-            final SequentFormula oldcf = it.next();
-            final SequentFormula newcf = replace(oldcf);
+            final Term oldcf = it.next();
+            final Term newcf = replace(oldcf);
 
             if (newcf != oldcf) {
                 result.combine(result.semisequent().replace(formulaNumber, newcf));
@@ -197,22 +196,6 @@ public SemisequentChangeInfo replace(Semisequent s) {
         return result;
     }
 
-
-    /**
-     * replaces in a constrained formula
-     */
-    public SequentFormula replace(SequentFormula cf) {
-        SequentFormula result = cf;
-
-        final Term newFormula = replace(cf.formula());
-
-        if (newFormula != cf.formula()) {
-            result = new SequentFormula(newFormula);
-        }
-        return result;
-    }
-
-
     private Term replaceProgramVariable(Term t) {
         final ProgramVariable pv = (ProgramVariable) t.op();
         ProgramVariable o = map.get(pv);
@@ -222,7 +205,6 @@ private Term replaceProgramVariable(Term t) {
         return t;
     }
 
-
     private Term standardReplace(Term t) {
         Term result = t;
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/Proof.java b/key.core/src/main/java/de/uka/ilkd/key/proof/Proof.java
index 1fb6157a6c0..e8121005091 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/Proof.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/Proof.java
@@ -242,7 +242,7 @@ public Proof(String name, Sequent problem, String header, InitConfig initConfig,
     public Proof(String name, Term problem, String header, InitConfig initConfig) {
         this(name,
             Sequent.createSuccSequent(
-                Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(problem)).semisequent()),
+                Semisequent.EMPTY_SEMISEQUENT.insert(0, problem).semisequent()),
             initConfig.createTacletIndex(), initConfig.createBuiltInRuleIndex(), initConfig);
         problemHeader = header;
     }
@@ -490,7 +490,6 @@ public ImmutableList<Goal> openEnabledGoals() {
         return filterEnabledGoals(openGoals);
     }
 
-
     /**
      * filter those goals from a list which are enabled
      *
@@ -509,15 +508,14 @@ private ImmutableList<Goal> filterEnabledGoals(ImmutableList<Goal> goals) {
         return enabledGoals;
     }
 
-
     /**
      * removes the given goal and adds the new goals in list
      *
      * @param oldGoal the old goal that has to be removed from list
-     * @param newGoals the IList<Goal> with the new goals that were result of a rule application on
-     *        goal
+     * @param newGoals the Iterable<Goal> with the new goals that were result of a rule application
+     *        on goal
      */
-    public void replace(Goal oldGoal, ImmutableList<Goal> newGoals) {
+    public void replace(Goal oldGoal, Iterable<Goal> newGoals) {
         openGoals = openGoals.removeAll(oldGoal);
 
         if (closed()) {
@@ -632,6 +630,21 @@ public void add(ImmutableList<Goal> goals) {
         fireProofGoalsAdded(goals);
     }
 
+    /**
+     * adds a list with new goals to the list of open goals
+     *
+     * @param goals the Iterable<Goal> to be prepended
+     */
+    public void add(Iterable<Goal> goals) {
+        ImmutableList<Goal> addGoals;
+        if (goals instanceof ImmutableList<Goal> asList) {
+            addGoals = asList;
+        } else {
+            addGoals = ImmutableList.fromList(goals);
+        }
+        add(addGoals);
+    }
+
 
     /**
      * returns true if the root node is marked as closed and all goals have been removed
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/ReplacementMap.java b/key.core/src/main/java/de/uka/ilkd/key/proof/ReplacementMap.java
index 88fe0af0499..a6df47649fb 100755
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/ReplacementMap.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/ReplacementMap.java
@@ -11,11 +11,12 @@
 import de.uka.ilkd.key.logic.TermFactory;
 import de.uka.ilkd.key.logic.label.OriginTermLabel;
 import de.uka.ilkd.key.logic.label.TermLabelManager;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.settings.ProofSettings;
 import de.uka.ilkd.key.settings.TermLabelSettings;
 import de.uka.ilkd.key.util.LinkedHashMap;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * A map to be used in an {@link OpReplacer}. It maps operators that should be replaced to their
  * replacements.
@@ -25,7 +26,7 @@
  * @param <S> the type of the elements to replace.
  * @param <T> the type of the replacements.
  */
-public interface ReplacementMap<S extends SVSubstitute, T> extends Map<S, T> {
+public interface ReplacementMap<S extends SyntaxElement, T> extends Map<S, T> {
 
     /**
      * Creates a new replacement map.
@@ -36,7 +37,7 @@ public interface ReplacementMap<S extends SVSubstitute, T> extends Map<S, T> {
      * @param proof the currently loaded proof, or {@code null} if no proof is loaded.
      * @return a new replacement map.
      */
-    static <S extends SVSubstitute, T> ReplacementMap<S, T> create(TermFactory tf,
+    static <S extends SyntaxElement, T> ReplacementMap<S, T> create(TermFactory tf,
             Proof proof) {
         var noIrrelevantTermLabelsMap = proof == null
                 ? ProofSettings.DEFAULT_SETTINGS.getTermLabelSettings().getUseOriginLabels()
@@ -58,7 +59,7 @@ static <S extends SVSubstitute, T> ReplacementMap<S, T> create(TermFactory tf,
      * @param initialMappings a map whose mapping should be added to the new replacement map.
      * @return a new replacement map.
      */
-    static <S extends SVSubstitute, T> ReplacementMap<S, T> create(TermFactory tf,
+    static <S extends SyntaxElement, T> ReplacementMap<S, T> create(TermFactory tf,
             Proof proof, Map<S, T> initialMappings) {
         ReplacementMap<S, T> result = create(tf, proof);
         result.putAll(initialMappings);
@@ -77,7 +78,7 @@ static <S extends SVSubstitute, T> ReplacementMap<S, T> create(TermFactory tf,
      * @param <S> the type of the operators to replace.
      * @param <T> the type of the replacements.
      */
-    class DefaultReplacementMap<S extends SVSubstitute, T> extends LinkedHashMap<S, T>
+    class DefaultReplacementMap<S extends SyntaxElement, T> extends LinkedHashMap<S, T>
             implements ReplacementMap<S, T> {
         private static final long serialVersionUID = 6223486569442129676L;
     }
@@ -98,7 +99,7 @@ class DefaultReplacementMap<S extends SVSubstitute, T> extends LinkedHashMap<S,
      *
      * @see OriginTermLabel
      */
-    class NoIrrelevantLabelsReplacementMap<S extends SVSubstitute, T>
+    class NoIrrelevantLabelsReplacementMap<S extends SyntaxElement, T>
             implements ReplacementMap<S, T> {
 
         /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/SemisequentTacletAppIndex.java b/key.core/src/main/java/de/uka/ilkd/key/proof/SemisequentTacletAppIndex.java
index f70243418f7..4a8c236ee6b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/SemisequentTacletAppIndex.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/SemisequentTacletAppIndex.java
@@ -24,7 +24,7 @@ public class SemisequentTacletAppIndex {
     public static final AtomicLong PERF_ADD = new AtomicLong();
     public static final AtomicLong PERF_REMOVE = new AtomicLong();
 
-    private ImmutableMap<SequentFormula, TermTacletAppIndex> termIndices =
+    private ImmutableMap<Term, TermTacletAppIndex> termIndices =
         DefaultImmutableMap.nilMap();
 
     private TermTacletAppIndexCacheSet indexCaches;
@@ -38,10 +38,10 @@ public class SemisequentTacletAppIndex {
      * Add indices for the given formulas to the map <code>termIndices</code>. Existing entries are
      * replaced with the new indices. Note: destructive, use only when constructing new index
      */
-    private void addTermIndices(ImmutableList<SequentFormula> cfmas, Services services,
+    private void addTermIndices(ImmutableList<Term> cfmas, Services services,
             TacletIndex tacletIndex, NewRuleListener listener) {
         while (!cfmas.isEmpty()) {
-            final SequentFormula cfma = cfmas.head();
+            final Term cfma = cfmas.head();
             cfmas = cfmas.tail();
             addTermIndex(cfma, services, tacletIndex, listener);
         }
@@ -51,7 +51,7 @@ private void addTermIndices(ImmutableList<SequentFormula> cfmas, Services servic
      * Add an index for the given formula to the map <code>termIndices</code>. An existing entry is
      * replaced with the new one. Note: destructive, use only when constructing new index
      */
-    private void addTermIndex(SequentFormula cfma, Services services,
+    private void addTermIndex(Term cfma, Services services,
             TacletIndex tacletIndex, NewRuleListener listener) {
         final PosInOccurrence pos = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), antec);
         termIndices = termIndices.put(cfma, TermTacletAppIndex.create(pos, services, tacletIndex,
@@ -63,7 +63,7 @@ private void addTermIndex(SequentFormula cfma, Services services,
      * <code>termIndices</code>, by adding the taclets that are selected by <code>filter</code>
      * Note: destructive, use only when constructing new index
      */
-    private void addTaclets(RuleFilter filter, SequentFormula cfma, Services services,
+    private void addTaclets(RuleFilter filter, Term cfma, Services services,
             TacletIndex tacletIndex, NewRuleListener listener) {
         final TermTacletAppIndex oldIndex = termIndices.get(cfma);
         assert oldIndex != null : "Term index that is supposed to be updated " + "does not exist";
@@ -78,8 +78,8 @@ private void addTaclets(RuleFilter filter, SequentFormula cfma, Services service
      * Remove the indices for the given formulas from the map <code>termIndices</code>. Note:
      * destructive, use only when constructing new index
      */
-    private void removeTermIndices(ImmutableList<SequentFormula> cfmas) {
-        for (SequentFormula cfma : cfmas) {
+    private void removeTermIndices(ImmutableList<Term> cfmas) {
+        for (Term cfma : cfmas) {
             removeTermIndex(cfma);
         }
     }
@@ -88,7 +88,7 @@ private void removeTermIndices(ImmutableList<SequentFormula> cfmas) {
      * Remove the index for the given formula from the map <code>termIndices</code>. Note:
      * destructive, use only when constructing new index
      */
-    private void removeTermIndex(SequentFormula cfma) {
+    private void removeTermIndex(Term cfma) {
         termIndices = termIndices.remove(cfma);
     }
 
@@ -102,7 +102,7 @@ private List<TermTacletAppIndex> removeFormulas(ImmutableList<FormulaChangeInfo>
         var oldIndices = new ArrayList<TermTacletAppIndex>(infos.size());
 
         for (FormulaChangeInfo info : infos) {
-            final SequentFormula oldFor = info.getOriginalFormula();
+            final Term oldFor = info.getOriginalFormula();
 
             oldIndices.add(termIndices.get(oldFor));
             removeTermIndex(oldFor);
@@ -125,7 +125,7 @@ private void updateTermIndices(List<TermTacletAppIndex> oldIndices,
 
         while (infoIt.hasNext()) {
             final FormulaChangeInfo info = infoIt.next();
-            final SequentFormula newFor = info.newFormula();
+            final Term newFor = info.newFormula();
             final TermTacletAppIndex oldIndex = oldIndexIt.next();
 
             if (oldIndex == null)
@@ -184,7 +184,7 @@ public SemisequentTacletAppIndex copy() {
      * Get term index for the formula to which position <code>pos</code> points
      */
     private TermTacletAppIndex getTermIndex(PosInOccurrence pos) {
-        return termIndices.get(pos.sequentFormula());
+        return termIndices.get(pos.sequentLevelFormula());
     }
 
     /**
@@ -240,7 +240,7 @@ public SemisequentTacletAppIndex sequentChanged(SequentChangeInfo sci, Services
     public SemisequentTacletAppIndex addTaclets(RuleFilter filter, Services services,
             TacletIndex tacletIndex, NewRuleListener listener) {
         final SemisequentTacletAppIndex result = copy();
-        final Iterator<SequentFormula> it = termIndices.keyIterator();
+        final Iterator<Term> it = termIndices.keyIterator();
 
         while (it.hasNext()) {
             result.addTaclets(filter, it.next(), services, tacletIndex, listener);
@@ -254,8 +254,8 @@ public SemisequentTacletAppIndex addTaclets(RuleFilter filter, Services services
      * taclet app.
      */
     void reportRuleApps(NewRuleListener l) {
-        for (final ImmutableMapEntry<SequentFormula, TermTacletAppIndex> entry : termIndices) {
-            final SequentFormula cfma = entry.key();
+        for (final ImmutableMapEntry<Term, TermTacletAppIndex> entry : termIndices) {
+            final Term cfma = entry.key();
             final TermTacletAppIndex index = entry.value();
             final PosInOccurrence pio = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), antec);
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/TermTacletAppIndex.java b/key.core/src/main/java/de/uka/ilkd/key/proof/TermTacletAppIndex.java
index 1af43522d9f..5b044a194db 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/TermTacletAppIndex.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/TermTacletAppIndex.java
@@ -91,9 +91,9 @@ private static ImmutableList<NoPosTacletApp> getFindTaclet(PosInOccurrence pos,
 
 
     /**
-     * collects all AntecedentTaclet instantiations for the given heuristics and SequentFormula
+     * collects all AntecedentTaclet instantiations for the given heuristics and Term
      *
-     * @param pos the PosInOccurrence of the SequentFormula the taclets have to be connected to (pos
+     * @param pos the PosInOccurrence of the Term the taclets have to be connected to (pos
      *        must point to the top level formula, i.e. <tt>pos.isTopLevel()</tt> must be true)
      * @param services the Services object encapsulating information about the java datastructures
      *        like (static)types etc.
@@ -105,9 +105,9 @@ private static ImmutableList<NoPosTacletApp> antecTaclet(PosInOccurrence pos, Ru
     }
 
     /**
-     * collects all SuccedentTaclet instantiations for the given heuristics and SequentFormula
+     * collects all SuccedentTaclet instantiations for the given heuristics and Term
      *
-     * @param pos the PosInOccurrence of the SequentFormula the taclets have to be connected to (pos
+     * @param pos the PosInOccurrence of the Term the taclets have to be connected to (pos
      *        must point to the top level formula, i.e. <tt>pos.isTopLevel()</tt> must be true)
      * @param services the Services object encapsulating information about the java datastructures
      *        like (static)types etc.
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/delayedcut/DelayedCutProcessor.java b/key.core/src/main/java/de/uka/ilkd/key/proof/delayedcut/DelayedCutProcessor.java
index cd0b76007b2..ee89b1abafc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/delayedcut/DelayedCutProcessor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/delayedcut/DelayedCutProcessor.java
@@ -186,7 +186,7 @@ protected boolean filter(Taclet taclet) {
      */
     private ImmutableList<Goal> hide(DelayedCut cut, Goal goal) {
 
-        SequentFormula sf = getSequentFormula(goal, cut.isDecisionPredicateInAntecendet());
+        Term sf = getTerm(goal, cut.isDecisionPredicateInAntecendet());
 
         PosInOccurrence pio =
             new PosInOccurrence(sf, PosInTerm.getTopLevel(), cut.isDecisionPredicateInAntecendet());
@@ -208,9 +208,9 @@ private int getGoalForHiding(ImmutableList<Goal> goals, DelayedCut cut) {
             String side = cut.isDecisionPredicateInAntecendet() ? "TRUE" : "FALSE";
 
             if (goal[i].node().getNodeInfo().getBranchLabel().endsWith(side)) {
-                SequentFormula formula =
-                    getSequentFormula(goal[i], cut.isDecisionPredicateInAntecendet());
-                if (formula.formula() == cut.getFormula()) {
+                Term formula =
+                    getTerm(goal[i], cut.isDecisionPredicateInAntecendet());
+                if (formula == cut.getFormula()) {
                     return i;
                 }
             }
@@ -223,7 +223,7 @@ private String getHideTacletName(DelayedCut cut) {
         return cut.isDecisionPredicateInAntecendet() ? HIDE_LEFT_TACLET : HIDE_RIGHT_TACLET;
     }
 
-    private SequentFormula getSequentFormula(Goal goal, boolean decPredInAnte) {
+    private Term getTerm(Goal goal, boolean decPredInAnte) {
         return decPredInAnte ? goal.sequent().antecedent().get(DEC_PRED_INDEX)
                 : goal.sequent().succedent().get(DEC_PRED_INDEX);
 
@@ -390,7 +390,7 @@ private PosInOccurrence translate(NodeGoalPair pair, TermServices services) {
         }
         int formulaNumber =
             pair.node.sequent().formulaNumberInSequent(oldRuleApp.posInOccurrence().isInAntec(),
-                oldRuleApp.posInOccurrence().sequentFormula());
+                oldRuleApp.posInOccurrence().sequentLevelFormula());
         return PosInOccurrence.findInSequent(pair.goal.sequent(), formulaNumber,
             oldRuleApp.posInOccurrence().posInTerm());
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/init/ProblemInitializer.java b/key.core/src/main/java/de/uka/ilkd/key/proof/init/ProblemInitializer.java
index 4c089e3a4b5..0b2c712662f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/init/ProblemInitializer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/init/ProblemInitializer.java
@@ -17,7 +17,6 @@
 import de.uka.ilkd.key.ldt.HeapLDT;
 import de.uka.ilkd.key.logic.Namespace;
 import de.uka.ilkd.key.logic.NamespaceSet;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.OriginTermLabelFactory;
 import de.uka.ilkd.key.logic.op.*;
@@ -377,8 +376,8 @@ private void populateNamespaces(Term term, NamespaceSet namespaces, Goal rootGoa
     private void populateNamespaces(Proof proof) {
         final NamespaceSet namespaces = proof.getNamespaces();
         final Goal rootGoal = proof.openGoals().head();
-        for (SequentFormula cf : proof.root().sequent()) {
-            populateNamespaces(cf.formula(), namespaces, rootGoal);
+        for (Term cf : proof.root().sequent()) {
+            populateNamespaces(cf, namespaces, rootGoal);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/io/IntermediateProofReplayer.java b/key.core/src/main/java/de/uka/ilkd/key/proof/io/IntermediateProofReplayer.java
index b40ef0409c1..7992e507085 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/io/IntermediateProofReplayer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/io/IntermediateProofReplayer.java
@@ -495,7 +495,7 @@ private TacletApp constructTacletApp(TacletAppIntermediate currInterm, Goal curr
             NamespaceSet nss = currGoal.getLocalNamespaces();
             Term term = parseTerm(ifFormulaStr, proof, nss.variables(), nss.programVariables(),
                 nss.functions());
-            ifFormulaList = ifFormulaList.append(new IfFormulaInstDirect(new SequentFormula(term)));
+            ifFormulaList = ifFormulaList.append(new IfFormulaInstDirect(term));
         }
 
         if (!ourApp.ifInstsCorrectSize(ifFormulaList)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/io/OutputStreamProofSaver.java b/key.core/src/main/java/de/uka/ilkd/key/proof/io/OutputStreamProofSaver.java
index 9bfd785e9e4..cf4e70129e7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/io/OutputStreamProofSaver.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/io/OutputStreamProofSaver.java
@@ -172,8 +172,8 @@ public void save(OutputStream out) throws IOException {
                 strategyProperties.put(StrategyProperties.INF_FLOW_CHECK_PROPERTY,
                     StrategyProperties.INF_FLOW_CHECK_TRUE);
                 strategySettings.setActiveStrategyProperties(strategyProperties);
-                for (final SequentFormula s : proof.root().sequent().succedent().asList()) {
-                    ((InfFlowProof) proof).addLabeledTotalTerm(s.formula());
+                for (final Term s : proof.root().sequent().succedent().asList()) {
+                    ((InfFlowProof) proof).addLabeledTotalTerm(s);
                 }
             } else {
                 strategyProperties.put(StrategyProperties.INF_FLOW_CHECK_PROPERTY,
@@ -694,7 +694,8 @@ public static String posInOccurrence2Proof(Sequent seq, PosInOccurrence pos) {
         if (pos == null) {
             return "";
         }
-        return " (formula \"" + seq.formulaNumberInSequent(pos.isInAntec(), pos.sequentFormula())
+        return " (formula \""
+            + seq.formulaNumberInSequent(pos.isInAntec(), pos.sequentLevelFormula())
             + "\")" + posInTerm2Proof(pos.posInTerm());
     }
 
@@ -754,15 +755,16 @@ public String ifFormulaInsts(Node node, ImmutableList<IfFormulaInstantiation> l)
         StringBuilder s = new StringBuilder();
         for (final IfFormulaInstantiation aL : l) {
             if (aL instanceof IfFormulaInstSeq) {
-                final SequentFormula f = aL.getConstrainedFormula();
+                final Term f = aL.getConstrainedFormula();
                 s.append(" (ifseqformula \"")
                         .append(node.sequent()
                                 .formulaNumberInSequent(((IfFormulaInstSeq) aL).inAntec(), f))
                         .append("\")");
             } else if (aL instanceof IfFormulaInstDirect) {
 
+                Term fml = aL.getConstrainedFormula();
                 final String directInstantiation =
-                    printTerm(aL.getConstrainedFormula().formula(), node.proof().getServices());
+                    printTerm(fml, node.proof().getServices());
 
                 s.append(" (ifdirectformula \"").append(escapeCharacters(directInstantiation))
                         .append("\")");
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinIsApplicable.java b/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinIsApplicable.java
index 2568f3fe8cd..072a2aa0474 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinIsApplicable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinIsApplicable.java
@@ -7,7 +7,6 @@
 import java.util.List;
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
@@ -87,8 +86,8 @@ private ProspectivePartner areProspectivePartners(Goal g1, PosInOccurrence pio,
             referenceFormula.op() instanceof UpdateApplication ? referenceFormula.sub(1)
                     : referenceFormula;
 
-        for (SequentFormula sf : g2.sequent().succedent()) {
-            Term formula = sf.formula();
+        for (Term sf : g2.sequent().succedent()) {
+            Term formula = sf;
             Term update2 = tb.skip();
             if (formula.op() instanceof UpdateApplication
                     && !formula.equalsModProperty(referenceFormula, RENAMING_PROPERTY)) {
@@ -98,7 +97,8 @@ private ProspectivePartner areProspectivePartners(Goal g1, PosInOccurrence pio,
 
             }
             if (formula.equalsModProperty(referenceFormula, RENAMING_PROPERTY)) {
-                return new ProspectivePartner(referenceFormula, g1.node(), pio.sequentFormula(),
+                return new ProspectivePartner(referenceFormula, g1.node(),
+                    pio.sequentLevelFormula(),
                     update1, g2.node(), sf, update2);
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinProcessor.java b/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinProcessor.java
index 48bf81f8d66..8f8429f1d06 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinProcessor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/join/JoinProcessor.java
@@ -115,15 +115,15 @@ private void processJoin() {
     }
 
     private void orRight(Goal goal) {
-        SequentFormula sf = goal.sequent().succedent().get(0);
+        Term sf = goal.sequent().succedent().get(0);
         PosInOccurrence pio = new PosInOccurrence(sf, PosInTerm.getTopLevel(), false);
         apply(new String[] { OR_RIGHT_TACLET }, goal, pio);
 
     }
 
-    private SequentFormula findFormula(Sequent sequent, Term content, boolean antecedent) {
-        for (SequentFormula sf : (antecedent ? sequent.antecedent() : sequent.succedent())) {
-            if (sf.formula().equals(content)) {
+    private Term findFormula(Sequent sequent, Term content, boolean antecedent) {
+        for (Term sf : (antecedent ? sequent.antecedent() : sequent.succedent())) {
+            if (sf.equals(content)) {
                 return sf;
             }
         }
@@ -132,7 +132,7 @@ private SequentFormula findFormula(Sequent sequent, Term content, boolean antece
 
     private Goal simplifyUpdate(Goal goal, DelayedCut cut) {
 
-        SequentFormula sf = findFormula(goal.sequent(), cut.getFormula(), false);
+        Term sf = findFormula(goal.sequent(), cut.getFormula(), false);
 
         PosInOccurrence pio = new PosInOccurrence(sf, PosInTerm.getTopLevel().down(0), false);
         Goal result = apply(SIMPLIFY_UPDATE, goal, pio).head();
@@ -203,10 +203,12 @@ private Term createPhi() {
             partner.getSequent(1).succedent(), partner.getCommonFormula());
         Collection<Term> commonGamma = computeCommonFormulas(partner.getSequent(0).antecedent(),
             partner.getSequent(1).antecedent(), partner.getCommonFormula());
+        Term partnerFormula = partner.getFormula(0);
         Collection<Term> delta1 = computeDifference(partner.getSequent(0).succedent(), commonDelta,
-            partner.getFormula(0).formula());
+            partnerFormula);
+        Term formula = partner.getFormula(1);
         Collection<Term> delta2 = computeDifference(partner.getSequent(1).succedent(), commonDelta,
-            partner.getFormula(1).formula());
+            formula);
 
         Collection<Term> gamma1 =
             computeDifference(partner.getSequent(0).antecedent(), commonGamma, null);
@@ -262,9 +264,9 @@ private Collection<Term> createConstrainedTerms(Collection<Term> terms, Term pre
     private Collection<Term> computeCommonFormulas(Semisequent s1, Semisequent s2, Term exclude) {
         TreeSet<Term> formulas1 = createTree(s1, exclude);
         TreeSet<Term> result = createTree();
-        for (SequentFormula sf : s2) {
-            if (formulas1.contains(sf.formula())) {
-                result.add(sf.formula());
+        for (Term sf : s2) {
+            if (formulas1.contains(sf)) {
+                result.add(sf);
             }
         }
         return result;
@@ -273,9 +275,11 @@ private Collection<Term> computeCommonFormulas(Semisequent s1, Semisequent s2, T
     private Collection<Term> computeDifference(Semisequent s, Collection<Term> excludeSet,
             Term exclude) {
         LinkedList<Term> result = new LinkedList<>();
-        for (SequentFormula sf : s) {
-            if (sf.formula() != exclude && !excludeSet.contains(sf.formula())) {
-                result.add(sf.formula());
+        for (Term sf : s) {
+            if (sf != exclude) {
+                if (!excludeSet.contains(sf)) {
+                    result.add(sf);
+                }
             }
         }
         return result;
@@ -283,9 +287,9 @@ private Collection<Term> computeDifference(Semisequent s, Collection<Term> exclu
 
     private TreeSet<Term> createTree(Semisequent semisequent, Term exclude) {
         TreeSet<Term> set = createTree();
-        for (SequentFormula sf : semisequent) {
-            if (sf.formula() != exclude) {
-                set.add(sf.formula());
+        for (Term sf : semisequent) {
+            if (sf != exclude) {
+                set.add(sf);
             }
         }
         return set;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/join/LateApplicationCheck.java b/key.core/src/main/java/de/uka/ilkd/key/proof/join/LateApplicationCheck.java
index 1b9db61523b..076c8782067 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/join/LateApplicationCheck.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/join/LateApplicationCheck.java
@@ -7,7 +7,7 @@
 import java.util.List;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Node;
 import de.uka.ilkd.key.proof.delayedcut.ApplicationCheck;
 
@@ -27,8 +27,8 @@ public List<String> check(Node node, Node cutNode, ApplicationCheck check) {
 
     private List<String> check(ApplicationCheck check, Sequent sequent, Node cutNode) {
         List<String> conflicts = new LinkedList<>();
-        for (SequentFormula sf : sequent) {
-            String result = check.check(cutNode, sf.formula());
+        for (Term sf : sequent) {
+            String result = check.check(cutNode, sf);
             if (result != null) {
                 conflicts.add(result);
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/join/ProspectivePartner.java b/key.core/src/main/java/de/uka/ilkd/key/proof/join/ProspectivePartner.java
index f7a26bc2dce..4d54f573f9f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/join/ProspectivePartner.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/join/ProspectivePartner.java
@@ -4,7 +4,6 @@
 package de.uka.ilkd.key.proof.join;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Node;
 
@@ -16,11 +15,11 @@
 public class ProspectivePartner {
     private final Term[] updates = new Term[2];
     private final Term commonFormula;
-    private final SequentFormula[] formula = new SequentFormula[2];
+    private final Term[] formula = new Term[2];
     private final Node[] nodes = new Node[2];
     private Term commonPredicate = null;
     private Node commonParent = null;
-    private SequentFormula formulaForHiding = null;
+    private Term formulaForHiding = null;
 
     /**
      * Constructs a new prospective partner object, i.e. a structure comprising the information
@@ -35,8 +34,8 @@ public class ProspectivePartner {
      * @param formula2 The second join formula.
      * @param update2 The second symbolic state.
      */
-    public ProspectivePartner(Term commonFormula, Node node1, SequentFormula formula1, Term update1,
-            Node node2, SequentFormula formula2, Term update2) {
+    public ProspectivePartner(Term commonFormula, Node node1, Term formula1, Term update1,
+            Node node2, Term formula2, Term update2) {
         super();
         this.commonFormula = commonFormula;
         formula[0] = formula1;
@@ -72,15 +71,15 @@ public void setCommonParent(Node commonParent) {
         if (commonParent.getAppliedRuleApp() != null
                 && commonParent.getAppliedRuleApp().posInOccurrence() != null) {
             setFormulaForHiding(
-                commonParent.getAppliedRuleApp().posInOccurrence().sequentFormula());
+                commonParent.getAppliedRuleApp().posInOccurrence().sequentLevelFormula());
         }
     }
 
-    private void setFormulaForHiding(SequentFormula formulaForHiding) {
+    private void setFormulaForHiding(Term formulaForHiding) {
         this.formulaForHiding = formulaForHiding;
     }
 
-    public SequentFormula getFormulaForHiding() {
+    public Term getFormulaForHiding() {
         return formulaForHiding;
     }
 
@@ -92,7 +91,7 @@ public Sequent getSequent(int index) {
         return getNode(index).sequent();
     }
 
-    public SequentFormula getFormula(int i) {
+    public Term getFormula(int i) {
         return formula[i];
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/mgt/SpecificationRepository.java b/key.core/src/main/java/de/uka/ilkd/key/proof/mgt/SpecificationRepository.java
index ac8404f0b4e..ef826a9216e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/mgt/SpecificationRepository.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/mgt/SpecificationRepository.java
@@ -189,7 +189,8 @@ private static Taclet getUnlimitedToLimitedTaclet(IObserverFunction limited,
         // create taclet
         final RewriteTacletBuilder<RewriteTaclet> tacletBuilder = new RewriteTacletBuilder<>();
         tacletBuilder.setFind(tb.func(unlimited, subs));
-        final SequentFormula cf = new SequentFormula(tb.equals(limitedTerm, unlimitedTerm));
+        Term uAssumptions = tb.equals(limitedTerm, unlimitedTerm);
+        final Term cf = uAssumptions;
         final Sequent addedSeq =
             Sequent.createAnteSequent(Semisequent.EMPTY_SEMISEQUENT.insertFirst(cf).semisequent());
         tacletBuilder.addTacletGoalTemplate(new RewriteTacletGoalTemplate(addedSeq,
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/proofevent/NodeReplacement.java b/key.core/src/main/java/de/uka/ilkd/key/proof/proofevent/NodeReplacement.java
index 46f9447818b..6d1c9f0b213 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/proofevent/NodeReplacement.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/proofevent/NodeReplacement.java
@@ -12,7 +12,7 @@
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
 import de.uka.ilkd.key.logic.SequentChangeInfo;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Node;
 
 import org.key_project.util.collection.ImmutableList;
@@ -55,7 +55,7 @@ private void addNodeChanges() {
     }
 
     private void addNodeChange(SequentChangeInfo p_sci) {
-        Iterator<SequentFormula> it;
+        Iterator<Term> it;
         Iterator<FormulaChangeInfo> it2;
 
         // ---
@@ -72,13 +72,13 @@ private void addNodeChange(SequentChangeInfo p_sci) {
         // Information about modified formulas is currently not used
         it2 = p_sci.modifiedFormulas(true).iterator();
         while (it2.hasNext()) {
-            addRemovedChange(it2.next().positionOfModification().sequentFormula(), true);
+            addRemovedChange(it2.next().positionOfModification().sequentLevelFormula(), true);
         }
 
         // Information about modified formulas is currently not used
         it2 = p_sci.modifiedFormulas(false).iterator();
         while (it2.hasNext()) {
-            addRemovedChange(it2.next().positionOfModification().sequentFormula(), false);
+            addRemovedChange(it2.next().positionOfModification().sequentLevelFormula(), false);
         }
 
         it = p_sci.addedFormulas(true).iterator();
@@ -119,7 +119,7 @@ private void addNodeChange(SequentChangeInfo p_sci) {
 
     }
 
-    private void addAddedChange(SequentFormula p_cf, boolean p_inAntec) {
+    private void addAddedChange(Term p_cf, boolean p_inAntec) {
         Sequent oldS = parent.sequent();
         Semisequent oldSS = (p_inAntec ? oldS.antecedent() : oldS.succedent());
         Sequent newS = node.sequent();
@@ -140,7 +140,7 @@ private void addAddedChange(SequentFormula p_cf, boolean p_inAntec) {
      * @param p_cf
      * @param p_inAntec
      */
-    private void addAddedRedundantChange(SequentFormula p_cf, boolean p_inAntec) {
+    private void addAddedRedundantChange(Term p_cf, boolean p_inAntec) {
 
         final PosInOccurrence pio = new PosInOccurrence(p_cf, PosInTerm.getTopLevel(), p_inAntec);
         addNodeChange(new NodeRedundantAddChange(pio));
@@ -149,7 +149,7 @@ private void addAddedRedundantChange(SequentFormula p_cf, boolean p_inAntec) {
 
 
 
-    private void addRemovedChange(SequentFormula p_cf, boolean p_inAntec) {
+    private void addRemovedChange(Term p_cf, boolean p_inAntec) {
         Sequent oldS = parent.sequent();
         Semisequent oldSS = (p_inAntec ? oldS.antecedent() : oldS.succedent());
 
@@ -165,7 +165,7 @@ private void addNodeChange(NodeChange p_nc) {
         changes = changes.prepend(p_nc);
     }
 
-    private void removeNodeChanges(SequentFormula p_cf, boolean p_inAntec) {
+    private void removeNodeChanges(Term p_cf, boolean p_inAntec) {
         Iterator<NodeChange> it = changes.iterator();
         changes = ImmutableSLList.nil();
         NodeChange oldNC;
@@ -176,7 +176,7 @@ private void removeNodeChanges(SequentFormula p_cf, boolean p_inAntec) {
 
             if (oldNC instanceof NodeChangeARFormula) {
                 oldPio = oldNC.getPos();
-                if (oldPio.isInAntec() == p_inAntec && oldPio.sequentFormula().equals(p_cf)) {
+                if (oldPio.isInAntec() == p_inAntec && oldPio.sequentLevelFormula().equals(p_cf)) {
                     continue;
                 }
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/proof/replay/AbstractProofReplayer.java b/key.core/src/main/java/de/uka/ilkd/key/proof/replay/AbstractProofReplayer.java
index 48538a003f3..278b897a38b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/proof/replay/AbstractProofReplayer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/proof/replay/AbstractProofReplayer.java
@@ -14,8 +14,8 @@
 import de.uka.ilkd.key.logic.PosInTerm;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.proof.Node;
@@ -304,10 +304,10 @@ private TacletApp constructTacletApp(Node originalStep, Goal currGoal) {
             if (oldFormulaPioSpec.second) {
                 ifFormulaList = ifFormulaList.append(
                     new IfFormulaInstSeq(currGoal.sequent(), oldFormulaPio.isInAntec(),
-                        newPio.sequentFormula()));
+                        newPio.sequentLevelFormula()));
             } else {
                 ifFormulaList = ifFormulaList.append(
-                    new IfFormulaInstDirect(newPio.sequentFormula()));
+                    new IfFormulaInstDirect(newPio.sequentLevelFormula()));
             }
         }
 
@@ -333,11 +333,12 @@ private TacletApp constructTacletApp(Node originalStep, Goal currGoal) {
      * @return the formula in the sequent, or null if not found
      */
     private PosInOccurrence findInNewSequent(PosInOccurrence oldPos, Sequent newSequent) {
-        SequentFormula oldFormula = oldPos.sequentFormula();
+        Term oldFormula = oldPos.sequentLevelFormula();
         Semisequent semiSeq = oldPos.isInAntec() ? newSequent.antecedent()
                 : newSequent.succedent();
-        for (SequentFormula newFormula : semiSeq.asList()) {
-            if (newFormula.equalsModProofIrrelevancy(oldFormula)) {
+        for (Term newFormula : semiSeq.asList()) {
+            if (newFormula.equalsModProperty(oldFormula,
+                ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY)) {
                 return oldPos.replaceConstrainedFormula(newFormula);
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/prover/impl/ApplyStrategy.java b/key.core/src/main/java/de/uka/ilkd/key/prover/impl/ApplyStrategy.java
index 05b6f74d9dd..5d69be261c3 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/prover/impl/ApplyStrategy.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/prover/impl/ApplyStrategy.java
@@ -267,9 +267,9 @@ private ProofTreeListener prepareStrategy(Proof proof, ImmutableList<Goal> goals
         ProofTreeListener treeListener = new ProofTreeAdapter() {
             @Override
             public void proofGoalsAdded(ProofTreeEvent e) {
-                ImmutableList<Goal> newGoals = e.getGoals();
+                Iterable<Goal> newGoals = e.getGoals();
                 // Check for a closed goal ...
-                if (newGoals.size() == 0) {
+                if (!newGoals.iterator().hasNext()) {
                     // No new goals have been generated ...
                     closedGoals++;
                 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBlockContractRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBlockContractRule.java
index dfae6550d37..8e118b9ebd3 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBlockContractRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBlockContractRule.java
@@ -24,7 +24,6 @@
 import de.uka.ilkd.key.java.statement.JavaStatement;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.ProgramElementName;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -294,7 +293,7 @@ protected static Term buildInfFlowPostAssumption(ProofObligationVars instVars,
         return afterAssumptions;
     }
 
-    static SequentFormula buildBodyPreservesSequent(InfFlowPOSnippetFactory f, InfFlowProof proof) {
+    static Term buildBodyPreservesSequent(InfFlowPOSnippetFactory f, InfFlowProof proof) {
         Term selfComposedExec =
             f.create(InfFlowPOSnippetFactory.Snippet.SELFCOMPOSED_BLOCK_WITH_PRE_RELATION);
         Term post = f.create(InfFlowPOSnippetFactory.Snippet.INF_FLOW_INPUT_OUTPUT_RELATION);
@@ -304,7 +303,7 @@ static SequentFormula buildBodyPreservesSequent(InfFlowPOSnippetFactory f, InfFl
             tb.imp(tb.label(selfComposedExec, ParameterlessTermLabel.SELF_COMPOSITION_LABEL), post);
         proof.addLabeledIFSymbol(selfComposedExec);
 
-        return new SequentFormula(finalTerm);
+        return finalTerm;
     }
 
     private static ProofObligationVars generateProofObligationVariables(
@@ -347,7 +346,7 @@ private static void addProofObligation(final Goal infFlowGoal, final InfFlowProo
         InfFlowPOSnippetFactory infFlowFactory =
             POSnippetFactory.getInfFlowFactory(contract, ifVars.c1, ifVars.c2, ec, services);
 
-        final SequentFormula poFormula = buildBodyPreservesSequent(infFlowFactory, proof);
+        final Term poFormula = buildBodyPreservesSequent(infFlowFactory, proof);
 
         // add proof obligation to goal
         infFlowGoal.addFormula(poFormula, false, true);
@@ -399,7 +398,7 @@ protected void setUpInfFlowPartOfUsageGoal(final Goal usageGoal,
             tb.applySequential(new Term[] { contextUpdate, remembranceUpdate },
                 tb.and(infFlowValitidyData.preAssumption,
                     tb.apply(anonymisationUpdate, infFlowValitidyData.postAssumption)));
-        usageGoal.addFormula(new SequentFormula(uAssumptions), true, false);
+        usageGoal.addFormula(uAssumptions, true, false);
     }
 
     protected InfFlowValidityData setUpInfFlowValidityGoal(final Goal infFlowGoal,
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBuiltInRuleApp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBuiltInRuleApp.java
index cc0f21552f8..7b58514ee7b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBuiltInRuleApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/AbstractBuiltInRuleApp.java
@@ -9,6 +9,7 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.proof.Goal;
 
