%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM129+1 : TPTP v8.1.2. Released v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 : Wed Aug 30 18:44:32 EDT 2023 % Result : Theorem 16.82s 3.05s % Output : Proof 20.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM129+1 : TPTP v8.1.2. Released v6.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 13:08:03 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.68 ________ _____ % 0.20/0.68 ___ __ \_________(_)________________________________ % 0.20/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.68 % 0.20/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.68 (2023-06-19) % 0.20/0.68 % 0.20/0.68 (c) Philipp Rümmer, 2009-2023 % 0.20/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.68 Amanda Stjerna. % 0.20/0.68 Free software under BSD-3-Clause. % 0.20/0.68 % 0.20/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.68 % 0.20/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.69 Running up to 7 provers in parallel. % 0.20/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.78/1.53 Prover 4: Preprocessing ... % 5.78/1.53 Prover 1: Preprocessing ... % 5.78/1.55 Prover 5: Preprocessing ... % 5.78/1.55 Prover 2: Preprocessing ... % 5.78/1.55 Prover 6: Preprocessing ... % 5.78/1.55 Prover 0: Preprocessing ... % 5.78/1.55 Prover 3: Preprocessing ... % 12.15/2.41 Prover 3: Constructing countermodel ... % 12.15/2.41 Prover 1: Constructing countermodel ... % 12.51/2.47 Prover 6: Proving ... % 12.51/2.47 Prover 4: Constructing countermodel ... % 13.62/2.63 Prover 5: Proving ... % 14.01/2.64 Prover 3: gave up % 14.01/2.64 Prover 1: gave up % 14.01/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.01/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.09/2.66 Prover 6: gave up % 14.09/2.66 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 14.09/2.66 Prover 0: Proving ... % 14.09/2.66 Prover 4: gave up % 14.09/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.09/2.69 Prover 2: Proving ... % 14.54/2.74 Prover 7: Preprocessing ... % 14.54/2.75 Prover 8: Preprocessing ... % 14.54/2.76 Prover 9: Preprocessing ... % 14.98/2.85 Prover 10: Preprocessing ... % 16.82/3.04 Prover 2: proved (2340ms) % 16.82/3.04 % 16.82/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.82/3.05 % 16.82/3.06 Prover 0: stopped % 16.82/3.06 Prover 5: stopped % 16.82/3.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.82/3.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.82/3.08 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 16.82/3.12 Prover 8: Warning: ignoring some quantifiers % 16.82/3.13 Prover 7: Warning: ignoring some quantifiers % 17.41/3.15 Prover 8: Constructing countermodel ... % 17.41/3.16 Prover 11: Preprocessing ... % 17.41/3.16 Prover 7: Constructing countermodel ... % 17.41/3.16 Prover 10: Warning: ignoring some quantifiers % 17.41/3.17 Prover 16: Preprocessing ... % 17.41/3.17 Prover 13: Preprocessing ... % 17.41/3.19 Prover 10: Constructing countermodel ... % 18.53/3.25 Prover 9: Constructing countermodel ... % 18.53/3.27 Prover 9: stopped % 18.53/3.27 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 18.78/3.32 Prover 10: Found proof (size 14) % 18.78/3.32 Prover 10: proved (635ms) % 18.78/3.32 Prover 8: stopped % 18.78/3.32 Prover 7: stopped % 19.24/3.33 Prover 16: stopped % 19.24/3.33 Prover 19: Preprocessing ... % 19.90/3.46 Prover 13: Warning: ignoring some quantifiers % 20.15/3.47 Prover 11: Constructing countermodel ... % 20.15/3.48 Prover 13: Constructing countermodel ... % 20.15/3.49 Prover 11: stopped % 20.15/3.49 Prover 13: stopped % 20.15/3.51 Prover 19: Warning: ignoring some quantifiers % 20.15/3.52 Prover 19: Constructing countermodel ... % 20.15/3.53 Prover 19: stopped % 20.15/3.53 % 20.15/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.15/3.53 % 20.53/3.54 % SZS output start Proof for theBenchmark % 20.53/3.55 Assumptions after simplification: % 20.53/3.55 --------------------------------- % 20.53/3.55 % 20.53/3.55 (fresh-free-2) % 20.67/3.