%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM215_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Tue May 5 06:21:35 PM UTC 2026 % Result : Theorem 18.45s 3.29s % Output : Proof 28.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM215_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n025.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Mon May 4 18:50:58 EDT 2026 % 0.16/0.35 % CPUTime : % 0.51/0.62 ________ _____ % 0.51/0.62 ___ __ \_________(_)________________________________ % 0.51/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.62 (2023-06-19) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2023 % 0.51/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.62 Amanda Stjerna. % 0.51/0.62 Free software under BSD-3-Clause. % 0.51/0.62 % 0.51/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.63 Running up to 7 provers in parallel. % 0.68/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.13/1.45 Prover 4: Preprocessing ... % 5.13/1.45 Prover 1: Preprocessing ... % 5.13/1.46 Prover 6: Preprocessing ... % 5.13/1.46 Prover 0: Preprocessing ... % 5.13/1.46 Prover 5: Preprocessing ... % 5.13/1.46 Prover 2: Preprocessing ... % 5.13/1.47 Prover 3: Preprocessing ... % 11.70/2.39 Prover 1: Warning: ignoring some quantifiers % 12.41/2.46 Prover 1: Constructing countermodel ... % 12.41/2.49 Prover 6: Proving ... % 13.20/2.55 Prover 3: Warning: ignoring some quantifiers % 13.20/2.57 Prover 3: Constructing countermodel ... % 13.96/2.62 Prover 5: Proving ... % 13.96/2.68 Prover 4: Warning: ignoring some quantifiers % 14.71/2.73 Prover 4: Constructing countermodel ... % 14.71/2.78 Prover 0: Proving ... % 16.26/2.91 Prover 2: Proving ... % 18.45/3.29 Prover 5: proved (2640ms) % 18.45/3.29 % 18.45/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.45/3.29 % 18.45/3.29 Prover 0: stopped % 18.45/3.30 Prover 6: stopped % 19.20/3.30 Prover 2: stopped % 19.20/3.31 Prover 3: stopped % 19.20/3.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.20/3.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.20/3.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.20/3.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.20/3.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.63/3.58 Prover 8: Preprocessing ... % 20.63/3.58 Prover 11: Preprocessing ... % 21.35/3.60 Prover 7: Preprocessing ... % 21.35/3.61 Prover 13: Preprocessing ... % 21.35/3.61 Prover 10: Preprocessing ... % 23.69/3.90 Prover 7: Warning: ignoring some quantifiers % 23.69/3.90 Prover 8: Warning: ignoring some quantifiers % 23.69/3.91 Prover 7: Constructing countermodel ... % 23.69/3.93 Prover 8: Constructing countermodel ... % 23.69/3.97 Prover 10: Warning: ignoring some quantifiers % 23.69/3.98 Prover 10: Constructing countermodel ... % 24.54/4.08 Prover 11: Warning: ignoring some quantifiers % 24.54/4.11 Prover 11: Constructing countermodel ... % 25.32/4.15 Prover 13: Warning: ignoring some quantifiers % 25.32/4.17 Prover 13: Constructing countermodel ... % 27.55/4.47 Prover 7: Found proof (size 20) % 27.55/4.47 Prover 7: proved (1176ms) % 27.55/4.47 Prover 10: stopped % 27.55/4.47 Prover 13: stopped % 27.55/4.47 Prover 8: stopped % 27.55/4.47 Prover 1: stopped % 27.55/4.47 Prover 11: stopped % 27.55/4.47 Prover 4: stopped % 27.55/4.47 % 27.55/4.