@@ -55,7 +56,7 @@ public BuiltInRule rule() {
     }
 
     /**
-     * returns the PositionInOccurrence (representing a SequentFormula and a position in the
+     * returns the PositionInOccurrence (representing a Term and a position in the
      * corresponding formula) of this rule application
      */
     @Override
@@ -171,7 +172,8 @@ public boolean equalsModProofIrrelevancy(Object obj) {
     @Override
     public int hashCodeModProofIrrelevancy() {
         return Objects.hash(rule(), getHeapContext(),
-            posInOccurrence().sequentFormula().hashCodeModProofIrrelevancy(),
+            ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY
+                    .hashCodeModThisProperty(posInOccurrence().sequentLevelFormula()),
             posInOccurrence().posInTerm());
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/AuxiliaryContractBuilders.java b/key.core/src/main/java/de/uka/ilkd/key/rule/AuxiliaryContractBuilders.java
index 4991bac41dc..4edccc048ef 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/AuxiliaryContractBuilders.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/AuxiliaryContractBuilders.java
@@ -1355,7 +1355,7 @@ public Term setUpWdGoal(final Goal goal, final BlockContract contract, final Ter
             services.getSpecificationRepository().addWdStatement(bwd);
             final LocationVariable heapAtPre = variables.remembranceHeaps.get(heap);
             final Term anon = anonHeap != null ? services.getTermBuilder().func(anonHeap) : null;
-            final SequentFormula wdBlock = bwd.generateSequent(variables.self, variables.exception,
+            final Term wdBlock = bwd.generateSequent(variables.self, variables.exception,
                 variables.result, heap, heapAtPre, anon, localIns, update, anonUpdate, services);
 
             if (goal != null) {
@@ -1363,7 +1363,7 @@ public Term setUpWdGoal(final Goal goal, final BlockContract contract, final Ter
                 goal.changeFormula(wdBlock, occurrence);
             }
 
-            return wdBlock.formula();
+            return wdBlock;
         }
 
         /**
@@ -1394,8 +1394,9 @@ public Term setUpValidityGoal(final Goal goal, final Term[] updates,
 
             Term term;
             if (goal != null) {
+                Term uAssumptions = tb.applySequential(updates, tb.and(assumptions));
                 goal.addFormula(
-                    new SequentFormula(tb.applySequential(updates, tb.and(assumptions))), true,
+                    uAssumptions, true,
                     false);
 
                 ImmutableArray<TermLabel> labels = TermLabelManager.instantiateLabels(
@@ -1408,7 +1409,7 @@ public Term setUpValidityGoal(final Goal goal, final Term[] updates,
                 term = tb.applySequential(updates,
                     tb.prog(instantiation.modality().kind(), newJavaBlock, newPost, labels));
 
-                goal.changeFormula(new SequentFormula(term), occurrence);
+                goal.changeFormula(term, occurrence);
                 TermLabelManager.refactorGoal(termLabelState, services, occurrence,
                     application.rule(), goal, null, null);
                 addInfFlow(goal);
@@ -1512,7 +1513,7 @@ public Term setUpLoopValidityGoal(final Goal goal, final LoopContract contract,
             if (goal != null) {
                 goal.setBranchLabel("Validity");
                 addInfFlow(goal);
-                goal.changeFormula(new SequentFormula(term), occurrence);
+                goal.changeFormula(term, occurrence);
             }
             return term;
         }
@@ -1532,7 +1533,7 @@ public void setUpPreconditionGoal(final Goal goal, final Term update,
             fullPrecondition =
                 TermLabelManager.refactorTerm(termLabelState, services, null, fullPrecondition,
                     rule, goal, BlockContractInternalRule.FULL_PRECONDITION_TERM_HINT, null);
-            goal.changeFormula(new SequentFormula(fullPrecondition), occurrence);
+            goal.changeFormula(fullPrecondition, occurrence);
             TermLabelManager.refactorGoal(termLabelState, services, occurrence, application.rule(),
                 goal, null, null);
         }
@@ -1549,9 +1550,10 @@ public void setUpUsageGoal(final Goal goal, final Term[] updates,
             final TermBuilder tb = services.getTermBuilder();
             goal.setBranchLabel("Usage");
             Term uAssumptions = tb.applySequential(updates, tb.and(assumptions));
-            goal.addFormula(new SequentFormula(uAssumptions), true, false);
+            goal.addFormula(uAssumptions, true, false);
+            Term uAssumptions1 = tb.applySequential(updates, buildUsageFormula(goal));
             goal.changeFormula(
-                new SequentFormula(tb.applySequential(updates, buildUsageFormula(goal))),
+                uAssumptions1,
                 occurrence);
             TermLabelManager.refactorGoal(termLabelState, services, occurrence, application.rule(),
                 goal, null, null);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/BlockContractInternalRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/BlockContractInternalRule.java
index 50f3a0ec633..5b57624c749 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/BlockContractInternalRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/BlockContractInternalRule.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -355,7 +354,8 @@ private void setUpValidityGoal(final ImmutableList<Goal> result, final boolean i
                     updates[1], updates[2], tb);
             } else {
                 // nothing to prove -> set up trivial goal
-                validityGoal.addFormula(new SequentFormula(tb.tt()), false, true);
+                Term uAssumptions = tb.tt();
+                validityGoal.addFormula(uAssumptions, false, true);
             }
         }
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/BoundUniquenessChecker.java b/key.core/src/main/java/de/uka/ilkd/key/rule/BoundUniquenessChecker.java
index 5b20688062a..d25d73c54c2 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/BoundUniquenessChecker.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/BoundUniquenessChecker.java
@@ -7,7 +7,6 @@
 import java.util.LinkedHashSet;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
 
@@ -52,8 +51,8 @@ public void addTerm(Term term) {
      * @param seq the Sequent with the formulas to add
      */
     public void addAll(Sequent seq) {
-        for (final SequentFormula cf : seq) {
-            terms = terms.prepend(cf.formula());
+        for (final Term cf : seq) {
+            terms = terms.prepend(cf);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstDirect.java b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstDirect.java
index 710c9da1949..dc9fcca4607 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstDirect.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstDirect.java
@@ -4,7 +4,7 @@
 package de.uka.ilkd.key.rule;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.io.ProofSaver;
 
 
@@ -17,16 +17,16 @@ public class IfFormulaInstDirect implements IfFormulaInstantiation {
     /**
      * Simply the formula
      */
-    private final SequentFormula cf;
+    private final Term cf;
 
-    public IfFormulaInstDirect(SequentFormula p_cf) {
+    public IfFormulaInstDirect(Term p_cf) {
         cf = p_cf;
     }
 
     /**
      * @return the cf this is pointing to
      */
-    public SequentFormula getConstrainedFormula() {
+    public Term getConstrainedFormula() {
         return cf;
     }
 
@@ -48,6 +48,6 @@ public int hashCode() {
     }
 
     public String toString(Services services) {
-        return ProofSaver.printAnything(cf.formula(), services);
+        return ProofSaver.printAnything(cf, services);
     }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstSeq.java b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstSeq.java
index d70b9e1a529..c082aa270b2 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstSeq.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstSeq.java
@@ -4,11 +4,7 @@
 package de.uka.ilkd.key.rule;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.proof.io.OutputStreamProofSaver;
 
 import org.key_project.util.collection.ImmutableArray;
@@ -25,9 +21,9 @@ public class IfFormulaInstSeq implements IfFormulaInstantiation {
      */
     private final Sequent seq;
     private final boolean antec; // formula is in antecedent?
-    private final SequentFormula cf;
+    private final Term cf;
 
-    public IfFormulaInstSeq(Sequent p_seq, boolean antec, SequentFormula p_cf) {
+    public IfFormulaInstSeq(Sequent p_seq, boolean antec, Term p_cf) {
         seq = p_seq;
         this.antec = antec;
         cf = p_cf;
@@ -43,7 +39,7 @@ public IfFormulaInstSeq(Sequent seq, int formulaNr) {
      * @return the cf this is pointing to
      */
     @Override
-    public SequentFormula getConstrainedFormula() {
+    public Term getConstrainedFormula() {
         return cf;
     }
 
@@ -93,7 +89,7 @@ public String toString() {
 
     @Override
     public String toString(Services services) {
-        return OutputStreamProofSaver.printAnything(cf.formula(), services);
+        return OutputStreamProofSaver.printAnything(cf, services);
     }
 
     @Override
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstantiation.java b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstantiation.java
index 9abb3fc3b5a..a7ab7433c88 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstantiation.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/IfFormulaInstantiation.java
@@ -4,7 +4,8 @@
 package de.uka.ilkd.key.rule;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 
 import org.key_project.util.EqualsModProofIrrelevancy;
 
@@ -18,7 +19,7 @@ public interface IfFormulaInstantiation extends EqualsModProofIrrelevancy {
     /**
      * @return the cf this is pointing to
      */
-    SequentFormula getConstrainedFormula();
+    Term getConstrainedFormula();
 
     String toString(Services services);
 
@@ -27,11 +28,13 @@ default boolean equalsModProofIrrelevancy(Object obj) {
         if (!(obj instanceof IfFormulaInstantiation that)) {
             return false;
         }
-        return getConstrainedFormula().equalsModProofIrrelevancy(that.getConstrainedFormula());
+        return getConstrainedFormula().equalsModProperty(that.getConstrainedFormula(),
+            ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY);
     }
 
     @Override
     default int hashCodeModProofIrrelevancy() {
-        return getConstrainedFormula().hashCodeModProofIrrelevancy();
+        return getConstrainedFormula()
+                .hashCodeModProperty(ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY);
     }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/JmlAssertRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/JmlAssertRule.java
index 87b9131b154..b3f641c0a87 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/JmlAssertRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/JmlAssertRule.java
@@ -158,7 +158,8 @@ public IBuiltInRuleApp createApp(PosInOccurrence occurrence, TermServices servic
     private void setUpValidityRule(Goal goal, PosInOccurrence occurrence, Term update,
             Term condition, TermBuilder tb) {
         goal.setBranchLabel("Validity");
-        goal.changeFormula(new SequentFormula(tb.apply(update, condition)), occurrence);
+        Term uAssumptions = tb.apply(update, condition);
+        goal.changeFormula(uAssumptions, occurrence);
     }
 
     private void setUpUsageGoal(Goal goal, PosInOccurrence occurrence, Term update, Term target,
@@ -169,7 +170,7 @@ private void setUpUsageGoal(Goal goal, PosInOccurrence occurrence, Term update,
             tb.imp(condition,
                 tb.prog(((Modality) target.op()).kind(), javaBlock, target.sub(0), null)));
 
-        goal.changeFormula(new SequentFormula(newTerm), occurrence);
+        goal.changeFormula(newTerm, occurrence);
     }
 
     @Override
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/LoopApplyHeadRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/LoopApplyHeadRule.java
index c2ed88a8cde..728bb34a756 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/LoopApplyHeadRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/LoopApplyHeadRule.java
@@ -9,7 +9,6 @@
 import de.uka.ilkd.key.java.visitor.ProgramElementReplacer;
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -96,9 +95,9 @@ public class LoopApplyHeadRule implements BuiltInRule {
         }
 
         Goal result = goal.split(1).head();
+        Term uAssumptions = tb.apply(update, tb.prog(modality.kind(), newJavaBlock, target.sub(0)));
         result.changeFormula(
-            new SequentFormula(
-                tb.apply(update, tb.prog(modality.kind(), newJavaBlock, target.sub(0)))),
+            uAssumptions,
             ruleApp.pio);
         return ImmutableSLList.<Goal>nil().append(goal);
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/LoopScopeInvariantRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/LoopScopeInvariantRule.java
index 3ae2aaed6cb..1e35409edc0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/LoopScopeInvariantRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/LoopScopeInvariantRule.java
@@ -21,7 +21,6 @@
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.ProgramPrefix;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.label.ParameterlessTermLabel;
@@ -240,9 +239,9 @@ private void constructPresrvAndUCGoal(Services services, RuleApp ruleApp, Goal p
             uBeforeLoopDefAnonVariant, invTerm);
 
         presrvAndUCGoal.setBranchLabel("Invariant Preserved and Used");
-        presrvAndUCGoal.addFormula(new SequentFormula(uAnonInv), true, false);
-        presrvAndUCGoal.addFormula(new SequentFormula(wellFormedAnon), true, false);
-        presrvAndUCGoal.changeFormula(new SequentFormula(newFormula), ruleApp.posInOccurrence());
+        presrvAndUCGoal.addFormula(uAnonInv, true, false);
+        presrvAndUCGoal.addFormula(wellFormedAnon, true, false);
+        presrvAndUCGoal.changeFormula(newFormula, ruleApp.posInOccurrence());
     }
 
     // -------------------------------------------------------------------------
@@ -323,7 +322,7 @@ private ProgramElement newProgram(Services services, final While loop,
     }
 
     /**
-     * Creates the {@link SequentFormula} for the "initially valid" goal.
+     * Creates the {@link Term} for the "initially valid" goal.
      *
      * @param termLabelState The {@link TermLabelState}.
      * @param inst The {@link Instantiation} for this rule application.
@@ -331,9 +330,9 @@ private ProgramElement newProgram(Services services, final While loop,
      * @param reachableState The reachable state formula.
      * @param services The {@link Services} object.
      * @param initGoal The goal containing the "initially valid" PO.
-     * @return The {@link SequentFormula} for the "initially valid" goal.
+     * @return The {@link Term} for the "initially valid" goal.
      */
-    private SequentFormula initFormula(TermLabelState termLabelState, Instantiation inst,
+    private Term initFormula(TermLabelState termLabelState, Instantiation inst,
             final Term invTerm, Term reachableState, Services services, Goal initGoal) {
         final TermBuilder tb = services.getTermBuilder();
 
@@ -341,7 +340,7 @@ private SequentFormula initFormula(TermLabelState termLabelState, Instantiation
         sfTerm = TermLabelManager.refactorTerm(termLabelState, services, null, sfTerm, this,
             initGoal, INITIAL_INVARIANT_ONLY_HINT, null);
 
-        return new SequentFormula(sfTerm);
+        return sfTerm;
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/NoPosTacletApp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/NoPosTacletApp.java
index 2b6434e380e..df86c6ca0c0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/NoPosTacletApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/NoPosTacletApp.java
@@ -282,7 +282,7 @@ protected ImmutableSet<QuantifiableVariable> contextVars(SchemaVariable sv) {
 
 
     /**
-     * returns the PositionInOccurrence (representing a SequentFormula and a position in the
+     * returns the PositionInOccurrence (representing a Term and a position in the
      * corresponding formula)
      *
      * @return the PosInOccurrence
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/ObserverToUpdateRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/ObserverToUpdateRule.java
index 000bd93dc5f..e48fde9cd4d 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/ObserverToUpdateRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/ObserverToUpdateRule.java
@@ -18,7 +18,6 @@
 import de.uka.ilkd.key.java.reference.TypeReference;
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -194,8 +193,9 @@ private ImmutableList<Goal> applyForModelFields(Goal goal, ModelFieldInstantiati
         // ---- create "Null Reference" branch
         if (nullGoal != null) {
             final Term actualSelfNotNull = tb.not(tb.equals(inst.receiver, tb.NULL()));
+            Term uAssumptions = tb.apply(inst.update, actualSelfNotNull, null);
             nullGoal.changeFormula(
-                new SequentFormula(tb.apply(inst.update, actualSelfNotNull, null)),
+                uAssumptions,
                 ruleApp.posInOccurrence());
         }
 
@@ -216,7 +216,7 @@ private ImmutableList<Goal> applyForModelFields(Goal goal, ModelFieldInstantiati
         Term update = tb.elementary(lhs,
             makeCall(services, inst.observerSymbol, inst.receiver, ImmutableList.of()));
         Term normalPost = tb.apply(update, modalityTerm);
-        contGoal.changeFormula(new SequentFormula(tb.apply(inst.update, normalPost, null)),
+        contGoal.changeFormula(tb.apply(inst.update, normalPost, null),
             ruleApp.posInOccurrence());
 
         TermLabelManager.refactorGoal(termLabelState, services, ruleApp.posInOccurrence(), this,
@@ -256,7 +256,8 @@ private ImmutableList<Goal> applyForMethods(Goal goal, Instantiation inst, Servi
         // ---- create "Null Reference" branch
         if (nullGoal != null) {
             final Term actualSelfNotNull = tb.not(tb.equals(inst.actualSelf, tb.NULL()));
-            nullGoal.changeFormula(new SequentFormula(tb.apply(inst.u, actualSelfNotNull, null)),
+            Term uAssumptions = tb.apply(inst.u, actualSelfNotNull, null);
+            nullGoal.changeFormula(uAssumptions,
                 ruleApp.posInOccurrence());
         }
 
@@ -274,7 +275,7 @@ private ImmutableList<Goal> applyForMethods(Goal goal, Instantiation inst, Servi
         Term update =
             tb.elementary(lhs, makeCall(services, inst.pm, inst.actualSelf, inst.actualParams));
         Term normalPost = tb.apply(update, modalityTerm);
-        contGoal.changeFormula(new SequentFormula(tb.apply(inst.u, normalPost, null)),
+        contGoal.changeFormula(tb.apply(inst.u, normalPost, null),
             ruleApp.posInOccurrence());
 
         TermLabelManager.refactorGoal(termLabelState, services, ruleApp.posInOccurrence(), this,
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/OneStepSimplifier.java b/key.core/src/main/java/de/uka/ilkd/key/rule/OneStepSimplifier.java
index feec9a03cae..19d726d810b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/OneStepSimplifier.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/OneStepSimplifier.java
@@ -15,7 +15,6 @@
 import de.uka.ilkd.key.logic.PosInTerm;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.label.TermLabel;
@@ -83,7 +82,7 @@ public static final class Protocol extends ArrayList<RuleApp> {
             .append("update_apply").append("update_join").append("elimQuantifier");
 
     private static final boolean[] bottomUp = { false, false, true, true, true, false };
-    private final Map<SequentFormula, Boolean> applicabilityCache =
+    private final Map<Term, Boolean> applicabilityCache =
         new LRUCache<>(APPLICABILITY_CACHE_SIZE);
 
     private Proof lastProof;
@@ -241,7 +240,7 @@ public boolean isShutdown() {
      *
      * @param protocol
      */
-    private SequentFormula simplifyPos(Goal goal, Services services, PosInOccurrence pos,
+    private Term simplifyPos(Goal goal, Services services, PosInOccurrence pos,
             int indexNr, Protocol protocol) {
         final ImmutableList<NoPosTacletApp> apps =
             indices[indexNr].getRewriteTaclet(pos, TacletFilter.TRUE, services);
@@ -257,13 +256,13 @@ private SequentFormula simplifyPos(Goal goal, Services services, PosInOccurrence
                 }
             }
             RewriteTaclet taclet = (RewriteTaclet) app.rule();
-            SequentFormula result =
+            Term result =
                 taclet.getRewriteResult(goal, new TermLabelState(), services, app);
             if (protocol != null) {
                 protocol.add(app);
             }
             return result;
-            // TODO Idea: return new Pair<TacletApp, SequentFormula>(null, null);
+            // TODO Idea: return new Pair<TacletApp, Term>(null, null);
         }
         return null;
     }
@@ -275,10 +274,10 @@ private SequentFormula simplifyPos(Goal goal, Services services, PosInOccurrence
      *
      * @param protocol
      */
-    private SequentFormula simplifySub(Goal goal, Services services, PosInOccurrence pos,
+    private Term simplifySub(Goal goal, Services services, PosInOccurrence pos,
             int indexNr, Protocol protocol) {
         for (int i = 0, n = pos.subTerm().arity(); i < n; i++) {
-            SequentFormula result =
+            Term result =
                 simplifyPosOrSub(goal, services, pos.down(i), indexNr, protocol);
             if (result != null) {
                 return result;
@@ -294,14 +293,14 @@ private SequentFormula simplifySub(Goal goal, Services services, PosInOccurrence
      *
      * @param protocol
      */
-    private SequentFormula simplifyPosOrSub(Goal goal, Services services, PosInOccurrence pos,
+    private Term simplifyPosOrSub(Goal goal, Services services, PosInOccurrence pos,
             int indexNr, Protocol protocol) {
         final Term term = pos.subTerm();
         if (notSimplifiableCaches[indexNr].get(term) != null) {
             return null;
         }
 
-        SequentFormula result;
+        Term result;
         if (bottomUp[indexNr]) {
             result = simplifySub(goal, services, pos, indexNr, protocol);
             if (result == null) {
@@ -376,20 +375,20 @@ private Term replaceKnownHelper(Map<TermReplacementKey, PosInOccurrence> map, Te
      * (hardcoded here). The context formulas available for replace-known are passed in as
      * "context". The positions of the actually used context formulas are passed out as "ifInsts".
      */
-    private SequentFormula replaceKnown(Services services, SequentFormula cf, boolean inAntecedent,
+    private Term replaceKnown(Services services, Term cf, boolean inAntecedent,
             Map<TermReplacementKey, PosInOccurrence> context,
             /* out */ List<PosInOccurrence> ifInsts, Protocol protocol, Goal goal,
             RuleApp ruleApp) {
         if (context == null) {
             return null;
         }
-        final Term formula = cf.formula();
+        final Term formula = cf;
         final Term simplifiedFormula = replaceKnownHelper(context, formula, inAntecedent, ifInsts,
             protocol, services, goal, ruleApp);
         if (simplifiedFormula.equals(formula)) {
             return null;
         } else {
-            return new SequentFormula(simplifiedFormula);
+            return simplifiedFormula;
         }
     }
 
@@ -406,18 +405,18 @@ private RuleApp makeReplaceKnownTacletApp(Term formula, boolean inAntecedent,
 
         SVInstantiations svi = SVInstantiations.EMPTY_SVINSTANTIATIONS;
         FormulaSV sv = SchemaVariableFactory.createFormulaSV(new Name("b"));
-        svi.add(sv, pio.sequentFormula().formula(), lastProof.getServices());
+        svi.add(sv, pio.sequentLevelFormula(), lastProof.getServices());
 
         PosInOccurrence applicatinPIO =
-            new PosInOccurrence(new SequentFormula(formula), PosInTerm.getTopLevel(), // TODO: This
-                                                                                      // should be
-                                                                                      // the precise
-                                                                                      // sub term
+            new PosInOccurrence(formula, PosInTerm.getTopLevel(), // TODO: This
+                                                                  // should be
+                                                                  // the precise
+                                                                  // sub term
                 inAntecedent); // It is required to create a new PosInOccurrence because formula and
                                // pio.constrainedFormula().formula() are only equals module
                                // renamings and term labels
         ImmutableList<IfFormulaInstantiation> ifInst = ImmutableSLList.nil();
-        ifInst = ifInst.append(new IfFormulaInstDirect(pio.sequentFormula()));
+        ifInst = ifInst.append(new IfFormulaInstDirect(pio.sequentLevelFormula()));
         TacletApp ta = PosTacletApp.createPosTacletApp(taclet, svi, ifInst, applicatinPIO,
             lastProof.getServices());
         return ta;
@@ -429,11 +428,11 @@ private RuleApp makeReplaceKnownTacletApp(Term formula, boolean inAntecedent,
      *
      * @param protocol
      */
-    private SequentFormula simplifyConstrainedFormula(Services services, SequentFormula cf,
+    private Term simplifyConstrainedFormula(Services services, Term cf,
             boolean inAntecedent, Map<TermReplacementKey, PosInOccurrence> context,
             /* out */ List<PosInOccurrence> ifInsts, Protocol protocol, Goal goal,
             RuleApp ruleApp) {
-        SequentFormula result =
+        Term result =
             replaceKnown(services, cf, inAntecedent, context, ifInsts, protocol, goal, ruleApp);
         if (result != null) {
             return result;
@@ -461,24 +460,28 @@ private Instantiation computeInstantiation(Services services, PosInOccurrence os
         // collect context formulas (potential if-insts for replace-known)
         final Map<TermReplacementKey, PosInOccurrence> context =
             new LinkedHashMap<>();
-        final SequentFormula cf = ossPIO.sequentFormula();
-        for (SequentFormula ante : seq.antecedent()) {
-            if (!ante.equals(cf) && ante.formula().op() != Junctor.TRUE) {
-                context.put(new TermReplacementKey(ante.formula()),
-                    new PosInOccurrence(ante, PosInTerm.getTopLevel(), true));
+        final Term cf = ossPIO.sequentLevelFormula();
+        for (Term ante : seq.antecedent()) {
+            if (!ante.equals(cf)) {
+                if (ante.op() != Junctor.TRUE) {
+                    context.put(new TermReplacementKey(ante),
+                        new PosInOccurrence(ante, PosInTerm.getTopLevel(), true));
+                }
             }
         }
-        for (SequentFormula succ : seq.succedent()) {
-            if (!succ.equals(cf) && succ.formula().op() != Junctor.FALSE) {
-                context.put(new TermReplacementKey(succ.formula()),
-                    new PosInOccurrence(succ, PosInTerm.getTopLevel(), false));
+        for (Term succ : seq.succedent()) {
+            if (!succ.equals(cf)) {
+                if (succ.op() != Junctor.FALSE) {
+                    context.put(new TermReplacementKey(succ),
+                        new PosInOccurrence(succ, PosInTerm.getTopLevel(), false));
+                }
             }
         }
         final List<PosInOccurrence> ifInsts = new ArrayList<>(seq.size());
 
         // simplify as long as possible
-        ImmutableList<SequentFormula> list = ImmutableSLList.nil();
-        SequentFormula simplifiedCf = cf;
+        ImmutableList<Term> list = ImmutableSLList.nil();
+        Term simplifiedCf = cf;
         while (true) {
             simplifiedCf = simplifyConstrainedFormula(services, simplifiedCf, ossPIO.isInAntec(),
                 context, ifInsts, protocol, goal, ruleApp);
@@ -500,14 +503,14 @@ private Instantiation computeInstantiation(Services services, PosInOccurrence os
     /**
      * Tells whether the passed formula can be simplified
      */
-    private synchronized boolean applicableTo(Services services, SequentFormula cf,
+    private synchronized boolean applicableTo(Services services, Term cf,
             boolean inAntecedent, Goal goal, RuleApp ruleApp) {
         final Boolean b = applicabilityCache.get(cf);
         if (b != null) {
             return b;
         } else {
             // try one simplification step without replace-known
-            final SequentFormula simplifiedCf = simplifyConstrainedFormula(services, cf,
+            final Term simplifiedCf = simplifyConstrainedFormula(services, cf,
                 inAntecedent, null, null, null, goal, ruleApp);
             final boolean result = simplifiedCf != null && !simplifiedCf.equals(cf);
             applicabilityCache.put(cf, result);
@@ -572,7 +575,8 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
         }
 
         // applicable to the formula?
-        return applicableTo(goal.proof().getServices(), pio.sequentFormula(), pio.isInAntec(), goal,
+        return applicableTo(goal.proof().getServices(), pio.sequentLevelFormula(), pio.isInAntec(),
+            goal,
             null);
     }
 
@@ -594,21 +598,21 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
         if (((OneStepSimplifierRuleApp) ruleApp).shouldRestrictAssumeInsts()
                 && !disableOSSRestriction) {
             ImmutableList<PosInOccurrence> ifInsts = ((OneStepSimplifierRuleApp) ruleApp).ifInsts();
-            ImmutableList<SequentFormula> anteFormulas = ImmutableSLList.nil();
-            ImmutableList<SequentFormula> succFormulas = ImmutableSLList.nil();
+            ImmutableList<Term> anteFormulas = ImmutableSLList.nil();
+            ImmutableList<Term> succFormulas = ImmutableSLList.nil();
             if (ifInsts != null) {
                 for (PosInOccurrence it : ifInsts) {
                     if (it.isInAntec()) {
-                        anteFormulas = anteFormulas.prepend(it.sequentFormula());
+                        anteFormulas = anteFormulas.prepend(it.sequentLevelFormula());
                     } else {
-                        succFormulas = succFormulas.prepend(it.sequentFormula());
+                        succFormulas = succFormulas.prepend(it.sequentLevelFormula());
                     }
                 }
             }
             if (pos.isInAntec()) {
-                anteFormulas = anteFormulas.prepend(pos.sequentFormula());
+                anteFormulas = anteFormulas.prepend(pos.sequentLevelFormula());
             } else {
-                succFormulas = succFormulas.prepend(pos.sequentFormula());
+                succFormulas = succFormulas.prepend(pos.sequentLevelFormula());
             }
             Semisequent antecedent = anteFormulas.isEmpty() ? Semisequent.EMPTY_SEMISEQUENT
                     : new Semisequent(anteFormulas);
@@ -673,11 +677,11 @@ public Set<NoPosTacletApp> getCapturedTaclets() {
     // -------------------------------------------------------------------------
 
     private static final class Instantiation {
-        private final SequentFormula cf;
+        private final Term cf;
         private final int numAppliedRules;
         private final ImmutableList<PosInOccurrence> ifInsts;
 
-        public Instantiation(SequentFormula cf, int numAppliedRules,
+        public Instantiation(Term cf, int numAppliedRules,
                 ImmutableList<PosInOccurrence> ifInsts) {
             assert numAppliedRules >= 0;
             this.cf = cf;
@@ -685,7 +689,7 @@ public Instantiation(SequentFormula cf, int numAppliedRules,
             this.ifInsts = ifInsts;
         }
 
-        public SequentFormula getCf() {
+        public Term getCf() {
             return cf;
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/PosTacletApp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/PosTacletApp.java
index 6c5d92442ad..0baf6550866 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/PosTacletApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/PosTacletApp.java
@@ -10,6 +10,7 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
@@ -277,7 +278,7 @@ public boolean complete() {
     }
 
     /**
-     * returns the PositionInOccurrence (representing a SequentFormula and a position in the
+     * returns the PositionInOccurrence (representing a Term and a position in the
      * corresponding formula)
      *
      * @return the PosInOccurrence
@@ -319,7 +320,8 @@ public boolean equalsModProofIrrelevancy(Object o) {
     @Override
     public int hashCodeModProofIrrelevancy() {
         return Objects.hash(super.hashCodeModProofIrrelevancy(),
-            pos.sequentFormula().hashCodeModProofIrrelevancy(),
+            ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY
+                    .hashCodeModThisProperty(pos.sequentLevelFormula()),
             pos.posInTerm());
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/QueryExpand.java b/key.core/src/main/java/de/uka/ilkd/key/rule/QueryExpand.java
index 492c155c269..3ffe39389eb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/QueryExpand.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/QueryExpand.java
@@ -88,7 +88,7 @@ public class QueryExpand implements BuiltInRule {
         tb.addRuleSet(new RuleSet(new Name("concrete")));
 
         // move the query call directly to the succedent. Use box instead of diamond?
-        g.addFormula(new SequentFormula(queryEval.first), true, true);
+        g.addFormula(queryEval.first, true, true);
         g.addTaclet(tb.getTaclet(), SVInstantiations.EMPTY_SVINSTANTIATIONS, true);
         return newGoal;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/RewriteTaclet.java b/key.core/src/main/java/de/uka/ilkd/key/rule/RewriteTaclet.java
index 6e506a3f31b..696e7405cf2 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/RewriteTaclet.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/RewriteTaclet.java
@@ -258,7 +258,7 @@ public RewriteTacletExecutor<? extends RewriteTaclet> getExecutor() {
         return (RewriteTacletExecutor<? extends RewriteTaclet>) executor;
     }
 
-    public SequentFormula getRewriteResult(Goal goal, TermLabelState termLabelState,
+    public Term getRewriteResult(Goal goal, TermLabelState termLabelState,
             Services services, TacletApp app) {
         return getExecutor().getRewriteResult(goal, termLabelState, services, app);
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/Rule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/Rule.java
index af71ed4c8ec..09f069deb69 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/Rule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/Rule.java
@@ -39,5 +39,7 @@ ImmutableList<Goal> apply(Goal goal, Services services, RuleApp ruleApp)
     /**
      * returns the display name of the rule
      */
-    String displayName();
+    default String displayName() {
+        return name().toString();
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/RuleAbortException.java b/key.core/src/main/java/de/uka/ilkd/key/rule/RuleAbortException.java
index 96e67cb4ea9..e10f101bd10 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/RuleAbortException.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/RuleAbortException.java
@@ -10,9 +10,7 @@
  *         This Exception signals the abort of a rule Application
  *
  */
-
-
-public class RuleAbortException extends Exception {
+public class RuleAbortException extends RuntimeException {
 
     private static final long serialVersionUID = -645034125571021135L;
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/RuleApp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/RuleApp.java
index 8c505c74360..c55bd34bd9a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/RuleApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/RuleApp.java
@@ -23,7 +23,7 @@ public interface RuleApp extends EqualsModProofIrrelevancy {
     Rule rule();
 
     /**
-     * returns the PositionInOccurrence (representing a SequentFormula and a position in the
+     * returns the PositionInOccurrence (representing a Term and a position in the
      * corresponding formula) of this rule application
      */
     PosInOccurrence posInOccurrence();
@@ -33,11 +33,10 @@ public interface RuleApp extends EqualsModProofIrrelevancy {
      * instantiated
      *
      * @param goal the Goal where to apply the rule
-     * @param services the Services encapsulating all java information
      * @return list of new created goals
      */
-    @Nullable
-    ImmutableList<Goal> execute(Goal goal, Services services);
+    // @Nullable
+    // <G extends ProofGoal> ImmutableList<G> execute(G goal);
 
     /**
      * returns true if all variables are instantiated
@@ -46,6 +45,17 @@ public interface RuleApp extends EqualsModProofIrrelevancy {
      */
     boolean complete();
 
+    /**
+     * applies the specified rule at the specified position if all schema variables have been
+     * instantiated
+     *
+     * @param goal the Goal where to apply the rule
+     * @param services the Services encapsulating all java information
+     * @return list of new created goals
+     */
+    @Nullable
+    ImmutableList<Goal> execute(Goal goal, Services services);
+
     /**
      * @return user-friendly name for this rule-application
      */
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/SVNameCorrespondenceCollector.java b/key.core/src/main/java/de/uka/ilkd/key/rule/SVNameCorrespondenceCollector.java
index b86aa18d2bf..dfe05eb9e5a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/SVNameCorrespondenceCollector.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/SVNameCorrespondenceCollector.java
@@ -7,7 +7,6 @@
 import de.uka.ilkd.key.logic.DefaultVisitor;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.JFunction;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
@@ -84,8 +83,8 @@ public ImmutableMap<SchemaVariable, SchemaVariable> getCorrespondences() {
      * @param semiseq the Semisequent to visit
      */
     private void visit(Semisequent semiseq) {
-        for (SequentFormula cf : semiseq) {
-            cf.formula().execPostOrder(this);
+        for (Term cf : semiseq) {
+            cf.execPostOrder(this);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/SetStatementRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/SetStatementRule.java
index 6e29239f3eb..94082faab59 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/SetStatementRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/SetStatementRule.java
@@ -113,7 +113,7 @@ public IBuiltInRuleApp createApp(PosInOccurrence occurrence, TermServices servic
         Term newTerm = tb.apply(update, tb.apply(newUpdate, term));
 
         ImmutableList<Goal> result = goal.split(1);
-        result.head().changeFormula(new SequentFormula(newTerm), occurrence);
+        result.head().changeFormula(newTerm, occurrence);
         return result;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/Taclet.java b/key.core/src/main/java/de/uka/ilkd/key/rule/Taclet.java
index 5f61d57f92b..c1adfe7c326 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/Taclet.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/Taclet.java
@@ -7,6 +7,7 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.*;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.logic.label.TermLabel;
 import de.uka.ilkd.key.logic.op.Operator;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
@@ -491,17 +492,19 @@ public boolean equalsModProofIrrelevancy(Object o) {
         if ((ifSequent == null && t2.ifSequent != null)
                 || (ifSequent != null && t2.ifSequent == null)) {
             return false;
+        } else if (ifSequent.size() != t2.ifSequent.size()) {
+            return false;
         } else {
-            ImmutableList<SequentFormula> if1 = ifSequent.asList();
-            ImmutableList<SequentFormula> if2 = t2.ifSequent.asList();
-            while (!if1.isEmpty() && !if2.isEmpty()
-                    && if1.head().equalsModProofIrrelevancy(if2.head())) {
+            ImmutableList<Term> if1 = ifSequent.asList();
+            ImmutableList<Term> if2 = t2.ifSequent.asList();
+            while (!if1.isEmpty()) {
+                if (!ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY
+                        .equalsModThisProperty(if1.head(), if2.head())) {
+                    return false;
+                }
                 if1 = if1.tail();
                 if2 = if2.tail();
             }
-            if (!if1.isEmpty() || !if2.isEmpty()) {
-                return false;
-            }
         }
 
         if (!choices.equals(t2.choices)) {
@@ -529,7 +532,9 @@ public int hashCode() {
     @Override
     public int hashCodeModProofIrrelevancy() {
         if (hashcode2 == 0) {
-            hashcode2 = ifSequent.getFormulabyNr(1).hashCodeModProofIrrelevancy();
+            Term term = ifSequent.getFormulabyNr(1);
+            hashcode2 =
+                ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY.hashCodeModThisProperty(term);
             if (hashcode2 == 0) {
                 hashcode2 = -1;
             }
@@ -740,8 +745,8 @@ public Set<SchemaVariable> collectSchemaVars() {
 
 
     private void collectSchemaVarsHelper(Sequent s, OpCollector oc) {
-        for (SequentFormula cf : s) {
-            cf.formula().execPostOrder(oc);
+        for (Term cf : s) {
+            cf.execPostOrder(oc);
         }
     }
 
@@ -762,9 +767,9 @@ public static class TacletLabelHint {
         private final Sequent sequent;
 
         /**
-         * The optional {@link SequentFormula} contained in {@link #getSequent()}.
+         * The optional {@link Term} contained in {@link #getSequent()}.
          */
-        private final SequentFormula sequentFormula;
+        private final Term seqFormula;
 
         /**
          * The optional replace {@link Term} of the taclet.
@@ -788,7 +793,7 @@ public TacletLabelHint(TacletOperation tacletOperation, Sequent sequent) {
             assert sequent != null;
             this.tacletOperation = tacletOperation;
             this.sequent = sequent;
-            this.sequentFormula = null;
+            this.seqFormula = null;
             this.term = null;
         }
 
@@ -796,30 +801,30 @@ public TacletLabelHint(TacletOperation tacletOperation, Sequent sequent) {
          * Constructor creating a hint indicating
          * {@link TacletOperation#REPLACE_TERM} as the currently performed operation.
          *
-         * @param term The optional replace {@link Term} of the taclet.
+         * @param replaceTerm The optional replace {@link Term} of the taclet.
          */
-        public TacletLabelHint(Term term) {
-            assert term != null;
+        public TacletLabelHint(Term replaceTerm) {
+            assert replaceTerm != null;
             this.tacletOperation = TacletOperation.REPLACE_TERM;
             this.sequent = null;
-            this.sequentFormula = null;
-            this.term = term;
+            this.seqFormula = null;
+            this.term = seqFormula;
         }
 
         /**
          * Constructor.
          *
          * @param labelHint The previous {@link TacletLabelHint} which is now specialised.
-         * @param sequentFormula The optional {@link SequentFormula} contained in
+         * @param formula The optional {@link Term} contained in
          *        {@link #getSequent()}.
          */
-        public TacletLabelHint(TacletLabelHint labelHint, SequentFormula sequentFormula) {
+        public TacletLabelHint(TacletLabelHint labelHint, Term formula) {
             assert labelHint != null;
             assert !TacletOperation.REPLACE_TERM.equals(labelHint.getTacletOperation());
-            assert sequentFormula != null;
+            assert formula != null;
             this.tacletOperation = labelHint.getTacletOperation();
             this.sequent = labelHint.getSequent();
-            this.sequentFormula = sequentFormula;
+            this.seqFormula = formula;
             this.term = labelHint.getTerm();
         }
 
@@ -842,12 +847,12 @@ public Sequent getSequent() {
         }
 
         /**
-         * Returns the optional {@link SequentFormula} contained in {@link #getSequent()}.
+         * Returns the optional {@link Term} contained in {@link #getSequent()}.
          *
-         * @return The optional {@link SequentFormula} contained in {@link #getSequent()}.
+         * @return The optional {@link Term} contained in {@link #getSequent()}.
          */
-        public SequentFormula getSequentFormula() {
-            return sequentFormula;
+        public Term getSeqFormula() {
+            return seqFormula;
         }
 
         /**
@@ -883,7 +888,7 @@ public Term getTerm() {
         @Override
         public String toString() {
             return tacletOperation + ", sequent = " + sequent + ", sequent formula = "
-                + sequentFormula + ", term = " + term;
+                + seqFormula + ", term = " + term;
         }
 
         /**
@@ -894,20 +899,20 @@ public String toString() {
         public enum TacletOperation {
             /**
              * Add clause of a {@link Taclet} applied to the antecedent. Available information are
-             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSeqFormula()}.
              */
             ADD_ANTECEDENT,
 
             /**
              * Add clause of a {@link Taclet} applied to the succedent. Available information are
-             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSeqFormula()}.
              */
             ADD_SUCCEDENT,
 
             /**
              * Replace clause of a {@link Taclet} provides a {@link Sequent} and currently
              * additional adds to the antecedent are performed. Available information are
-             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSeqFormula()}.
              */
             REPLACE_TO_ANTECEDENT,
 
@@ -915,7 +920,7 @@ public enum TacletOperation {
              * Replace clause of a {@link Taclet} provides a {@link Sequent} and currently the
              * current {@link PosInOccurrence} on the succedent is modified. Available information
              * are {@link TacletLabelHint#getSequent()} and
-             * {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSeqFormula()}.
              */
             REPLACE_AT_SUCCEDENT,
 
