├── .github ├── runAll.sh └── workflows │ └── ci.yml ├── .gitignore ├── .scalafix.conf ├── .scalafmt.conf ├── CHANGES.md ├── LICENSE ├── README.md ├── bin ├── egg-sc-tptp ├── egg-sc-tptp.exe ├── goeland_linux_release └── sctptpUtils.jar ├── lisa-examples ├── goeland │ ├── Example.buveurs2.p │ └── Example.buveurs2_sol.p └── src │ └── main │ └── scala │ ├── ADTExample.scala │ ├── ATPExample.scala │ ├── Example.scala │ ├── ExampleKernel.scala │ └── Lattices.scala ├── lisa-kernel └── src │ └── main │ └── scala │ └── lisa │ └── kernel │ ├── fol │ ├── FOL.scala │ ├── OLEquivalenceChecker.scala │ └── Syntax.scala │ └── proof │ ├── Judgement.scala │ ├── RunningTheory.scala │ ├── SCProof.scala │ ├── SCProofChecker.scala │ └── SequentCalculus.scala ├── lisa-sets └── src │ ├── main │ └── scala │ │ └── lisa │ │ ├── Main.scala │ │ ├── SetTheoryLibrary.scala │ │ ├── Tests.scala │ │ ├── automation │ │ ├── CommonTactics.scala │ │ ├── Congruence.scala │ │ ├── Substitution.scala │ │ ├── Tableau.scala │ │ ├── Tautology.scala │ │ └── atp │ │ │ ├── Egg.scala │ │ │ ├── Goeland.scala │ │ │ └── Prover9.scala │ │ ├── maths │ │ ├── Quantifiers.scala │ │ └── SetTheory │ │ │ ├── Base │ │ │ ├── CartesianProduct.scala │ │ │ ├── Class.scala │ │ │ ├── Comprehension.scala │ │ │ ├── Difference.scala │ │ │ ├── EmptySet.scala │ │ │ ├── Extensionality.scala │ │ │ ├── FoundationAxiom.scala │ │ │ ├── Intersection.scala │ │ │ ├── Pair.scala │ │ │ ├── PowerSet.scala │ │ │ ├── Predef.scala │ │ │ ├── Replacement.scala │ │ │ ├── Singleton.scala │ │ │ ├── Subset.scala │ │ │ ├── Symbols.scala │ │ │ ├── Union.scala │ │ │ ├── UnorderedPair.scala │ │ │ └── WellFounded.scala │ │ │ ├── Functions │ │ │ ├── BasicTheorems.scala │ │ │ ├── Examples │ │ │ │ └── ConstantFunction.scala │ │ │ ├── Function.scala │ │ │ ├── Operations │ │ │ │ ├── Composition.scala │ │ │ │ ├── Restriction.scala │ │ │ │ └── Union.scala │ │ │ ├── Pi.scala │ │ │ ├── Predef.scala │ │ │ └── Sigma.scala │ │ │ ├── Order │ │ │ ├── BasicTheorems.scala │ │ │ ├── Examples │ │ │ │ └── EmptyOrder.scala │ │ │ ├── Extrema.scala │ │ │ ├── LowerSet.scala │ │ │ ├── OrderIsomorphism.scala │ │ │ ├── PartialOrder.scala │ │ │ ├── Predef.scala │ │ │ ├── TotalOrder.scala │ │ │ └── WellOrders │ │ │ │ ├── InitialSegment.scala │ │ │ │ ├── OldRecursion.scala │ │ │ │ ├── WellOrder.scala │ │ │ │ ├── WellOrderedInduction.scala │ │ │ │ └── WellOrderedRecursion.scala │ │ │ ├── Ordinals │ │ │ ├── Arithmetic.scala │ │ │ ├── Integer.scala │ │ │ ├── Ordinal.scala │ │ │ ├── TransfiniteInduction.scala │ │ │ ├── TransfiniteRecursion.scala │ │ │ └── TransitiveSet.scala │ │ │ ├── Relations │ │ │ ├── BasicTheorems.scala │ │ │ ├── Equivalence.scala │ │ │ ├── Examples │ │ │ │ ├── EmptyRelation.scala │ │ │ │ ├── IdentityRelation.scala │ │ │ │ ├── MembershipRelation.scala │ │ │ │ └── UniversalRelation.scala │ │ │ ├── Operations │ │ │ │ ├── Closure.scala │ │ │ │ ├── Complement.scala │ │ │ │ ├── Composition.scala │ │ │ │ ├── Converse.scala │ │ │ │ └── Union.scala │ │ │ ├── Predef.scala │ │ │ ├── Properties.scala │ │ │ ├── Relation.scala │ │ │ └── WellFoundedRelation.scala │ │ │ ├── SetTheory.scala │ │ │ └── Types │ │ │ ├── ADT │ │ │ ├── Frontend.scala │ │ │ ├── Functions.scala │ │ │ ├── Helpers.scala │ │ │ ├── Tactics.scala │ │ │ ├── Typed.scala │ │ │ ├── Untyped.scala │ │ │ └── package.scala │ │ │ └── TypeSystem.scala │ │ └── tptp │ │ ├── Example.scala │ │ ├── KernelParser.scala │ │ ├── ProblemGatherer.scala │ │ ├── ProofParser.scala │ │ ├── ProofPrinter.scala │ │ ├── TPTP_Lisa.scala │ │ └── package.scala │ └── test │ ├── resources │ ├── goeland_test_1.p │ ├── level2_steps │ │ └── instMult.p │ ├── p9_test_1.p │ ├── p9_test_2.p │ ├── p9_test_3.p │ └── steps_tests │ │ ├── cut.p │ │ ├── hyp.p │ │ ├── instFun.p │ │ ├── instPred.p │ │ ├── leftAnd.p │ │ ├── leftExists.p │ │ ├── leftForall.p │ │ ├── leftIff.p │ │ ├── leftImplies.p │ │ ├── leftNot.p │ │ ├── leftOr.p │ │ ├── leftSubst.p │ │ ├── leftSubstIff.p │ │ ├── leftWeaken.p │ │ ├── rightAnd.p │ │ ├── rightExists.p │ │ ├── rightForall.p │ │ ├── rightIff.p │ │ ├── rightImplies.p │ │ ├── rightNot.p │ │ ├── rightOr.p │ │ ├── rightRefl.p │ │ ├── rightSubst.p │ │ ├── rightSubstIff.p │ │ └── rightWeaken.p │ └── scala │ └── lisa │ ├── automation │ ├── CongruenceTest.scala │ └── TableauTest.scala │ ├── examples │ └── peano_example │ │ ├── Peano.scala │ │ ├── PeanoArithmetics.scala │ │ └── PeanoArithmeticsLibrary.scala │ ├── proven │ └── InitialProofsTests.scala │ ├── tptp │ ├── ATPProofs.scala │ ├── LVL1Test.scala │ └── LVL2Test.scala │ └── utilities │ ├── SerializationTest.scala │ ├── SubstitutionTacticTest.scala │ └── TestMain.scala ├── lisa-utils └── src │ ├── main │ └── scala │ │ └── lisa │ │ └── utils │ │ ├── K.scala │ │ ├── KernelHelpers.scala │ │ ├── LisaException.scala │ │ ├── Printing.scala │ │ ├── ProofsShrink.scala │ │ ├── Serialization.scala │ │ ├── collection │ │ ├── Extensions.scala │ │ └── VecSet.scala │ │ ├── fol │ │ ├── ExprOps.scala │ │ ├── FOL.scala │ │ ├── Predef.scala │ │ ├── Sequents.scala │ │ └── Syntax.scala │ │ ├── memoization │ │ └── Memoized.scala │ │ ├── prooflib │ │ ├── BasicMain.scala │ │ ├── BasicStepTactic.scala │ │ ├── Exports.scala │ │ ├── Library.scala │ │ ├── OutputManager.scala │ │ ├── ProofPrinter.scala │ │ ├── ProofTacticLib.scala │ │ ├── ProofsHelpers.scala │ │ ├── SimpleDeducedSteps.scala │ │ └── WithTheorems.scala │ │ └── unification │ │ └── UnificationUtils.scala │ └── test │ └── scala │ └── lisa │ ├── ProofCheckerSuite.scala │ ├── ProofTacticTestLib.scala │ ├── TestTheory.scala │ ├── TestTheoryAxioms.scala │ ├── TestTheoryLibrary.scala │ ├── kernel │ ├── EquivalenceCheckerTests.scala │ ├── IncorrectProofsTests.scala │ ├── InvalidProofPathTests.scala │ ├── ProofTests.scala │ ├── SubstitutionTest.scala │ └── TheoriesHelpersTest.scala │ └── utils │ ├── BasicTacticTest.scala │ ├── ParserTest.scala │ ├── PrinterTest.scala │ ├── TestUtils.scala │ └── UnificationTest.scala ├── project ├── build.properties └── plugins.sbt └── refman ├── 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