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.55/4.47 % 27.55/4.48 % SZS output start Proof for theBenchmark % 27.55/4.48 Assumptions after simplification: % 27.55/4.48 --------------------------------- % 27.55/4.48 % 27.55/4.48 (DIFF-Succ-Pred) % 28.24/4.51 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ( ~ (vPred(v1) = v2) | ~ % 28.24/4.51 (vSucc(v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0)) % 28.24/4.51 % 28.24/4.51 (DIFF-Zero-Pred) % 28.24/4.51 vTerm(vZero) & ! [v0: vTerm] : ( ~ (vPred(v0) = vZero) | ~ vTerm(v0)) % 28.24/4.51 % 28.24/4.51 (PlusPreservation-Pred) % 28.24/4.51 vTy(vNat) & vTerm(vt2) & ? [v0: vTerm] : ? [v1: vTerm] : ? [v2: vTerm] : % 28.24/4.51 (vplusop(v1, v0) = v2 & vPred(vt2) = v0 & vTerm(v2) & vTerm(v1) & vTerm(v0) & % 28.24/4.51 vptchecksimple(v1, vNat) & vptchecksimple(v0, vNat) & ~ vptchecksimple(v2, % 28.24/4.51 vNat)) % 28.24/4.51 % 28.24/4.51 (plusop-2) % 28.24/4.51 vTerm(vZero) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v2 = v0 | % 28.24/4.51 v0 = vZero | ~ (vplusop(v1, v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? % 28.24/4.51 [v3: vTerm] : (vSucc(v3) = v0 & vTerm(v3))) % 28.24/4.51 % 28.24/4.51 Further assumptions not needed in the proof: % 28.24/4.51 -------------------------------------------- % 28.24/4.51 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 28.24/4.51 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 28.24/4.51 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 28.24/4.51 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 28.24/4.51 DIFF-Succ-Plus, DIFF-True-False, DIFF-True-Ifelse, DIFF-True-Iszero, % 28.24/4.51 DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, DIFF-True-Zero, % 28.24/4.51 DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Succ, DIFF-noTerm-someTerm, % 28.24/4.51 EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, EQ-Succ, EQ-someTerm, % 28.24/4.51 PlusPreservation-Pred-IH0, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, % 28.24/4.51 TPred_inv1, TPred_inv2, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, % 28.24/4.51 Tif, Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 28.24/4.51 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 28.24/4.51 isNV-false-INV, isNV-true-INV, isSomeTerm-0, isSomeTerm-1, isSomeTerm-false-INV, % 28.24/4.51 isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, isValue-false-INV, % 28.24/4.51 isValue-true-INV, plusop-0, plusop-1, plusop-INV, reduce-0, reduce-1, reduce-10, % 28.24/4.51 reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, reduce-17, % 28.24/4.51 reduce-18, reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, reduce-23, % 28.24/4.51 reduce-3, reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV % 28.24/4.51 % 28.24/4.51 Those formulas are unsatisfiable: % 28.24/4.51 --------------------------------- % 28.24/4.51 % 28.24/4.51 Begin of proof % 28.24/4.51 | % 28.24/4.51 | ALPHA: (DIFF-Zero-Pred) implies: % 28.24/4.51 | (1) ! [v0: vTerm] : ( ~ (vPred(v0) = vZero) | ~ vTerm(v0)) % 28.24/4.51 | % 28.24/4.51 | ALPHA: (plusop-2) implies: % 28.24/4.52 | (2) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v2 = v0 | v0 = % 28.24/4.52 | vZero | ~ (vplusop(v1, v0) = v2) | ~ vTerm(v1) | ~ vTerm(v0) | ? % 28.24/4.52 | [v3: vTerm] : (vSucc(v3) = v0 & vTerm(v3))) % 28.24/4.52 | % 28.24/4.52 | ALPHA: (PlusPreservation-Pred) implies: % 28.24/4.52 | (3) vTerm(vt2) % 28.24/4.52 | (4) ? [v0: vTerm] : ? [v1: vTerm] : ? [v2: vTerm] : (vplusop(v1, v0) = % 28.24/4.52 | v2 & vPred(vt2) = v0 & vTerm(v2) & vTerm(v1) & vTerm(v0) & % 28.24/4.52 | vptchecksimple(v1, vNat) & vptchecksimple(v0, vNat) & ~ % 28.24/4.52 | vptchecksimple(v2, vNat)) % 28.24/4.52 | % 28.24/4.52 | DELTA: instantiating (4) with fresh symbols all_104_0, all_104_1, all_104_2 % 28.24/4.52 | gives: % 28.24/4.52 | (5) vplusop(all_104_1, all_104_2) = all_104_0 & vPred(vt2) = all_104_2 & % 28.24/4.52 | vTerm(all_104_0) & vTerm(all_104_1) & vTerm(all_104_2) & % 28.24/4.52 | vptchecksimple(all_104_1, vNat) & vptchecksimple(all_104_2, vNat) & ~ % 28.24/4.52 | vptchecksimple(all_104_0, vNat) % 28.24/4.52 | % 28.24/4.52 | ALPHA: (5) implies: % 28.24/4.52 | (6) ~ vptchecksimple(all_104_0, vNat) % 28.24/4.52 | (7) vptchecksimple(all_104_2, vNat) % 28.24/4.52 | (8) vTerm(all_104_2) % 28.24/4.52 | (9) vTerm(all_104_1) % 28.24/4.52 | (10) vPred(vt2) = all_104_2 % 28.24/4.52 | (11) vplusop(all_104_1, all_104_2) = all_104_0 % 28.24/4.52 | % 28.24/4.52 | PRED_UNIFY: (6), (7) imply: % 28.24/4.52 | (12) ~ (all_104_0 = all_104_2) % 28.24/4.52 | % 28.24/4.52 | GROUND_INST: instantiating (1) with vt2, simplifying with (3) gives: % 28.24/4.52 | (13) ~ (vPred(vt2) = vZero) % 28.24/4.52 | % 28.24/4.52 | GROUND_INST: instantiating (2) with all_104_2, all_104_1, all_104_0, % 28.24/4.52 | simplifying with (8), (9), (11) gives: % 28.24/4.52 | (14) all_104_0 = all_104_2 | all_104_2 = vZero | ? [v0: vTerm] : % 28.24/4.52 | (vSucc(v0) = all_104_2 & vTerm(v0)) % 28.24/4.52 | % 28.24/4.52 | PRED_UNIFY: (10), (13) imply: % 28.24/4.52 | (15) ~ (all_104_2 = vZero) % 28.24/4.52 | % 28.24/4.52 | BETA: splitting (14) gives: % 28.24/4.52 | % 28.24/4.52 | Case 1: % 28.24/4.52 | | % 28.24/4.52 | | (16) all_104_2 = vZero % 28.24/4.52 | | % 28.24/4.52 | | REDUCE: (15), (16) imply: % 28.24/4.52 | | (17) $false % 28.24/4.52 | | % 28.24/4.52 | | CLOSE: (17) is inconsistent. % 28.24/4.52 | | % 28.24/4.52 | Case 2: % 28.24/4.52 | | % 28.24/4.52 | | (18) all_104_0 = all_104_2 | ? [v0: vTerm] : (vSucc(v0) = all_104_2 & % 28.24/4.52 | | vTerm(v0)) % 28.24/4.52 | | % 28.24/4.52 | | BETA: splitting (18) gives: % 28.24/4.52 | | % 28.24/4.52 | | Case 1: % 28.24/4.52 | | | % 28.24/4.52 | | | (19) all_104_0 = all_104_2 % 28.24/4.52 | | | % 28.24/4.52 | | | REDUCE: (12), (19) imply: % 28.24/4.52 | | | (20) $false % 28.24/4.52 | | | % 28.24/4.52 | | | CLOSE: (20) is inconsistent. % 28.24/4.52 | | | % 28.24/4.52 | | Case 2: % 28.24/4.52 | | | % 28.24/4.52 | | | (21) ? [v0: vTerm] : (vSucc(v0) = all_104_2 & vTerm(v0)) % 28.24/4.53 | | | % 28.24/4.53 | | | DELTA: instantiating (21) with fresh symbol all_170_0 gives: % 28.24/4.53 | | | (22) vSucc(all_170_0) = all_104_2 & vTerm(all_170_0) % 28.24/4.53 | | | % 28.24/4.53 | | | ALPHA: (22) implies: % 28.24/4.53 | | | (23) vTerm(all_170_0) % 28.24/4.53 | | | (24) vSucc(all_170_0) = all_104_2 % 28.24/4.53 | | | % 28.24/4.53 | | | GROUND_INST: instantiating (DIFF-Succ-Pred) with all_170_0, vt2, % 28.24/4.53 | | | all_104_2, simplifying with (3), (10), (23), (24) gives: % 28.24/4.53 | | | (25) $false % 28.24/4.53 | | | % 28.24/4.53 | | | CLOSE: (25) is inconsistent. % 28.24/4.53 | | | % 28.24/4.53 | | End of split % 28.24/4.53 | | % 28.24/4.53 | End of split % 28.24/4.53 | % 28.24/4.53 End of proof % 28.24/4.53 % SZS output end Proof for theBenchmark % 28.24/4.53 % 28.24/4.53 3909ms %------------------------------------------------------------------------------