@@ -923,21 +928,21 @@ public enum TacletOperation {
              * Replace clause of a {@link Taclet} provides a {@link Sequent} and currently the
              * current {@link PosInOccurrence} on the antecedent is modified. Available information
              * are {@link TacletLabelHint#getSequent()} and
-             * {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSeqFormula()}.
              */
             REPLACE_AT_ANTECEDENT,
 
             /**
              * Replace clause of a {@link Taclet} provides a {@link Sequent} and currently
              * additional adds to the succedent are performed. Available information are
-             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSequentFormula()}.
+             * {@link TacletLabelHint#getSequent()} and {@link TacletLabelHint#getSeqFormula()}.
              */
             REPLACE_TO_SUCCEDENT,
 
             /**
              * Replace clause of a {@link Taclet} provides a {@link Term} which is currently used to
              * modify the {@link PosInOccurrence}. Available information are
-             * {@link TacletLabelHint#getTerm()}.
+             * {@link TacletLabelHint#getSeqFormula()}.
              */
             REPLACE_TERM
         }
@@ -955,7 +960,7 @@ public enum TacletOperation {
      */
     @Override
     public @NonNull ImmutableList<Goal> apply(Goal goal, Services services, RuleApp tacletApp) {
-        return getExecutor().apply(goal, services, tacletApp);
+        return getExecutor().apply((Goal) goal, services, tacletApp);
     }
 
     public TacletExecutor<? extends Taclet> getExecutor() {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletApp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletApp.java
index a98632eb8ef..feecc41cc5d 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletApp.java
@@ -236,8 +236,8 @@ private static Term getTermBelowQuantifier(SchemaVariable varSV, Term term) {
      * @return the term below the given quantifier in the find and if-parts of the Taclet
      */
     private static Term getTermBelowQuantifier(Taclet taclet, SchemaVariable varSV) {
-        for (SequentFormula sequentFormula : taclet.ifSequent()) {
-            Term result = getTermBelowQuantifier(varSV, sequentFormula.formula());
+        for (Term assumesFml : taclet.ifSequent()) {
+            Term result = getTermBelowQuantifier(varSV, assumesFml);
             if (result != null) {
                 return result;
             }
@@ -895,7 +895,7 @@ public ImmutableList<TacletApp> findIfFormulaInstantiations(Sequent seq, Service
      * @return a list of tacletapps with the found if formula instantiations
      */
     private ImmutableList<TacletApp> findIfFormulaInstantiationsHelp(
-            ImmutableList<SequentFormula> ruleSuccTail, ImmutableList<SequentFormula> ruleAntecTail,
+            ImmutableList<Term> ruleSuccTail, ImmutableList<Term> ruleAntecTail,
             ImmutableArray<IfFormulaInstantiation> instSucc,
             ImmutableArray<IfFormulaInstantiation> instAntec,
             ImmutableList<IfFormulaInstantiation> instAlreadyMatched, MatchConditions matchCond,
@@ -918,8 +918,8 @@ private ImmutableList<TacletApp> findIfFormulaInstantiationsHelp(
         }
 
         // Match the current formula
-        IfMatchResult mr = taclet().getMatcher().matchIf(instSucc, ruleSuccTail.head().formula(),
-            matchCond, services);
+        Term fml = ruleSuccTail.head();
+        IfMatchResult mr = taclet().getMatcher().matchIf(instSucc, fml, matchCond, services);
 
         // For each matching formula call the method again to match
         // the remaining terms
@@ -935,10 +935,10 @@ private ImmutableList<TacletApp> findIfFormulaInstantiationsHelp(
         return res;
     }
 
-    private ImmutableList<SequentFormula> createSemisequentList(Semisequent p_ss) {
-        ImmutableList<SequentFormula> res = ImmutableSLList.nil();
+    private ImmutableList<Term> createSemisequentList(Semisequent p_ss) {
+        ImmutableList<Term> res = ImmutableSLList.nil();
 
-        for (SequentFormula p_s : p_ss) {
+        for (Term p_s : p_ss) {
             res = res.prepend(p_s);
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletMatcher.java b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletMatcher.java
index 567b38b68f1..9ca5be95b01 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletMatcher.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletMatcher.java
@@ -6,9 +6,10 @@
 import de.uka.ilkd.key.java.ProgramElement;
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Term;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 
+import org.key_project.logic.SyntaxElement;
+
 public interface TacletMatcher {
 
     /**
@@ -69,7 +70,7 @@ MatchConditions checkConditions(MatchConditions p_matchconditions,
      *         <code>instantiationCandidate</code> or <code>null</code> if a match was not possible
      */
     MatchConditions checkVariableConditions(SchemaVariable var,
-            SVSubstitute instantiationCandidate, MatchConditions matchCond, Services services);
+            SyntaxElement instantiationCandidate, MatchConditions matchCond, Services services);
 
     /**
      * matches the given term against the taclet's find term if the taclet has no find term or the
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletSchemaVariableCollector.java b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletSchemaVariableCollector.java
index 04d610c2326..60356bf5e21 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/TacletSchemaVariableCollector.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/TacletSchemaVariableCollector.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabel;
 import de.uka.ilkd.key.logic.op.*;
@@ -159,8 +158,8 @@ public boolean contains(SchemaVariable var) {
      * @param semiseq the Semisequent to visit
      */
     private void visit(Semisequent semiseq) {
-        for (SequentFormula aSemiseq : semiseq) {
-            aSemiseq.formula().execPostOrder(this);
+        for (Term aSemiseq : semiseq) {
+            aSemiseq.execPostOrder(this);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/UseDependencyContractRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/UseDependencyContractRule.java
index 6b9fe73e9e1..9e3dd9ac82c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/UseDependencyContractRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/UseDependencyContractRule.java
@@ -56,8 +56,8 @@ private UseDependencyContractRule() {
 
     private static List<Term> getEqualityDefs(Term term, Sequent seq) {
         final List<Term> result = new LinkedList<>();
-        for (SequentFormula cf : seq.antecedent()) {
-            final Term formula = cf.formula();
+        for (Term cf : seq.antecedent()) {
+            final Term formula = cf;
             if (formula.op() instanceof Equality && formula.sub(1).equals(term)) {
                 result.add(formula.sub(0));
             }
@@ -69,8 +69,8 @@ private static List<Term> getEqualityDefs(Term term, Sequent seq) {
     private static List<Pair<Term, PosInOccurrence>> getEqualityDefsAndPos(Term term, Sequent seq) {
         final List<Pair<Term, PosInOccurrence>> result =
             new LinkedList<>();
-        for (SequentFormula cf : seq.antecedent()) {
-            final Term formula = cf.formula();
+        for (Term cf : seq.antecedent()) {
+            final Term formula = cf;
             if (formula.op() instanceof Equality && formula.sub(1).equals(term)) {
                 final PosInOccurrence pos = new PosInOccurrence(cf, PosInTerm.getTopLevel(), true);
                 result.add(new Pair<>(formula.sub(0), pos));
@@ -83,8 +83,8 @@ private static List<Pair<Term, PosInOccurrence>> getEqualityDefsAndPos(Term term
     private ImmutableSet<Term> addEqualDefs(ImmutableSet<Term> terms, Goal g) {
         ImmutableList<Term> result = ImmutableSLList.nil();
 
-        for (SequentFormula cf : g.sequent().antecedent()) {
-            final Term formula = cf.formula();
+        for (Term cf : g.sequent().antecedent()) {
+            final Term formula = cf;
             if (formula.op() instanceof Equality && terms.contains(formula.sub(1))) {
                 result = result.prepend(formula.sub(0));
             }
@@ -234,11 +234,11 @@ private static void collectBaseOccsHelper(Term focus, PosInOccurrence pos,
     private static Map<Term, PosInOccurrence> collectBaseOccs(Term focus, Sequent seq) {
         assert focus.op() instanceof IObserverFunction;
         final Map<Term, PosInOccurrence> result = new LinkedHashMap<>();
-        for (SequentFormula cf : seq.antecedent()) {
+        for (Term cf : seq.antecedent()) {
             final PosInOccurrence pos = new PosInOccurrence(cf, PosInTerm.getTopLevel(), true);
             collectBaseOccsHelper(focus, pos, result);
         }
-        for (SequentFormula cf : seq.succedent()) {
+        for (Term cf : seq.succedent()) {
             final PosInOccurrence pos = new PosInOccurrence(cf, PosInTerm.getTopLevel(), false);
             collectBaseOccsHelper(focus, pos, result);
         }
@@ -537,7 +537,7 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
         final ImmutableList<Goal> result = goal.split(1);
         final Term termWithBaseHeap = TB.func(target, subs);
         final Term implication = TB.imp(cutFormula, TB.equals(focus, termWithBaseHeap));
-        result.head().addFormula(new SequentFormula(implication), true, false);
+        result.head().addFormula(implication, true, false);
 
         return result;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/UseOperationContractRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/UseOperationContractRule.java
index c5e3d287d09..819622e7098 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/UseOperationContractRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/UseOperationContractRule.java
@@ -40,7 +40,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.PosInProgram;
 import de.uka.ilkd.key.logic.ProgramPrefix;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermFactory;
@@ -430,13 +429,13 @@ private static void applyInfFlow(Goal goal, final FunctionalOperationContract co
         Taclet informationFlowContractApp = ifContractBuilder.buildTaclet(goal);
 
         // add term and taclet to post goal
-        goal.addFormula(new SequentFormula(contractApplPredTerm), true, false);
+        goal.addFormula(contractApplPredTerm, true, false);
         goal.addTaclet(informationFlowContractApp, SVInstantiations.EMPTY_SVINSTANTIATIONS, true);
 
         // information flow proofs might get easier if we add the (proved)
         // method contract precondition as an assumption to the post goal
         // (in case the precondition cannot be proved easily)
-        goal.addFormula(new SequentFormula(finalPreTerm), true, false);
+        goal.addFormula(finalPreTerm, true, false);
         final InfFlowProof proof = (InfFlowProof) goal.proof();
         proof.addIFSymbol(contractApplPredTerm);
         proof.addIFSymbol(informationFlowContractApp);
@@ -745,7 +744,7 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
 
         finalPreTerm = TermLabelManager.refactorTerm(termLabelState, services, null, finalPreTerm,
             this, preGoal, FINAL_PRE_TERM_HINT, null);
-        preGoal.changeFormula(new SequentFormula(finalPreTerm), ruleApp.posInOccurrence());
+        preGoal.changeFormula(finalPreTerm, ruleApp.posInOccurrence());
 
         TermLabelManager.refactorGoal(termLabelState, services, ruleApp.posInOccurrence(), this,
             preGoal, null, null);
@@ -769,10 +768,11 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
                         new ImmutableArray<>(inst.progPost.sub(0)), null,
                         inst.progPost.getLabels()))),
             null);
-        postGoal.addFormula(new SequentFormula(wellFormedAnon), true, false);
-        postGoal.changeFormula(new SequentFormula(tb.apply(inst.u, normalPost, null)),
+        postGoal.addFormula(wellFormedAnon, true, false);
+        Term uAssumptions2 = tb.apply(inst.u, normalPost, null);
+        postGoal.changeFormula(uAssumptions2,
             ruleApp.posInOccurrence());
-        postGoal.addFormula(new SequentFormula(postAssumption), true, false);
+        postGoal.addFormula(postAssumption, true, false);
 
         applyInfFlow(postGoal, contract, inst, contractSelf, contractParams, contractResult,
             tb.var(excVar), mby, atPreUpdates, finalPreTerm, anonUpdateDatas, services);
@@ -792,15 +792,17 @@ public boolean isApplicable(Goal goal, PosInOccurrence pio) {
             null);
         final Term excPost =
             globalDefs == null ? originalExcPost : tb.apply(globalDefs, originalExcPost);
-        excPostGoal.addFormula(new SequentFormula(wellFormedAnon), true, false);
-        excPostGoal.changeFormula(new SequentFormula(tb.apply(inst.u, excPost, null)),
+        excPostGoal.addFormula(wellFormedAnon, true, false);
+        Term uAssumptions1 = tb.apply(inst.u, excPost, null);
+        excPostGoal.changeFormula(uAssumptions1,
             ruleApp.posInOccurrence());
-        excPostGoal.addFormula(new SequentFormula(excPostAssumption), true, false);
+        excPostGoal.addFormula(excPostAssumption, true, false);
 
         // create "Null Reference" branch
         if (nullGoal != null) {
             final Term actualSelfNotNull = tb.not(tb.equals(inst.actualSelf, tb.NULL()));
-            nullGoal.changeFormula(new SequentFormula(tb.apply(inst.u, actualSelfNotNull, null)),
+            Term uAssumptions = tb.apply(inst.u, actualSelfNotNull, null);
+            nullGoal.changeFormula(uAssumptions,
                 ruleApp.posInOccurrence());
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/VariableCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/VariableCondition.java
index aa9cc4495e5..1907547ddc7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/VariableCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/VariableCondition.java
@@ -4,9 +4,10 @@
 package de.uka.ilkd.key.rule;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * The instantiations of a schemavariable can be restricted on rule scope by attaching conditions on
@@ -30,7 +31,8 @@ public interface VariableCondition {
      * @return modified match results if the condition can be satisfied, or <code>null</code>
      *         otherwise
      */
-    MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions matchCond,
+    MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions matchCond,
             Services services);
 
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/VariableConditionAdapter.java b/key.core/src/main/java/de/uka/ilkd/key/rule/VariableConditionAdapter.java
index cb29e713636..d2c19ec07fb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/VariableConditionAdapter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/VariableConditionAdapter.java
@@ -4,10 +4,11 @@
 package de.uka.ilkd.key.rule;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * The variable condition adapter can be used by variable conditions which can either fail or be
@@ -24,13 +25,13 @@ public abstract class VariableConditionAdapter implements VariableCondition {
      * @param services the program information object
      * @return true iff condition is fulfilled
      */
-    public abstract boolean check(SchemaVariable var, SVSubstitute instCandidate,
+    public abstract boolean check(SchemaVariable var, SyntaxElement instCandidate,
             SVInstantiations instMap, Services services);
 
 
 
     @Override
-    public final MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public final MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions mc, Services services) {
         return check(var, instCandidate, mc.getInstantiations(), services) ? mc : null;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/WhileInvariantRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/WhileInvariantRule.java
index 4ed438b1b8a..95cc1230556 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/WhileInvariantRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/WhileInvariantRule.java
@@ -34,7 +34,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.ProgramElementName;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -414,7 +413,7 @@ private static void setUpInfFlowPartOfUseGoal(final InfFlowData infData, final T
         final Term infFlowAssumptions = tb.apply(infData.updates.first, tb.and(beforeAssumptions,
             tb.apply(infData.updates.second, tb.and(afterAssumptions, infData.applPredTerm))));
 
-        goal.addFormula(new SequentFormula(infFlowAssumptions), true, false);
+        goal.addFormula(infFlowAssumptions, true, false);
         goal.addTaclet(infData.infFlowApp, SVInstantiations.EMPTY_SVINSTANTIATIONS, true);
         final InfFlowProof proof = (InfFlowProof) goal.proof();
         proof.addIFSymbol(infData.applPredTerm);
@@ -464,7 +463,7 @@ private static InfFlowData setUpInfFlowValidityGoal(Goal infFlowGoal,
         final Term finalTerm =
             tb.imp(tb.label(selfComposedExec, ParameterlessTermLabel.SELF_COMPOSITION_LABEL), post);
         ((InfFlowProof) infFlowGoal.proof()).addLabeledIFSymbol(selfComposedExec);
-        infFlowGoal.addFormula(new SequentFormula(finalTerm), false, true);
+        infFlowGoal.addFormula(finalTerm, false, true);
 
         return infFlowData;
     }
@@ -545,13 +544,13 @@ private Term bodyTerm(TermLabelState termLabelState, Services services, RuleApp
     }
 
 
-    private SequentFormula initFormula(TermLabelState termLabelState, Instantiation inst,
+    private Term initFormula(TermLabelState termLabelState, Instantiation inst,
             final Term invTerm, Term reachableState, Services services, Goal initGoal) {
         final TermBuilder tb = services.getTermBuilder();
         Term sfTerm = tb.apply(inst.u, tb.and(invTerm, reachableState), null);
         sfTerm = TermLabelManager.refactorTerm(termLabelState, services, null, sfTerm, this,
             initGoal, INITIAL_INVARIANT_ONLY_HINT, null);
-        return new SequentFormula(sfTerm);
+        return sfTerm;
     }
 
     private Term useCaseFormula(TermLabelState termLabelState, Services services, RuleApp ruleApp,
@@ -614,15 +613,16 @@ private void prepareBodyPreservesBranch(TermLabelState termLabelState, Services
             final Term[] uBeforeLoopDefAnonVariant, final Term uAnonInv) {
         final TermBuilder tb = services.getTermBuilder();
         bodyGoal.setBranchLabel(BODY_PRESERVES_INVARIANT_LABEL);
-        bodyGoal.addFormula(new SequentFormula(wellFormedAnon), true, false);
+        bodyGoal.addFormula(wellFormedAnon, true, false);
 
-        bodyGoal.addFormula(new SequentFormula(uAnonInv), true, false);
+        bodyGoal.addFormula(uAnonInv, true, false);
 
         Term guardTrueBody = bodyTerm(termLabelState, services, ruleApp, applicationSequent, inst,
             invTerm, frameCondition, variantPO, bodyGoal, guardJb, guardTrueTerm);
 
+        Term uAssumptions = tb.applySequential(uBeforeLoopDefAnonVariant, guardTrueBody);
         bodyGoal.changeFormula(
-            new SequentFormula(tb.applySequential(uBeforeLoopDefAnonVariant, guardTrueBody)),
+            uAssumptions,
             ruleApp.posInOccurrence());
     }
 
@@ -632,13 +632,14 @@ private void prepareUseCaseBranch(TermLabelState termLabelState, Services servic
             final JavaBlock guardJb, final Term guardFalseTerm, final Term[] uAnon,
             final Term uAnonInv) {
         useGoal.setBranchLabel("Use Case");
-        useGoal.addFormula(new SequentFormula(wellFormedAnon), true, false);
-        useGoal.addFormula(new SequentFormula(uAnonInv), true, false);
+        useGoal.addFormula(wellFormedAnon, true, false);
+        useGoal.addFormula(uAnonInv, true, false);
         final TermBuilder tb = services.getTermBuilder();
 
         Term guardFalseRestPsi = useCaseFormula(termLabelState, services, ruleApp, inst, useGoal,
             guardJb, guardFalseTerm);
-        useGoal.changeFormula(new SequentFormula(tb.applySequential(uAnon, guardFalseRestPsi)),
+        Term uAssumptions = tb.applySequential(uAnon, guardFalseRestPsi);
+        useGoal.changeFormula(uAssumptions,
             ruleApp.posInOccurrence());
     }
 
@@ -696,7 +697,7 @@ private void setupWdGoal(final Goal goal, final LoopSpecification inv, final Ter
             self = null;
         }
         services.getSpecificationRepository().addWdStatement(lwd);
-        final SequentFormula wdInv =
+        final Term wdInv =
             lwd.generateSequent(self, heap, anonHeap, localIns, update, localAnonUpdate, services);
         goal.changeFormula(wdInv, pio);
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AbstractOrInterfaceType.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AbstractOrInterfaceType.java
index 396d872b368..8ff2d7edcb0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AbstractOrInterfaceType.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AbstractOrInterfaceType.java
@@ -4,11 +4,11 @@
 package de.uka.ilkd.key.rule.conditions;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -34,7 +34,7 @@ public TypeResolver getTypeResolver() {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         final Sort sort = resolver.resolveSort(var, instCandidate, instMap, services);
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AlternativeVariableCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AlternativeVariableCondition.java
index 5ac5d19f8b3..8b1455e32bb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AlternativeVariableCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/AlternativeVariableCondition.java
@@ -5,11 +5,12 @@
 
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * disjoin two variable conditions
@@ -30,7 +31,7 @@ public AlternativeVariableCondition(VariableConditionAdapter delegate0,
      * check whether any of the two delegates apply
      */
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
         return delegate0.check(var, subst, svInst, services)
                 || delegate1.check(var, subst, svInst, services);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ApplyUpdateOnRigidCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ApplyUpdateOnRigidCondition.java
index 78f40a82ba6..511ce913b22 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ApplyUpdateOnRigidCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ApplyUpdateOnRigidCondition.java
@@ -13,6 +13,7 @@
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 import org.key_project.util.collection.ImmutableSet;
 
@@ -198,7 +199,8 @@ private static boolean nameIsAlreadyUsed(Name name, ImmutableSet<QuantifiableVar
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         Term uInst = (Term) svInst.getInstantiation(u);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayComponentTypeCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayComponentTypeCondition.java
index 4a99d1b5bfa..95af112a2f5 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayComponentTypeCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayComponentTypeCondition.java
@@ -8,12 +8,12 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.reference.TypeReference;
 import de.uka.ilkd.key.logic.Term;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ArraySort;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -47,7 +47,7 @@ public boolean isCheckReferenceType() {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
         if (var != this.var) {
             return true;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayLengthCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayLengthCondition.java
index ff12e2bc8ec..a8d42005d63 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayLengthCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayLengthCondition.java
@@ -7,11 +7,12 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.reference.FieldReference;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 public final class ArrayLengthCondition extends VariableConditionAdapter {
 
@@ -26,7 +27,7 @@ public ArrayLengthCondition(SchemaVariable reference, boolean negation) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
         if (var == reference) {
             ProgramVariable attribute;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayTypeCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayTypeCondition.java
index 316d7507014..16d8ca6010d 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayTypeCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ArrayTypeCondition.java
@@ -8,12 +8,12 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.reference.TypeReference;
 import de.uka.ilkd.key.logic.Term;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ArraySort;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -42,7 +42,7 @@ public ArrayTypeCondition(SchemaVariable var, boolean negated) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
         if (var != this.var) {
             return true;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ConstantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ConstantCondition.java
index 9f330e539e4..2446796c1a4 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ConstantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ConstantCondition.java
@@ -7,12 +7,13 @@
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.AbstractSortedOperator;
 import de.uka.ilkd.key.logic.op.FormulaSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.TermSV;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * This variable condition checks if an instantiation is a constant formula or term, i.e. its arity
  * is equal to zero.
@@ -30,7 +31,7 @@ public ConstantCondition(AbstractSortedOperator t, boolean negated) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         if ((!(var instanceof TermSV) || var != this.t)
                 && (!(var instanceof FormulaSV) || var != this.t)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ContainsAssignmentCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ContainsAssignmentCondition.java
index d0d86c71485..b55d9901ce9 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ContainsAssignmentCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ContainsAssignmentCondition.java
@@ -10,10 +10,11 @@
 import de.uka.ilkd.key.java.visitor.JavaASTVisitor;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * This variable condition can be used to check whether an assignment expression occurs as a
@@ -56,7 +57,7 @@ public ContainsAssignmentCondition(SchemaVariable x, boolean negated) {
      * {@inheritDoc}
      */
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         if (var != expression) {
             return true;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentFields.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentFields.java
index ad85c70dd3c..d1d53dda392 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentFields.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentFields.java
@@ -5,11 +5,11 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Term;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.op.Function;
 
 
@@ -27,7 +27,7 @@ public DifferentFields(SchemaVariable var1, SchemaVariable var2) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
 
         if (var == var1) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentInstantiationCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentInstantiationCondition.java
index 430a7511ea9..513f2656bfd 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentInstantiationCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DifferentInstantiationCondition.java
@@ -5,11 +5,11 @@
 
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 
 
 public final class DifferentInstantiationCondition extends VariableConditionAdapter {
@@ -23,7 +23,7 @@ public DifferentInstantiationCondition(SchemaVariable var1, SchemaVariable var2)
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
         if (var == var1) {
             final Object inst2 = svInst.getInstantiation(var2);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessElementariesCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessElementariesCondition.java
index 0dd3be764b2..a8ac743343e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessElementariesCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessElementariesCondition.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.op.ElementaryUpdate;
 import de.uka.ilkd.key.logic.op.LocationVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
 import de.uka.ilkd.key.logic.op.UpdateJunctor;
@@ -20,6 +19,8 @@
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 public final class DropEffectlessElementariesCondition implements VariableCondition {
     private final UpdateSV u;
@@ -85,7 +86,8 @@ private static Term dropEffectlessElementaries(Term update, Term target, Service
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         Term uInst = (Term) svInst.getInstantiation(u);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessStoresCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessStoresCondition.java
index 819c1c38797..d49c3d47269 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessStoresCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/DropEffectlessStoresCondition.java
@@ -7,13 +7,13 @@
 import de.uka.ilkd.key.ldt.HeapLDT;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermServices;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.TermSV;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.op.Function;
 import org.key_project.util.collection.DefaultImmutableSet;
 import org.key_project.util.collection.ImmutableSet;
@@ -68,7 +68,8 @@ private static Term dropEffectlessStores(Term t, Services services) {
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         Term hInst = (Term) svInst.getInstantiation(h);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumConstantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumConstantCondition.java
index b91bf9833d2..89f301379fb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumConstantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumConstantCondition.java
@@ -9,11 +9,12 @@
 import de.uka.ilkd.key.java.reference.FieldReference;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * ensures that the given instantiation for the schemavariable denotes a constant of an enum type.
@@ -36,7 +37,7 @@ public EnumConstantCondition(SchemaVariable reference) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
 
         if (var == reference) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumTypeCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumTypeCondition.java
index 49e3c00e918..cfd28e10638 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumTypeCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EnumTypeCondition.java
@@ -6,11 +6,11 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.java.declaration.EnumClassDeclaration;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 import org.slf4j.Logger;
@@ -41,7 +41,7 @@ public EnumTypeCondition(TypeResolver resolver, boolean negated) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
 
         if (!resolver.isComplete(var, candidate, svInst, services)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EqualUniqueCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EqualUniqueCondition.java
index c3d59761404..12ebba29f5a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EqualUniqueCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/EqualUniqueCondition.java
@@ -12,6 +12,7 @@
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.op.Function;
 
 
@@ -46,7 +47,8 @@ private static Term equalUnique(Term t1, Term t2, TermServices services) {
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         Term tInst = (Term) svInst.getInstantiation(t);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FieldTypeToSortCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FieldTypeToSortCondition.java
index eb0549b986c..6e24994aef6 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FieldTypeToSortCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FieldTypeToSortCondition.java
@@ -14,6 +14,7 @@
 import de.uka.ilkd.key.rule.inst.GenericSortCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 /**
@@ -42,7 +43,7 @@ public static boolean checkSortedSV(final OperatorSV exprOrTypeSV) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute svSubst,
+    public MatchConditions check(SchemaVariable var, SyntaxElement svSubst,
             MatchConditions matchCond, Services services) {
 
         if (var != exprOrTypeSV) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FinalReferenceCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FinalReferenceCondition.java
index 0ef0eb93abf..5843abad72e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FinalReferenceCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FinalReferenceCondition.java
@@ -8,11 +8,12 @@
 import de.uka.ilkd.key.java.reference.FieldReference;
 import de.uka.ilkd.key.logic.op.ProgramConstant;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * ensures that the given instantiation for the schema variable denotes a final field
@@ -34,7 +35,7 @@ public FinalReferenceCondition(SchemaVariable reference, boolean negation) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
 
         if (var == reference) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FreeLabelInVariableCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FreeLabelInVariableCondition.java
index a143fc73812..4af726b1533 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FreeLabelInVariableCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/FreeLabelInVariableCondition.java
@@ -7,11 +7,12 @@
 import de.uka.ilkd.key.java.ProgramElement;
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.visitor.FreeLabelFinder;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 public final class FreeLabelInVariableCondition extends VariableConditionAdapter {
 
@@ -29,7 +30,7 @@ public FreeLabelInVariableCondition(SchemaVariable label, SchemaVariable stateme
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         Label prgLabel = null;
         ProgramElement program = null;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/HasLoopInvariantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/HasLoopInvariantCondition.java
index 91d31ef7b6d..dcade88a885 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/HasLoopInvariantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/HasLoopInvariantCondition.java
@@ -15,7 +15,6 @@
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.logic.op.Modality;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
@@ -23,6 +22,8 @@
 import de.uka.ilkd.key.speclang.LoopSpecification;
 import de.uka.ilkd.key.util.MiscTools;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Checks whether a loop has an invariant (either normal or "free").
  *
@@ -38,7 +39,7 @@ public HasLoopInvariantCondition(ProgramSV loopStmtSV, SchemaVariable modalitySV
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/InStrictFp.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/InStrictFp.java
index e71205389db..9f69ae63bfc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/InStrictFp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/InStrictFp.java
@@ -8,11 +8,12 @@
 import de.uka.ilkd.key.java.declaration.ClassDeclaration;
 import de.uka.ilkd.key.java.reference.ExecutionContext;
 import de.uka.ilkd.key.logic.op.IProgramMethod;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * This variable condition checks if a context is affected by the strictfp modifier
@@ -30,7 +31,7 @@ public boolean isNegated() {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
 
         ExecutionContext ec = instMap.getExecutionContext();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsLabeledCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsLabeledCondition.java
index 5dfb2263f6e..3cef0e6b48e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsLabeledCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsLabeledCondition.java
@@ -11,12 +11,13 @@
 import de.uka.ilkd.key.java.statement.LabeledStatement;
 import de.uka.ilkd.key.logic.ProgramPrefix;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Checks whether the given statement is labeled, i.e., actual a LabeledStatement. This information
  * is obtained from the program prefix.
@@ -33,7 +34,7 @@ public IsLabeledCondition(ProgramSV stmtSV, boolean negated) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable sv, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable sv, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsThisReference.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsThisReference.java
index a294b1f669d..11f330b6f5b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsThisReference.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/IsThisReference.java
@@ -6,13 +6,13 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.reference.ThisReference;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ProgramSVSort;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
 import org.key_project.logic.ParsableVariable;
+import org.key_project.logic.SyntaxElement;
 
 
 /**
@@ -36,7 +36,7 @@ public boolean isNegated() {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         if (var != this.var) {
             return true;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/JavaTypeToSortCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/JavaTypeToSortCondition.java
index da44d2c07fd..70490a2ce19 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/JavaTypeToSortCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/JavaTypeToSortCondition.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.java.reference.TypeReference;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.OperatorSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ArraySort;
 import de.uka.ilkd.key.logic.sort.GenericSort;
@@ -20,6 +19,7 @@
 import de.uka.ilkd.key.rule.inst.SortException;
 import de.uka.ilkd.key.util.Debug;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -55,7 +55,7 @@ public static boolean checkSortedSV(final OperatorSV exprOrTypeSV) {
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute svSubst,
+    public MatchConditions check(SchemaVariable var, SyntaxElement svSubst,
             MatchConditions matchCond, Services services) {
         if (var != exprOrTypeSV) {
             return matchCond;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LocalVariableCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LocalVariableCondition.java
index 5d460646591..892319029db 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LocalVariableCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LocalVariableCondition.java
@@ -7,11 +7,12 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.op.ProgramSV;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Ensures the given ProgramElement denotes a local variable
  */
@@ -30,7 +31,7 @@ public LocalVariableCondition(SchemaVariable var, boolean neg) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
 
         if (var != this.var) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopFreeInvariantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopFreeInvariantCondition.java
index 69989310270..0b1a44ebd34 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopFreeInvariantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopFreeInvariantCondition.java
@@ -16,7 +16,6 @@
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.logic.op.Modality;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
@@ -24,6 +23,8 @@
 import de.uka.ilkd.key.speclang.LoopSpecification;
 import de.uka.ilkd.key.util.MiscTools;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Extracts the free loop invariants for the given loop term. Free invariants are only assumed, but
  * not proven (like an axiom).
@@ -43,7 +44,7 @@ public LoopFreeInvariantCondition(ProgramSV loopStmtSV, SchemaVariable modalityS
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
         final TermBuilder tb = services.getTermBuilder();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopInvariantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopInvariantCondition.java
index 95b261845ce..7fa589f3e82 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopInvariantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopInvariantCondition.java
@@ -16,7 +16,6 @@
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.logic.op.Modality;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
@@ -24,6 +23,8 @@
 import de.uka.ilkd.key.speclang.LoopSpecification;
 import de.uka.ilkd.key.util.MiscTools;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Extracts the loop invariants for a loop term (for all applicable heap contexts).
  *
@@ -42,7 +43,7 @@ public LoopInvariantCondition(ProgramSV loopStmtSV, SchemaVariable modalitySV,
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
         final TermBuilder tb = services.getTermBuilder();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopVariantCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopVariantCondition.java
index 918a37afcbb..7921bc7b80f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopVariantCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/LoopVariantCondition.java
@@ -7,13 +7,14 @@
 import de.uka.ilkd.key.java.statement.LoopStatement;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 import de.uka.ilkd.key.speclang.LoopSpecification;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Extracts the variant for a loop term.
  *
@@ -29,7 +30,7 @@ public LoopVariantCondition(ProgramSV loopStmtSV, SchemaVariable variantSV) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MayExpandMethodCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MayExpandMethodCondition.java
index 3be1356bd16..6ff5aa9edf6 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MayExpandMethodCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MayExpandMethodCondition.java
@@ -17,11 +17,11 @@
 import de.uka.ilkd.key.java.reference.MethodReference;
 import de.uka.ilkd.key.java.reference.ReferencePrefix;
 import de.uka.ilkd.key.logic.op.IProgramMethod;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 
 
@@ -111,7 +111,7 @@ private static ImmutableArray<Expression> toExpArray(
 
     @SuppressWarnings("unchecked")
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
         Map<String, String> tacletOptions =
             services.getProof().getSettings().getChoiceSettings().getDefaultChoices();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MetaDisjointCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MetaDisjointCondition.java
index 58f2f5e8ef4..a657c581069 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MetaDisjointCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/MetaDisjointCondition.java
@@ -10,6 +10,7 @@
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.op.Function;
 import org.key_project.util.collection.DefaultImmutableSet;
 import org.key_project.util.collection.ImmutableSet;
@@ -66,7 +67,7 @@ private static boolean clearlyDisjoint(Term t1, Term t2, Services services) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
         final Term s1Inst = (Term) svInst.getInstantiation(var1);
         final Term s2Inst = (Term) svInst.getInstantiation(var2);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ModelFieldCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ModelFieldCondition.java
index 84b479a3a64..cfcc8aa1240 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ModelFieldCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ModelFieldCondition.java
@@ -20,11 +20,12 @@
 import de.uka.ilkd.key.java.reference.FieldReference;
 import de.uka.ilkd.key.logic.op.ProgramConstant;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * This variable condition checks if the instantiation of a schemavariable (of
  * type Field) refers to a Java field declared as "model".
@@ -47,7 +48,7 @@ public ModelFieldCondition(SchemaVariable field, boolean negated) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst,
+    public boolean check(SchemaVariable var, SyntaxElement subst,
             SVInstantiations instMap, Services services) {
 
         if (var == field) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/NewJumpLabelCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/NewJumpLabelCondition.java
index 063b580d813..4823f007a09 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/NewJumpLabelCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/NewJumpLabelCondition.java
@@ -12,7 +12,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.visitor.LabelCollector;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ProgramSVSort;
 import de.uka.ilkd.key.rule.MatchConditions;
@@ -20,6 +19,7 @@
 import de.uka.ilkd.key.rule.inst.InstantiationEntry;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableMapEntry;
 
 /**
@@ -41,11 +41,11 @@ public NewJumpLabelCondition(SchemaVariable sv) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         if (var != labelSV && matchCond.getInstantiations().isInstantiated(labelSV)) {
             var = labelSV;
-            instCandidate = (SVSubstitute) matchCond.getInstantiations().getInstantiation(labelSV);
+            instCandidate = (SyntaxElement) matchCond.getInstantiations().getInstantiation(labelSV);
         }
 
         if (var == labelSV) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ObserverCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ObserverCondition.java
index 88695c74bd0..8c877c2cc6c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ObserverCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/ObserverCondition.java
@@ -7,13 +7,14 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.IObserverFunction;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.TermSV;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 public final class ObserverCondition implements VariableCondition {
 
@@ -28,7 +29,8 @@ public ObserverCondition(TermSV obs, TermSV heap) {
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         final Term obsInst = (Term) svInst.getInstantiation(obs);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SameObserverCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SameObserverCondition.java
index 52287cf0a6f..2249534b53e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SameObserverCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SameObserverCondition.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.IObserverFunction;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.UseDependencyContractRule;
@@ -17,6 +16,7 @@
 import de.uka.ilkd.key.speclang.Contract;
 
 import org.key_project.logic.ParsableVariable;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableSet;
 
 /**
@@ -70,7 +70,8 @@ public SameObserverCondition(ParsableVariable schema1, ParsableVariable schema2)
 
     // explanation see class javadoc.
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
         final Term term1 = (Term) svInst.getInstantiation(schema1);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SimplifyIfThenElseUpdateCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SimplifyIfThenElseUpdateCondition.java
index 980911205ec..7b64f04a5c5 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SimplifyIfThenElseUpdateCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SimplifyIfThenElseUpdateCondition.java
@@ -17,6 +17,7 @@
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
 import org.key_project.logic.Named;
+import org.key_project.logic.SyntaxElement;
 
 public class SimplifyIfThenElseUpdateCondition implements VariableCondition {
 
@@ -151,7 +152,8 @@ private Term simplify(Term phi, Term u1, Term u2, Term t, TermServices services)
 
 
     @Override
-    public MatchConditions check(SchemaVariable var, SVSubstitute instCandidate, MatchConditions mc,
+    public MatchConditions check(SchemaVariable var, SyntaxElement instCandidate,
+            MatchConditions mc,
             Services services) {
         SVInstantiations svInst = mc.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticFieldCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticFieldCondition.java
index 2d942802bf8..f850a1d42be 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticFieldCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticFieldCondition.java
@@ -10,6 +10,8 @@
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * This variable condition checks if the instantiation of a schemavariable (of type Field) refers to
  * a Java field declared as "static".
@@ -31,7 +33,7 @@ public StaticFieldCondition(SchemaVariable field, boolean negated) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         final Object o = instMap.getInstantiation(field);
         if (!(o instanceof Term f)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticMethodCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticMethodCondition.java
index 2ce44dab8b6..10524eba651 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticMethodCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticMethodCondition.java
@@ -13,12 +13,12 @@
 import de.uka.ilkd.key.java.reference.ReferencePrefix;
 import de.uka.ilkd.key.logic.op.IProgramMethod;
 import de.uka.ilkd.key.logic.op.LocationVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.NullSort;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 
 
@@ -58,7 +58,7 @@ private static ImmutableArray<Expression> toExpArray(
 
     @SuppressWarnings("unchecked")
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
 
         ReferencePrefix rp = (ReferencePrefix) svInst.getInstantiation(caller);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticReferenceCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticReferenceCondition.java
index c3ce83b2aa2..332bba35df2 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticReferenceCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StaticReferenceCondition.java
@@ -8,11 +8,12 @@
 import de.uka.ilkd.key.java.reference.FieldReference;
 import de.uka.ilkd.key.logic.op.ProgramConstant;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 
 /**
  * ensures that the given instantiation for the schemavariable denotes a static field
@@ -34,7 +35,7 @@ public StaticReferenceCondition(SchemaVariable reference, boolean negation) {
 
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
 
         if (var == reference) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreStmtInCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreStmtInCondition.java
index 74f87909a8f..a92a20bdb21 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreStmtInCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreStmtInCondition.java
@@ -9,13 +9,14 @@
 import de.uka.ilkd.key.logic.JavaBlock;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.ProgramSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.LightweightSyntacticalReplaceVisitor;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Stores the given {@link Statement}, after substitution of {@link SchemaVariable}s, into the given
  * {@link ProgramSV} for later use in other conditions and transformers. The arguments are a
@@ -37,7 +38,7 @@ public StoreStmtInCondition(ProgramSV resultVarSV, Term term) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable sv, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable sv, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreTermInCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreTermInCondition.java
index a155d62dc1c..6b6e31e5b4e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreTermInCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/StoreTermInCondition.java
@@ -5,13 +5,14 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Term;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.LightweightSyntacticalReplaceVisitor;
 import de.uka.ilkd.key.rule.MatchConditions;
 import de.uka.ilkd.key.rule.VariableCondition;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * Stores the given {@link Term}, after substitution of {@link SchemaVariable}s, into the given
  * {@link SchemaVariable} for later use in other conditions and transformers.
@@ -28,7 +29,7 @@ public StoreTermInCondition(SchemaVariable resultVarSV, Term term) {
     }
 