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.67/3.59 $i] : ? [v6: $i] : (vgensym(v6) = v2 & vapp(v4, v5) = v6 & vapp(v0, v3) = % 20.67/3.59 v4 & vvar(v1) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 20.67/3.59 $i(v0) & visFreeVar(v2, v3)) % 20.67/3.59 % 20.67/3.59 (fresh-unequal-var-3) % 20.67/3.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.67/3.59 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vapp(v0, v1) = v3) | ~ (vvar(v2) = v4) % 20.67/3.59 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ( ~ (v6 = v2) & % 20.67/3.59 vgensym(v5) = v6 & $i(v6))) % 20.67/3.59 % 20.67/3.59 (gensym-is-fresh) % 20.67/3.59 ! [v0: $i] : ! [v1: $i] : ( ~ (vgensym(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 20.67/3.59 ~ visFreeVar(v0, v1)) % 20.67/3.59 % 20.67/3.60 (isFreeVar2) % 20.67/3.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v2, v3) = % 20.67/3.60 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ visFreeVar(v0, % 20.67/3.60 v3) | visFreeVar(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.67/3.60 [v3: $i] : ( ~ (vapp(v2, v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.67/3.60 $i(v0) | ~ visFreeVar(v0, v2) | visFreeVar(v0, v1)) & ! [v0: $i] : ! [v1: % 20.67/3.60 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v2, v3) = v1) | ~ $i(v3) | ~ % 20.67/3.60 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ visFreeVar(v0, v1) | visFreeVar(v0, v3) % 20.67/3.60 | visFreeVar(v0, v2)) % 20.67/3.60 % 20.67/3.60 (function-axioms) % 20.67/3.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 20.67/3.61 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: $i] % 20.67/3.61 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 20.67/3.61 (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0)) & ! [v0: $i] : ! % 20.67/3.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vabs(v4, % 20.67/3.61 v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 20.67/3.61 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, v2) = v1) | ~ % 20.67/3.61 (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 20.67/3.61 $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) & ! % 20.67/3.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, % 20.67/3.61 v2) = v1) | ~ (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.67/3.61 [v2: $i] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: % 20.67/3.61 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ % 20.67/3.61 (vgetSomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 20.67/3.61 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: % 20.67/3.61 $i] : ! [v2: $i] : (v1 = v0 | ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = % 20.67/3.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.67/3.61 (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = v0)) & ! [v0: $i] : ! % 20.67/3.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 20.67/3.61 (vsomeType(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 20.67/3.61 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 20.67/3.61 % 20.67/3.61 Further assumptions not needed in the proof: % 20.67/3.61 -------------------------------------------- % 20.67/3.61 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, % 20.67/3.61 DIFF-var-abs, DIFF-var-app, EQ-abs, EQ-app, EQ-arrow, EQ-bind, EQ-empty, % 20.67/3.61 EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Context-Duplicate, % 20.67/3.61 T-Context-Swap, T-Strong, T-Weak, T-Weak-FreeVar, T-abs, T-app, T-inv, % 20.67/3.61 T-subst-abs-2-gen, T-var, alpha-equiv-FreeVar, alpha-equiv-refl, % 20.67/3.61 alpha-equiv-subst-abs, alpha-equiv-sym, alpha-equiv-trans, alpha-equiv-typing, % 20.67/3.61 getSomeExp0, getSomeType0, isFreeVar0, isFreeVar1, isSomeExp0, isSomeExp1, % 20.67/3.61 isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, lookup0, % 20.67/3.61 lookup1, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4, % 20.67/3.61 reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5 % 20.67/3.61 % 20.67/3.61 Those formulas are unsatisfiable: % 20.67/3.61 --------------------------------- % 20.67/3.61 % 20.67/3.61 Begin of proof % 20.67/3.61 | % 20.67/3.61 | ALPHA: (isFreeVar2) implies: % 20.67/3.