     @Override
-    public MatchConditions check(SchemaVariable sv, SVSubstitute instCandidate,
+    public MatchConditions check(SchemaVariable sv, SyntaxElement instCandidate,
             MatchConditions matchCond, Services services) {
         final SVInstantiations svInst = matchCond.getInstantiations();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SubFormulaCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SubFormulaCondition.java
index 7787df797dd..2ac0c4428a2 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SubFormulaCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/SubFormulaCondition.java
@@ -7,11 +7,12 @@
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.FormulaSV;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
+
 /**
  * This variable condition checks if an instantiation for a formula has sub formulas which are
  * formulas. It returns false for an arity equal to zero or no sub formulas. This is needed to
@@ -32,7 +33,7 @@ public SubFormulaCondition(FormulaSV a, boolean negated) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         if (!(var instanceof FormulaSV) || var != this.a) {
             return false;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TermLabelCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TermLabelCondition.java
index 1f29050176e..6bccef558d5 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TermLabelCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TermLabelCondition.java
@@ -5,13 +5,13 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.label.TermLabel;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.TermLabelSV;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 
 /**
@@ -33,7 +33,7 @@ public TermLabelCondition(TermLabelSV l, String t, boolean negated) {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute instCandidate, SVInstantiations instMap,
+    public boolean check(SchemaVariable var, SyntaxElement instCandidate, SVInstantiations instMap,
             Services services) {
         assert instMap.getInstantiation(l) instanceof ImmutableArray<?>;
         ImmutableArray<?> tInsts = (ImmutableArray<?>) instMap.getInstantiation(l);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeComparisonCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeComparisonCondition.java
index 6d49717e70d..3c28d087433 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeComparisonCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeComparisonCondition.java
@@ -12,7 +12,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.java.declaration.InterfaceDeclaration;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.ArraySort;
 import de.uka.ilkd.key.logic.sort.NullSort;
@@ -20,6 +19,7 @@
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -72,7 +72,7 @@ public Mode getMode() {
     }
 
     @Override
-    public boolean check(SchemaVariable var, SVSubstitute subst, SVInstantiations svInst,
+    public boolean check(SchemaVariable var, SyntaxElement subst, SVInstantiations svInst,
             Services services) {
 
         if (!fst.isComplete(var, subst, svInst, services)
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeCondition.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeCondition.java
index febb37096b7..7f041a3731a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeCondition.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeCondition.java
@@ -5,13 +5,13 @@
 
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.NullSort;
 import de.uka.ilkd.key.logic.sort.ProxySort;
 import de.uka.ilkd.key.rule.VariableConditionAdapter;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 
@@ -55,7 +55,7 @@ public boolean getNonNull() {
 
 
     @Override
-    public boolean check(SchemaVariable p_var, SVSubstitute candidate, SVInstantiations svInst,
+    public boolean check(SchemaVariable p_var, SyntaxElement candidate, SVInstantiations svInst,
             Services services) {
 
         if (!resolver.isComplete(p_var, candidate, svInst, services)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeResolver.java b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeResolver.java
index f7dd7617ab8..f313becfd78 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeResolver.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/conditions/TypeResolver.java
@@ -11,13 +11,13 @@
 import de.uka.ilkd.key.logic.op.IObserverFunction;
 import de.uka.ilkd.key.logic.op.Operator;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.sort.GenericSort;
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 import de.uka.ilkd.key.util.Debug;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.op.Function;
 import org.key_project.logic.sort.Sort;
 
@@ -50,10 +50,10 @@ public static TypeResolver createNonGenericSortResolver(Sort s) {
     }
 
 
-    public abstract boolean isComplete(SchemaVariable sv, SVSubstitute instCandidate,
+    public abstract boolean isComplete(SchemaVariable sv, SyntaxElement instCandidate,
             SVInstantiations instMap, TermServices services);
 
-    public abstract Sort resolveSort(SchemaVariable sv, SVSubstitute instCandidate,
+    public abstract Sort resolveSort(SchemaVariable sv, SyntaxElement instCandidate,
             SVInstantiations instMap, Services services);
 
 
@@ -74,13 +74,13 @@ public GenericSort getGenericSort() {
         }
 
         @Override
-        public boolean isComplete(SchemaVariable sv, SVSubstitute instCandidate,
+        public boolean isComplete(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, TermServices services) {
             return instMap.getGenericSortInstantiations().getInstantiation(gs) != null;
         }
 
         @Override
-        public Sort resolveSort(SchemaVariable sv, SVSubstitute instCandidate,
+        public Sort resolveSort(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, Services services) {
             return instMap.getGenericSortInstantiations().getInstantiation(gs);
         }
@@ -100,13 +100,13 @@ public NonGenericSortResolver(Sort s) {
         }
 
         @Override
-        public boolean isComplete(SchemaVariable sv, SVSubstitute instCandidate,
+        public boolean isComplete(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, TermServices services) {
             return true;
         }
 
         @Override
-        public Sort resolveSort(SchemaVariable sv, SVSubstitute instCandidate,
+        public Sort resolveSort(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, Services services) {
             return s;
         }
@@ -130,18 +130,18 @@ public ElementTypeResolverForSV(SchemaVariable sv) {
         }
 
         @Override
-        public boolean isComplete(SchemaVariable sv, SVSubstitute instCandidate,
+        public boolean isComplete(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, TermServices services) {
             return resolveSV == sv || instMap.getInstantiation(resolveSV) != null;
         }
 
         @Override
-        public Sort resolveSort(SchemaVariable sv, SVSubstitute instCandidate,
+        public Sort resolveSort(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, Services services) {
 
             final Sort s;
 
-            final SVSubstitute inst = (SVSubstitute) (resolveSV == sv ? instCandidate
+            final SyntaxElement inst = (SyntaxElement) (resolveSV == sv ? instCandidate
                     : instMap.getInstantiation(resolveSV));
 
             if (inst instanceof ProgramVariable) {
@@ -178,18 +178,18 @@ public ContainerTypeResolver(SchemaVariable sv) {
         }
 
         @Override
-        public boolean isComplete(SchemaVariable sv, SVSubstitute instCandidate,
+        public boolean isComplete(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, TermServices services) {
 
             return sv == memberSV || instMap.getInstantiation(memberSV) != null;
         }
 
         @Override
-        public Sort resolveSort(SchemaVariable sv, SVSubstitute instCandidate,
+        public Sort resolveSort(SchemaVariable sv, SyntaxElement instCandidate,
                 SVInstantiations instMap, Services services) {
             final Sort result;
 
-            final SVSubstitute inst = (SVSubstitute) (memberSV == sv ? instCandidate
+            final SyntaxElement inst = (SyntaxElement) (memberSV == sv ? instCandidate
                     : instMap.getInstantiation(memberSV));
 
             if (inst instanceof Operator) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/AntecTacletExecutor.java b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/AntecTacletExecutor.java
index 2033daf4d37..311577b10eb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/AntecTacletExecutor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/AntecTacletExecutor.java
@@ -7,7 +7,7 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
 import de.uka.ilkd.key.logic.SequentChangeInfo;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabelState;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.rule.AntecTaclet;
@@ -60,7 +60,7 @@ matchCond, new TacletLabelHint(TacletOperation.REPLACE_AT_ANTECEDENT, replWith),
     /**
      * applies the {@code add}-expressions of taclet goal descriptions
      *
-     * @param add the {@link Sequent} with the uninstantiated {@link SequentFormula}'s to be added
+     * @param add the {@link Sequent} with the uninstantiated {@link Term}'s to be added
      *        to the goal's sequent
      * @param termLabelState The {@link TermLabelState} of the current rule application.
      * @param currentSequent the {@link SequentChangeInfo} which is the current (intermediate)
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/FindTacletExecutor.java b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/FindTacletExecutor.java
index 2866c6d0e12..03c1c6b5c33 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/FindTacletExecutor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/FindTacletExecutor.java
@@ -52,7 +52,7 @@ protected abstract void applyReplacewith(TacletGoalTemplate gt, TermLabelState t
     /**
      * applies the {@code add}-expressions of taclet goal descriptions
      *
-     * @param add the {@link Sequent} with the uninstantiated {@link SequentFormula}'s to be added
+     * @param add the {@link Sequent} with the uninstantiated {@link Term}'s to be added
      *        to the goal's sequent
      * @param termLabelState The {@link TermLabelState} of the current rule application.
      * @param currentSequent the {@link SequentChangeInfo} which is the current (intermediate)
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/RewriteTacletExecutor.java b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/RewriteTacletExecutor.java
index 0ea5c2ecb63..793053ae10a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/RewriteTacletExecutor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/RewriteTacletExecutor.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
 import de.uka.ilkd.key.logic.SequentChangeInfo;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabelManager;
 import de.uka.ilkd.key.logic.label.TermLabelState;
@@ -64,26 +63,26 @@ private Term replace(Term term, Term with, TermLabelState termLabelState,
     }
 
 
-    private SequentFormula applyReplacewithHelper(Goal goal, TermLabelState termLabelState,
+    private Term applyReplacewithHelper(Goal goal, TermLabelState termLabelState,
             RewriteTacletGoalTemplate gt, PosInOccurrence posOfFind, Services services,
             MatchConditions matchCond, RuleApp ruleApp) {
-        final Term term = posOfFind.sequentFormula().formula();
+        final Term term = posOfFind.sequentLevelFormula();
         final IntIterator it = posOfFind.posInTerm().iterator();
         final Term rwTemplate = gt.replaceWith();
 
         Term formula = replace(term, rwTemplate, termLabelState, new TacletLabelHint(rwTemplate),
             posOfFind, it, matchCond, term.sort(), goal, services, ruleApp);
-        formula = TermLabelManager.refactorSequentFormula(termLabelState, services, formula,
+        formula = TermLabelManager.refactorTerm(termLabelState, services, formula,
             posOfFind, taclet, goal, null, rwTemplate);
         if (term == formula) {
-            return posOfFind.sequentFormula();
+            return posOfFind.sequentLevelFormula();
         } else {
-            return new SequentFormula(formula);
+            return formula;
         }
     }
 
 
-    public SequentFormula getRewriteResult(Goal goal, TermLabelState termLabelState,
+    public Term getRewriteResult(Goal goal, TermLabelState termLabelState,
             Services services, TacletApp app) {
         assert taclet.goalTemplates().size() == 1;
         assert taclet.goalTemplates().head().sequent().isEmpty();
@@ -104,19 +103,19 @@ protected void applyReplacewith(TacletGoalTemplate gt, TermLabelState termLabelS
             SequentChangeInfo currentSequent, PosInOccurrence posOfFind, MatchConditions matchCond,
             Goal goal, RuleApp ruleApp, Services services) {
         if (gt instanceof RewriteTacletGoalTemplate) {
-            final SequentFormula cf = applyReplacewithHelper(goal, termLabelState,
+            final Term cf = applyReplacewithHelper(goal, termLabelState,
                 (RewriteTacletGoalTemplate) gt, posOfFind, services, matchCond, ruleApp);
             currentSequent.combine(currentSequent.sequent().changeFormula(cf, posOfFind));
         } else {
             // Then there was no replacewith...
             // This is strange in a RewriteTaclet, but who knows...
             // However, term label refactorings have to be performed.
-            final Term oldFormula = posOfFind.sequentFormula().formula();
-            final Term newFormula = TermLabelManager.refactorSequentFormula(termLabelState,
+            final Term oldFormula = posOfFind.sequentLevelFormula();
+            final Term newFormula = TermLabelManager.refactorTerm(termLabelState,
                 services, oldFormula, posOfFind, taclet, goal, null, null);
             if (oldFormula != newFormula) {
                 currentSequent.combine(currentSequent.sequent()
-                        .changeFormula(new SequentFormula(newFormula), posOfFind));
+                        .changeFormula(newFormula, posOfFind));
             }
         }
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/TacletExecutor.java b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/TacletExecutor.java
index e9ca72c22c6..c49c334b9bb 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/TacletExecutor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/executor/javadl/TacletExecutor.java
@@ -13,7 +13,6 @@
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.SemisequentChangeInfo;
 import de.uka.ilkd.key.logic.SequentChangeInfo;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.VariableNamer;
@@ -89,17 +88,17 @@ protected Term syntacticalReplace(Term term, TermLabelState termLabelState,
     }
 
     /**
-     * adds SequentFormula to antecedent or succedent depending on position information or the
+     * adds Term to antecedent or succedent depending on position information or the
      * boolean antec contrary to "addToPos" frm will not be modified
      *
-     * @param frm the {@link SequentFormula} that should be added
+     * @param frm the {@link Term} that should be added
      * @param currentSequent the {@link SequentChangeInfo} which is the current (intermediate)
      *        result of applying the taclet
      * @param pos the {@link PosInOccurrence} describing the place in the sequent
      * @param antec boolean true(false) if elements have to be added to the antecedent(succedent)
      *        (only looked at if pos == null)
      */
-    private void addToPosWithoutInst(SequentFormula frm, SequentChangeInfo currentSequent,
+    private void addToPosWithoutInst(Term frm, SequentChangeInfo currentSequent,
             PosInOccurrence pos, boolean antec) {
         if (pos != null) {
             currentSequent.combine(currentSequent.sequent().addFormula(frm, pos));
@@ -116,23 +115,23 @@ private void addToPosWithoutInst(SequentFormula frm, SequentChangeInfo currentSe
      * instantiated formula) is returned.
      *
      * @param termLabelState The {@link TermLabelState} of the current rule application.
-     * @param schemaFormula the SequentFormula to be instantiated
+     * @param schemaFormula the Term to be instantiated
      * @param services the Services object carrying ja related information
      * @param matchCond the MatchConditions object with the instantiations of the schemavariables,
      *        constraints etc.
      * @param applicationPosInOccurrence The {@link PosInOccurrence} of the {@link Term} which is
      *        rewritten
      * @param labelHint The hint used to maintain {@link TermLabel}s.
-     * @return the as far as possible instantiated SequentFormula
+     * @return the as far as possible instantiated Term
      */
-    private SequentFormula instantiateReplacement(TermLabelState termLabelState,
-            SequentFormula schemaFormula, Services services, MatchConditions matchCond,
+    private Term instantiateReplacement(TermLabelState termLabelState,
+            Term schemaFormula, Services services, MatchConditions matchCond,
             PosInOccurrence applicationPosInOccurrence, TacletLabelHint labelHint, Goal goal,
             RuleApp tacletApp) {
 
         final SVInstantiations svInst = matchCond.getInstantiations();
 
-        Term instantiatedFormula = syntacticalReplace(schemaFormula.formula(), termLabelState,
+        Term instantiatedFormula = syntacticalReplace(schemaFormula, termLabelState,
             new TacletLabelHint(labelHint, schemaFormula), applicationPosInOccurrence, matchCond,
             goal, tacletApp, services);
 
@@ -141,7 +140,7 @@ private SequentFormula instantiateReplacement(TermLabelState termLabelState,
                     .applyUpdatePairsSequential(svInst.getUpdateContext(), instantiatedFormula);
         }
 
-        return new SequentFormula(instantiatedFormula);
+        return instantiatedFormula;
     }
 
     /**
@@ -157,14 +156,14 @@ private SequentFormula instantiateReplacement(TermLabelState termLabelState,
      * @param services the Services
      * @return the instantiated formulas of the semisequent as list
      */
-    protected ImmutableList<SequentFormula> instantiateSemisequent(Semisequent semi,
+    protected ImmutableList<Term> instantiateSemisequent(Semisequent semi,
             TermLabelState termLabelState, TacletLabelHint labelHint,
             PosInOccurrence applicationPosInOccurrence, MatchConditions matchCond, Goal goal,
             RuleApp tacletApp, Services services) {
 
-        ImmutableList<SequentFormula> replacements = ImmutableSLList.nil();
+        ImmutableList<Term> replacements = ImmutableSLList.nil();
 
-        for (SequentFormula sf : semi) {
+        for (Term sf : semi) {
             replacements = replacements.append(instantiateReplacement(termLabelState, sf, services,
                 matchCond, applicationPosInOccurrence, labelHint, goal, tacletApp));
         }
@@ -191,7 +190,7 @@ protected ImmutableList<SequentFormula> instantiateSemisequent(Semisequent semi,
     protected void replaceAtPos(Semisequent semi, TermLabelState termLabelState,
             SequentChangeInfo currentSequent, PosInOccurrence pos, MatchConditions matchCond,
             TacletLabelHint labelHint, Goal goal, RuleApp ruleApp, Services services) {
-        final ImmutableList<SequentFormula> replacements = instantiateSemisequent(semi,
+        final ImmutableList<Term> replacements = instantiateSemisequent(semi,
             termLabelState, labelHint, pos, matchCond, goal, ruleApp, services);
         currentSequent.combine(currentSequent.sequent().changeFormula(replacements, pos));
     }
@@ -219,7 +218,7 @@ private void addToPos(Semisequent semi, TermLabelState termLabelState,
             PosInOccurrence applicationPosInOccurrence, boolean antec, TacletLabelHint labelHint,
             MatchConditions matchCond, Goal goal, Services services, RuleApp tacletApp) {
 
-        final ImmutableList<SequentFormula> replacements =
+        final ImmutableList<Term> replacements =
             instantiateSemisequent(semi, termLabelState, labelHint, applicationPosInOccurrence,
                 matchCond, goal, tacletApp, services);
         if (pos != null) {
@@ -230,7 +229,7 @@ private void addToPos(Semisequent semi, TermLabelState termLabelState,
     }
 
     /**
-     * adds SequentFormula to antecedent depending on position information (if none is handed over
+     * adds Term to antecedent depending on position information (if none is handed over
      * it is added at the head of the antecedent). Of course it has to be ensured that the position
      * information describes one occurrence in the antecedent of the sequent.
      *
@@ -256,7 +255,7 @@ protected void addToAntec(Semisequent semi, TermLabelState termLabelState,
     }
 
     /**
-     * adds SequentFormula to succedent depending on position information (if none is handed over it
+     * adds Term to succedent depending on position information (if none is handed over it
      * is added at the head of the succedent). Of course it has to be ensured that the position
      * information describes one occurrence in the succedent of the sequent.
      *
@@ -419,7 +418,7 @@ protected ImmutableList<SequentChangeInfo> checkIfGoals(Goal p_goal,
             for (final IfFormulaInstantiation inst : p_list) {
                 if (!(inst instanceof IfFormulaInstSeq)) {
                     // build the if obligation formula
-                    ifPart = inst.getConstrainedFormula().formula();
+                    ifPart = inst.getConstrainedFormula();
 
                     // negate formulas of the if-succedent
                     final TermServices services = p_goal.proof().getServices();
@@ -470,7 +469,7 @@ protected ImmutableList<SequentChangeInfo> checkIfGoals(Goal p_goal,
                 seq = itNewGoalSequents.next();
             }
 
-            addToPosWithoutInst(new SequentFormula(ifObl), seq, null, false);
+            addToPosWithoutInst(ifObl, seq, null, false);
         }
 
         return res;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/inst/ProgramList.java b/key.core/src/main/java/de/uka/ilkd/key/rule/inst/ProgramList.java
index 408e0b82b92..e5f38ccbc06 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/inst/ProgramList.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/inst/ProgramList.java
@@ -4,11 +4,11 @@
 package de.uka.ilkd.key.rule.inst;
 
 import de.uka.ilkd.key.java.ProgramElement;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 
-public class ProgramList implements SVSubstitute {
+public class ProgramList implements SyntaxElement {
 
     private final ImmutableArray<ProgramElement> list;
 
@@ -34,4 +34,14 @@ public int hashCode() {
         return list.hashCode();
     }
 
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        return list.get(n);
+    }
+
+    @Override
+    public int getChildCount() {
+        return list.size();
+    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/label/OriginTermLabelRefactoring.java b/key.core/src/main/java/de/uka/ilkd/key/rule/label/OriginTermLabelRefactoring.java
index 3fc16ba6428..9b964549cfb 100755
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/label/OriginTermLabelRefactoring.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/label/OriginTermLabelRefactoring.java
@@ -129,8 +129,8 @@ private Set<Origin> collectSubtermOrigins(Term term, Set<Origin> result) {
         TermLabel label = term.getLabel(OriginTermLabel.NAME);
 
         if (label != null) {
-            result.add((Origin) label.getChild(0));
-            result.addAll((Set<Origin>) label.getChild(1));
+            result.add((Origin) label.getTLChild(0));
+            result.addAll((Set<Origin>) label.getTLChild(1));
         }
 
         ImmutableArray<Term> subterms = term.subs();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelMerger.java b/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelMerger.java
index dd2fa9e20fb..a1e0d567191 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelMerger.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelMerger.java
@@ -7,7 +7,6 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabel;
 import de.uka.ilkd.key.logic.label.TermLabelManager;
@@ -16,7 +15,7 @@
  * <p>
  * A {@link TermLabelMerger} is used by
  * {@link TermLabelManager#mergeLabels(Services, de.uka.ilkd.key.logic.SequentChangeInfo)} to merge
- * {@link TermLabel}s in case a {@link SequentFormula} was rejected to be added to the resulting
+ * {@link TermLabel}s in case a {@link Term} was rejected to be added to the resulting
  * {@link Sequent}.
  * </p>
  * <p>
@@ -32,18 +31,18 @@ public interface TermLabelMerger {
     /**
      * Merges the existing and the rejected {@link TermLabel} by updating the merged {@link List}.
      *
-     * @param existingSF The existing {@link SequentFormula}.
-     * @param existingTerm The {@link Term} of the existing {@link SequentFormula}.
+     * @param existingSF The existing {@link Term}.
+     * @param existingTerm The {@link Term} of the existing {@link Term}.
      * @param existingLabel The existing {@link TermLabel} if available or {@code null} otherwise.
-     * @param rejectedSF The rejected {@link SequentFormula}.
-     * @param rejectedTerm The {@link Term} of the rejected {@link SequentFormula}.
+     * @param rejectedSF The rejected {@link Term}.
+     * @param rejectedTerm The {@link Term} of the rejected {@link Term}.
      * @param rejectedLabel The rejected {@link TermLabel}.
      * @param mergedLabels The {@link List} with new {@link TermLabel}s which will be visible in the
      *        resulting {@link Sequent}.
      * @return {@code true} if the {@link List} of {@link TermLabel} was modified and {@code false}
      *         otherwise.
      */
-    boolean mergeLabels(SequentFormula existingSF, Term existingTerm,
-            TermLabel existingLabel, SequentFormula rejectedSF, Term rejectedTerm,
+    boolean mergeLabels(Term existingSF, Term existingTerm,
+            TermLabel existingLabel, Term rejectedSF, Term rejectedTerm,
             TermLabel rejectedLabel, List<TermLabel> mergedLabels);
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelRefactoring.java b/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelRefactoring.java
index 85fed275c36..606cc7262a0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelRefactoring.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/label/TermLabelRefactoring.java
@@ -6,7 +6,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.label.LabelCollection;
@@ -161,7 +160,7 @@ enum RefactoringScope {
         APPLICATION_CHILDREN_AND_GRANDCHILDREN_SUBTREE,
 
         /**
-         * Refactor the {@link SequentFormula} on which the rule is applied.
+         * Refactor the {@link Term} on which the rule is applied.
          */
         APPLICATION_CHILDREN_AND_GRANDCHILDREN_SUBTREE_AND_PARENTS,
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/match/vm/VMTacletMatcher.java b/key.core/src/main/java/de/uka/ilkd/key/rule/match/vm/VMTacletMatcher.java
index ef2d5270d82..409bb2008e9 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/match/vm/VMTacletMatcher.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/match/vm/VMTacletMatcher.java
@@ -9,11 +9,9 @@
 import de.uka.ilkd.key.java.ProgramElement;
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.Operator;
 import de.uka.ilkd.key.logic.op.QuantifiableVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
 import de.uka.ilkd.key.rule.FindTaclet;
@@ -30,6 +28,7 @@
 import de.uka.ilkd.key.rule.match.TacletMatcherKit;
 import de.uka.ilkd.key.rule.match.vm.instructions.MatchSchemaVariableInstruction;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
 import org.key_project.util.collection.ImmutableSet;
@@ -101,8 +100,8 @@ public VMTacletMatcher(Taclet taclet) {
             findMatchProgram = TacletMatchProgram.EMPTY_PROGRAM;
         }
 
-        for (SequentFormula sf : assumesSequent) {
-            assumesMatchPrograms.put(sf.formula(), TacletMatchProgram.createProgram(sf.formula()));
+        for (Term sf : assumesSequent) {
+            assumesMatchPrograms.put(sf, TacletMatchProgram.createProgram(sf));
         }
     }
 
@@ -132,7 +131,7 @@ public final IfMatchResult matchIf(Iterable<IfFormulaInstantiation> p_toMatch,
         }
 
         for (var cf : p_toMatch) {
-            Term formula = cf.getConstrainedFormula().formula();
+            Term formula = cf.getConstrainedFormula();
 
             if (updateContextPresent) {
                 formula = matchUpdateContext(context, formula);
@@ -189,8 +188,8 @@ private Term matchUpdateContext(ImmutableList<UpdateLabelPair> context, Term for
     public final MatchConditions matchIf(Iterable<IfFormulaInstantiation> p_toMatch,
             MatchConditions p_matchCond, Services p_services) {
 
-        final Iterator<SequentFormula> anteIterator = assumesSequent.antecedent().iterator();
-        final Iterator<SequentFormula> succIterator = assumesSequent.succedent().iterator();
+        final Iterator<Term> anteIterator = assumesSequent.antecedent().iterator();
+        final Iterator<Term> succIterator = assumesSequent.succedent().iterator();
 
         ImmutableList<MatchConditions> newMC;
 
@@ -204,13 +203,13 @@ public final MatchConditions matchIf(Iterable<IfFormulaInstantiation> p_toMatch,
                             // Default: just take the next ante formula, else succ formula
                             && anteIterator.hasNext();
 
-            Iterator<SequentFormula> itIfSequent = candidateInAntec ? anteIterator : succIterator;
+            Iterator<Term> itIfSequent = candidateInAntec ? anteIterator : succIterator;
             // Fix end
 
             assert itIfSequent.hasNext()
                     : "p_toMatch and assumes sequent must have same number of elements";
             newMC = matchIf(ImmutableSLList.<IfFormulaInstantiation>nil().prepend(candidateInst),
-                itIfSequent.next().formula(), p_matchCond, p_services).getMatchConditions();
+                itIfSequent.next(), p_matchCond, p_services).getMatchConditions();
 
             if (newMC.isEmpty()) {
                 return null;
@@ -239,8 +238,8 @@ public final MatchConditions checkConditions(MatchConditions cond, Services serv
             while (result != null && svIterator.hasNext()) {
                 final SchemaVariable sv = svIterator.next();
                 final Object o = result.getInstantiations().getInstantiation(sv);
-                if (o instanceof SVSubstitute) {
-                    result = checkVariableConditions(sv, (SVSubstitute) o, result, services);
+                if (o instanceof SyntaxElement) {
+                    result = checkVariableConditions(sv, (SyntaxElement) o, result, services);
                 }
             }
         }
@@ -279,7 +278,7 @@ private boolean varIsBound(SchemaVariable v) {
      */
     @Override
     public final MatchConditions checkVariableConditions(SchemaVariable var,
-            SVSubstitute instantiationCandidate, MatchConditions matchCond, Services services) {
+            SyntaxElement instantiationCandidate, MatchConditions matchCond, Services services) {
         if (matchCond != null) {
             if (instantiationCandidate instanceof Term term) {
                 if (!(term.op() instanceof QuantifiableVariable)) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/merge/CloseAfterMerge.java b/key.core/src/main/java/de/uka/ilkd/key/rule/merge/CloseAfterMerge.java
index 19b3b4b36e2..b3c8e4d7d63 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/merge/CloseAfterMerge.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/merge/CloseAfterMerge.java
@@ -13,7 +13,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -133,7 +132,7 @@ public void proofGoalsAdded(ProofTreeEvent e) {
                 // a closed goal when loading a proof without the GUI (e.g.
                 // in a JUnit test).
 
-                if (e.getGoals().size() == 0 && mergeNodeF.isClosed()) {
+                if (e.getGoals().isEmpty() && mergeNodeF.isClosed()) {
                     // The merged node was closed; now also close this node.
 
                     e.getSource().closeGoal(linkedGoal);
@@ -154,7 +153,7 @@ public void proofGoalsAdded(ProofTreeEvent e) {
             // Delete previous sequents
             clearSemisequent(ruleIsWeakeningGoal, true);
             clearSemisequent(ruleIsWeakeningGoal, false);
-            ruleIsWeakeningGoal.addFormula(new SequentFormula(isWeakeningForm), false, true);
+            ruleIsWeakeningGoal.addFormula(isWeakeningForm, false, true);
             TermLabelManager.refactorGoal(termLabelState, services, ruleApp.posInOccurrence(), this,
                 ruleIsWeakeningGoal, null, null);
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/merge/MergeRule.java b/key.core/src/main/java/de/uka/ilkd/key/rule/merge/MergeRule.java
index 3b83dceb151..332a94aed64 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/merge/MergeRule.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/merge/MergeRule.java
@@ -14,7 +14,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.PosInTerm;
 import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -235,13 +234,13 @@ public String toString() {
 
         // Add new antecedent (path condition)
         for (Term antecedentFormula : getConjunctiveElementsFor(resultPathCondition)) {
-            final SequentFormula newAntecedent = new SequentFormula(antecedentFormula);
+            final Term newAntecedent = antecedentFormula;
             newGoal.addFormula(newAntecedent, true, false);
         }
 
         // Add new succedent (symbolic state & program counter)
         final Term succedentFormula = tb.apply(mergedState.first, thisSEState.third);
-        final SequentFormula newSuccedent = new SequentFormula(succedentFormula);
+        final Term newSuccedent = succedentFormula;
         newGoal.addFormula(newSuccedent,
             new PosInOccurrence(newSuccedent, PosInTerm.getTopLevel(), false));
 
@@ -276,7 +275,7 @@ public String toString() {
                 clearSemisequent(sideConditionGoal, false);
                 final Term sideCondition = sideCondIt.next();
 
-                sideConditionGoal.addFormula(new SequentFormula(sideCondition),
+                sideConditionGoal.addFormula(sideCondition,
                     new PosInOccurrence(newSuccedent, PosInTerm.getTopLevel(), false));
 
                 i++;
@@ -686,7 +685,7 @@ public static ImmutableList<MergePartner> findPotentialMergePartners(Goal goal,
             if (!g.equals(goal) && !g.isLinked()) {
                 Semisequent succedent = g.sequent().succedent();
                 for (int i = 0; i < succedent.size(); i++) {
-                    final SequentFormula f = succedent.get(i);
+                    final Term f = succedent.get(i);
 
                     final PosInTerm pit = PosInTerm.getTopLevel();
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/RewriteTacletBuilderSchemaVarCollector.java b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/RewriteTacletBuilderSchemaVarCollector.java
index 0e933eec771..de0dcc617fa 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/RewriteTacletBuilderSchemaVarCollector.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/RewriteTacletBuilderSchemaVarCollector.java
@@ -7,7 +7,6 @@
 import java.util.Set;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.rule.RewriteTaclet;
@@ -86,8 +85,8 @@ public void subtreeLeft(Term subtreeRoot) {
     private Set<SchemaVariable> collectSchemaVariables(Sequent s) {
         Set<SchemaVariable> result = new LinkedHashSet<>();
 
-        for (final SequentFormula cf : s) {
-            result.addAll(collectSchemaVariables(cf.formula()));
+        for (final Term cf : s) {
+            result.addAll(collectSchemaVariables(cf));
         }
 
         return result;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletBuilder.java b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletBuilder.java
index a52fd22bfb0..724dd06fb98 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletBuilder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletBuilder.java
@@ -67,8 +67,8 @@ private static boolean containsFreeVarSV(Term t) {
     }
 
     private static boolean containsFreeVarSV(Sequent sequent) {
-        for (final SequentFormula cf : sequent) {
-            if (containsFreeVarSV(cf.formula())) {
+        for (final Term cf : sequent) {
+            if (containsFreeVarSV(cf)) {
                 return true;
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletGenerator.java
index 4f513fef8dd..59469dd9487 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletGenerator.java
@@ -52,7 +52,7 @@ public static TacletGenerator getInstance() {
 
 
     private TacletGoalTemplate createAxiomGoalTemplate(Term goalTerm) {
-        final SequentFormula axiomSf = new SequentFormula(goalTerm);
+        final Term axiomSf = goalTerm;
         final Semisequent axiomSemiSeq =
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(axiomSf).semisequent();
         final Sequent axiomSeq = Sequent.createAnteSequent(axiomSemiSeq);
@@ -146,7 +146,7 @@ public Taclet generateRelationalRepresentsTaclet(Name tacletName, Term originalA
         final TermAndBoundVarPair schemaAxiom = createSchemaTerm(originalAxiom, pvs, svs, services);
 
         // create goal template
-        SequentFormula guardedSchemaAxiom = generateGuard(kjt, target, services, selfSV, heapSVs,
+        Term guardedSchemaAxiom = generateGuard(kjt, target, services, selfSV, heapSVs,
             paramSVs, schemaAxiom.term, tacletBuilder, satisfiabilityGuard);
         final Sequent addedSeq = Sequent.createAnteSequent(
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(guardedSchemaAxiom).semisequent());
@@ -249,14 +249,14 @@ public ImmutableSet<Taclet> generateFunctionalRepresentsTaclets(Name name, Term
              */
             // ifSeq = null;
             final Term ifFormula = TB.equals(TB.var(selfSV), TB.NULL());
-            final SequentFormula ifCf = new SequentFormula(ifFormula);
+            final Term ifCf = ifFormula;
             final Semisequent ifSemiSeq =
                 Semisequent.EMPTY_SEMISEQUENT.insertFirst(ifCf).semisequent();
             ifSeq = Sequent.createSuccSequent(ifSemiSeq);
         } else {
             /* \assumes ( Sort.exactInstance(self) ==> ) */
             final Term ifFormula = TB.exactInstance(kjt.getSort(), TB.var(selfSV));
-            final SequentFormula ifCf = new SequentFormula(ifFormula);
+            final Term ifCf = ifFormula;
             final Semisequent ifSemiSeq =
                 Semisequent.EMPTY_SEMISEQUENT.insertFirst(ifCf).semisequent();
             ifSeq = Sequent.createAnteSequent(ifSemiSeq);
@@ -351,7 +351,7 @@ private void functionalRepresentsAddSatisfiabilityBranch(IObserverFunction targe
             final RewriteTacletBuilder<? extends RewriteTaclet> tacletBuilder) {
         final Term axiomSatisfiable = functionalRepresentsSatisfiability(target, services, heapSVs,
             selfSV, paramSVs, schemaRepresents, tacletBuilder);
-        SequentFormula addedCf = new SequentFormula(axiomSatisfiable);
+        Term addedCf = axiomSatisfiable;
         final Semisequent addedSemiSeq =
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(addedCf).semisequent();
         final Sequent addedSeq = Sequent.createSuccSequent(addedSemiSeq);
@@ -526,7 +526,7 @@ public ImmutableSet<Taclet> generateContractAxiomTaclets(Name name, Term origina
             pvs, svs, services);
 
         final Term addedFormula = schemaAdd.term;
-        final SequentFormula addedCf = new SequentFormula(addedFormula);
+        final Term addedCf = addedFormula;
         final Semisequent addedSemiSeq =
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(addedCf).semisequent();
         final Sequent addedSeq = Sequent.createAnteSequent(addedSemiSeq);
@@ -662,7 +662,7 @@ public ImmutableSet<Taclet> generatePartialInvTaclet(Name name, List<TermSV> hea
         result = result.union(limited.second);
 
         // create added sequent
-        final SequentFormula addedCf = new SequentFormula(limitedAxiom);
+        final Term addedCf = limitedAxiom;
         final Semisequent addedSemiSeq =
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(addedCf).semisequent();
         final Sequent addedSeq = Sequent.createAnteSequent(addedSemiSeq);
@@ -707,8 +707,8 @@ public ImmutableSet<Taclet> generatePartialInvTaclet(Name name, List<TermSV> hea
             // \assumes( self = EQ ==> EQ = null )
             final Term selfEQ = TB.equals(TB.var(selfSV), TB.var(eqSV));
             final Term eqNull = TB.equals(TB.var(eqSV), TB.NULL());
-            final SequentFormula selfEQSF = new SequentFormula(selfEQ);
-            final SequentFormula eqNullSF = new SequentFormula(eqNull);
+            final Term selfEQSF = selfEQ;
+            final Term eqNullSF = eqNull;
             final Semisequent succ =
                 Semisequent.EMPTY_SEMISEQUENT.insertFirst(selfEQSF).semisequent();
             final Semisequent ant =
@@ -718,7 +718,7 @@ public ImmutableSet<Taclet> generatePartialInvTaclet(Name name, List<TermSV> hea
         } else if (!isStatic) {
             // \assumes( ==> self = null )
             final Term selfNull = TB.equals(TB.var(selfSV), TB.NULL());
-            final SequentFormula selfNullSF = new SequentFormula(selfNull);
+            final Term selfNullSF = selfNull;
             final Semisequent succ =
                 Semisequent.EMPTY_SEMISEQUENT.insertFirst(selfNullSF).semisequent();
             final Sequent ifSeq = Sequent.createSuccSequent(succ);
@@ -930,7 +930,7 @@ private Pair<Term, ImmutableSet<Taclet>> limitTerm(Term t,
     }
 
 
-    private SequentFormula generateGuard(KeYJavaType kjt, IObserverFunction target,
+    private Term generateGuard(KeYJavaType kjt, IObserverFunction target,
             TermServices services, final OperatorSV selfSV, List<TermSV> heapSVs,
             ImmutableList<OperatorSV> paramSVs, final Term schemaAxiom,
             final RewriteTacletBuilder<? extends RewriteTaclet> tacletBuilder, boolean addGuard) {
@@ -942,7 +942,7 @@ private SequentFormula generateGuard(KeYJavaType kjt, IObserverFunction target,
                 : TB.tt();
         // assemble formula
         final Term guardedAxiom = TB.imp(TB.and(exactInstance, axiomSatisfiable), schemaAxiom);
-        final SequentFormula guardedAxiomCf = new SequentFormula(guardedAxiom);
+        final Term guardedAxiomCf = guardedAxiom;
         return guardedAxiomCf;
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletPrefixBuilder.java b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletPrefixBuilder.java
index c7574e69260..948b838fb76 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletPrefixBuilder.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/rule/tacletbuilder/TacletPrefixBuilder.java
@@ -6,7 +6,6 @@
 import java.util.Iterator;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.label.TermLabel;
 import de.uka.ilkd.key.logic.op.*;
@@ -103,8 +102,8 @@ private void visit(Term t) {
     }
 
     private void visit(Sequent s) {
-        for (final SequentFormula cf : s) {
-            visit(cf.formula());
+        for (final Term cf : s) {
+            visit(cf);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTFocusResults.java b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTFocusResults.java
index 4a20c0867c4..08d0ae975db 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTFocusResults.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTFocusResults.java
@@ -71,7 +71,7 @@ public static boolean focus(SMTProblem smtProblem, Services services) {
         Semisequent succedent = goalNode.sequent().succedent();
 
         int i = 1;
-        for (SequentFormula sf : antecedent) {
+        for (Term sf : antecedent) {
             PosInOccurrence pio =
                 PosInOccurrence.findInSequent(goalNode.sequent(), i, PosInTerm.getTopLevel());
             if (!unsatCore.contains(pio)) {
@@ -80,13 +80,13 @@ public static boolean focus(SMTProblem smtProblem, Services services) {
                 TacletApp app = PosTacletApp.createPosTacletApp(hideLeft, new MatchConditions(),
                     new PosInOccurrence(sf, PosInTerm.getTopLevel(), true),
                     services);
-                app = app.addCheckedInstantiation(schema, sf.formula(), services, true);
+                app = app.addCheckedInstantiation(schema, sf, services, true);
                 goal = goal.apply(app).iterator().next();
             }
             i++;
         }
 
-        for (SequentFormula sf : succedent) {
+        for (Term sf : succedent) {
             PosInOccurrence pio =
                 PosInOccurrence.findInSequent(goalNode.sequent(), i, PosInTerm.getTopLevel());
             if (!unsatCore.contains(pio)) {
@@ -96,7 +96,7 @@ public static boolean focus(SMTProblem smtProblem, Services services) {
                     PosTacletApp.createPosTacletApp(hideRight, new MatchConditions(),
                         new PosInOccurrence(sf, PosInTerm.getTopLevel(), false),
                         services);
-                app = app.addCheckedInstantiation(schema, sf.formula(), services, true);
+                app = app.addCheckedInstantiation(schema, sf, services, true);
                 goal = goal.apply(app).iterator().next();
             }
             i++;
@@ -146,7 +146,7 @@ public static ImmutableList<PosInOccurrence> getUnsatCore(SMTProblem problem) {
 
         Semisequent antecedent = goalNode.sequent().antecedent();
         int i = 1;
-        for (SequentFormula sf : antecedent) {
+        for (Term sf : antecedent) {
             if (unsatCore.contains(i)) {
                 unsatCoreFormulas = unsatCoreFormulas.prepend(PosInOccurrence
                         .findInSequent(goalNode.sequent(), i, PosInTerm.getTopLevel()));
@@ -155,7 +155,7 @@ public static ImmutableList<PosInOccurrence> getUnsatCore(SMTProblem problem) {
         }
 
         Semisequent succedent = goalNode.sequent().succedent();
-        for (SequentFormula sf : succedent) {
+        for (Term sf : succedent) {
             if (unsatCore.contains(i)) {
                 unsatCoreFormulas = unsatCoreFormulas.prepend(PosInOccurrence
                         .findInSequent(goalNode.sequent(), i, PosInTerm.getTopLevel()));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTProblem.java b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTProblem.java
index 79176217814..e6cfce8a099 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTProblem.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTProblem.java
@@ -8,7 +8,6 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.proof.Goal;
@@ -162,14 +161,14 @@ public static Term sequentToTerm(Sequent s, Services services) {
 
         final TermBuilder tb = services.getTermBuilder();
         ante = ante.append(tb.tt());
-        for (SequentFormula f : s.antecedent()) {
-            ante = ante.append(f.formula());
+        for (Term f : s.antecedent()) {
+            ante = ante.append(f);
         }
 
         ImmutableList<Term> succ = ImmutableSLList.nil();
         succ = succ.append(tb.ff());
-        for (SequentFormula f : s.succedent()) {
-            succ = succ.append(f.formula());
+        for (Term f : s.succedent()) {
+            succ = succ.append(f);
         }
 
         return tb.imp(tb.and(ante), tb.or(succ));
@@ -183,14 +182,14 @@ private Term sequentToTerm(Sequent s) {
 
         final TermBuilder tb = goal.proof().getServices().getTermBuilder();
         ante = ante.append(tb.tt());
-        for (SequentFormula f : s.antecedent()) {
-            ante = ante.append(f.formula());
+        for (Term f : s.antecedent()) {
+            ante = ante.append(f);
         }
 
         ImmutableList<Term> succ = ImmutableSLList.nil();
         succ = succ.append(tb.ff());
-        for (SequentFormula f : s.succedent()) {
-            succ = succ.append(f.formula());
+        for (Term f : s.succedent()) {
+            succ = succ.append(f);
         }
 
         return tb.imp(tb.and(ante), tb.or(succ));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTRuleApp.java b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTRuleApp.java
index 9674a9ed1b8..cfb03d9e9cd 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/smt/SMTRuleApp.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/smt/SMTRuleApp.java
@@ -160,10 +160,10 @@ public SMTRuleApp tryToInstantiate(Goal goal) {
         SMTRuleApp app = RULE.createApp(pio, goal.proof().getServices());
         Sequent seq = goal.sequent();
         List<PosInOccurrence> ifInsts = new ArrayList<>();
-        for (SequentFormula ante : seq.antecedent()) {
+        for (Term ante : seq.antecedent()) {
             ifInsts.add(new PosInOccurrence(ante, PosInTerm.getTopLevel(), true));
         }
-        for (SequentFormula succ : seq.succedent()) {
+        for (Term succ : seq.succedent()) {
             ifInsts.add(new PosInOccurrence(succ, PosInTerm.getTopLevel(), false));
         }
         return app.setIfInsts(ImmutableList.fromList(ifInsts));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/smt/newsmt2/ModularSMTLib2Translator.java b/key.core/src/main/java/de/uka/ilkd/key/smt/newsmt2/ModularSMTLib2Translator.java
index fc459866dd8..d31949e01fc 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/smt/newsmt2/ModularSMTLib2Translator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/smt/newsmt2/ModularSMTLib2Translator.java
@@ -13,7 +13,6 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.smt.SMTSettings;
@@ -226,11 +225,11 @@ private static String readResource(String s) {
     private List<Term> getTermsFromSequent(Sequent seq, Services serv) {
         TermBuilder tb = serv.getTermBuilder();
         List<Term> res = new LinkedList<>();
-        for (SequentFormula sf : seq.antecedent()) {
-            res.add(sf.formula());
+        for (Term sf : seq.antecedent()) {
+            res.add(sf);
         }
-        for (SequentFormula sf : seq.succedent()) {
-            res.add(tb.not(sf.formula()));
+        for (Term sf : seq.succedent()) {
+            res.add(tb.not(sf));
         }
         return res;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/BlockWellDefinedness.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/BlockWellDefinedness.java
index 84ff36c0880..3baba545c88 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/BlockWellDefinedness.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/BlockWellDefinedness.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.java.declaration.modifier.VisibilityModifier;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -68,12 +67,12 @@ public BlockWellDefinedness map(UnaryOperator<Term> op, Services services) {
     }
 
     @Override
-    SequentFormula generateSequent(SequentTerms seq, TermServices services) {
+    Term generateSequent(SequentTerms seq, TermServices services) {
         // wd(pre) & (pre & wf(anon) -> wd(modifiable) & {anon^modifiable}(wd(post)))
         final Term imp =
             TB.imp(TB.and(seq.pre, seq.wfAnon), TB.and(seq.wdModifiable, seq.anonWdPost));
         final Term wdPre = TB.wd(seq.pre);
-        return new SequentFormula(TB.apply(seq.context, TB.and(wdPre, imp)));
+        return TB.apply(seq.context, TB.and(wdPre, imp));
     }
 
     @Override
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/DependencyContractImpl.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/DependencyContractImpl.java
index 6d2947127e1..1f72b3d0149 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/DependencyContractImpl.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/DependencyContractImpl.java
@@ -14,7 +14,6 @@
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.IObserverFunction;
 import de.uka.ilkd.key.logic.op.LocationVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.pp.LogicPrinter;
 import de.uka.ilkd.key.proof.OpReplacer;
 import de.uka.ilkd.key.proof.init.ContractPO;
@@ -22,6 +21,7 @@
 import de.uka.ilkd.key.proof.init.InitConfig;
 import de.uka.ilkd.key.proof.init.ProofOblInput;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.java.MapUtil;
 
@@ -145,7 +145,7 @@ public Term getPre(LocationVariable heap, LocationVariable selfVar,
         assert paramVars != null;
         assert paramVars.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         if (originalSelfVar != null) {
             map.put(originalSelfVar, selfVar);
         }
@@ -192,7 +192,7 @@ public Term getPre(LocationVariable heap, Term heapTerm, Term selfTerm,
         assert paramTerms != null;
         assert paramTerms.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         map.put(services.getTermBuilder().var(heap), heapTerm);
         if (originalSelfVar != null) {
             map.put(services.getTermBuilder().var(originalSelfVar), selfTerm);
@@ -259,7 +259,7 @@ public Term getMby(LocationVariable selfVar, ImmutableList<LocationVariable> par
         assert paramVars != null;
         assert paramVars.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         if (originalSelfVar != null) {
             map.put(originalSelfVar, selfVar);
         }
@@ -281,7 +281,7 @@ public Term getMby(Map<LocationVariable, Term> heapTerms, Term selfTerm,
         assert paramTerms != null;
         assert paramTerms.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         for (LocationVariable heap : heapTerms.keySet()) {
             map.put(services.getTermBuilder().var(heap), heapTerms.get(heap));
         }
@@ -370,7 +370,7 @@ public Term getDep(LocationVariable heap, boolean atPre, LocationVariable selfVa
         assert paramVars != null;
         assert paramVars.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         if (originalSelfVar != null) {
             map.put(originalSelfVar, selfVar);
         }
@@ -400,7 +400,7 @@ public Term getDep(LocationVariable heap, boolean atPre, Term heapTerm, Term sel
         assert paramTerms != null;
         assert paramTerms.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         map.put(services.getTermBuilder().var(heap), heapTerm);
         if (originalSelfVar != null) {
             map.put(services.getTermBuilder().var(originalSelfVar), selfTerm);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/FunctionalOperationContractImpl.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/FunctionalOperationContractImpl.java
index d3d6b4819d4..675c1393eda 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/FunctionalOperationContractImpl.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/FunctionalOperationContractImpl.java
@@ -29,6 +29,7 @@
 import de.uka.ilkd.key.proof.init.ProofOblInput;
 
 import org.key_project.logic.Named;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.collection.ImmutableArray;
 import org.key_project.util.collection.ImmutableList;
 import org.key_project.util.collection.ImmutableSLList;
@@ -744,7 +745,7 @@ public static String getText(FunctionalOperationContract contract,
 
 
     private static String getSignatureText(IProgramMethod pm, Operator originalResultVar,
-            Operator originalSelfVar, ImmutableList<? extends SVSubstitute> originalParamVars,
+            Operator originalSelfVar, ImmutableList<? extends SyntaxElement> originalParamVars,
             LocationVariable originalExcVar, Services services, boolean usePrettyPrinting,
             boolean useUnicodeSymbols) {
         final StringBuilder sig = new StringBuilder();
@@ -761,7 +762,7 @@ private static String getSignatureText(IProgramMethod pm, Operator originalResul
         }
         sig.append(pm.getName());
         sig.append("(");
-        for (SVSubstitute subst : originalParamVars) {
+        for (SyntaxElement subst : originalParamVars) {
             if (subst instanceof Named named) {
                 sig.append(named.name()).append(", ");
             } else if (subst instanceof Term) {
@@ -868,7 +869,7 @@ private static String getPostText(Map<LocationVariable, Term> originalPosts,
     }
 
     private static String getText(IProgramMethod pm, Operator originalResultVar,
-            Operator originalSelfVar, ImmutableList<? extends SVSubstitute> originalParamVars,
+            Operator originalSelfVar, ImmutableList<? extends SyntaxElement> originalParamVars,
             LocationVariable originalExcVar, boolean hasMby, Term originalMby,
             Map<LocationVariable, Term> originalModifiables,
             Map<LocationVariable, Boolean> hasRealModifiable, Term globalDefs,
@@ -1300,7 +1301,7 @@ public Term getDep(LocationVariable heap, boolean atPre, LocationVariable selfVa
         assert paramVars != null;
         assert paramVars.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         if (originalSelfVar != null) {
             map.put(originalSelfVar, selfVar);
         }
@@ -1328,7 +1329,7 @@ public Term getDep(LocationVariable heap, boolean atPre, Term heapTerm, Term sel
         assert paramTerms != null;
         assert paramTerms.size() == originalParamVars.size();
         assert services != null;
-        Map<SVSubstitute, SVSubstitute> map = new LinkedHashMap<>();
+        Map<SyntaxElement, SyntaxElement> map = new LinkedHashMap<>();
         map.put(tb.var(heap), heapTerm);
         if (originalSelfVar != null) {
             map.put(tb.var(originalSelfVar), selfTerm);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopContractImpl.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopContractImpl.java
index cb8f34c0291..86207d1f136 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopContractImpl.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopContractImpl.java
@@ -41,13 +41,13 @@
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.logic.op.Modality;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
 import de.uka.ilkd.key.proof.OpReplacer;
 import de.uka.ilkd.key.proof.mgt.SpecificationRepository;
 import de.uka.ilkd.key.rule.metaconstruct.EnhancedForElimination;
 import de.uka.ilkd.key.speclang.jml.pretranslation.Behavior;
 import de.uka.ilkd.key.util.InfFlowSpec;
 
+import org.key_project.logic.SyntaxElement;
 import org.key_project.util.ExtList;
 import org.key_project.util.collection.DefaultImmutableSet;
 import org.key_project.util.collection.ImmutableList;
@@ -331,7 +331,7 @@ public static LoopContract combine(ImmutableSet<LoopContract> contracts, Service
      */
     private static OpReplacer createOpReplacer(final ProgramVariable index,
             final ProgramVariable values, Services services) {
-        final Map<SVSubstitute, SVSubstitute> replacementMap = new HashMap<>();
+        final Map<SyntaxElement, SyntaxElement> replacementMap = new HashMap<>();
         if (index != null) {
             replacementMap.put(services.getTermBuilder().index(),
                 services.getTermBuilder().var(index));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopWellDefinedness.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopWellDefinedness.java
index e72c4a12f91..7fad4eab5c7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopWellDefinedness.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/LoopWellDefinedness.java
@@ -8,7 +8,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.java.declaration.modifier.VisibilityModifier;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -48,14 +47,14 @@ public LoopWellDefinedness(LoopSpecification inv, ImmutableSet<LocationVariable>
     }
 
     @Override
-    SequentFormula generateSequent(SequentTerms seq, TermServices services) {
+    Term generateSequent(SequentTerms seq, TermServices services) {
         // wd(phi) & (phi & wf(anon) -> wd(modifiable) & wd(variant) & {anon^modifiable}(wd(phi) &
         // wd(variant)))
         final Term imp =
             TB.imp(TB.and(seq.pre, seq.wfAnon),
                 TB.and(seq.wdModifiable, seq.wdRest, seq.anonWdPost));
         final Term wdPre = TB.wd(seq.pre);
-        return new SequentFormula(TB.apply(seq.context, TB.and(wdPre, imp)));
+        return TB.apply(seq.context, TB.and(wdPre, imp));
     }
 
     @Override
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/QueryAxiom.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/QueryAxiom.java
index e35290909cd..05b4cd65e5a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/QueryAxiom.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/QueryAxiom.java
@@ -18,7 +18,6 @@
 import de.uka.ilkd.key.logic.ProgramElementName;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.op.*;
@@ -188,7 +187,7 @@ public ImmutableSet<Taclet> getTaclets(ImmutableSet<Pair<Sort, IObserverFunction
             ifSeq = null;
         } else {
             final Term ifFormula = tb.exactInstance(kjt.getSort(), tb.var(selfSV));
-            final SequentFormula ifCf = new SequentFormula(ifFormula);
+            final Term ifCf = ifFormula;
             final Semisequent ifSemiSeq =
                 Semisequent.EMPTY_SEMISEQUENT.insertFirst(ifCf).semisequent();
             ifSeq = Sequent.createAnteSequent(ifSemiSeq);
@@ -217,7 +216,7 @@ public ImmutableSet<Taclet> getTaclets(ImmutableSet<Pair<Sort, IObserverFunction
         // create added sequent
         final Term addedFormula =
             tb.apply(update, tb.prog(Modality.JavaModalityKind.BOX, jb, post), null);
-        final SequentFormula addedCf = new SequentFormula(addedFormula);
+        final Term addedCf = addedFormula;
         final Semisequent addedSemiSeq =
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(addedCf).semisequent();
         final Sequent addedSeq = Sequent.createAnteSequent(addedSemiSeq);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/ReplacementMap.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/ReplacementMap.java
index 0e1617da870..3bfcaf07435 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/ReplacementMap.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/ReplacementMap.java
@@ -13,7 +13,8 @@
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.op.LocationVariable;
 import de.uka.ilkd.key.logic.op.ProgramVariable;
-import de.uka.ilkd.key.logic.op.SVSubstitute;
+
+import org.key_project.logic.SyntaxElement;
 
 /**
  * A map from some type to the same type.
@@ -22,7 +23,7 @@
  *
  * @author lanzinger
  */
-public abstract class ReplacementMap<S extends Sorted & SVSubstitute>
+public abstract class ReplacementMap<S extends Sorted & SyntaxElement>
         extends de.uka.ilkd.key.proof.ReplacementMap.NoIrrelevantLabelsReplacementMap<S, S> {
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/speclang/StatementWellDefinedness.java b/key.core/src/main/java/de/uka/ilkd/key/speclang/StatementWellDefinedness.java
index 30241f0272c..9ed3e01c66c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/speclang/StatementWellDefinedness.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/speclang/StatementWellDefinedness.java
@@ -8,7 +8,6 @@
 import java.util.function.UnaryOperator;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -54,7 +53,7 @@ public abstract class StatementWellDefinedness extends WellDefinednessCheck {
      * @param services
      * @return
      */
-    abstract SequentFormula generateSequent(SequentTerms seqTerms, TermServices services);
+    abstract Term generateSequent(SequentTerms seqTerms, TermServices services);
 
     public abstract SpecificationElement getStatement();
 
@@ -121,7 +120,7 @@ final SequentTerms createSeqTerms(POTerms po, Variables vars, Term leadingUpdate
      * @param services The current services reference
      * @return The proof sequent for the well-definedness check
      */
-    public SequentFormula generateSequent(LocationVariable self, LocationVariable exception,
+    public Term generateSequent(LocationVariable self, LocationVariable exception,
             LocationVariable result, LocationVariable heap, LocationVariable heapAtPre,
             Term anonHeap,
             ImmutableSet<LocationVariable> ps, Term leadingUpdate, Term localAnonUpdate,
@@ -153,7 +152,7 @@ public SequentFormula generateSequent(LocationVariable self, LocationVariable ex
      * @param services
      * @return The proof sequent for the well-definedness check
      */
-    public SequentFormula generateSequent(LocationVariable self, LocationVariable heap,
+    public Term generateSequent(LocationVariable self, LocationVariable heap,
             Term anonHeap, ImmutableSet<LocationVariable> ps, Term leadingUpdate,
             Term localAnonUpdate, Services services) {
         return generateSequent(self, null, null, heap, null, anonHeap, ps, leadingUpdate,
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/BuiltInRuleAppContainer.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/BuiltInRuleAppContainer.java
index 5e47e52d8d0..a853dea7996 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/BuiltInRuleAppContainer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/BuiltInRuleAppContainer.java
@@ -64,7 +64,8 @@ private boolean isStillApplicable(Goal goal) {
                 // the formula does not exist anymore, bail out
                 return false;
             } else {
-                return topPos.sequentFormula().equals(applicationPosition.sequentFormula());
+                return topPos.sequentLevelFormula()
+                        .equals(applicationPosition.sequentLevelFormula());
             }
         }
     }
@@ -78,7 +79,7 @@ private PosInOccurrence getPosInOccurrence(Goal p_goal) {
 
         assert topPos != null;
 
-        return applicationPosition.replaceConstrainedFormula(topPos.sequentFormula());
+        return applicationPosition.replaceConstrainedFormula(topPos.sequentLevelFormula());
     }
 
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/FindTacletAppContainer.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/FindTacletAppContainer.java
index 10313f11e9e..0ed3573d86a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/FindTacletAppContainer.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/FindTacletAppContainer.java
@@ -6,7 +6,6 @@
 import de.uka.ilkd.key.logic.FormulaChangeInfo;
 import de.uka.ilkd.key.logic.PIOPathIterator;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.Modality;
 import de.uka.ilkd.key.logic.op.Operator;
@@ -79,8 +78,8 @@ private boolean subformulaOrPreceedingUpdateHasChanged(Goal goal) {
             final FormulaChangeInfo info = infoList.head();
             infoList = infoList.tail();
 
-            final SequentFormula newFormula = info.newFormula();
-            if (newFormula == applicationPosition.sequentFormula()) {
+            final Term newFormula = info.newFormula();
+            if (newFormula == applicationPosition.sequentLevelFormula()) {
                 // then there were no relevant modifications since the creation
                 // of the rule app object
                 return false;
@@ -106,7 +105,7 @@ private boolean subformulaOrPreceedingUpdateHasChanged(Goal goal) {
      *         formulas) and no indirect relationship exists which is established by a modification
      *         that occurred inside an update
      */
-    private boolean independentSubformulas(PosInOccurrence changePos, SequentFormula newFormula) {
+    private boolean independentSubformulas(PosInOccurrence changePos, Term newFormula) {
         final PIOPathIterator changePIO = changePos.iterator();
         final PIOPathIterator appPIO = applicationPosition.iterator();
 
@@ -172,7 +171,7 @@ private boolean updateContextIsRecorded() {
     protected PosInOccurrence getPosInOccurrence(Goal p_goal) {
         final PosInOccurrence topPos = p_goal.getFormulaTagManager().getPosForTag(positionTag);
         assert topPos != null;
-        return applicationPosition.replaceConstrainedFormula(topPos.sequentFormula());
+        return applicationPosition.replaceConstrainedFormula(topPos.sequentLevelFormula());
     }
 
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/FocussedRuleApplicationManager.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/FocussedRuleApplicationManager.java
index 7a0153fb9a9..dabc0f36297 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/FocussedRuleApplicationManager.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/FocussedRuleApplicationManager.java
@@ -140,7 +140,7 @@ public void rulesAdded(ImmutableList<? extends RuleApp> rules, PosInOccurrence p
 
     private boolean isSameFormula(PosInOccurrence pio1, PosInOccurrence pio2) {
         return pio2.isInAntec() == pio1.isInAntec()
-                && pio2.sequentFormula().equals(pio1.sequentFormula());
+                && pio2.sequentLevelFormula().equals(pio1.sequentLevelFormula());
     }
 
     private PosInOccurrence getPIOForFocussedSubterm() {
@@ -150,7 +150,7 @@ private PosInOccurrence getPIOForFocussedSubterm() {
             return null;
         }
 
-        return focussedSubterm.replaceConstrainedFormula(formula.sequentFormula());
+        return focussedSubterm.replaceConstrainedFormula(formula.sequentLevelFormula());
     }
 
     private boolean isBelow(PosInOccurrence over, PosInOccurrence under) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/IfInstantiator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/IfInstantiator.java
index ae00ddba01d..c64397f7005 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/IfInstantiator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/IfInstantiator.java
@@ -6,10 +6,7 @@
 import java.util.Iterator;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.proof.FormulaTag;
 import de.uka.ilkd.key.proof.FormulaTagManager;
 import de.uka.ilkd.key.proof.Goal;
@@ -94,21 +91,21 @@ private Taclet getTaclet() {
      * @return a list of potential if-formula instantiations (analogously to
      *         <code>IfFormulaInstSeq.createList</code>)
      */
-    private ImmutableArray<IfFormulaInstantiation> getSequentFormulas(boolean p_antec,
+    private ImmutableArray<IfFormulaInstantiation> getTerms(boolean p_antec,
             boolean p_all) {
         if (p_all) {
-            return getAllSequentFormulas(p_antec);
+            return getAllTerms(p_antec);
         }
 
         final ImmutableArray<IfFormulaInstantiation> cache =
-            getNewSequentFormulasFromCache(p_antec);
+            getNewTermsFromCache(p_antec);
         if (cache != null) {
             return cache;
         }
 
         final ImmutableArray<IfFormulaInstantiation> newFormulas = selectNewFormulas(p_antec);
 
-        addNewSequentFormulasToCache(newFormulas, p_antec);
+        addNewTermsToCache(newFormulas, p_antec);
 
         return newFormulas;
     }
@@ -120,12 +117,12 @@ private ImmutableArray<IfFormulaInstantiation> getSequentFormulas(boolean p_ante
      *         <code>true</code>
      */
     private ImmutableArray<IfFormulaInstantiation> selectNewFormulas(boolean p_antec) {
-        final ImmutableArray<IfFormulaInstantiation> allSequentFormulas =
-            getAllSequentFormulas(p_antec);
-        final IfFormulaInstantiation[] res = new IfFormulaInstantiation[allSequentFormulas.size()];
+        final ImmutableArray<IfFormulaInstantiation> allTerms =
+            getAllTerms(p_antec);
+        final IfFormulaInstantiation[] res = new IfFormulaInstantiation[allTerms.size()];
 
         int i = 0;
-        for (final IfFormulaInstantiation ifInstantiation : allSequentFormulas) {
+        for (final IfFormulaInstantiation ifInstantiation : allTerms) {
             if (isNewFormulaDirect((IfFormulaInstSeq) ifInstantiation)) {
                 res[i] = ifInstantiation;
                 ++i;
@@ -142,7 +139,7 @@ private ImmutableArray<IfFormulaInstantiation> selectNewFormulas(boolean p_antec
     private boolean isNewFormula(IfFormulaInstSeq p_ifInstantiation) {
         final boolean antec = p_ifInstantiation.inAntec();
 
-        final ImmutableArray<IfFormulaInstantiation> cache = getNewSequentFormulasFromCache(antec);
+        final ImmutableArray<IfFormulaInstantiation> cache = getNewTermsFromCache(antec);
 
         if (cache != null) {
             return cache.contains(p_ifInstantiation);
@@ -159,7 +156,7 @@ private boolean isNewFormula(IfFormulaInstSeq p_ifInstantiation) {
     private boolean isNewFormulaDirect(IfFormulaInstSeq p_ifInstantiation) {
         final boolean antec = p_ifInstantiation.inAntec();
 
-        final SequentFormula cfma = p_ifInstantiation.getConstrainedFormula();
+        final Term cfma = p_ifInstantiation.getConstrainedFormula();
         final PosInOccurrence pio = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), antec);
 
         final FormulaTagManager tagManager = goal.getFormulaTagManager();
@@ -173,17 +170,17 @@ private boolean isNewFormulaDirect(IfFormulaInstSeq p_ifInstantiation) {
         return tacletAppContainer.getAge() < formulaAge;
     }
 
-    private ImmutableArray<IfFormulaInstantiation> getNewSequentFormulasFromCache(boolean p_antec) {
+    private ImmutableArray<IfFormulaInstantiation> getNewTermsFromCache(boolean p_antec) {
         return ifInstCache.get(p_antec, tacletAppContainer.getAge());
     }
 
-    private void addNewSequentFormulasToCache(ImmutableArray<IfFormulaInstantiation> p_list,
+    private void addNewTermsToCache(ImmutableArray<IfFormulaInstantiation> p_list,
             boolean p_antec) {
         ifInstCache.put(p_antec, tacletAppContainer.getAge(), p_list);
     }
 
 
-    private ImmutableArray<IfFormulaInstantiation> getAllSequentFormulas(boolean p_antec) {
+    private ImmutableArray<IfFormulaInstantiation> getAllTerms(boolean p_antec) {
         return p_antec ? allAntecFormulas : allSuccFormulas;
     }
 
@@ -197,8 +194,8 @@ private ImmutableArray<IfFormulaInstantiation> getAllSequentFormulas(boolean p_a
      * @param p_alreadyMatchedNewFor at least one new formula has already been matched, i.e. a
      *        formula that has been modified recently
      */
-    private void findIfFormulaInstantiationsHelp(ImmutableList<SequentFormula> p_ifSeqTail,
-            ImmutableList<SequentFormula> p_ifSeqTail2nd,
+    private void findIfFormulaInstantiationsHelp(ImmutableList<Term> p_ifSeqTail,
+            ImmutableList<Term> p_ifSeqTail2nd,
             ImmutableList<IfFormulaInstantiation> p_alreadyMatched,
             MatchConditions p_matchCond, boolean p_alreadyMatchedNewFor) {
 
@@ -219,9 +216,9 @@ private void findIfFormulaInstantiationsHelp(ImmutableList<SequentFormula> p_ifS
         final boolean lastIfFormula =
             p_ifSeqTail.size() == 1 && (p_ifSeqTail2nd == null || p_ifSeqTail2nd.isEmpty());
         final ImmutableArray<IfFormulaInstantiation> formulas =
-            getSequentFormulas(antec, !lastIfFormula || p_alreadyMatchedNewFor);
+            getTerms(antec, !lastIfFormula || p_alreadyMatchedNewFor);
         final IfMatchResult mr = getTaclet().getMatcher().matchIf(formulas,
-            p_ifSeqTail.head().formula(), p_matchCond, getServices());
+            p_ifSeqTail.head(), p_matchCond, getServices());
 
         // For each matching formula call the method again to match
         // the remaining terms
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/JavaCardDLStrategy.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/JavaCardDLStrategy.java
index 960cd033f50..bd322207345 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/JavaCardDLStrategy.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/JavaCardDLStrategy.java
@@ -1919,9 +1919,9 @@ private RuleSetDispatchFeature setupApprovalDispatcher() {
 
         bindRuleSet(d, "apply_select_eq",
             add(isInstantiated("s"), isInstantiated("t1"),
+                NoSelfApplicationFeature.INSTANCE,
                 or(applyTF("s", rec(any(), SimplifiedSelectTermFeature.create(heapLDT))),
-                    add(NoSelfApplicationFeature.INSTANCE,
-                        applyTF("t1", IsSelectSkolemConstantTermFeature.INSTANCE)))));
+                    add(applyTF("t1", IsSelectSkolemConstantTermFeature.INSTANCE)))));
         bindRuleSet(d, "apply_auxiliary_eq",
             add(NoSelfApplicationFeature.INSTANCE, isInstantiated("s"),
                 applyTF("s",
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/AbstractBetaFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/AbstractBetaFeature.java
index 512404467a9..88a5b4ff43b 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/AbstractBetaFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/AbstractBetaFeature.java
@@ -329,7 +329,7 @@ public RuleAppCost computeCost(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
         assert pos != null : "Feature is only applicable to rules with find";
 
-        final Term findTerm = pos.sequentFormula().formula();
+        final Term findTerm = pos.sequentLevelFormula();
 
         return doComputation(pos, findTerm, goal.proof().getServices().getCaches());
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/CheckApplyEqFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/CheckApplyEqFeature.java
index 3951cae6d33..754c253c535 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/CheckApplyEqFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/CheckApplyEqFeature.java
@@ -39,7 +39,7 @@ protected boolean filter(TacletApp p_app, PosInOccurrence pos, Goal goal, Mutabl
 
     private boolean isNotSelfApplication(PosInOccurrence pos, IfFormulaInstantiation ifInst) {
         if (!(ifInst instanceof IfFormulaInstSeq)
-                || ifInst.getConstrainedFormula() != pos.sequentFormula()
+                || ifInst.getConstrainedFormula() != pos.sequentLevelFormula()
                 || ((IfFormulaInstSeq) ifInst).inAntec() != pos.isInAntec()) {
             return true;
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/DiffFindAndIfFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/DiffFindAndIfFeature.java
index 624855765f9..dfdead87396 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/DiffFindAndIfFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/DiffFindAndIfFeature.java
@@ -4,7 +4,7 @@
 package de.uka.ilkd.key.strategy.feature;
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.rule.IfFormulaInstSeq;
 import de.uka.ilkd.key.rule.IfFormulaInstantiation;
@@ -28,7 +28,7 @@ protected boolean filter(TacletApp app, PosInOccurrence pos, Goal goal, MutableS
         assert pos != null : "Feature is only applicable to rules with find";
 
         ImmutableList<IfFormulaInstantiation> list = app.ifFormulaInstantiations();
-        final SequentFormula findFormula = pos.sequentFormula();
+        final Term findFormula = pos.sequentLevelFormula();
         final boolean findIsInAntec = pos.isInAntec();
 
         assert list != null;
@@ -36,7 +36,7 @@ protected boolean filter(TacletApp app, PosInOccurrence pos, Goal goal, MutableS
         for (final IfFormulaInstantiation aList : list) {
             final IfFormulaInstSeq iffi = (IfFormulaInstSeq) aList;
             assert iffi != null;
-            final SequentFormula ifFormula = iffi.getConstrainedFormula();
+            final Term ifFormula = iffi.getConstrainedFormula();
 
             final boolean result =
                 findIsInAntec != iffi.inAntec() || !findFormula.equals(ifFormula);
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FocusIsSubFormulaOfInfFlowContractAppFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FocusIsSubFormulaOfInfFlowContractAppFeature.java
index 7f758b320d7..cee42d2d437 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FocusIsSubFormulaOfInfFlowContractAppFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FocusIsSubFormulaOfInfFlowContractAppFeature.java
@@ -46,7 +46,7 @@ public RuleAppCost computeCost(RuleApp ruleApp, PosInOccurrence pos, Goal goal,
             return NumberRuleAppCost.getZeroCost();
         }
 
-        final Term focusFor = pos.sequentFormula().formula();
+        final Term focusFor = pos.sequentLevelFormula();
         ImmutableList<Term> contractAppls =
             goal.getStrategyInfo(InfFlowContractAppTacletExecutor.INF_FLOW_CONTRACT_APPL_PROPERTY);
         if (contractAppls == null) {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FormulaAddedByRuleFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FormulaAddedByRuleFeature.java
index 59ce82fc587..e9020db82a7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FormulaAddedByRuleFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/FormulaAddedByRuleFeature.java
@@ -5,7 +5,7 @@
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.proof.Node;
 import de.uka.ilkd.key.proof.rulefilter.RuleFilter;
@@ -31,7 +31,7 @@ public static Feature create(RuleFilter p_filter) {
     public boolean filter(RuleApp app, PosInOccurrence pos, Goal goal, MutableState mState) {
         assert pos != null : "Feature is only applicable to rules with find";
 
-        final SequentFormula cfma = pos.sequentFormula();
+        final Term cfma = pos.sequentLevelFormula();
         final boolean antec = pos.isInAntec();
 
         Node node = goal.node();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/InfFlowContractAppFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/InfFlowContractAppFeature.java
index 0c9588ccb8d..05db3ffad2c 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/InfFlowContractAppFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/InfFlowContractAppFeature.java
@@ -10,10 +10,7 @@
 import de.uka.ilkd.key.informationflow.po.InfFlowContractPO;
 import de.uka.ilkd.key.informationflow.po.LoopInvExecutionPO;
 import de.uka.ilkd.key.informationflow.po.SymbolicExecutionPO;
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.logic.op.SchemaVariable;
 import de.uka.ilkd.key.logic.op.SkolemTermSV;
 import de.uka.ilkd.key.logic.op.VariableSV;
@@ -59,7 +56,7 @@ protected boolean comparePio(TacletApp newApp, TacletApp oldApp, PosInOccurrence
      * Check whether a semisequent contains a formula. Again, one can either search for the same or
      * an equal formula
      */
-    protected boolean semiSequentContains(Semisequent semisequent, SequentFormula cfma) {
+    protected boolean semiSequentContains(Semisequent semisequent, Term cfma) {
         return semisequent.containsEqual(cfma);
     }
 
@@ -155,9 +152,9 @@ protected boolean duplicateFindTaclet(TacletApp app, PosInOccurrence pos, Goal g
         assert app.ifFormulaInstantiations().size() >= 1
                 : "Featureis only applicable to rules with at least one assumes.";
 
-        final SequentFormula focusFor = pos.sequentFormula();
+        final Term focusFor = pos.sequentLevelFormula();
         final boolean antec = pos.isInAntec();
-        final SequentFormula assumesFor =
+        final Term assumesFor =
             app.ifFormulaInstantiations().iterator().next().getConstrainedFormula();
 
         // assumtion has to occour before the find-term in the sequent in order
@@ -220,11 +217,11 @@ public RuleAppCost computeCost(RuleApp ruleApp, PosInOccurrence pos, Goal goal,
 
         // only relate the n-th called method in execution A with the n-th
         // called method in execution B automatically
-        final SequentFormula focusFor = pos.sequentFormula();
-        final SequentFormula assumesFor =
+        final Term focusFor = pos.sequentLevelFormula();
+        final Term assumesFor =
             app.ifFormulaInstantiations().iterator().next().getConstrainedFormula();
 
-        ArrayList<SequentFormula> relatesTerms = getRelatesTerms(goal);
+        ArrayList<Term> relatesTerms = getRelatesTerms(goal);
         final int numOfContractAppls = relatesTerms.size() / 2;
         int assumesApplNumber = 0;
         for (int i = 0; i < numOfContractAppls; i++) {
@@ -249,11 +246,11 @@ private boolean isInfFlowProof(Proof proof) {
     }
 
 
-    private ArrayList<SequentFormula> getRelatesTerms(Goal goal) {
-        ArrayList<SequentFormula> list = new ArrayList<>();
+    private ArrayList<Term> getRelatesTerms(Goal goal) {
+        ArrayList<Term> list = new ArrayList<>();
         Semisequent antecedent = goal.node().sequent().antecedent();
-        for (SequentFormula f : antecedent) {
-            if (f.formula().op().toString().startsWith("RELATED_BY_")) {
+        for (Term f : antecedent) {
+            if (f.op().toString().startsWith("RELATED_BY_")) {
                 list.add(f);
             }
         }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/NoSelfApplicationFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/NoSelfApplicationFeature.java
index de00a63a054..263e6bf2eb6 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/NoSelfApplicationFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/NoSelfApplicationFeature.java
@@ -38,7 +38,7 @@ protected boolean filter(TacletApp p_app, PosInOccurrence pos, Goal goal, Mutabl
         boolean noSelfApplication = true;
         for (IfFormulaInstantiation ifInst : ifInsts) {
             noSelfApplication =
-                noSelfApplication && (ifInst.getConstrainedFormula() != pos.sequentFormula());
+                noSelfApplication && (ifInst.getConstrainedFormula() != pos.sequentLevelFormula());
         }
         return noSelfApplication;
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/SeqContainsExecutableCodeFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/SeqContainsExecutableCodeFeature.java
index fc204cf81f4..9a4a2f74c14 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/SeqContainsExecutableCodeFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/feature/SeqContainsExecutableCodeFeature.java
@@ -7,7 +7,7 @@
 
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.rule.RuleApp;
 import de.uka.ilkd.key.strategy.termfeature.BinaryTermFeature;
@@ -36,10 +36,10 @@ protected boolean filter(RuleApp app, PosInOccurrence pos, Goal goal, MutableSta
                     goal.proof().getServices());
     }
 
-    private boolean containsExec(Iterator<SequentFormula> it, MutableState mState,
+    private boolean containsExec(Iterator<Term> it, MutableState mState,
             Services services) {
         while (it.hasNext()) {
-            if (tf.compute(it.next().formula(), mState, services)
+            if (tf.compute(it.next(), mState, services)
                     .equals(BinaryTermFeature.ZERO_COST)) {
                 return true;
             }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/ExistentiallyConnectedFormulasFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/ExistentiallyConnectedFormulasFeature.java
index 1eebfa51ed5..1bf8efb4e0a 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/ExistentiallyConnectedFormulasFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/ExistentiallyConnectedFormulasFeature.java
@@ -30,7 +30,7 @@ public static Feature create(ProjectionToTerm for0, ProjectionToTerm for1) {
     protected boolean filter(TacletApp app, PosInOccurrence pos, Goal goal, MutableState mState) {
         assert pos != null : "Feature is only applicable to rules with find";
 
-        final ClausesGraph graph = ClausesGraph.create(pos.sequentFormula().formula(),
+        final ClausesGraph graph = ClausesGraph.create(pos.sequentLevelFormula(),
             goal.proof().getServices().getCaches());
 
         return graph.connected(for0.toTerm(app, pos, goal, mState),
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/HeuristicInstantiation.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/HeuristicInstantiation.java
index 6aa01776eec..225659251ba 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/HeuristicInstantiation.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/HeuristicInstantiation.java
@@ -30,7 +30,7 @@ public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
         assert pos != null : "Feature is only applicable to rules with find";
 
-        final Term qf = pos.sequentFormula().formula();
+        final Term qf = pos.sequentLevelFormula();
         final Instantiation ia =
             Instantiation.create(qf, goal.sequent(), goal.proof().getServices());
         final QuantifiableVariable var = qf.varsBoundHere(0).last();
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Instantiation.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Instantiation.java
index ad1fee4514c..1bf26258226 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Instantiation.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Instantiation.java
@@ -9,7 +9,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.op.Operator;
@@ -76,8 +75,8 @@ static Instantiation create(Term qf, Sequent seq, Services services) {
 
     private static ImmutableSet<Term> sequentToTerms(Sequent seq) {
         ImmutableList<Term> res = ImmutableSLList.nil();
-        for (final SequentFormula cf : seq) {
-            res = res.prepend(cf.formula());
+        for (final Term cf : seq) {
+            res = res.prepend(cf);
         }
         return DefaultImmutableSet.fromImmutableList(res);
     }
@@ -148,15 +147,15 @@ private void addInstance(Substitution sub, long cost) {
      */
     private ImmutableSet<Term> initAssertLiterals(Sequent seq, TermServices services) {
         ImmutableList<Term> assertLits = ImmutableSLList.nil();
-        for (final SequentFormula cf : seq.antecedent()) {
-            final Term atom = cf.formula();
+        for (final Term cf : seq.antecedent()) {
+            final Term atom = cf;
             final Operator op = atom.op();
             if (!(op == Quantifier.ALL || op == Quantifier.EX)) {
                 assertLits = assertLits.prepend(atom);
             }
         }
-        for (final SequentFormula cf : seq.succedent()) {
-            final Term atom = cf.formula();
+        for (final Term cf : seq.succedent()) {
+            final Term atom = cf;
             final Operator op = atom.op();
             if (!(op == Quantifier.ALL || op == Quantifier.EX)) {
                 assertLits = assertLits.prepend(services.getTermBuilder().not(atom));
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/InstantiationCost.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/InstantiationCost.java
index 28e96e73d5b..7710d80ab67 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/InstantiationCost.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/InstantiationCost.java
@@ -34,7 +34,7 @@ public RuleAppCost computeCost(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
         assert pos != null : "Projection is only applicable to rules with find";
 
-        final Term formula = pos.sequentFormula().formula();
+        final Term formula = pos.sequentLevelFormula();
         final Term instance = varInst.toTerm(app, pos, goal, mState);
 
         return Instantiation.computeCost(instance, formula, goal.sequent(),
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Metavariable.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Metavariable.java
index 76edd2ab297..44fb3a27177 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Metavariable.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/Metavariable.java
@@ -8,11 +8,12 @@
 
 import org.key_project.logic.Name;
 import org.key_project.logic.ParsableVariable;
+import org.key_project.logic.TerminalSyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 @Deprecated
 public final class Metavariable extends AbstractSortedOperator
-        implements ParsableVariable, Comparable<Metavariable> {
+        implements ParsableVariable, Comparable<Metavariable>, TerminalSyntaxElement {
 