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v2, % 20.67/3.61 | v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 20.67/3.61 | visFreeVar(v0, v2) | visFreeVar(v0, v1)) % 20.67/3.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v2, % 20.67/3.61 | v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 20.67/3.61 | visFreeVar(v0, v3) | visFreeVar(v0, v1)) % 20.67/3.61 | % 20.67/3.61 | ALPHA: (function-axioms) implies: % 20.67/3.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vgensym(v2) = % 20.67/3.61 | v1) | ~ (vgensym(v2) = v0)) % 20.67/3.61 | % 20.67/3.61 | DELTA: instantiating (fresh-free-2) with fresh symbols all_60_0, all_60_1, % 20.67/3.61 | all_60_2, all_60_3, all_60_4, all_60_5, all_60_6 gives: % 20.67/3.61 | (4) vgensym(all_60_0) = all_60_4 & vapp(all_60_2, all_60_1) = all_60_0 & % 20.67/3.61 | vapp(all_60_6, all_60_3) = all_60_2 & vvar(all_60_5) = all_60_1 & % 20.67/3.61 | $i(all_60_0) & $i(all_60_1) & $i(all_60_2) & $i(all_60_3) & % 20.67/3.61 | $i(all_60_4) & $i(all_60_5) & $i(all_60_6) & visFreeVar(all_60_4, % 20.67/3.61 | all_60_3) % 20.67/3.61 | % 20.67/3.61 | ALPHA: (4) implies: % 20.67/3.61 | (5) visFreeVar(all_60_4, all_60_3) % 20.67/3.62 | (6) $i(all_60_6) % 20.67/3.62 | (7) $i(all_60_5) % 20.67/3.62 | (8) $i(all_60_4) % 20.67/3.62 | (9) $i(all_60_3) % 20.67/3.62 | (10) $i(all_60_2) % 20.67/3.62 | (11) $i(all_60_1) % 20.67/3.62 | (12) $i(all_60_0) % 20.67/3.62 | (13) vvar(all_60_5) = all_60_1 % 20.67/3.62 | (14) vapp(all_60_6, all_60_3) = all_60_2 % 20.67/3.62 | (15) vapp(all_60_2, all_60_1) = all_60_0 % 20.67/3.62 | (16) vgensym(all_60_0) = all_60_4 % 20.67/3.62 | % 20.67/3.62 | GROUND_INST: instantiating (2) with all_60_4, all_60_2, all_60_6, all_60_3, % 20.67/3.62 | simplifying with (5), (6), (8), (9), (10), (14) gives: % 20.67/3.62 | (17) visFreeVar(all_60_4, all_60_2) % 20.67/3.62 | % 20.67/3.62 | GROUND_INST: instantiating (fresh-unequal-var-3) with all_60_6, all_60_3, % 20.67/3.62 | all_60_5, all_60_2, all_60_1, all_60_0, simplifying with (6), % 20.67/3.62 | (7), (9), (13), (14), (15) gives: % 20.67/3.62 | (18) ? [v0: any] : ( ~ (v0 = all_60_5) & vgensym(all_60_0) = v0 & $i(v0)) % 20.67/3.62 | % 20.67/3.62 | DELTA: instantiating (18) with fresh symbol all_76_0 gives: % 20.67/3.62 | (19) ~ (all_76_0 = all_60_5) & vgensym(all_60_0) = all_76_0 & $i(all_76_0) % 20.67/3.62 | % 20.67/3.62 | ALPHA: (19) implies: % 20.67/3.62 | (20) $i(all_76_0) % 20.67/3.62 | (21) vgensym(all_60_0) = all_76_0 % 20.67/3.62 | % 20.67/3.62 | GROUND_INST: instantiating (3) with all_60_4, all_76_0, all_60_0, simplifying % 20.67/3.62 | with (16), (21) gives: % 20.67/3.62 | (22) all_76_0 = all_60_4 % 20.67/3.62 | % 20.67/3.62 | GROUND_INST: instantiating (1) with all_60_4, all_60_0, all_60_2, all_60_1, % 20.67/3.62 | simplifying with (8), (10), (11), (12), (15), (17) gives: % 20.67/3.62 | (23) visFreeVar(all_60_4, all_60_0) % 20.67/3.62 | % 20.67/3.62 | GROUND_INST: instantiating (gensym-is-fresh) with all_60_4, all_60_0, % 20.67/3.62 | simplifying with (8), (12), (16), (23) gives: % 20.67/3.62 | (24) $false % 20.67/3.62 | % 20.67/3.62 | CLOSE: (24) is inconsistent. % 20.67/3.62 | % 20.67/3.62 End of proof % 20.67/3.62 % SZS output end Proof for theBenchmark % 20.67/3.62 % 20.67/3.62 2946ms %------------------------------------------------------------------------------