     // Used to define an alternative order of all existing
     // metavariables
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/SplittableQuantifiedFormulaFeature.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/SplittableQuantifiedFormulaFeature.java
index 4b6ee9436cd..91b737e8eb0 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/SplittableQuantifiedFormulaFeature.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/quantifierHeuristics/SplittableQuantifiedFormulaFeature.java
@@ -28,7 +28,7 @@ protected boolean filter(RuleApp app, PosInOccurrence pos, Goal goal, MutableSta
         assert pos != null : "Feature is only applicable to rules with find";
 
         final Analyser analyser = new Analyser();
-        if (!analyser.analyse(pos.sequentFormula().formula())) {
+        if (!analyser.analyse(pos.sequentLevelFormula())) {
             return false;
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/AssumptionProjection.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/AssumptionProjection.java
index 4119f587f55..29f2bb0ccf7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/AssumptionProjection.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/AssumptionProjection.java
@@ -36,6 +36,6 @@ public Term toTerm(RuleApp app, PosInOccurrence pos, Goal goal, MutableState mut
                 : "Projection is only applicable to taclet apps with assumptions," + " but got "
                     + app;
 
-        return tapp.ifFormulaInstantiations().take(no).head().getConstrainedFormula().formula();
+        return tapp.ifFormulaInstantiations().take(no).head().getConstrainedFormula();
     }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/FocusFormulaProjection.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/FocusFormulaProjection.java
index eca4c0ffe95..01bc65e77af 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/FocusFormulaProjection.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termProjection/FocusFormulaProjection.java
@@ -18,7 +18,7 @@ private FocusFormulaProjection() {}
     public Term toTerm(RuleApp app, PosInOccurrence pos, Goal goal, MutableState mutableState) {
         assert pos != null : "Projection is only applicable to rules with find";
 
-        return pos.sequentFormula().formula();
+        return pos.sequentLevelFormula();
     }
 
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/AllowedCutPositionsGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/AllowedCutPositionsGenerator.java
index d4263852cca..816ccc9b945 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/AllowedCutPositionsGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/AllowedCutPositionsGenerator.java
@@ -26,7 +26,7 @@ private AllowedCutPositionsGenerator() {}
 
     public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
-        return new ACPIterator(pos.sequentFormula().formula(), pos.isInAntec());
+        return new ACPIterator(pos.sequentLevelFormula(), pos.isInAntec());
     }
 
     private static class ACPIterator implements Iterator<Term> {
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/HeapGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/HeapGenerator.java
index 4e292f35a5e..bbe48e9b74f 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/HeapGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/HeapGenerator.java
@@ -9,7 +9,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.UpdateApplication;
 import de.uka.ilkd.key.proof.Goal;
@@ -40,8 +39,8 @@ public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
         LinkedHashSet<Term> heaps = new LinkedHashSet<>();
         Sequent seq = goal.sequent();
-        for (SequentFormula sf : seq) {
-            collectHeaps(sf.formula(), heaps, goal.proof().getServices());
+        for (Term sf : seq) {
+            collectHeaps(sf, heaps, goal.proof().getServices());
         }
         return heaps.iterator();
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/MultiplesModEquationsGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/MultiplesModEquationsGenerator.java
index 2e95e5be36a..f73c27c5371 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/MultiplesModEquationsGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/MultiplesModEquationsGenerator.java
@@ -11,7 +11,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.ldt.IntegerLDT;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.op.Equality;
 import de.uka.ilkd.key.proof.Goal;
@@ -145,9 +144,9 @@ private List<CofactorPolynomial> extractPolys(Goal goal, Services services) {
 
         final List<CofactorPolynomial> res = new ArrayList<>();
 
-        for (final SequentFormula cfm : goal.sequent().antecedent()) {
+        for (final Term cfm : goal.sequent().antecedent()) {
 
-            final Term t = cfm.formula();
+            final Term t = cfm;
             if (t.op() != Equality.EQUALS || t.sub(0).sort() != numbers.targetSort()
                     || t.sub(1).sort() != numbers.targetSort()) {
                 continue;
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SequentFormulasGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SequentFormulasGenerator.java
index 0f54c39ae17..8baf0daefdd 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SequentFormulasGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SequentFormulasGenerator.java
@@ -6,7 +6,6 @@
 import java.util.Iterator;
 
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.rule.RuleApp;
@@ -21,7 +20,7 @@ protected SequentFormulasGenerator() {}
 
     public static SequentFormulasGenerator antecedent() {
         return new SequentFormulasGenerator() {
-            protected Iterator<SequentFormula> generateForIt(Goal goal) {
+            protected Iterator<Term> generateForIt(Goal goal) {
                 return goal.sequent().antecedent().iterator();
             }
         };
@@ -29,7 +28,7 @@ protected Iterator<SequentFormula> generateForIt(Goal goal) {
 
     public static SequentFormulasGenerator succedent() {
         return new SequentFormulasGenerator() {
-            protected Iterator<SequentFormula> generateForIt(Goal goal) {
+            protected Iterator<Term> generateForIt(Goal goal) {
                 return goal.sequent().succedent().iterator();
             }
         };
@@ -37,40 +36,17 @@ protected Iterator<SequentFormula> generateForIt(Goal goal) {
 
     public static SequentFormulasGenerator sequent() {
         return new SequentFormulasGenerator() {
-            protected Iterator<SequentFormula> generateForIt(Goal goal) {
+            protected Iterator<Term> generateForIt(Goal goal) {
                 return goal.sequent().iterator();
             }
         };
     }
 
-    protected abstract Iterator<SequentFormula> generateForIt(Goal goal);
+    protected abstract Iterator<Term> generateForIt(Goal goal);
 
     public Iterator<Term> generate(RuleApp app, PosInOccurrence pos, Goal goal,
             MutableState mState) {
-        return new SFIterator(generateForIt(goal));
+        return generateForIt(goal);
     }
 
-    private static class SFIterator implements Iterator<Term> {
-        private final Iterator<SequentFormula> forIt;
-
-        public boolean hasNext() {
-            return forIt.hasNext();
-        }
-
-        public Term next() {
-            return forIt.next().formula();
-        }
-
-        public SFIterator(Iterator<SequentFormula> forIt) {
-            this.forIt = forIt;
-        }
-
-        /**
-         * throw an unsupported operation exception
-         */
-        public void remove() {
-            throw new UnsupportedOperationException();
-        }
-
-    }
 }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SuperTermGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SuperTermGenerator.java
index c3a3b2599d0..49368cb1602 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SuperTermGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/SuperTermGenerator.java
@@ -19,6 +19,7 @@
 
 import org.key_project.logic.Name;
 import org.key_project.logic.TermCreationException;
+import org.key_project.logic.TerminalSyntaxElement;
 import org.key_project.logic.op.Modifier;
 import org.key_project.logic.op.SortedOperator;
 import org.key_project.logic.sort.Sort;
@@ -95,7 +96,8 @@ protected Term generateOneTerm(Term superterm, int child) {
             return services.getTermBuilder().tf().createTerm(binFunc, superterm, index);
         }
 
-        private static class SuperTermGeneratedOp implements SortedOperator, Operator {
+        private static class SuperTermGeneratedOp
+                implements SortedOperator, Operator, TerminalSyntaxElement {
             private final Name NAME;
             private final IntegerLDT numbers;
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/TriggeredInstantiations.java b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/TriggeredInstantiations.java
index 95fb98f2926..d4cb7624dde 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/TriggeredInstantiations.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/strategy/termgenerator/TriggeredInstantiations.java
@@ -12,7 +12,6 @@
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermServices;
 import de.uka.ilkd.key.logic.label.TermLabelState;
@@ -156,12 +155,12 @@ private void collectAxiomsAndCandidateTerms(final Set<Term> terms, final Set<Ter
             final IntegerLDT integerLDT, Semisequent antecedent, boolean inAntecedent,
             TermServices services) {
 
-        for (SequentFormula sf : antecedent) {
-            collectTerms(sf.formula(), terms, integerLDT);
-            if (sf.formula().op() instanceof JFunction
-                    || sf.formula().op() == Equality.EQUALS) {
+        for (Term sf : antecedent) {
+            collectTerms(sf, terms, integerLDT);
+            if (sf.op() instanceof JFunction
+                    || sf.op() == Equality.EQUALS) {
                 axioms.add(
-                    inAntecedent ? sf.formula() : services.getTermBuilder().not(sf.formula()));
+                    inAntecedent ? sf : services.getTermBuilder().not(sf));
             }
         }
     }
diff --git a/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/SkeletonGenerator.java b/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/SkeletonGenerator.java
index 6ed1844efbf..897881461d7 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/SkeletonGenerator.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/SkeletonGenerator.java
@@ -5,7 +5,6 @@
 
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.logic.TermServices;
@@ -72,8 +71,8 @@ protected Term translate(Sequent s, TermServices services) {
      */
     private ImmutableList<Term> getFormulaeOfSemisequent(Semisequent s) {
         ImmutableList<Term> terms = ImmutableSLList.nil();
-        for (SequentFormula cf : s) {
-            terms = terms.append(cf.formula());
+        for (Term cf : s) {
+            terms = terms.append(cf);
         }
         return terms;
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/TacletVisitor.java b/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/TacletVisitor.java
index 39885889d7f..14e2520941e 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/TacletVisitor.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/taclettranslation/TacletVisitor.java
@@ -3,10 +3,7 @@
  * SPDX-License-Identifier: GPL-2.0-only */
 package de.uka.ilkd.key.taclettranslation;
 
-import de.uka.ilkd.key.logic.DefaultVisitor;
-import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.rule.FindTaclet;
 import de.uka.ilkd.key.rule.Taclet;
 import de.uka.ilkd.key.rule.tacletbuilder.AntecSuccTacletGoalTemplate;
@@ -19,8 +16,8 @@ public abstract class TacletVisitor implements DefaultVisitor {
     private String failureDescription = null;
 
     private void visit(Semisequent semiseq) {
-        for (SequentFormula aSemiseq : semiseq) {
-            aSemiseq.formula().execPostOrder(this);
+        for (Term aSemiseq : semiseq) {
+            aSemiseq.execPostOrder(this);
         }
     }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/util/HelperClassForTests.java b/key.core/src/main/java/de/uka/ilkd/key/util/HelperClassForTests.java
index 1033dfe3f41..e6ad15022b4 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/util/HelperClassForTests.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/util/HelperClassForTests.java
@@ -95,7 +95,7 @@ public ProofAggregate parseThrowException(File file, Profile profile)
     }
 
     public Term extractProblemTerm(Proof p) {
-        return p.root().sequent().succedent().iterator().next().formula();
+        return p.root().sequent().succedent().iterator().next();
     }
 
     /**
diff --git a/key.core/src/main/java/de/uka/ilkd/key/util/ProofStarter.java b/key.core/src/main/java/de/uka/ilkd/key/util/ProofStarter.java
index d0b1454bedd..72be773d293 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/util/ProofStarter.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/util/ProofStarter.java
@@ -6,7 +6,6 @@
 import de.uka.ilkd.key.java.abstraction.KeYJavaType;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.proof.Proof;
@@ -63,7 +62,7 @@ public UserProvidedInput(Sequent seq, ProofEnvironment env, String proofName) {
 
         public UserProvidedInput(Term formula, ProofEnvironment env) {
             this(Sequent.createSuccSequent(Semisequent.EMPTY_SEMISEQUENT
-                    .insertFirst(new SequentFormula(formula)).semisequent()),
+                    .insertFirst(formula).semisequent()),
                 env);
         }
 
diff --git a/key.core/src/main/java/de/uka/ilkd/key/util/mergerule/MergeRuleUtils.java b/key.core/src/main/java/de/uka/ilkd/key/util/mergerule/MergeRuleUtils.java
index aeb78f68cde..571607cb435 100644
--- a/key.core/src/main/java/de/uka/ilkd/key/util/mergerule/MergeRuleUtils.java
+++ b/key.core/src/main/java/de/uka/ilkd/key/util/mergerule/MergeRuleUtils.java
@@ -236,8 +236,8 @@ public static HashSet<LocationVariable> getLocationVariablesHashSet(Sequent sequ
             Services services) {
         HashSet<LocationVariable> result = new HashSet<>();
 
-        for (SequentFormula f : sequent) {
-            result.addAll(getLocationVariablesHashSet(f.formula(), services));
+        for (Term f : sequent) {
+            result.addAll(getLocationVariablesHashSet(f, services));
         }
 
         return result;
@@ -800,7 +800,7 @@ public static Term trySimplify(final Proof parentProof, final Term term,
     public static void clearSemisequent(Goal goal, boolean antec) {
         final Semisequent semiseq =
             antec ? goal.sequent().antecedent() : goal.sequent().succedent();
-        for (final SequentFormula f : semiseq) {
+        for (final Term f : semiseq) {
             final PosInOccurrence gPio = new PosInOccurrence(f, PosInTerm.getTopLevel(), antec);
             goal.removeFormula(gPio);
         }
@@ -1055,15 +1055,16 @@ public static SymbolicExecutionState sequentToSEPair(Node node, PosInOccurrence
     public static SymbolicExecutionStateWithProgCnt sequentToSETriple(Node node,
             PosInOccurrence pio, Services services) {
 
-        ImmutableList<SequentFormula> pathConditionSet = ImmutableSLList.nil();
+        ImmutableList<Term> pathConditionSet = ImmutableSLList.nil();
         pathConditionSet = pathConditionSet.prepend(node.sequent().antecedent().asList());
 
         Term selected = pio.subTerm();
 
-        for (SequentFormula sf : node.sequent().succedent()) {
-            if (!sf.formula().equals(selected)) {
+        for (Term sf : node.sequent().succedent()) {
+            if (!sf.equals(selected)) {
+                Term uAssumptions = services.getTermBuilder().not(sf);
                 pathConditionSet = pathConditionSet
-                        .prepend(new SequentFormula(services.getTermBuilder().not(sf.formula())));
+                        .prepend(uAssumptions);
             }
         }
 
@@ -1373,14 +1374,14 @@ public static LocationVariable rename(Name newName, LocationVariable lv) {
      * @param services The services object.
      * @return And-formula connecting the given terms.
      */
-    private static Term joinListToAndTerm(ImmutableList<SequentFormula> formulae,
+    private static Term joinListToAndTerm(ImmutableList<Term> formulae,
             Services services) {
         if (formulae.size() == 0) {
             return services.getTermBuilder().tt();
         } else if (formulae.size() == 1) {
-            return formulae.head().formula();
+            return formulae.head();
         } else {
-            return services.getTermBuilder().and(formulae.head().formula(),
+            return services.getTermBuilder().and(formulae.head(),
                 joinListToAndTerm(formulae.tail(), services));
         }
     }
@@ -1471,7 +1472,7 @@ private static ApplyStrategyInfo tryToProve(Term toProve, Services services, boo
             String sideProofName, int timeout) throws ProofInputException {
         return tryToProve(Sequent.createSequent(
             // Sequent to prove
-            Semisequent.EMPTY_SEMISEQUENT, new Semisequent(new SequentFormula(toProve))), services,
+            Semisequent.EMPTY_SEMISEQUENT, new Semisequent(toProve)), services,
             doSplit, sideProofName, timeout);
     }
 
@@ -1620,12 +1621,12 @@ private static Term sequentToFormula(Sequent sequent, Services services) {
         ImmutableList<Term> succedentForms = ImmutableSLList.nil();
 
         // Shift antecedent formulae to the succedent by negation
-        for (SequentFormula sf : sequent.antecedent().asList()) {
-            negAntecedentForms = negAntecedentForms.prepend(tb.not(sf.formula()));
+        for (Term sf : sequent.antecedent().asList()) {
+            negAntecedentForms = negAntecedentForms.prepend(tb.not(sf));
         }
 
-        for (SequentFormula sf : sequent.succedent().asList()) {
-            succedentForms = succedentForms.prepend(sf.formula());
+        for (Term sf : sequent.succedent().asList()) {
+            succedentForms = succedentForms.prepend(sf);
         }
 
         return tb.or(negAntecedentForms.prepend(succedentForms));
diff --git a/key.core/src/main/java/org/key_project/proof/LocationVariableTracker.java b/key.core/src/main/java/org/key_project/proof/LocationVariableTracker.java
index 52f96ac8848..ac859d6d395 100644
--- a/key.core/src/main/java/org/key_project/proof/LocationVariableTracker.java
+++ b/key.core/src/main/java/org/key_project/proof/LocationVariableTracker.java
@@ -56,9 +56,9 @@ public void ruleApplied(ProofEvent e) {
                 var it = x.getNodeChanges();
                 while (it.hasNext()) {
                     var change = it.next();
-                    var sf = change.getPos().sequentFormula();
+                    var sf = change.getPos().sequentLevelFormula();
                     var collect = new OpCollectorJavaBlock();
-                    sf.formula().execPreOrder(collect);
+                    sf.execPreOrder(collect);
                     for (var op : collect.ops()) {
                         if (!(op instanceof LocationVariable) || createdBy.containsKey(op)) {
                             continue;
diff --git a/key.core/src/test/java/de/uka/ilkd/key/logic/TestPosInOcc.java b/key.core/src/test/java/de/uka/ilkd/key/logic/TestPosInOcc.java
index dfa27b88653..028228d5d9b 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/logic/TestPosInOcc.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/logic/TestPosInOcc.java
@@ -41,7 +41,7 @@ public void testIterator() {
         terms[2] = TB.func(p, new Term[] { terms[1] });
 
         PosInOccurrence pio =
-            new PosInOccurrence(new SequentFormula(terms[2]), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(terms[2], PosInTerm.getTopLevel(), true);
 
         PIOPathIterator it = pio.iterator();
 
@@ -84,14 +84,14 @@ public void testReplaceConstrainedFormula() {
         terms[0] = TB.var(x);
         terms[1] = TB.func(f, new Term[] { terms[0] });
         terms[2] = TB.func(p, new Term[] { terms[1] });
-        SequentFormula cfma = new SequentFormula(terms[2]);
+        Term cfma = terms[2];
 
         Term[] terms2 = new Term[4];
         terms2[0] = TB.func(c);
         terms2[1] = TB.func(f, new Term[] { terms2[0] });
         terms2[2] = TB.func(f, new Term[] { terms2[1] });
         terms2[3] = TB.func(p, new Term[] { terms2[2] });
-        SequentFormula cfma2 = new SequentFormula(terms2[3]);
+        Term cfma2 = terms2[3];
 
         final PosInOccurrence topPIO = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), true);
 
diff --git a/key.core/src/test/java/de/uka/ilkd/key/logic/TestSemisequent.java b/key.core/src/test/java/de/uka/ilkd/key/logic/TestSemisequent.java
index 8df3490b235..0bdb3d2b24b 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/logic/TestSemisequent.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/logic/TestSemisequent.java
@@ -25,7 +25,7 @@
 
 public class TestSemisequent {
 
-    private SequentFormula[] con;
+    private Term[] con;
 
     @BeforeEach
     public void setUp() {
@@ -48,14 +48,14 @@ public void setUp() {
         Term t_c = TB.func(c, new Term[] {});
 
 
-        con = new SequentFormula[7];
-        con[0] = new SequentFormula(t_p);
-        con[1] = new SequentFormula(t_q);
-        con[2] = new SequentFormula(t_r);
-        con[3] = new SequentFormula(t_r);
-        con[4] = new SequentFormula(t_a);
-        con[5] = new SequentFormula(t_b);
-        con[6] = new SequentFormula(t_c);
+        con = new Term[7];
+        con[0] = t_p;
+        con[1] = t_q;
+        con[2] = t_r;
+        con[3] = t_r;
+        con[4] = t_a;
+        con[5] = t_b;
+        con[6] = t_c;
 
         Sort s = new SortImpl(new Name("test"));
         Function f = new JFunction(new Name("f"), s, new Sort[] {});
@@ -75,7 +75,8 @@ public void testContains() {
         Semisequent seq = Semisequent.EMPTY_SEMISEQUENT;
         seq = extract(seq.insert(0, con[0]));
         seq = extract(seq.insert(1, con[1]));
-        SequentFormula eq2con0 = new SequentFormula(con[0].formula());
+        TermBuilder TB = TacletForTests.services().getTermBuilder(false);
+        Term eq2con0 = TB.func((JFunction) con[0].op(), new Term[] {});
         assertFalse(seq.contains(eq2con0), "Contains should test of identity and not equality.");
     }
 
@@ -84,7 +85,7 @@ public void testContainsEquals() {
         Semisequent seq = Semisequent.EMPTY_SEMISEQUENT;
         seq = extract(seq.insert(0, con[0]));
         seq = extract(seq.insert(1, con[1]));
-        SequentFormula eq2con0 = new SequentFormula(con[0].formula());
+        Term eq2con0 = con[0];
         assertTrue(seq.containsEqual(eq2con0),
             "Contains tests of equality and should find the formula.");
     }
@@ -238,7 +239,7 @@ public void testListInsert() {
 
         Semisequent expected = extract(
             extract(extract(origin.insertLast(con[4])).insertLast(con[5])).insertLast(con[6]));
-        ImmutableList<SequentFormula> insertionList = ImmutableSLList.<SequentFormula>nil()
+        ImmutableList<Term> insertionList = ImmutableSLList.<Term>nil()
                 .prepend(con[0]).prepend(con[1]).prepend(con[6]).prepend(con[5]).prepend(con[4]);
         Semisequent result = extract(origin.insert(origin.size(), insertionList));
         assertEquals(expected, result, "Both semisequents should be equal.");
@@ -252,7 +253,7 @@ public void testListInsertInMid() {
                     .insertLast(con[2]));
         Semisequent expected =
             extract(extract(extract(origin.insert(2, con[4])).insert(3, con[5])).insert(4, con[6]));
-        ImmutableList<SequentFormula> insertionList = ImmutableSLList.<SequentFormula>nil()
+        ImmutableList<Term> insertionList = ImmutableSLList.<Term>nil()
                 .prepend(con[0]).prepend(con[1]).prepend(con[6]).prepend(con[5]).prepend(con[4]);
         Semisequent result = extract(origin.insert(origin.size() - 1, insertionList));
         assertEquals(expected, result, "Both semisequents should be equal.");
@@ -270,16 +271,16 @@ public void testListReplace() {
             extract(extract(extract(origin.remove(2)).insertLast(con[4])).insertLast(con[5]))
                     .insertLast(con[6]));
         // insert: [a,b,c,q,p]
-        ImmutableList<SequentFormula> insertionList = ImmutableSLList.<SequentFormula>nil()
+        ImmutableList<Term> insertionList = ImmutableSLList.<Term>nil()
                 .prepend(con[0]).prepend(con[1]).prepend(con[6]).prepend(con[5]).prepend(con[4]);
 
         SemisequentChangeInfo result = origin.replace(origin.size() - 1, insertionList);
 
         assertEquals(
-            ImmutableSLList.<SequentFormula>nil().prepend(con[4]).prepend(con[5]).prepend(con[6]),
+            ImmutableSLList.<Term>nil().prepend(con[4]).prepend(con[5]).prepend(con[6]),
             result.addedFormulas(),
             "SemisequentChangeInfo is corrupt due to wrong added formula list:");
-        assertEquals(ImmutableSLList.<SequentFormula>nil().prepend(con[2]),
+        assertEquals(ImmutableSLList.<Term>nil().prepend(con[2]),
             result.removedFormulas(),
             "SemisequentChangeInfo is corrupt due to wrong removed formula list:");
         assertEquals(expected, extract(result), "Both semisequents should be equal.");
@@ -296,17 +297,17 @@ public void testListReplaceAddRedundantList() {
             extract(extract(origin.insertLast(con[4])).insertLast(con[5])).insertLast(con[6]))
                     .insertLast(con[2]));
         // insert:[a,b,c,r,r,q,p]
-        ImmutableList<SequentFormula> insertionList =
-            ImmutableSLList.<SequentFormula>nil().prepend(con[0]).prepend(con[1]).prepend(con[2])
+        ImmutableList<Term> insertionList =
+            ImmutableSLList.<Term>nil().prepend(con[0]).prepend(con[1]).prepend(con[2])
                     .prepend(con[3]).prepend(con[6]).prepend(con[5]).prepend(con[4]);
 
         SemisequentChangeInfo sci = origin.replace(origin.size(), insertionList);
         assertEquals(
-            ImmutableSLList.<SequentFormula>nil().prepend(con[4]).prepend(con[5]).prepend(con[6])
+            ImmutableSLList.<Term>nil().prepend(con[4]).prepend(con[5]).prepend(con[6])
                     .prepend(con[3]),
             sci.addedFormulas(),
             "SemisequentChangeInfo is corrupt due to wrong added formula list:");
-        assertEquals(ImmutableSLList.<SequentFormula>nil(), sci.removedFormulas(),
+        assertEquals(ImmutableSLList.<Term>nil(), sci.removedFormulas(),
             "SemisequentChangeInfo is corrupt due to wrong removed formula list:");
         assertEquals(expected, extract(sci), "Both semisequents should be equal.");
     }
diff --git a/key.core/src/test/java/de/uka/ilkd/key/logic/TestTermLabelManager.java b/key.core/src/test/java/de/uka/ilkd/key/logic/TestTermLabelManager.java
index 517a5a78a8c..7bdcc70c978 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/logic/TestTermLabelManager.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/logic/TestTermLabelManager.java
@@ -119,9 +119,11 @@ protected void doRefactoringTestLogging(boolean ruleChanged, boolean notSupporte
         one = TB.label(one, new ParameterlessTermLabel(new Name("APPLICATION")));
         two = TB.label(two, new ParameterlessTermLabel(new Name("APPLICATION")));
         Sequent sequent = Sequent.EMPTY_SEQUENT;
-        sequent = sequent.addFormula(new SequentFormula(TB.inInt(one)), true, true).sequent();
-        sequent = sequent.addFormula(pos.sequentFormula(), true, false).sequent();
-        sequent = sequent.addFormula(new SequentFormula(TB.inInt(two)), false, true).sequent();
+        Term uAssumptions1 = TB.inInt(one);
+        sequent = sequent.addFormula(uAssumptions1, true, true).sequent();
+        sequent = sequent.addFormula(pos.sequentLevelFormula(), true, false).sequent();
+        Term uAssumptions = TB.inInt(two);
+        sequent = sequent.addFormula(uAssumptions, false, true).sequent();
         // Test supported rule
         Rule rule = new DummyRule("rule");
         Term taclet = TB.tt();
@@ -147,12 +149,12 @@ protected Goal createGoal(InitConfig initConfig, Sequent sequent) {
 
     protected void compareSequents(Sequent expected, Sequent current, boolean changed,
             RefactoringScope scope) {
-        Iterator<SequentFormula> expectedIter = expected.iterator();
-        Iterator<SequentFormula> currentIter = current.iterator();
+        Iterator<Term> expectedIter = expected.iterator();
+        Iterator<Term> currentIter = current.iterator();
         while (expectedIter.hasNext() && currentIter.hasNext()) {
-            SequentFormula expectedSF = expectedIter.next();
-            SequentFormula currentSF = currentIter.next();
-            compareTerms(expectedSF.formula(), currentSF.formula(), changed, scope);
+            Term expectedSF = expectedIter.next();
+            Term currentSF = currentIter.next();
+            compareTerms(expectedSF, currentSF, changed, scope);
         }
         assertFalse(expectedIter.hasNext());
         assertFalse(currentIter.hasNext());
@@ -450,7 +452,7 @@ public void testInstantiateLabels_modalityTermPolicies() {
         Term updateApp = TB.apply(update, modality,
             new ImmutableArray<>(new ParameterlessTermLabel(new Name("UPDATE-APPLICATION"))));
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(updateApp), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(updateApp, PosInTerm.getTopLevel(), true);
         Term taclet = TB.tt();
         Rule rule = new DummyRule("rule");
         // Create labels
@@ -526,7 +528,7 @@ public void testInstantiateLabels_null() {
     protected PosInOccurrence createTestPosInOccurrence(Services services) {
         Term testTerm = createTestTerm(services);
         Term inInt = services.getTermBuilder().inInt(testTerm);
-        return new PosInOccurrence(new SequentFormula(inInt), PosInTerm.parseReverseString("0"),
+        return new PosInOccurrence(inInt, PosInTerm.parseReverseString("0"),
             true);
     }
 
@@ -557,18 +559,18 @@ public void testParseLabel() throws TermLabelException {
         TermLabel label = manager.parseLabel("ONE", null, services);
         assertTrue(label instanceof LoggingTermLabel);
         assertEquals("ONE", label.name().toString());
-        assertEquals(0, label.getChildCount());
+        assertEquals(0, label.getTLChildCount());
         // Test empty parameter
         label = manager.parseLabel("TWO", null, services);
         assertTrue(label instanceof LoggingTermLabel);
         assertEquals("TWO", label.name().toString());
-        assertEquals(0, label.getChildCount());
+        assertEquals(0, label.getTLChildCount());
         // Test with parameter
         label = manager.parseLabel("THREE", Collections.singletonList("Param"), services);
         assertTrue(label instanceof LoggingTermLabel);
         assertEquals("THREE", label.name().toString());
-        assertEquals(1, label.getChildCount());
-        assertEquals("Param", label.getChild(0));
+        assertEquals(1, label.getTLChildCount());
+        assertEquals("Param", label.getTLChild(0));
         // Test unsupported
         try {
             manager.parseLabel("UNKNOWN", null, services);
@@ -850,12 +852,12 @@ public Name name() {
         }
 
         @Override
-        public Object getChild(int i) {
+        public Object getTLChild(int i) {
             return arguments.get(i);
         }
 
         @Override
-        public int getChildCount() {
+        public int getTLChildCount() {
             return arguments != null ? arguments.size() : 0;
         }
     }
diff --git a/key.core/src/test/java/de/uka/ilkd/key/logic/TestVariableNamer.java b/key.core/src/test/java/de/uka/ilkd/key/logic/TestVariableNamer.java
index 25570005100..5e5e42ac945 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/logic/TestVariableNamer.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/logic/TestVariableNamer.java
@@ -45,9 +45,9 @@ public class TestVariableNamer {
     private final LocationVariable x_2 = constructProgramVariable("x_2");
     private final LocationVariable var_1 = constructProgramVariable("var_1");
     private final LocationVariable var_2 = constructProgramVariable("var_2");
-    private final SequentFormula formulaWithX = constructFormula(x);
-    private final SequentFormula formulaWithX_1 = constructFormula(x_1);
-    private final SequentFormula formulaWithVar_1 = constructFormula(var_1);
+    private final Term formulaWithX = constructFormula(x);
+    private final Term formulaWithX_1 = constructFormula(x_1);
+    private final Term formulaWithVar_1 = constructFormula(var_1);
     private final SchemaVariable variableSV = SchemaVariableFactory
             .createProgramSV(new ProgramElementName("sv"), ProgramSVSort.VARIABLE, false);
 
@@ -63,23 +63,23 @@ private LocationVariable constructProgramVariable(String name) {
         return constructProgramVariable(pen);
     }
 
-    private SequentFormula constructFormula(ProgramVariable containedVar) {
+    private Term constructFormula(ProgramVariable containedVar) {
         Statement statement = new PostIncrement(containedVar);
         StatementBlock statementBlock = new StatementBlock(statement);
         JavaBlock javaBlock = JavaBlock.createJavaBlock(statementBlock);
 
         Term term = services.getTermBuilder().dia(javaBlock, services.getTermBuilder().tt());
 
-        return new SequentFormula(term);
+        return term;
     }
 
 
-    private PosInOccurrence constructPIO(SequentFormula formula) {
+    private PosInOccurrence constructPIO(Term formula) {
         return new PosInOccurrence(formula, PosInTerm.getTopLevel(), true);
     }
 
 
-    private Goal constructGoal(SequentFormula containedFormula) {
+    private Goal constructGoal(Term containedFormula) {
         Semisequent empty = Semisequent.EMPTY_SEMISEQUENT;
         Semisequent ante = empty.insert(0, containedFormula).semisequent();
 
@@ -148,7 +148,7 @@ private void testTemporaryNames(VariableNamer vn) {
         assertNotEquals("x", name.getProgramName());
 
         LocationVariable v = constructProgramVariable(name);
-        SequentFormula formula = constructFormula(v);
+        Term formula = constructFormula(v);
         Goal goal = constructGoal(formula);
         PosInOccurrence pio = constructPIO(formula);
         v = vn.rename(v, goal, pio);
diff --git a/key.core/src/test/java/de/uka/ilkd/key/parser/TestTacletParser.java b/key.core/src/test/java/de/uka/ilkd/key/parser/TestTacletParser.java
index 3a83e98d474..404e477f4a3 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/parser/TestTacletParser.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/parser/TestTacletParser.java
@@ -95,8 +95,8 @@ public Term parseFma(String s) {
         return parseTerm(s);
     }
 
-    public SequentFormula cf(String s) {
-        return new SequentFormula(parseFma(s));
+    public Term cf(String s) {
+        return parseFma(s);
     }
 
     public Semisequent sseq(String s) {
diff --git a/key.core/src/test/java/de/uka/ilkd/key/proof/TestGoal.java b/key.core/src/test/java/de/uka/ilkd/key/proof/TestGoal.java
index 5e186bcbe8c..a56f54d288c 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/proof/TestGoal.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/proof/TestGoal.java
@@ -8,7 +8,7 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.init.AbstractProfile;
 import de.uka.ilkd.key.proof.init.InitConfig;
 import de.uka.ilkd.key.rule.TacletForTests;
@@ -43,8 +43,9 @@ public void tearDown() {
 
     @Test
     public void testSetBack0() {
+        Term uAssumptions = TacletForTests.parseTerm("A");
         Sequent seq = Sequent.createSuccSequent(Semisequent.EMPTY_SEMISEQUENT
-                .insert(0, new SequentFormula(TacletForTests.parseTerm("A"))).semisequent());
+                .insert(0, uAssumptions).semisequent());
 
         final InitConfig initConfig =
             new InitConfig(new Services(AbstractProfile.getDefaultProfile()));
@@ -85,8 +86,9 @@ public void testSetBack0() {
 
     @Test
     public void testSetBack1() throws Exception {
+        Term uAssumptions = TacletForTests.parseTerm("A");
         Sequent seq = Sequent.createSuccSequent(Semisequent.EMPTY_SEMISEQUENT
-                .insert(0, new SequentFormula(TacletForTests.parseTerm("A"))).semisequent());
+                .insert(0, uAssumptions).semisequent());
         Node root = new Node(proof, seq);
         proof.setRoot(root);
         Goal g = new Goal(root, TacletIndexKit.getKit().createTacletIndex(),
diff --git a/key.core/src/test/java/de/uka/ilkd/key/proof/TestProofTree.java b/key.core/src/test/java/de/uka/ilkd/key/proof/TestProofTree.java
index 58fb09fa3ca..fa8e6dfb90d 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/proof/TestProofTree.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/proof/TestProofTree.java
@@ -62,25 +62,25 @@ public void setUp() {
         Term t_b7 = tf.createTerm(Equality.EQUALS, tf.createTerm(b7), tf.createTerm(b7));
 
         Sequent s1 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b1)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b1).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s2 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b2)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b2).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s3 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b3)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b3).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s4 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b4)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b4).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s5 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b5)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b5).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s6 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b6)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b6).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
         Sequent s7 = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t_b7)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t_b7).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
 
         p = new Proof("TestProofTree",
diff --git a/key.core/src/test/java/de/uka/ilkd/key/proof/TestTacletIndex.java b/key.core/src/test/java/de/uka/ilkd/key/proof/TestTacletIndex.java
index f2813d73211..bf1039a55dc 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/proof/TestTacletIndex.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/proof/TestTacletIndex.java
@@ -115,7 +115,7 @@ public void disabled_testNonInteractiveIsShownOnlyIfHeuristicIsMissed() {
         ImmutableList<RuleSet> listofHeuristic = ImmutableSLList.nil();
         listofHeuristic = listofHeuristic.prepend(h3);
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(term_p1), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(term_p1, PosInTerm.getTopLevel(), true);
         assertTrue(
             isRuleIn(variante_one.getAntecedentTaclet(pos,
                 new IHTacletFilter(true, listofHeuristic), null), ruleRewriteNonH1H2),
@@ -150,7 +150,7 @@ public void testShownIfHeuristicFits() {
 
         Term term_p1 = TacletForTests.parseTerm("p(one, zero)");
 
-        SequentFormula cfma = new SequentFormula(term_p1);
+        Term cfma = term_p1;
 
         PosInOccurrence posSucc = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), false);
 
@@ -183,9 +183,9 @@ public void testNoMatchingFindRule() {
         Term term_p2 = TacletForTests.parseTerm("\\forall nat z; p(z, one)").sub(0);
 
         PosInOccurrence posAntec =
-            new PosInOccurrence(new SequentFormula(term_p2), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(term_p2, PosInTerm.getTopLevel(), true);
         PosInOccurrence posSucc =
-            new PosInOccurrence(new SequentFormula(term_p2), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(term_p2, PosInTerm.getTopLevel(), true);
 
 
         assertFalse(
@@ -216,7 +216,7 @@ public void testMatchConflictOccurs() {
 
         ImmutableList<RuleSet> listofHeuristic = ImmutableSLList.nil();
         PosInOccurrence posAntec =
-            new PosInOccurrence(new SequentFormula(term_p4), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(term_p4, PosInTerm.getTopLevel(), true);
 
         assertFalse(
             isRuleIn(ruleIdx.getAntecedentTaclet(posAntec,
@@ -231,7 +231,7 @@ public void testNotFreeInYConflict() {
         ruleIdx.add(notfreeconflict);
 
         Term term_p5 = TacletForTests.parseTerm("\\forall nat z; p(f(z), z)");
-        SequentFormula cfma_p5 = new SequentFormula(term_p5);
+        Term cfma_p5 = term_p5;
         Sequent seq_p5 = Sequent.createAnteSequent(
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(cfma_p5).semisequent());
         PosInOccurrence pio_p5 = new PosInOccurrence(cfma_p5, PosInTerm.getTopLevel(), true);
@@ -243,7 +243,7 @@ public void testNotFreeInYConflict() {
 
         Term term_p6 = TacletForTests.parseTerm("\\forall nat z; p(zero, z)");
 
-        SequentFormula cfma_p6 = new SequentFormula(term_p6);
+        Term cfma_p6 = term_p6;
         Sequent seq_p6 = Sequent.createAnteSequent(
             Semisequent.EMPTY_SEMISEQUENT.insertFirst(cfma_p6).semisequent());
         PosInOccurrence pio_p6 = new PosInOccurrence(cfma_p6, PosInTerm.getTopLevel(), true);
diff --git a/key.core/src/test/java/de/uka/ilkd/key/proof/TestTermTacletAppIndex.java b/key.core/src/test/java/de/uka/ilkd/key/proof/TestTermTacletAppIndex.java
index 78e1af4fa9d..1fd6e267c92 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/proof/TestTermTacletAppIndex.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/proof/TestTermTacletAppIndex.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.logic.PosInOccurrence;
 import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.PrefixTermTacletAppIndexCacheImpl.CacheKey;
 import de.uka.ilkd.key.proof.rulefilter.SetRuleFilter;
@@ -121,7 +120,7 @@ private void doTestIndex0(TermTacletAppIndexCacheSet cache) {
         ruleIdx.add(remove_zero);
 
         Term term = TacletForTests.parseTerm("f(f(f(zero)))=one");
-        SequentFormula cfma = new SequentFormula(term);
+        Term cfma = term;
 
         PosInOccurrence pio = new PosInOccurrence(cfma, PosInTerm.getTopLevel(), false);
 
@@ -138,7 +137,7 @@ private void doTestIndex0(TermTacletAppIndexCacheSet cache) {
 
         // now a real change
         Term term2 = TacletForTests.parseTerm("f(f(zero))=one");
-        SequentFormula cfma2 = new SequentFormula(term2);
+        Term cfma2 = term2;
         PosInOccurrence pio2 = new PosInOccurrence(cfma2, PosInTerm.getTopLevel(), false);
 
         termIdx = termIdx.update(pio2.down(0).down(0).down(0), serv, ruleIdx,
diff --git a/key.core/src/test/java/de/uka/ilkd/key/proof/runallproofs/performance/NodeData.java b/key.core/src/test/java/de/uka/ilkd/key/proof/runallproofs/performance/NodeData.java
index a5cedbd4ef4..ea43f21c613 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/proof/runallproofs/performance/NodeData.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/proof/runallproofs/performance/NodeData.java
@@ -7,7 +7,6 @@
 import java.util.Map;
 
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.proof.Node;
@@ -41,11 +40,11 @@ private static int countAST(Node n) {
 
     private static int countAST(Sequent sequent) {
         int sum = 0;
-        for (SequentFormula f : sequent.antecedent().asList()) {
-            sum += countAST(f.formula());
+        for (Term f : sequent.antecedent().asList()) {
+            sum += countAST(f);
         }
-        for (SequentFormula f : sequent.succedent().asList()) {
-            sum += countAST(f.formula());
+        for (Term f : sequent.succedent().asList()) {
+            sum += countAST(f);
         }
         return sum;
     }
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/CreateTacletForTests.java b/key.core/src/test/java/de/uka/ilkd/key/rule/CreateTacletForTests.java
index c9b0b017cd4..8b61d735ea5 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/CreateTacletForTests.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/CreateTacletForTests.java
@@ -247,13 +247,13 @@ public void setUp() throws IOException {
         Term t_test1 = null;
         try {
             t_test1 = io.load(test1).loadDeclarations().loadProblem().getProblem().succedent()
-                    .get(0).formula();
+                    .get(0);
         } catch (Exception e) {
             LOGGER.error("Parser Error or Input Error", e);
             fail("Parser Error");
         }
-        SequentFormula cf = new SequentFormula(t_test1);
-        SequentFormula cf2 = new SequentFormula(t_test1);
+        Term cf = t_test1;
+        Term cf2 = t_test1;
         seq_test1 = Sequent.createSequent(Semisequent.EMPTY_SEMISEQUENT,
             Semisequent.EMPTY_SEMISEQUENT.insert(0, cf).semisequent());
         seq_test2 = Sequent.createSequent(Semisequent.EMPTY_SEMISEQUENT.insert(0, cf).semisequent(),
@@ -288,13 +288,13 @@ public void setUp() throws IOException {
 
         // => (c+d) = ((d -1 +1) +c) -> (c +1)+d = (d+c) +1
         seq_testNat = Sequent.createSequent(Semisequent.EMPTY_SEMISEQUENT,
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(tnat)).semisequent());
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, tnat).semisequent());
 
 
         z = new LogicVariable(new Name("z"), sort1);
         Term t_z = tf.createTerm(z);
         Term t_allzpz = services.getTermBuilder().all(z, tf.createTerm(func_p, t_z));
-        SequentFormula cf3 = new SequentFormula(t_allzpz);
+        Term cf3 = t_allzpz;
         seq_testAll = Sequent.createSequent(Semisequent.EMPTY_SEMISEQUENT,
             Semisequent.EMPTY_SEMISEQUENT.insert(0, cf3).semisequent());
 
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/TestApplyTaclet.java b/key.core/src/test/java/de/uka/ilkd/key/rule/TestApplyTaclet.java
index 2052f3a8e75..df7f53e8dd0 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/TestApplyTaclet.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/TestApplyTaclet.java
@@ -68,8 +68,8 @@ private static Semisequent parseTermForSemisequent(String t) {
         if ("".equals(t)) {
             return Semisequent.EMPTY_SEMISEQUENT;
         }
-        SequentFormula cf0 = new SequentFormula(TacletForTests.parseTerm(t));
-        return Semisequent.EMPTY_SEMISEQUENT.insert(0, cf0).semisequent();
+        return Semisequent.EMPTY_SEMISEQUENT.insert(0,
+            TacletForTests.parseTerm(t)).semisequent();
     }
 
     @BeforeEach
@@ -100,7 +100,7 @@ public void tearDown() {
 
     @Test
     public void testSuccTacletWithoutIf() {
-        Term fma = proof[0].root().sequent().succedent().getFirst().formula();
+        Term fma = proof[0].root().sequent().succedent().getFirst();
         NoPosTacletApp impright = TacletForTests.getRules().lookup("imp_right");
         TacletIndex tacletIndex = TacletIndexKit.getKit().createTacletIndex();
         tacletIndex.add(impright);
@@ -115,16 +115,16 @@ public void testSuccTacletWithoutIf() {
         ImmutableList<Goal> goals = rApp.execute(goal, TacletForTests.services());
         assertEquals(1, goals.size(), "Too many or zero goals for imp-right.");
         Sequent seq = goals.head().sequent();
-        assertEquals(seq.antecedent().getFirst().formula(), fma.sub(0),
+        assertEquals(seq.antecedent().getFirst(), fma.sub(0),
             "Wrong antecedent after imp-right");
-        assertEquals(seq.succedent().getFirst().formula(), fma.sub(1),
+        assertEquals(seq.succedent().getFirst(), fma.sub(1),
             "Wrong succedent after imp-right");
     }
 
 
     @Test
     public void testAddingRule() {
-        Term fma = proof[0].root().sequent().succedent().getFirst().formula();
+        Term fma = proof[0].root().sequent().succedent().getFirst();
         NoPosTacletApp imprightadd =
             TacletForTests.getRules().lookup("TestApplyTaclet_imp_right_add");
         TacletIndex tacletIndex = TacletIndexKit.getKit().createTacletIndex();
@@ -140,9 +140,9 @@ public void testAddingRule() {
         ImmutableList<Goal> goals = rApp.execute(goal, TacletForTests.services());
         assertEquals(1, goals.size(), "Too many or zero goals for imp_right_add.");
         Sequent seq = goals.head().sequent();
-        assertEquals(seq.antecedent().getFirst().formula(), fma.sub(0),
+        assertEquals(seq.antecedent().getFirst(), fma.sub(0),
             "Wrong antecedent after imp_right_add");
-        assertEquals(seq.succedent().getFirst().formula(), fma.sub(1),
+        assertEquals(seq.succedent().getFirst(), fma.sub(1),
             "Wrong succedent after imp_right_add");
         ImmutableList<NoPosTacletApp> nfapp = goals.head().indexOfTaclets()
                 .getNoFindTaclet(new IHTacletFilter(true, ImmutableSLList.nil()), null);
@@ -158,12 +158,12 @@ public void testAddingRule() {
         Sequent seq2 = goals.tail().head().sequent();
         assertEquals(2, goals.size(), "Preinstantiated cut-rule should be executed");
         assertTrue(
-            seq1.succedent().getFirst().formula().equals(aimpb)
-                    || seq2.succedent().getFirst().formula().equals(aimpb)
+            seq1.succedent().getFirst().equals(aimpb)
+                    || seq2.succedent().getFirst().equals(aimpb)
                     || (seq1.succedent().get(1) != null
-                            && seq1.succedent().get(1).formula().equals(aimpb))
+                            && seq1.succedent().get(1).equals(aimpb))
                     || (seq2.succedent().get(1) != null
-                            && seq2.succedent().get(1).formula().equals(aimpb)),
+                            && seq2.succedent().get(1).equals(aimpb)),
             "A->B should be in the succedent of one of the new goals now, "
                 + "it's in the antecedent, anyway.");
     }
@@ -188,7 +188,7 @@ public void testSuccTacletAllRight() {
         Sequent seq = goals.head().sequent();
         assertEquals(seq.antecedent(), Semisequent.EMPTY_SEMISEQUENT,
             "Wrong antecedent after all-right");
-        assertEquals(seq.succedent().getFirst().formula().op(),
+        assertEquals(seq.succedent().getFirst().op(),
             TacletForTests.getFunctions().lookup(new Name("p")),
             "Wrong succedent after all-right (op mismatch)");
     }
@@ -230,7 +230,7 @@ public void testTacletWithIf() {
 
     @Test
     public void testAntecTacletWithoutIf() {
-        Term fma = proof[3].root().sequent().antecedent().getFirst().formula();
+        Term fma = proof[3].root().sequent().antecedent().getFirst();
         NoPosTacletApp impleft = TacletForTests.getRules().lookup("imp_left");
         TacletIndex tacletIndex = TacletIndexKit.getKit().createTacletIndex();
         tacletIndex.add(impleft);
@@ -246,19 +246,19 @@ public void testAntecTacletWithoutIf() {
         assertEquals(2, goals.size(), "Too many or zero goals for imp-left.");
         Sequent seq = goals.head().sequent();
         if (!seq.succedent().isEmpty()) {
-            assertEquals(seq.succedent().getFirst().formula(), fma.sub(0),
+            assertEquals(seq.succedent().getFirst(), fma.sub(0),
                 "Wrong succedent after imp-left");
             goals = goals.tail();
             seq = goals.head().node().sequent();
-            assertEquals(seq.antecedent().getFirst().formula(), fma.sub(1),
+            assertEquals(seq.antecedent().getFirst(), fma.sub(1),
                 "Wrong antecedent after imp-left");
         } else {
-            assertEquals(seq.antecedent().getFirst().formula(), fma.sub(1),
+            assertEquals(seq.antecedent().getFirst(), fma.sub(1),
                 "Wrong antecedent after imp-left");
             goals = goals.tail();
             seq = goals.head().node().sequent();
 
-            assertEquals(seq.succedent().getFirst().formula(), fma.sub(0),
+            assertEquals(seq.succedent().getFirst(), fma.sub(0),
                 "Wrong succedent after imp-left");
         }
     }
@@ -282,7 +282,7 @@ public void testRewriteTacletWithoutIf() {
         ImmutableList<Goal> goals = rApp.execute(goal, TacletForTests.services());
         assertEquals(1, goals.size(), "Too many or zero goals for contradiction.");
         Sequent seq = goals.head().sequent();
-        Term term = seq.succedent().getFirst().formula().sub(1).sub(0).sub(0);
+        Term term = seq.succedent().getFirst().sub(1).sub(0).sub(0);
         assertEquals(term, TacletForTests.parseTerm("!B -> !A"));
     }
 
@@ -308,17 +308,17 @@ public void testNoFindTacletWithoutIf() {
         Sequent seq1 = goals.head().sequent();
         goals = goals.tail();
         Sequent seq2 = goals.head().sequent();
-        if (!seq1.antecedent().isEmpty() && seq1.antecedent().getFirst().formula().equals(t_c)) {
+        if (!seq1.antecedent().isEmpty() && seq1.antecedent().getFirst().equals(t_c)) {
             assertTrue(
-                seq2.succedent().getFirst().formula().equals(t_c)
-                        || seq2.succedent().get(1).formula().equals(t_c),
+                seq2.succedent().getFirst().equals(t_c)
+                        || seq2.succedent().get(1).equals(t_c),
                 "D is in antecedent of 1st goal but not in succedent of 2nd");
         } else {
             assertTrue(
-                seq1.succedent().getFirst().formula().equals(t_c)
-                        || seq1.succedent().get(1).formula().equals(t_c),
+                seq1.succedent().getFirst().equals(t_c)
+                        || seq1.succedent().get(1).equals(t_c),
                 "D is not in antecedent and not in succedent " + "of first new goal");
-            assertEquals(seq2.antecedent().getFirst().formula(), t_c,
+            assertEquals(seq2.antecedent().getFirst(), t_c,
                 "D is in succedent of first new goal, but not in antecedent "
                     + "of second new goal");
         }
@@ -330,10 +330,10 @@ public void testNoFindTacletWithoutIf() {
      * public String automaticProof(Sequent initSeq, TacletIndex index){ String out=""; Proof
      * proof=new Proof(); proof.setRoot(new Node(proof, initSeq)); IList<Goal>
      * goals=ImmSLList.<Goal>nil(); Goal goal=new Goal(proof.root(),new RuleAppIndex(index));
-     * goals=goals.prepend(goal); while (goals.size()!=0) { SequentFormula cfma=null; SequentFormula
+     * goals=goals.prepend(goal); while (goals.size()!=0) { Term cfma=null; Term
      * userCfma=null; // in the real system the //user would select this IList<TacletApp>
      * rapplist=ImmSLList.<TacletApp>nil(); out="\n"+out+("Goals: "+goals+"\n"); goal=goals.head();
-     * Iterator<SequentFormula> it=goal.node().sequent().antecedent().iterator(); while
+     * Iterator<Term> it=goal.node().sequent().antecedent().iterator(); while
      * (it.hasNext()) { userCfma=it.next(); rapplist=rapplist.prepend(goal.ruleAppIndex().
      * getTacletAppAtAndBelow(TacletFilter.TRUE, new PosInOccurrence(userCfma, PosInTerm.TOP_LEVEL,
      * goal.node().sequent()))); } if (rapplist.isEmpty()) {
@@ -446,19 +446,22 @@ public void testBugBrokenApply() {
         ImmutableList<Goal> goals = rApplist.head().execute(goal, TacletForTests.services);
 
         assertEquals(2, goals.size(), "Expected two goals");
+        Term fml1 = goals.head().sequent().succedent().iterator().next();
+        Term fml2 = goals.head().sequent().antecedent().iterator().next();
         assertTrue(
             goals.head().sequent().antecedent().size() == 1
-                    && goals.head().sequent().antecedent().iterator().next().formula()
+                    && fml2
                             .op() == Quantifier.ALL
                     && goals.head().sequent().succedent().size() == 1
-                    && goals.head().sequent().succedent().iterator().next().formula()
+                    && fml1
                             .op() == Quantifier.ALL,
             "First goal should be 'b==>b', but is " + goals.head().sequent());
         goals = goals.tail();
+        Term succFml = goals.head().sequent().succedent().iterator().next();
         assertTrue(
             goals.head().sequent().antecedent().size() == 0
                     && goals.head().sequent().succedent().size() == 1
-                    && goals.head().sequent().succedent().iterator().next().formula()
+                    && succFml
                             .op() == Quantifier.ALL,
             "Second goal should be '==>b', but is " + goals.head().sequent());
 
@@ -506,11 +509,11 @@ public void testBugID177() {
 
 
         assertEquals(1, goals.size(), "Expected one goal");
-        Iterator<SequentFormula> it = goals.head().sequent().antecedent().iterator();
+        Iterator<Term> it = goals.head().sequent().antecedent().iterator();
         assertTrue(
             goals.head().sequent().antecedent().size() == 2
-                    && it.next().formula().equals(TacletForTests.parseTerm("A"))
-                    && it.next().formula().equals(TacletForTests.parseTerm("B")),
+                    && it.next().equals(TacletForTests.parseTerm("A"))
+                    && it.next().equals(TacletForTests.parseTerm("B")),
             "Expected 'A, B ==>', but is " + goals.head().sequent());
     }
 
@@ -546,13 +549,12 @@ public void testBugID188() {
 
         assertEquals(1, goals.size(), "Expected one goal");
 
-        Iterator<SequentFormula> it = goals.head().sequent().antecedent().iterator();
-
+        Iterator<Term> it = goals.head().sequent().antecedent().iterator();
         assertTrue(
             goals.head().sequent().antecedent().size() == 2
                     && goals.head().sequent().succedent().size() == 0
-                    && it.next().formula().equals(TacletForTests.parseTerm("A"))
-                    && it.next().formula().equals(TacletForTests.parseTerm("B")),
+                    && it.next().equals(TacletForTests.parseTerm("A"))
+                    && it.next().equals(TacletForTests.parseTerm("B")),
             "Expected 'A, B ==>', but is " + goals.head().sequent());
     }
 
@@ -611,10 +613,9 @@ public void testModalityLevel1() {
 
         assertEquals(0, appList.size(), "Did not expect a match.");
 
-        Term ifterm = TacletForTests.parseTerm("{i:=0}(f(const)=f(f(const)))");
-        SequentFormula ifformula = new SequentFormula(ifterm);
+        Term assumesFormula = TacletForTests.parseTerm("{i:=0}(f(const)=f(f(const)))");
         ImmutableList<IfFormulaInstantiation> ifInsts = ImmutableSLList
-                .<IfFormulaInstantiation>nil().prepend(new IfFormulaInstDirect(ifformula));
+                .<IfFormulaInstantiation>nil().prepend(new IfFormulaInstDirect(assumesFormula));
         appIt = rApplist.iterator();
         while (appIt.hasNext()) {
             TacletApp a =
@@ -632,13 +633,13 @@ public void testModalityLevel1() {
 
         { // Goal one
             Sequent correctSeq =
-                proof[11].root().sequent().addFormula(ifformula, true, true).sequent();
+                proof[11].root().sequent().addFormula(assumesFormula, true, true).sequent();
             assertEquals(goals.head().sequent(), correctSeq, "Wrong result");
         }
 
         { // Goal two
             Sequent correctSeq =
-                proof[10].root().sequent().addFormula(ifformula, false, true).sequent();
+                proof[10].root().sequent().addFormula(assumesFormula, false, true).sequent();
             assertEquals(goals.tail().head().sequent(), correctSeq, "Wrong result");
         }
     }
@@ -737,8 +738,8 @@ private void doTestCatchList(int p_proof) {
 
         Sequent correctSeq = proof[p_proof + 1].root().sequent();
 
-        Term resultFormula = goals.head().sequent().getFormulabyNr(1).formula();
-        Term correctFormula = correctSeq.getFormulabyNr(1).formula();
+        Term resultFormula = goals.head().sequent().getFormulabyNr(1);
+        Term correctFormula = correctSeq.getFormulabyNr(1);
 
         assertTrue(resultFormula.equalsModProperty(correctFormula, RENAMING_PROPERTY),
             "Wrong result. Expected:"
@@ -808,10 +809,12 @@ public void testCompleteContextAddBug() {
         assertEquals(1, goals.size(), "Expected one goal.");
 
         // the content of the diamond must not have changed
+        Term fml1 = proof[22].root().sequent().getFormulabyNr(1);
         ProgramElement expected =
-            proof[22].root().sequent().getFormulabyNr(1).formula().javaBlock().program();
+            fml1.javaBlock().program();
+        Term fml = goals.head().sequent().getFormulabyNr(1);
         ProgramElement is =
-            goals.head().sequent().getFormulabyNr(1).formula().sub(0).javaBlock().program();
+            fml.sub(0).javaBlock().program();
         assertEquals(expected, is, "Context has been thrown away.");
 
     }
@@ -844,8 +847,9 @@ public void testContextAdding() {
             TacletForTests.parsePrg("{try{ ; while (1==1) {if (1==2) {break;}} return 1==3; "
                 + "int i=17; } catch (Exception e) { return null;}}");
 
+        Term fml = goals.head().sequent().getFormulabyNr(1);
         ProgramElement is =
-            goals.head().sequent().getFormulabyNr(1).formula().javaBlock().program();
+            fml.javaBlock().program();
         // FIXME weigl: This test case is spurious:
         // actual.toString() == expected.toString() but internally there is a difference.
         assertTrue(expected.equalsModRenaming(is, new NameAbstractionTable()),
@@ -880,8 +884,7 @@ public void testRemoveEmptyBlock() {
             TacletForTests.parsePrg("{try{while (1==1) {if (1==2) {break;}} return 1==3; "
                 + "int i=17; } catch (Exception e) { return null;}}");
 
-        ProgramElement is =
-            goals.head().sequent().getFormulabyNr(1).formula().javaBlock().program();
+        ProgramElement is = goals.head().sequent().getFormulabyNr(1).javaBlock().program();
         assertTrue(expected.equalsModRenaming(is, new NameAbstractionTable()),
             "Expected:" + expected + "\n but was:" + is);
     }
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/TestCollisionResolving.java b/key.core/src/test/java/de/uka/ilkd/key/rule/TestCollisionResolving.java
index cc1acbca408..19b8b4c404a 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/TestCollisionResolving.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/TestCollisionResolving.java
@@ -120,7 +120,7 @@ public void testCollisionResolvingWithContext() {
             (FindTaclet) TacletForTests.getTaclet("TestCollisionResolving_coll_context").taclet();
 
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(term), PosInTerm.getTopLevel().down(0), true);
+            new PosInOccurrence(term, PosInTerm.getTopLevel().down(0), true);
 
         TacletApp result =
             PosTacletApp.createPosTacletApp(coll_varSV, coll_varSV.getMatcher().matchFind(
@@ -145,7 +145,7 @@ public void testVarNamespaceCreationWithContext() {
         FindTaclet taclet =
             (FindTaclet) TacletForTests.getTaclet("TestCollisionResolving_ns1").taclet();
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(term), PosInTerm.getTopLevel().down(0), true);
+            new PosInOccurrence(term, PosInTerm.getTopLevel().down(0), true);
         TacletApp app = PosTacletApp.createPosTacletApp(taclet,
             taclet.getMatcher().matchFind(term.sub(0), MatchConditions.EMPTY_MATCHCONDITIONS, null),
             pos, services);
@@ -214,10 +214,12 @@ public void testNameConflict1() {
         SchemaVariable v = TacletForTests.getSchemaVariables().lookup(new Name("v"));
         FindTaclet taclet =
             (FindTaclet) TacletForTests.getTaclet("TestCollisionResolving_name_conflict").taclet();
+        Term uAssumptions = TacletForTests.parseTerm("\\exists s x; p(x)");
+        Term uAssumptions1 = TacletForTests.parseTerm("\\forall s x; p(x)");
         Semisequent semiseq = Semisequent.EMPTY_SEMISEQUENT
-                .insert(0, new SequentFormula(TacletForTests.parseTerm("\\forall s x; p(x)")))
+                .insert(0, uAssumptions1)
                 .semisequent()
-                .insert(1, new SequentFormula(TacletForTests.parseTerm("\\exists s x; p(x)")))
+                .insert(1, uAssumptions)
                 .semisequent();
         Sequent seq = Sequent.createSuccSequent(semiseq);
         PosInOccurrence pos = new PosInOccurrence(semiseq.get(0), PosInTerm.getTopLevel(), false);
@@ -304,8 +306,8 @@ public void testNameConflictAfterInput() throws SVInstantiationException {
      * SchemaVariable v = TacletForTests.getVariables().lookup(new Name("v")); FindTaclet taclet =
      * (FindTaclet) TacletForTests.getTaclet
      * ("TestCollisionResolving_name_conflict_with_context").taclet(); Semisequent semiseq =
-     * Semisequent.EMPTY_SEMISEQUENT .insert(0, new SequentFormula(TacletForTests.parseTerm("ex x:s"
-     * +".p(x)"))) .insert(1, new SequentFormula(TacletForTests.parseTerm("all x:s" +".p(x)")));
+     * Semisequent.EMPTY_SEMISEQUENT .insert(0, Term.create(TacletForTests.parseTerm("ex x:s"
+     * +".p(x)"))) .insert(1, Term.create(TacletForTests.parseTerm("all x:s" +".p(x)")));
      * Sequent seq=Sequent.createSuccSequent(semiseq); PosInOccurrence pos=new
      * PosInOccurrence(semiseq.get(1), PosInTerm.TOP_LEVEL.down(0), seq); IList<SVInstantiations>
      * sviList=taclet.matchIf (seq, taclet.match(semiseq.get(1).formula().sub(0), taclet.find(),
@@ -327,7 +329,7 @@ public void testNameConflictWithContextAfterInput() throws SVInstantiationExcept
                 .getTaclet("TestCollisionResolving_name_conflict_with_context2").taclet();
         Term term = TacletForTests.parseTerm("\\forall s x; p(x)");
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(term), PosInTerm.getTopLevel().down(0), true);
+            new PosInOccurrence(term, PosInTerm.getTopLevel().down(0), true);
         MatchConditions mc =
             taclet.getMatcher().matchFind(term.sub(0), MatchConditions.EMPTY_MATCHCONDITIONS, null);
         TacletApp app = PosTacletApp.createPosTacletApp(taclet, mc, pos, services);
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/TestMatchTaclet.java b/key.core/src/test/java/de/uka/ilkd/key/rule/TestMatchTaclet.java
index f2e55c57052..448af059941 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/TestMatchTaclet.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/TestMatchTaclet.java
@@ -125,8 +125,9 @@ public void testVarOccursInIfAndAddRule() {
         // test at the subformula p(z) -> A that has a free variable
         // therefore no match should be found
 
+        Term uAssumptions = match.sub(0);
         Sequent seq = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(match.sub(0))).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, uAssumptions).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
 
         assertEquals(0,
@@ -137,7 +138,7 @@ public void testVarOccursInIfAndAddRule() {
 
         // we bind the free variable now a match should be found
         seq = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(match)).semisequent(),
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, match).semisequent(),
             Semisequent.EMPTY_SEMISEQUENT);
 
         assertNotEquals(0,
@@ -159,7 +160,7 @@ public void testVarOccursInFindAndAddRule() {
             find_addrule_conflict.getMatcher()
                     .matchFind(match.sub(0), MatchConditions.EMPTY_MATCHCONDITIONS, services)
                     .getInstantiations(),
-            new PosInOccurrence(new SequentFormula(match), PosInTerm.getTopLevel().down(0), true),
+            new PosInOccurrence(match, PosInTerm.getTopLevel().down(0), true),
             services);
 
 
@@ -173,7 +174,7 @@ public void testVarOccursInFindAndAddRule() {
             find_addrule_conflict.getMatcher()
                     .matchFind(match, MatchConditions.EMPTY_MATCHCONDITIONS, services)
                     .getInstantiations(),
-            new PosInOccurrence(new SequentFormula(match), PosInTerm.getTopLevel(), true),
+            new PosInOccurrence(match, PosInTerm.getTopLevel(), true),
             services);
         assertNotNull(app, "A match should have been found,"
             + " because here there formerly free variable is bound.");
@@ -188,13 +189,14 @@ public void testRWVarOccursFindAndIf() {
         // seq contains term that can match but has a free variable, so
         // matching to a should be not possible
         Term match = TacletForTests.parseTerm("\\forall testSort z; (p(z) -> A)");
+        Term uAssumptions = match.sub(0);
         TacletApp app = PosTacletApp
                 .createPosTacletApp(if_find_clash,
                     if_find_clash.getMatcher()
                             .matchFind(match.sub(0), MatchConditions.EMPTY_MATCHCONDITIONS,
                                 services)
                             .getInstantiations(),
-                    new PosInOccurrence(new SequentFormula(match.sub(0)),
+                    new PosInOccurrence(uAssumptions,
                         PosInTerm.getTopLevel().down(0), true),
                     services);
 
@@ -247,14 +249,14 @@ public void testCloseWithBoundRenaming() {
         Term closeable_one = TacletForTests.parseTerm("\\forall testSort z; p(z)");
         Term closeable_two = TacletForTests.parseTerm("\\forall testSort y; p(y)");
         Sequent seq = Sequent.createSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(closeable_one))
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, closeable_one)
                     .semisequent(),
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(closeable_two))
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, closeable_two)
                     .semisequent());
         TacletIndex index = TacletIndexKit.getKit().createTacletIndex();
         index.add(close_rule.taclet());
         PosInOccurrence pio =
-            new PosInOccurrence(new SequentFormula(closeable_two), PosInTerm.getTopLevel(), false);
+            new PosInOccurrence(closeable_two, PosInTerm.getTopLevel(), false);
 
         TacletApp tacletApp =
             index.getSuccedentTaclet(pio, new IHTacletFilter(true, ImmutableSLList.nil()), services)
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/TestSchemaModalOperators.java b/key.core/src/test/java/de/uka/ilkd/key/rule/TestSchemaModalOperators.java
index 00360649d89..cdbe9d57518 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/TestSchemaModalOperators.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/TestSchemaModalOperators.java
@@ -47,7 +47,8 @@ private static Semisequent parseTermForSemisequent(String t) {
         if ("".equals(t)) {
             return Semisequent.EMPTY_SEMISEQUENT;
         }
-        SequentFormula cf0 = new SequentFormula(TacletForTests.parseTerm(t));
+        Term uAssumptions = TacletForTests.parseTerm(t);
+        Term cf0 = uAssumptions;
         return Semisequent.EMPTY_SEMISEQUENT.insert(0, cf0).semisequent();
     }
 
@@ -94,8 +95,8 @@ public void setUp() {
          * consMV_f_c_X = Constraint.BOTTOM.unify(t_mv, t_f_c_X); consMV_f_X_c =
          * Constraint.BOTTOM.unify(t_mv, t_f_X_c);
          *
-         * SequentFormula cf1 = new SequentFormula(TacletForTests.parseTerm("A & B"), consMV_f_c_X);
-         * SequentFormula cf2 = new SequentFormula(TacletForTests.parseTerm("!(A | B)"),
+         * Term cf1 = Term.create(TacletForTests.parseTerm("A & B"), consMV_f_c_X);
+         * Term cf2 = Term.create(TacletForTests.parseTerm("!(A | B)"),
          * consMV_f_X_c);
          *
          * Sequent seq = Sequent.createSequent
@@ -152,10 +153,9 @@ public void testSchemaModalities1() {
         assertSame(Modality.JavaModalityKind.DIA, mc.getInstantiations().getInstantiation(osv));
 
         PosInOccurrence pos =
-            new PosInOccurrence(new SequentFormula(goal), PosInTerm.getTopLevel(), true);
+            new PosInOccurrence(goal, PosInTerm.getTopLevel(), true);
         PosTacletApp tacletApp = PosTacletApp.createPosTacletApp(t, mc, pos, services);
-        Term instReplace =
-            t.getRewriteResult(null, new TermLabelState(), services, tacletApp).formula();
+        Term instReplace = t.getRewriteResult(null, new TermLabelState(), services, tacletApp);
         assertNotNull(instReplace);
         assertSame(Modality.JavaModalityKind.DIA, ((Modality) instReplace.op()).kind());
     }
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/conditions/TestApplyUpdateOnRigidCondition.java b/key.core/src/test/java/de/uka/ilkd/key/rule/conditions/TestApplyUpdateOnRigidCondition.java
index 91ff2692110..fae51cc5a3e 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/conditions/TestApplyUpdateOnRigidCondition.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/conditions/TestApplyUpdateOnRigidCondition.java
@@ -12,6 +12,7 @@
 import de.uka.ilkd.key.rule.inst.SVInstantiations;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 
 import org.junit.jupiter.api.Test;
@@ -229,7 +230,7 @@ private Term applyUpdateOnTerm(Term term) {
      * @param tOrPhi the {@link SchemaVariable} that is instantiated with the term or formula in
      *        <code>term</code>
      * @param result the {@link SchemaVariable} that is instantiated with the result of a
-     *        {@link ApplyUpdateOnRigidCondition#check(SchemaVariable, SVSubstitute, MatchConditions, Services)}
+     *        {@link ApplyUpdateOnRigidCondition#check(SchemaVariable, SyntaxElement, MatchConditions, Services)}
      *        call
      *
      * @return the original formula or term if the update cannot be applied; else, the updated
diff --git a/key.core/src/test/java/de/uka/ilkd/key/rule/tacletbuilder/TestTacletBuild.java b/key.core/src/test/java/de/uka/ilkd/key/rule/tacletbuilder/TestTacletBuild.java
index 6cdd90af208..e97aea5da65 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/rule/tacletbuilder/TestTacletBuild.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/rule/tacletbuilder/TestTacletBuild.java
@@ -78,7 +78,7 @@ public void testUniquenessOfIfAndFindVarSVsInIfAndFind() {
         Term A = tf.createTerm(TacletForTests.getFunctions().lookup(new Name("A")), NO_SUBTERMS);
         Term t1 = tb.all((QuantifiableVariable) u, A);
         Sequent seq = Sequent.createSuccSequent(
-            Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t1)).semisequent());
+            Semisequent.EMPTY_SEMISEQUENT.insert(0, t1).semisequent());
         Term t2 = tb.ex((QuantifiableVariable) u, A);
         SuccTacletBuilder sb = new SuccTacletBuilder();
         sb.setIfSequent(seq);
@@ -100,8 +100,8 @@ public void testUniquenessOfIfAndFindVarSVBothInIf() {
         Term t1 = tb.all((QuantifiableVariable) u, A);
         Term t2 = tb.ex((QuantifiableVariable) u, A);
         Sequent seq = Sequent
-                .createSuccSequent(Semisequent.EMPTY_SEMISEQUENT.insert(0, new SequentFormula(t1))
-                        .semisequent().insert(1, new SequentFormula(t2)).semisequent());
+                .createSuccSequent(Semisequent.EMPTY_SEMISEQUENT.insert(0, t1)
+                        .semisequent().insert(1, t2).semisequent());
         SuccTacletBuilder sb = new SuccTacletBuilder();
         sb.setIfSequent(seq);
         sb.setFind(A);
diff --git a/key.core/src/test/java/de/uka/ilkd/key/smt/newsmt2/ProveSMTLemmasTest.java b/key.core/src/test/java/de/uka/ilkd/key/smt/newsmt2/ProveSMTLemmasTest.java
index b05f4767d35..1c4b18b9fcc 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/smt/newsmt2/ProveSMTLemmasTest.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/smt/newsmt2/ProveSMTLemmasTest.java
@@ -91,7 +91,7 @@ public void testSMTLemmaSoundness(String name, String lemmaString) throws Except
                     // and check if proofs are actually for the right theorem!
                     KeyIO io = new KeyIO(loadedProof.getServices());
                     Term parsedLemma = io.parseExpression(lemmaString);
-                    Term actual = loadedProof.root().sequent().succedent().get(0).formula();
+                    Term actual = loadedProof.root().sequent().succedent().get(0);
                     if (!actual.equalsModProperty(parsedLemma, RENAMING_PROPERTY)) {
                         LOGGER.info("Stored : {}", parsedLemma);
                         LOGGER.warn("Proven : {}", actual);
diff --git a/key.core/src/test/java/de/uka/ilkd/key/util/TestEqualsModProofIrrelevancy.java b/key.core/src/test/java/de/uka/ilkd/key/util/TestEqualsModProofIrrelevancy.java
index f8347da086e..5927c33693d 100644
--- a/key.core/src/test/java/de/uka/ilkd/key/util/TestEqualsModProofIrrelevancy.java
+++ b/key.core/src/test/java/de/uka/ilkd/key/util/TestEqualsModProofIrrelevancy.java
@@ -7,7 +7,8 @@
 
 import de.uka.ilkd.key.control.DefaultUserInterfaceControl;
 import de.uka.ilkd.key.control.KeYEnvironment;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.proof.Node;
 import de.uka.ilkd.key.proof.Proof;
 
@@ -48,9 +49,10 @@ void testJavaProof() throws Exception {
             Assertions.assertNotNull(node1);
             Assertions.assertNotNull(node2);
             for (int j = 1; j <= node1.sequent().size(); j++) {
-                SequentFormula sf1 = node1.sequent().getFormulabyNr(j);
-                SequentFormula sf2 = node2.sequent().getFormulabyNr(j);
-                Assertions.assertTrue(sf1.equalsModProofIrrelevancy(sf2));
+                Term sf1 = node1.sequent().getFormulabyNr(j);
+                Term sf2 = node2.sequent().getFormulabyNr(j);
+                Assertions.assertTrue(ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY
+                        .equalsModThisProperty(sf1, sf2));
             }
             if (node1.getAppliedRuleApp() != null) {
                 Assertions.assertTrue(
diff --git a/key.ncore/src/main/java/org/key_project/logic/SyntaxElement.java b/key.ncore/src/main/java/org/key_project/logic/SyntaxElement.java
index 244f53bbe4b..12f2c5be7e5 100644
--- a/key.ncore/src/main/java/org/key_project/logic/SyntaxElement.java
+++ b/key.ncore/src/main/java/org/key_project/logic/SyntaxElement.java
@@ -8,4 +8,22 @@
  * AST nodes.
  */
 public interface SyntaxElement {
+    /**
+     * Get the {@code n}-th child of this syntax element.
+     *
+     * @param n index of the child.
+     * @return the {@code n}-th child of this syntax element.
+     * @throws IndexOutOfBoundsException if there is no {@code n}-th child.
+     */
+    SyntaxElement getChild(int n);
+
+    /**
+     *
+     * @return the number of children of this syntax element.
+     */
+    int getChildCount();
+
+    default SyntaxElementCursor getCursor() {
+        return new SyntaxElementCursor(this);
+    }
 }
diff --git a/key.ncore/src/main/java/org/key_project/logic/SyntaxElementCursor.java b/key.ncore/src/main/java/org/key_project/logic/SyntaxElementCursor.java
new file mode 100644
index 00000000000..52a040d7819
--- /dev/null
+++ b/key.ncore/src/main/java/org/key_project/logic/SyntaxElementCursor.java
@@ -0,0 +1,101 @@
+/* This file is part of KeY - https://key-project.org
+ * KeY is licensed under the GNU General Public License Version 2
+ * SPDX-License-Identifier: GPL-2.0-only */
+package org.key_project.logic;
+
+import java.util.ArrayDeque;
+import java.util.Deque;
+
+/**
+ * A cursor (or walker) for navigating {@link SyntaxElement}s in pre-order. *
+ */
+public class SyntaxElementCursor {
+    private record ParentAndPosition(SyntaxElement parent, int index) {}
+
+    private final Deque<ParentAndPosition> path = new ArrayDeque<>();
+
+    private SyntaxElement node;
+
+    SyntaxElementCursor(SyntaxElement node) {
+        this.node = node;
+    }
+
+    public SyntaxElement getCurrentNode() {
+        return node;
+    }
+
+    /**
+     * Advance the cursor to the current node's first child if possible.
+     * Otherwise, no changes to the state occur.
+     *
+     * @return true iff the current node has at least one child.
+     */
+    public boolean gotoFirstChild() {
+        if (node.getChildCount() <= 0)
+            return false;
+        path.push(new ParentAndPosition(node, 0));
+        node = node.getChild(0);
+        return true;
+    }
+
+    /**
+     * Advance the cursor to the current node's next sibling if possible.
+     * Otherwise, no changes to the state occur.
+     *
+     * @return true iff the current node has at least one sibling not yet visited.
+     */
+    public boolean gotoNextSibling() {
+        if (path.isEmpty())
+            return false;
+        var pnp = path.pop();
+        SyntaxElement parent = pnp.parent;
+        int index = pnp.index + 1;
+        if (index >= parent.getChildCount()) {
+            path.push(pnp);
+            return false;
+        }
+        path.push(new ParentAndPosition(parent, index));
+        node = parent.getChild(index);
+        return true;
+    }
+
+    /**
+     * Advance the cursor to the current node's parent if possible.
+     * Otherwise, no changes to the state occur.
+     *
+     * @return true iff the current node is not the root.
+     */
+    public boolean gotoParent() {
+        if (path.isEmpty())
+            return false;
+        node = path.pop().parent;
+        return true;
+    }
+
+    /**
+     * Advance cursor to the next node.
+     * If the node has children, the cursor advances to the first child.
+     * Otherwise, if the node has unvisited siblings, the cursor advances to the next unvisited
+     * sibling.
+     * Otherwise, no changes to the state.
+     *
+     * @return true iff the node has children or an unvisited sibling.
+     */
+    public boolean goToNext() {
+        var ancestors = new ArrayDeque<ParentAndPosition>();
+        if (gotoFirstChild())
+            return true;
+        if (gotoNextSibling())
+            return true;
+        while (!path.isEmpty()) {
+            ancestors.add(path.pop());
+            if (gotoNextSibling())
+                return true;
+        }
+        // Nothing found; re-build stack
+        for (var ancestor : ancestors) {
+            path.push(ancestor);
+        }
+        return false;
+    }
+}
diff --git a/key.ncore/src/main/java/org/key_project/logic/Term.java b/key.ncore/src/main/java/org/key_project/logic/Term.java
index c08c5a866fd..5dc16e0ea29 100644
--- a/key.ncore/src/main/java/org/key_project/logic/Term.java
+++ b/key.ncore/src/main/java/org/key_project/logic/Term.java
@@ -91,4 +91,23 @@ public interface Term extends LogicElement, Sorted {
      * @param visitor the Visitor
      */
     <T extends Term> void execPreOrder(Visitor<T> visitor);
+
+    @Override
+    default int getChildCount() {
+        return 1 + boundVars().size() + subs().size();
+    }
+
+    @Override
+    default SyntaxElement getChild(int n) {
+        if (n == 0)
+            return op();
+        n--;
+        if (n < boundVars().size())
+            return boundVars().get(n);
+        n -= boundVars().size();
+        if (n < subs().size())
+            return sub(n);
+        throw new IndexOutOfBoundsException(
+            "Term " + this + " has only " + getChildCount() + " children");
+    }
 }
diff --git a/key.ncore/src/main/java/org/key_project/logic/TerminalSyntaxElement.java b/key.ncore/src/main/java/org/key_project/logic/TerminalSyntaxElement.java
new file mode 100644
index 00000000000..860f1e62a65
--- /dev/null
+++ b/key.ncore/src/main/java/org/key_project/logic/TerminalSyntaxElement.java
@@ -0,0 +1,16 @@
+/* This file is part of KeY - https://key-project.org
+ * KeY is licensed under the GNU General Public License Version 2
+ * SPDX-License-Identifier: GPL-2.0-only */
+package org.key_project.logic;
+
+public interface TerminalSyntaxElement extends SyntaxElement {
+    @Override
+    default SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException(this.getClass() + " " + this + " has no children");
+    }
+
+    @Override
+    default int getChildCount() {
+        return 0;
+    }
+}
diff --git a/key.ncore/src/main/java/org/key_project/logic/op/Function.java b/key.ncore/src/main/java/org/key_project/logic/op/Function.java
index 94b97468c93..ec55b5dcd44 100644
--- a/key.ncore/src/main/java/org/key_project/logic/op/Function.java
+++ b/key.ncore/src/main/java/org/key_project/logic/op/Function.java
@@ -4,6 +4,7 @@
 package org.key_project.logic.op;
 
 import org.key_project.logic.Name;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.sort.Sort;
 import org.key_project.util.collection.ImmutableArray;
 
@@ -51,4 +52,14 @@ public final boolean isSkolemConstant() {
     public final String toString() {
         return (name() + (whereToBind() == null ? "" : "{" + whereToBind() + "}"));
     }
+
+    @Override
+    public int getChildCount() {
+        return 0;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        throw new IndexOutOfBoundsException("Function " + name() + " has no children");
+    }
 }
diff --git a/key.ncore/src/main/java/org/key_project/logic/op/Modality.java b/key.ncore/src/main/java/org/key_project/logic/op/Modality.java
index 10d40f7a239..9c93156a847 100644
--- a/key.ncore/src/main/java/org/key_project/logic/op/Modality.java
+++ b/key.ncore/src/main/java/org/key_project/logic/op/Modality.java
@@ -5,9 +5,7 @@
 
 import java.util.Objects;
 
-import org.key_project.logic.Name;
-import org.key_project.logic.Named;
-import org.key_project.logic.Program;
+import org.key_project.logic.*;
 import org.key_project.logic.sort.Sort;
 
 import org.jspecify.annotations.Nullable;
@@ -41,10 +39,25 @@ public final <K extends Kind> K kind() {
      */
     public abstract Program program();
 
+    @Override
+    public int getChildCount() {
+        return 2;
+    }
+
+    @Override
+    public SyntaxElement getChild(int n) {
+        return switch (n) {
+        case 0 -> kind;
+        case 1 -> program();
+        default -> throw new IndexOutOfBoundsException(
+            "Modality " + name() + " has only two children");
+        };
+    }
+
     /**
      * Modality kinds like box and diamond.
      */
-    public abstract static class Kind implements Named {
+    public abstract static class Kind implements Named, TerminalSyntaxElement {
         private final Name name;
 
         public Kind(Name name) {
diff --git a/key.ncore/src/main/java/org/key_project/logic/op/Operator.java b/key.ncore/src/main/java/org/key_project/logic/op/Operator.java
index 3a4f900dde8..81fd39f426c 100644
--- a/key.ncore/src/main/java/org/key_project/logic/op/Operator.java
+++ b/key.ncore/src/main/java/org/key_project/logic/op/Operator.java
@@ -4,11 +4,12 @@
 package org.key_project.logic.op;
 
 import org.key_project.logic.Named;
+import org.key_project.logic.SyntaxElement;
 import org.key_project.logic.Term;
 import org.key_project.logic.TermCreationException;
 import org.key_project.logic.sort.Sort;
 
-public interface Operator extends Named {
+public interface Operator extends Named, SyntaxElement {
     /**
      * the arity of this operator
      */
diff --git a/key.ncore/src/test/java/org/key_project/logic/SyntaxElementCursorTest.java b/key.ncore/src/test/java/org/key_project/logic/SyntaxElementCursorTest.java
new file mode 100644
index 00000000000..86aafe4dba2
--- /dev/null
+++ b/key.ncore/src/test/java/org/key_project/logic/SyntaxElementCursorTest.java
@@ -0,0 +1,62 @@
+/* This file is part of KeY - https://key-project.org
+ * KeY is licensed under the GNU General Public License Version 2
+ * SPDX-License-Identifier: GPL-2.0-only */
+package org.key_project.logic;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+public class SyntaxElementCursorTest {
+    class Node implements SyntaxElement {
+        private final int value;
+        private final Node[] children;
+
+        public Node(int value, Node... children) {
+            this.value = value;
+            this.children = children;
+        }
+
+        public int getValue() {
+            return value;
+        }
+
+        @Override
+        public int getChildCount() {
+            return children.length;
+        }
+
+        @Override
+        public SyntaxElement getChild(int n) {
+            return children[n];
+        }
+    }
+
+    private Node example1() {
+        return new Node(0,
+            new Node(1, new Node(2), new Node(3)),
+            new Node(4, new Node(5), new Node(6)));
+    }
+
+    private List<Integer> traverse(Node n) {
+        var lst = new ArrayList<Integer>();
+        var cursor = n.getCursor();
+        do {
+            lst.add(((Node) cursor.getCurrentNode()).getValue());
+        } while (cursor.goToNext());
+        return lst;
+    }
+
+    @Test
+    void testOrder() {
+        var tree = example1();
+
+        assertEquals(
+            Arrays.asList(0, 1, 2, 3, 4, 5, 6),
+            traverse(tree));
+    }
+}
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/InspectorForDecisionPredicates.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/InspectorForDecisionPredicates.java
index 78df3ba18cb..5676ef78b9f 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/InspectorForDecisionPredicates.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/InspectorForDecisionPredicates.java
@@ -10,7 +10,6 @@
 import de.uka.ilkd.key.java.Services;
 import de.uka.ilkd.key.ldt.JavaDLTheory;
 import de.uka.ilkd.key.logic.Semisequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.nparser.KeyIO;
 import de.uka.ilkd.key.proof.Node;
@@ -50,8 +49,8 @@ public String check(String toBeChecked) {
         String position =
             cutMode == DelayedCut.DECISION_PREDICATE_IN_ANTECEDENT ? "antecedent" : "succedent";
 
-        for (SequentFormula sf : semisequent) {
-            if (sf.formula() == term) {
+        for (Term sf : semisequent) {
+            if (sf == term) {
                 return "Formula already exists in " + position + ".";
             }
         }
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/LoopInvariantRuleCompletion.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/LoopInvariantRuleCompletion.java
index fea7e23bb8c..2307cc5837a 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/LoopInvariantRuleCompletion.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/LoopInvariantRuleCompletion.java
@@ -10,6 +10,7 @@
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.rule.*;
+import de.uka.ilkd.key.rule.RuleAbortException;
 import de.uka.ilkd.key.speclang.LoopSpecImpl;
 import de.uka.ilkd.key.speclang.LoopSpecification;
 import de.uka.ilkd.key.util.MiscTools;
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/mergerule/MergePartnerSelectionDialog.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/mergerule/MergePartnerSelectionDialog.java
index a09d0a39715..609394256ea 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/mergerule/MergePartnerSelectionDialog.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/mergerule/MergePartnerSelectionDialog.java
@@ -431,16 +431,17 @@ private static boolean checkProvability(Sequent seq, Term formulaToProve, Servic
 
         Semisequent antecedent = seq.antecedent();
 
-        for (SequentFormula succedentFormula : seq.succedent()) {
-            if (!succedentFormula.formula().containsJavaBlockRecursive()) {
+        for (Term succedentFormula : seq.succedent()) {
+            if (!succedentFormula.containsJavaBlockRecursive()) {
+                Term uAssumptions = tb.not(succedentFormula);
                 antecedent =
-                    antecedent.insertFirst(new SequentFormula(tb.not(succedentFormula.formula())))
+                    antecedent.insertFirst(uAssumptions)
                             .semisequent();
             }
         }
 
         return MergeRuleUtils.isProvable(
-            Sequent.createSequent(antecedent, new Semisequent(new SequentFormula(formulaToProve))),
+            Sequent.createSequent(antecedent, new Semisequent(formulaToProve)),
             services, 1000);
     }
 
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/DragNDropInstantiator.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/DragNDropInstantiator.java
index ad048dbd1b3..79733ecce59 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/DragNDropInstantiator.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/DragNDropInstantiator.java
@@ -351,7 +351,7 @@ private ImmutableList<PosTacletApp> completeIfInstantiations(ImmutableList<PosTa
             ifFmlInst = null;
         } else {
             final IfFormulaInstSeq ifInst =
-                new IfFormulaInstSeq(seq, ifPIO.isInAntec(), ifPIO.sequentFormula());
+                new IfFormulaInstSeq(seq, ifPIO.isInAntec(), ifPIO.sequentLevelFormula());
             ifFmlInst = ImmutableSLList.<IfFormulaInstantiation>nil().prepend(ifInst);
         }
 
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/SequentView.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/SequentView.java
index 0db35e40024..c5ac08a3604 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/SequentView.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/nodeviews/SequentView.java
@@ -761,7 +761,7 @@ protected void updateHeatmapSFHighlights(int max_age, boolean newest) {
             }
         } else { // all formulas below MAX_AGE_FOR_HEATMAP are highlighted.
             for (SequentPrintFilterEntry entry : entryList) {
-                SequentFormula form = entry.getFilteredFormula();
+                Term form = entry.getFilteredFormula();
                 int age = computeSeqFormulaAge(getMainWindow().getMediator().getSelectedNode(),
                     form, max_age + 2);
                 if (age < max_age) {
@@ -806,15 +806,15 @@ protected void updateHeatmapTermHighlights(int max_age, boolean newest) {
         while (it.hasNext()) {
             node = it.next();
             if (node.getNodeInfo().getSequentChangeInfo() != null) {
-                ImmutableList<SequentFormula> added_ante =
+                ImmutableList<Term> added_ante =
                     node.getNodeInfo().getSequentChangeInfo().addedFormulas(true);
-                ImmutableList<SequentFormula> added_succ =
+                ImmutableList<Term> added_succ =
                     node.getNodeInfo().getSequentChangeInfo().addedFormulas(false);
-                for (SequentFormula sf : added_ante) {
+                for (Term sf : added_ante) {
                     pio_age_list.add(
                         new PIO_age(new PosInOccurrence(sf, PosInTerm.getTopLevel(), true), age));
                 }
-                for (SequentFormula sf : added_succ) {
+                for (Term sf : added_succ) {
                     pio_age_list.add(
                         new PIO_age(new PosInOccurrence(sf, PosInTerm.getTopLevel(), false), age));
                 }
@@ -824,7 +824,7 @@ protected void updateHeatmapTermHighlights(int max_age, boolean newest) {
                     PosInOccurrence positionOfMod = fci.positionOfModification();
                     pio_age_list.add(new PIO_age(positionOfMod, age));
                     for (PIO_age pair : pio_age_list) {
-                        if (pair.get_pio().sequentFormula().equals(fci.getOriginalFormula())) {
+                        if (pair.get_pio().sequentLevelFormula().equals(fci.getOriginalFormula())) {
                             if (positionOfMod.posInTerm().isPrefixOf(pair.get_pio().posInTerm())) {
                                 pair.active = false;
                             } else {
@@ -834,19 +834,19 @@ protected void updateHeatmapTermHighlights(int max_age, boolean newest) {
                         }
                     }
                 }
-                for (SequentFormula sf : node.getNodeInfo().getSequentChangeInfo()
+                for (Term sf : node.getNodeInfo().getSequentChangeInfo()
                         .removedFormulas(true)) {
                     for (PIO_age pair : pio_age_list) {
-                        if (pair.get_pio().sequentFormula().equals(sf)
+                        if (pair.get_pio().sequentLevelFormula().equals(sf)
                                 && pair.get_pio().isInAntec()) {
                             pair.active = false;
                         }
                     }
                 }
-                for (SequentFormula sf : node.getNodeInfo().getSequentChangeInfo()
+                for (Term sf : node.getNodeInfo().getSequentChangeInfo()
                         .removedFormulas(false)) {
                     for (PIO_age pair : pio_age_list) {
-                        if (pair.get_pio().sequentFormula().equals(sf)
+                        if (pair.get_pio().sequentLevelFormula().equals(sf)
                                 && !pair.get_pio().isInAntec()) {
                             pair.active = false;
                         }
@@ -930,7 +930,7 @@ private Color computeColorForAge(int max_age, int age) {
      * @param max_age the maximum age, specified in viewSettings
      * @return the sf's age
      */
-    private int computeSeqFormulaAge(Node node, SequentFormula form, int max_age) {
+    private int computeSeqFormulaAge(Node node, Term form, int max_age) {
         int age = -1;
         while (age < max_age && node != null && node.sequent().contains(form)) {
             age++;
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/originlabels/OriginTermLabelVisualizer.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/originlabels/OriginTermLabelVisualizer.java
index e08bdb030a5..0be5786e726 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/originlabels/OriginTermLabelVisualizer.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/originlabels/OriginTermLabelVisualizer.java
@@ -409,7 +409,7 @@ private PosInOccurrence convertPio(PosInOccurrence pio) {
         if (termPio == null) {
             return pio;
         } else if (pio == null) {
-            return new PosInOccurrence(termPio.sequentFormula(), termPio.posInTerm(),
+            return new PosInOccurrence(termPio.sequentLevelFormula(), termPio.posInTerm(),
                 termPio.isInAntec());
         } else {
             PosInTerm completePos = termPio.posInTerm();
@@ -419,7 +419,8 @@ private PosInOccurrence convertPio(PosInOccurrence pio) {
                 completePos = completePos.down(it.next());
             }
 
-            return new PosInOccurrence(termPio.sequentFormula(), completePos, termPio.isInAntec());
+            return new PosInOccurrence(termPio.sequentLevelFormula(), completePos,
+                termPio.isInAntec());
         }
     }
 
@@ -435,9 +436,9 @@ private void buildModel(TreeNode parentNode, PosInOccurrence parentPos,
         if (parentPos == null) {
             int index = 0;
 
-            ImmutableList<SequentFormula> children = sequent.antecedent().asList();
+            ImmutableList<Term> children = sequent.antecedent().asList();
 
-            for (SequentFormula child : children) {
+            for (Term child : children) {
                 PosInOccurrence childPos =
                     new PosInOccurrence(child, PosInTerm.getTopLevel(), true);
                 TreeNode childNode = new TreeNode(childPos);
@@ -450,7 +451,7 @@ private void buildModel(TreeNode parentNode, PosInOccurrence parentPos,
 
             children = sequent.succedent().asList();
 
-            for (SequentFormula child : children) {
+            for (Term child : children) {
                 PosInOccurrence childPos =
                     new PosInOccurrence(child, PosInTerm.getTopLevel(), false);
                 TreeNode childNode = new TreeNode(childPos);
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/proofdiff/ProofDifference.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/proofdiff/ProofDifference.java
index abcbed2365a..b10161c32e9 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/proofdiff/ProofDifference.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/proofdiff/ProofDifference.java
@@ -45,7 +45,9 @@ public static ProofDifference create(Node left, Node right, Function<Term, Strin
 
     private static List<String> initialise(Function<Term, String> printer,
             Semisequent semisequent) {
-        return semisequent.asList().stream().map(it -> printer.apply(it.formula()))
+        return semisequent.asList().stream().map(it -> {
+            return printer.apply(it);
+        })
                 .collect(Collectors.toList());
     }
 
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/prooftree/ProofTreeView.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/prooftree/ProofTreeView.java
index 5ccd3abc9fc..329ac53aae7 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/prooftree/ProofTreeView.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/prooftree/ProofTreeView.java
@@ -959,7 +959,8 @@ public void valueChanged(TreeSelectionEvent e) {
                     var ossParentNode = ((GUIProofTreeNode) ossNode.getParent());
                     var newSequent = ossParentNode.getNode().sequent();
                     var modifiedSequent = newSequent
-                            .replaceFormula(ossNode.getFormulaNr(), pio.sequentFormula()).sequent();
+                            .replaceFormula(ossNode.getFormulaNr(), pio.sequentLevelFormula())
+                            .sequent();
                     mediator.getSelectionModel().setSelectedSequentAndRuleApp(
                         ossParentNode.getNode(), modifiedSequent, ossNode.getRuleApp());
                 } else {
diff --git a/key.ui/src/main/java/de/uka/ilkd/key/gui/sourceview/SourceView.java b/key.ui/src/main/java/de/uka/ilkd/key/gui/sourceview/SourceView.java
index ea95cfdc20b..ccb351eef95 100644
--- a/key.ui/src/main/java/de/uka/ilkd/key/gui/sourceview/SourceView.java
+++ b/key.ui/src/main/java/de/uka/ilkd/key/gui/sourceview/SourceView.java
@@ -234,7 +234,7 @@ private void ensureProofJavaSourceCollectionExists(Proof proof) {
             proof.register(sources, ProofJavaSourceCollection.class);
             proof.root().sequent().forEach(formula -> {
                 OriginTermLabel originLabel =
-                    (OriginTermLabel) formula.formula().getLabel(OriginTermLabel.NAME);
+                    (OriginTermLabel) formula.getLabel(OriginTermLabel.NAME);
                 if (originLabel != null) {
                     if (originLabel.getOrigin() instanceof OriginTermLabel.FileOrigin) {
                         ((OriginTermLabel.FileOrigin) originLabel.getOrigin())
@@ -736,64 +736,71 @@ private LinkedList<Pair<Node, PositionInfo>> constructLinesSet(Node node) {
             // proof obligation belongs to is always loaded.
 
             node.sequent().forEach(
-                formula -> formula.formula().execPostOrder(new Visitor<Term>() {
+                formula -> {
+                    formula.execPostOrder(new Visitor<Term>() {
 
-                    @Override
-                    public boolean visitSubtree(Term visited) {
-                        return visited.containsJavaBlockRecursive();
-                    }
+                        @Override
+                        public boolean visitSubtree(Term visited) {
+                            return visited.containsJavaBlockRecursive();
+                        }
 
-                    @Override
-                    public void visit(Term visited) {}
-
-                    @Override
-                    public void subtreeLeft(Term subtreeRoot) {}
-
-                    @Override
-                    public void subtreeEntered(Term subtreeRoot) {
-                        if (subtreeRoot.javaBlock() != null) {
-                            JavaASTVisitor visitor =
-                                new JavaASTVisitor(subtreeRoot.javaBlock().program(),
-                                    mainWindow.getMediator().getServices()) {
-
-                                    @Override
-                                    protected void doDefaultAction(SourceElement el) {
-                                        if (el instanceof MethodBodyStatement mb) {
-                                            Statement body = mb.getBody(services);
-                                            PositionInfo posInf = null;
-                                            // try to find position information of the source
-                                            // element
-                                            if (body != null) {
-                                                posInf = body.getPositionInfo();
-                                            } else {
-                                                // the method is declared without a body
-                                                // -> we try to show the file either way
-                                                IProgramMethod pm = mb.getProgramMethod(services);
-                                                if (pm != null) {
-                                                    posInf = pm.getPositionInfo();
+                        @Override
+                        public void visit(Term visited) {}
+
+                        @Override
+                        public void subtreeLeft(Term subtreeRoot) {}
+
+                        @Override
+                        public void subtreeEntered(Term subtreeRoot) {
+                            if (subtreeRoot.javaBlock() != null) {
+                                JavaASTVisitor visitor =
+                                    new JavaASTVisitor(subtreeRoot.javaBlock().program(),
+                                        mainWindow.getMediator().getServices()) {
+
+                                        @Override
+                                        protected void doDefaultAction(SourceElement el) {
+                                            if (el instanceof MethodBodyStatement mb) {
+                                                Statement body = mb.getBody(services);
+                                                PositionInfo posInf = null;
+                                                // try to find position information of the source
+                                                // element
+                                                if (body != null) {
+                                                    posInf = body.getPositionInfo();
+                                                } else {
+                                                    // the method is declared without a body
+                                                    // -> we try to show the file either way
+                                                    IProgramMethod pm =
+                                                        mb.getProgramMethod(services);
+                                                    if (pm != null) {
+                                                        posInf = pm.getPositionInfo();
+                                                    }
                                                 }
-                                            }
-                                            if (posInf != null && posInf.getURI().isPresent()) {
-                                                // sometimes the useful file info is only stored in
-                                                // parentClassURI for some reason ...
-                                                if (posInf.getURI().isPresent()) {
-                                                    node.proof()
-                                                            .lookup(ProofJavaSourceCollection.class)
-                                                            .addRelevantFile(posInf.getURI().get());
-                                                } else if (posInf.getParentClassURI() != null) {
-                                                    node.proof()
-                                                            .lookup(ProofJavaSourceCollection.class)
-                                                            .addRelevantFile(
-                                                                posInf.getParentClassURI());
+                                                if (posInf != null && posInf.getURI().isPresent()) {
+                                                    // sometimes the useful file info is only stored
+                                                    // in
+                                                    // parentClassURI for some reason ...
+                                                    if (posInf.getURI().isPresent()) {
+                                                        node.proof()
+                                                                .lookup(
+                                                                    ProofJavaSourceCollection.class)
+                                                                .addRelevantFile(
+                                                                    posInf.getURI().get());
+                                                    } else if (posInf.getParentClassURI() != null) {
+                                                        node.proof()
+                                                                .lookup(
+                                                                    ProofJavaSourceCollection.class)
+                                                                .addRelevantFile(
+                                                                    posInf.getParentClassURI());
+                                                    }
                                                 }
                                             }
                                         }
-                                    }
-                                };
-                            visitor.start();
+                                    };
+                                visitor.start();
+                            }
                         }
-                    }
-                }));
+                    });
+                });
         }
 
         return list;
diff --git a/key.util/src/main/java/org/key_project/util/collection/ImmutableList.java b/key.util/src/main/java/org/key_project/util/collection/ImmutableList.java
index b46809d980a..b0b75675647 100644
--- a/key.util/src/main/java/org/key_project/util/collection/ImmutableList.java
+++ b/key.util/src/main/java/org/key_project/util/collection/ImmutableList.java
@@ -37,7 +37,7 @@ public interface ImmutableList<T extends @Nullable Object>
      * @param list a List.
      * @return an ImmutableList containing the same elements as the specified list.
      */
-    static <T extends @Nullable Object> ImmutableList<T> fromList(Collection<T> list) {
+    static <T extends @Nullable Object> ImmutableList<T> fromList(Iterable<T> list) {
         ImmutableList<T> result = ImmutableSLList.nil();
 
         for (T el : list) {
diff --git a/keyext.caching/src/main/java/de/uka/ilkd/key/proof/reference/ReferenceSearcher.java b/keyext.caching/src/main/java/de/uka/ilkd/key/proof/reference/ReferenceSearcher.java
index 14b5265c330..387f6eb45c2 100644
--- a/keyext.caching/src/main/java/de/uka/ilkd/key/proof/reference/ReferenceSearcher.java
+++ b/keyext.caching/src/main/java/de/uka/ilkd/key/proof/reference/ReferenceSearcher.java
@@ -5,12 +5,11 @@
 
 import java.util.*;
 import java.util.stream.Collectors;
-import javax.swing.*;
 
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.proof.Node;
 import de.uka.ilkd.key.proof.Proof;
 import de.uka.ilkd.key.rule.NoPosTacletApp;
@@ -146,10 +145,11 @@ public static ClosedBy findPreviousProof(List<Proof> previousProofs, Node newNod
      * @return whether all formulas are present
      */
     private static boolean containedIn(Semisequent superset, Semisequent subset) {
-        for (SequentFormula sf : subset) {
+        for (Term sf : subset) {
             boolean found = false;
-            for (SequentFormula sf2 : superset) {
-                if (sf2.equalsModProofIrrelevancy(sf)) {
+            for (Term sf2 : superset) {
+                if (ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY.equalsModThisProperty(sf2,
+                    sf)) {
                     found = true;
                     break;
                 }
@@ -173,7 +173,7 @@ public static boolean suitableForCloseByReference(Node node) {
         ProgramMethodFinder f = new ProgramMethodFinder();
         Sequent seq = node.sequent();
         for (int i = 1; i <= seq.size(); i++) {
-            Term term = seq.getFormulabyNr(i).formula();
+            Term term = seq.getFormulabyNr(i);
             // first, check for a java block
             if (term.containsJavaBlockRecursive()) {
                 // not suitable for caching
diff --git a/keyext.exploration/src/main/java/org/key_project/exploration/ProofExplorationService.java b/keyext.exploration/src/main/java/org/key_project/exploration/ProofExplorationService.java
index 310148a5efd..b0ccf0fedde 100644
--- a/keyext.exploration/src/main/java/org/key_project/exploration/ProofExplorationService.java
+++ b/keyext.exploration/src/main/java/org/key_project/exploration/ProofExplorationService.java
@@ -105,10 +105,10 @@ private FindTaclet getHideTaclet(boolean inAntec) {
     public @NonNull Node soundAddition(@NonNull Goal g, @NonNull Term t, boolean antecedent) {
         Taclet cut =
             g.proof().getEnv().getInitConfigForEnvironment().lookupActiveTaclet(new Name("cut"));
-        Semisequent semisequent = new Semisequent(new SequentFormula(t));
+        Semisequent semisequent = new Semisequent(t);
         TacletApp app = NoPosTacletApp.createNoPosTacletApp(cut);
         SchemaVariable sv = app.uninstantiatedVars().iterator().next();
-        app = app.addCheckedInstantiation(sv, semisequent.getFirst().formula(), services, true);
+        app = app.addCheckedInstantiation(sv, semisequent.getFirst(), services, true);
         ExplorationNodeData explorationNodeData = new ExplorationNodeData();
         if (antecedent) {
             explorationNodeData.setExplorationAction("Added " + t + " ==>");
@@ -186,11 +186,10 @@ public Node applyChangeFormula(@NonNull Goal g, @NonNull PosInOccurrence pio,
     private TacletApp soundChange(@NonNull PosInOccurrence pio, @NonNull Term term,
             @NonNull Term newTerm) {
         Taclet cut = getCutTaclet();
-        Semisequent semisequent = new Semisequent(new SequentFormula(newTerm));
+        Semisequent semisequent = new Semisequent(newTerm);
         TacletApp app = NoPosTacletApp.createNoPosTacletApp(cut);
         SchemaVariable sv = app.uninstantiatedVars().iterator().next();
-        app = app.addCheckedInstantiation(sv, semisequent.getFirst().formula(), services, true);
-        return app;
+        return app.addCheckedInstantiation(sv, semisequent.getFirst(), services, true);
     }
 
     public void soundHide(Goal g, PosInOccurrence pio, Term term) {
diff --git a/keyext.exploration/src/main/java/org/key_project/exploration/actions/EditFormulaAction.java b/keyext.exploration/src/main/java/org/key_project/exploration/actions/EditFormulaAction.java
index 754adf282d8..aed6f0c5186 100644
--- a/keyext.exploration/src/main/java/org/key_project/exploration/actions/EditFormulaAction.java
+++ b/keyext.exploration/src/main/java/org/key_project/exploration/actions/EditFormulaAction.java
@@ -7,7 +7,6 @@
 
 import de.uka.ilkd.key.gui.MainWindow;
 import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.SequentFormula;
 import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.logic.TermBuilder;
 import de.uka.ilkd.key.pp.PosInSequent;
@@ -50,7 +49,7 @@ public void actionPerformed(ActionEvent e) {
         TermBuilder tb = getMediator().getServices().getTermBuilder();
         PosInOccurrence pio = posInSeq.getPosInOccurrence();
         Term term = pio.subTerm();
-        SequentFormula sf = pio.sequentFormula();
+        Term sf = pio.sequentLevelFormula();
         Goal g = getMediator().getSelectedGoal();
         Term newTerm = promptForTerm(mainWindow, term);
 
@@ -59,8 +58,8 @@ public void actionPerformed(ActionEvent e) {
         }
 
         ProofExplorationService api = ProofExplorationService.get(getMediator());
-        Node toBeSelected = api.applyChangeFormula(g, pio, sf.formula(),
-            tb.replace(sf.formula(), pio.posInTerm(), newTerm));
+        Node toBeSelected = api.applyChangeFormula(g, pio, sf,
+            tb.replace(sf, pio.posInTerm(), newTerm));
         getMediator().getSelectionModel().setSelectedNode(toBeSelected);
     }
 }
diff --git a/keyext.exploration/src/test/java/org/key_project/exploration/ProofExplorationServiceTest.java b/keyext.exploration/src/test/java/org/key_project/exploration/ProofExplorationServiceTest.java
index b65232317fe..3faa2e75c6f 100644
--- a/keyext.exploration/src/test/java/org/key_project/exploration/ProofExplorationServiceTest.java
+++ b/keyext.exploration/src/test/java/org/key_project/exploration/ProofExplorationServiceTest.java
@@ -150,7 +150,7 @@ public void testChangeFormula() {
         Sequent sequent = goals.head().node().sequent();
         PosInOccurrence pio =
             new PosInOccurrence(sequent.succedent().get(0), PosInTerm.getTopLevel(), false);
-        expService.applyChangeFormula(goals.head(), pio, sequent.succedent().get(0).formula(),
+        expService.applyChangeFormula(goals.head(), pio, sequent.succedent().get(0),
             change);
         ImmutableList<Goal> newCreatedGoals = currentProof.openGoals();
 
@@ -199,7 +199,7 @@ private void testAddition(Goal withAddedTerm, Goal justification, Term added, bo
 
         assertSame(semiSeqAdded.size(), parentSemiSeqOfAdded.size() + 1,
             "The size of the added semisequent has changed");
-        assertEquals(semiSeqAdded.get(0).formula(), added, "Added Term is indeed added");
+        assertEquals(semiSeqAdded.get(0), added, "Added Term is indeed added");
         assertFalse(justification.isAutomatic(), "Justification branch is marked as interactive");
 
         assertSame(semiSeqUntouched.size(), parentSemiSeqOfUntouched.size(),
diff --git a/keyext.slicing/src/main/java/org/key_project/slicing/DependencyTracker.java b/keyext.slicing/src/main/java/org/key_project/slicing/DependencyTracker.java
index 1e629f71944..420dd23a323 100644
--- a/keyext.slicing/src/main/java/org/key_project/slicing/DependencyTracker.java
+++ b/keyext.slicing/src/main/java/org/key_project/slicing/DependencyTracker.java
@@ -11,9 +11,7 @@
 import java.util.WeakHashMap;
 import java.util.stream.Stream;
 
-import de.uka.ilkd.key.logic.PosInOccurrence;
-import de.uka.ilkd.key.logic.PosInTerm;
-import de.uka.ilkd.key.logic.Sequent;
+import de.uka.ilkd.key.logic.*;
 import de.uka.ilkd.key.proof.BranchLocation;
 import de.uka.ilkd.key.proof.Goal;
 import de.uka.ilkd.key.proof.Node;
@@ -146,7 +144,7 @@ private List<Pair<GraphNode, Boolean>> inputsOfNode(Node n, Set<PosInOccurrence>
             boolean added = false;
             for (int i = 0; i <= size; i++) {
                 TrackedFormula formula =
-                    new TrackedFormula(in.sequentFormula(), loc, in.isInAntec(),
+                    new TrackedFormula(in.sequentLevelFormula(), loc, in.isInAntec(),
                         proof.getServices());
                 if (graph.containsNode(formula)) {
                     input.add(new Pair<>(formula, removed.contains(in)));
@@ -159,12 +157,13 @@ private List<Pair<GraphNode, Boolean>> inputsOfNode(Node n, Set<PosInOccurrence>
             }
             if (!added) {
                 // should only happen if the formula is the initial proof obligation
-                if (!proof.root().sequent().contains(in.sequentFormula())) {
+                if (!proof.root().sequent().contains(in.sequentLevelFormula())) {
                     throw new IllegalStateException(
-                        "found formula that was not produced by any rule! " + in.sequentFormula());
+                        "found formula that was not produced by any rule! "
+                            + in.sequentLevelFormula());
                 }
                 TrackedFormula formula =
-                    new TrackedFormula(in.sequentFormula(), loc, in.isInAntec(),
+                    new TrackedFormula(in.sequentLevelFormula(), loc, in.isInAntec(),
                         proof.getServices());
                 input.add(new Pair<>(formula, removed.contains(in)));
             }
@@ -193,21 +192,26 @@ private Set<PosInOccurrence> formulasRemovedBy(RuleAppInfo ruleAppInfo) {
     }
 
     private Set<PosInOccurrence> formulasRemovedBy(Node node) {
-        Set<PosInOccurrence> removed = new HashSet<>();
         // compare parent sequent to new sequent
         Node parent = node.parent();
         if (parent == null) {
-            return removed;
+            return new HashSet<>();
         }
-        Sequent seqParent = parent.sequent();
-        var seqNew = new IdentityHashSet<>(node.sequent().asList());
-        int i = 1;
-        for (final var parentFormula : seqParent) {
+        var removed = computeRemovedFormulas(node.sequent().antecedent(),
+            parent.sequent().antecedent(), true);
+        removed.addAll(computeRemovedFormulas(node.sequent().succedent(),
+            parent.sequent().succedent(), false));
+        return removed;
+    }
+
+    private Set<PosInOccurrence> computeRemovedFormulas(Semisequent newSemi, Semisequent parentSemi,
+            boolean inAntec) {
+        final Set<PosInOccurrence> removed = new HashSet<>();
+        final var seqNew = new IdentityHashSet<>(newSemi.asList());
+        for (final var parentFormula : parentSemi) {
             if (!seqNew.contains(parentFormula)) {
-                removed.add(new PosInOccurrence(parentFormula, PosInTerm.getTopLevel(),
-                    seqParent.numberInAntec(i)));
+                removed.add(new PosInOccurrence(parentFormula, PosInTerm.getTopLevel(), inAntec));
             }
-            i++;
         }
         return removed;
     }
@@ -239,22 +243,27 @@ private List<Pair<PosInOccurrence, Integer>> outputsOfNode(Node node) {
         int sibling = 0;
         for (Node b : node.children()) {
             // compare sequents
-            var oldSeq = new IdentityHashSet<>(node.sequent().asList());
-            Sequent newSeq = b.sequent();
-            int index = 1;
-            for (var f : newSeq) {
-                if (!oldSeq.contains(f)) {
-                    var pio = new PosInOccurrence(f, PosInTerm.getTopLevel(),
-                        newSeq.numberInAntec(index));
-                    outputs.add(new Pair<>(pio, node.childrenCount() > 1 ? sibling : -1));
-                }
-                index++;
-            }
+            computeOutputForSemisequent(node, b, true, outputs, sibling);
+            computeOutputForSemisequent(node, b, false, outputs, sibling);
             sibling++;
         }
         return outputs;
     }
 
+    private void computeOutputForSemisequent(Node parent, Node child, boolean inAntec,
+            List<Pair<PosInOccurrence, Integer>> outputs, int sibling) {
+        ImmutableList<Term> oldSemi = inAntec ? parent.sequent().antecedent().asList()
+                : parent.sequent().succedent().asList();
+        Semisequent newSeq = inAntec ? child.sequent().antecedent() : child.sequent().succedent();
+        var oldSeq = new IdentityHashSet<>(oldSemi);
+        for (var f : newSeq) {
+            if (!oldSeq.contains(f)) {
+                var pio = new PosInOccurrence(f, PosInTerm.getTopLevel(), inAntec);
+                outputs.add(new Pair<>(pio, parent.childrenCount() > 1 ? sibling : -1));
+            }
+        }
+    }
+
     @Override
     public void ruleApplied(ProofEvent e) {
         if (e.getSource() != proof) {
@@ -272,14 +281,15 @@ public void ruleApplied(ProofEvent e) {
         // record any rules added by this rule application
         for (NodeReplacement newNode : ruleAppInfo.getReplacementNodes()) {
             for (NoPosTacletApp newRule : newNode.getNode().getLocalIntroducedRules()) {
+                Taclet newTaclet = newRule.taclet();
                 final var justification =
                     newNode.getNode().proof().getInitConfig().getJustifInfo()
-                            .getJustification(newRule.taclet());
+                            .getJustification(newTaclet);
                 if (justification instanceof RuleJustificationByAddRules justAddRule &&
                         justAddRule.node() == n) {
-                    AddedRule ruleNode = new AddedRule(newRule.rule().name().toString());
+                    AddedRule ruleNode = new AddedRule(newTaclet.name().toString());
                     output.add(ruleNode);
-                    dynamicRules.put((Taclet) newRule.rule(), ruleNode);
+                    dynamicRules.put(newTaclet, ruleNode);
                 }
             }
         }
@@ -302,7 +312,7 @@ public void ruleApplied(ProofEvent e) {
                 loc = loc.append(new Pair<>(n, out.second));
             }
             TrackedFormula formula = new TrackedFormula(
-                out.first.sequentFormula(),
+                out.first.sequentLevelFormula(),
                 loc,
                 out.first.isInAntec(),
                 proof.getServices());
@@ -386,7 +396,7 @@ public void trackNode(Node n) {
                 loc = loc.append(new Pair<>(n, out.second));
             }
             TrackedFormula formula = new TrackedFormula(
-                out.first.sequentFormula(),
+                out.first.sequentLevelFormula(),
                 loc,
                 out.first.isInAntec(),
                 proof.getServices());
diff --git a/keyext.slicing/src/main/java/org/key_project/slicing/analysis/AnalysisResults.java b/keyext.slicing/src/main/java/org/key_project/slicing/analysis/AnalysisResults.java
index 0b0e0b0e578..8175547b001 100644
--- a/keyext.slicing/src/main/java/org/key_project/slicing/analysis/AnalysisResults.java
+++ b/keyext.slicing/src/main/java/org/key_project/slicing/analysis/AnalysisResults.java
@@ -13,7 +13,7 @@
 import de.uka.ilkd.key.logic.PosInTerm;
 import de.uka.ilkd.key.logic.Semisequent;
 import de.uka.ilkd.key.logic.Sequent;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
 import de.uka.ilkd.key.proof.BranchLocation;
 import de.uka.ilkd.key.proof.Node;
 import de.uka.ilkd.key.proof.Proof;
@@ -164,8 +164,8 @@ public Sequent reduceSequent(Node node) {
     }
 
     private Semisequent reduce(Semisequent semi, Node node, boolean antec) {
-        var semiList = new ArrayList<SequentFormula>();
-        for (SequentFormula sf : semi) {
+        var semiList = new ArrayList<Term>();
+        for (Term sf : semi) {
             var graphNode = dependencyGraph.getGraphNode(node.proof(), node.getBranchLocation(),
                 new PosInOccurrence(sf, PosInTerm.getTopLevel(), antec));
             if (usefulNodes.contains(graphNode)) {
diff --git a/keyext.slicing/src/main/java/org/key_project/slicing/graph/DependencyGraph.java b/keyext.slicing/src/main/java/org/key_project/slicing/graph/DependencyGraph.java
index 02f109322a2..c0d23160060 100644
--- a/keyext.slicing/src/main/java/org/key_project/slicing/graph/DependencyGraph.java
+++ b/keyext.slicing/src/main/java/org/key_project/slicing/graph/DependencyGraph.java
@@ -350,7 +350,7 @@ public GraphNode getGraphNode(Proof proof, BranchLocation locationGuess, PosInOc
         }
         while (true) {
             TrackedFormula formula =
-                new TrackedFormula(pio.sequentFormula(), locationGuess, pio.isInAntec(),
+                new TrackedFormula(pio.sequentLevelFormula(), locationGuess, pio.isInAntec(),
                     proof.getServices());
             if (containsNode(formula)) {
                 return formula;
diff --git a/keyext.slicing/src/main/java/org/key_project/slicing/graph/TrackedFormula.java b/keyext.slicing/src/main/java/org/key_project/slicing/graph/TrackedFormula.java
index 2c24e4dbee0..f49e9683ed6 100644
--- a/keyext.slicing/src/main/java/org/key_project/slicing/graph/TrackedFormula.java
+++ b/keyext.slicing/src/main/java/org/key_project/slicing/graph/TrackedFormula.java
@@ -6,7 +6,8 @@
 import java.util.Objects;
 
 import de.uka.ilkd.key.java.Services;
-import de.uka.ilkd.key.logic.SequentFormula;
+import de.uka.ilkd.key.logic.Term;
+import de.uka.ilkd.key.logic.equality.ProofIrrelevancyProperty;
 import de.uka.ilkd.key.pp.LogicPrinter;
 import de.uka.ilkd.key.proof.BranchLocation;
 
@@ -30,7 +31,7 @@ public class TrackedFormula extends GraphNode implements EqualsModProofIrrelevan
     /**
      * The formula.
      */
-    public final SequentFormula formula;
+    public final Term formula;
     /**
      * Whether the formula is in the antecedent.
      */
@@ -49,7 +50,7 @@ public class TrackedFormula extends GraphNode implements EqualsModProofIrrelevan
      * @param services services
      */
     public TrackedFormula(
-            SequentFormula formula,
+            Term formula,
             BranchLocation branchLocation,
             boolean inAntec,
             Services services) {
@@ -70,7 +71,7 @@ public String toString(boolean abbreviated, boolean omitBranch) {
             return Integer.toHexString(hashCode());
         }
         String term = LogicPrinter.quickPrintTerm(
-            formula.formula(),
+            formula,
             services,
             true, // pretty print
             true // using unicode symbols
@@ -110,12 +111,15 @@ public boolean equalsModProofIrrelevancy(Object o) {
         }
         TrackedFormula that = (TrackedFormula) o;
         return inAntec == that.inAntec
-                && formula.equalsModProofIrrelevancy(that.formula)
+                && formula.equalsModProperty(that.formula,
+                    ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY)
                 && Objects.equals(branchLocation, that.branchLocation);
     }
 
     @Override
     public int hashCodeModProofIrrelevancy() {
-        return Objects.hash(inAntec, formula.hashCodeModProofIrrelevancy(), branchLocation);
+        return Objects.hash(inAntec,
+            formula.hashCodeModProperty(ProofIrrelevancyProperty.PROOF_IRRELEVANCY_PROPERTY),
+            branchLocation);
     }
 }
diff --git a/settings.gradle b/settings.gradle
index 171f3b1d56c..aa955f87e87 100644
--- a/settings.gradle
+++ b/settings.gradle
@@ -18,4 +18,4 @@ include 'keyext.caching'
 
 // ENABLE NULLNESS here or on the CLI
 // This flag is activated to enable the checker framework.
-// System.setProperty("ENABLE_NULLNESS", "true")
\ No newline at end of file
+// System.setProperty("ENABLE_NULLNESS", "true")