%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM130+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 : n028.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 15.97s 2.78s % Output : Proof 19.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM130+1 : TPTP v8.1.2. Released v6.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.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 13:29:55 EDT 2023 % 0.13/0.34 % CPUTime : % 0.51/0.60 ________ _____ % 0.51/0.61 ___ __ \_________(_)________________________________ % 0.51/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.61 % 0.51/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.61 (2023-06-19) % 0.51/0.61 % 0.51/0.61 (c) Philipp Rümmer, 2009-2023 % 0.51/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.61 Amanda Stjerna. % 0.51/0.61 Free software under BSD-3-Clause. % 0.51/0.61 % 0.51/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.61 % 0.51/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.51/0.62 Running up to 7 provers in parallel. % 0.51/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.28/1.40 Prover 1: Preprocessing ... % 5.28/1.41 Prover 4: Preprocessing ... % 5.69/1.44 Prover 0: Preprocessing ... % 5.69/1.44 Prover 6: Preprocessing ... % 5.69/1.44 Prover 5: Preprocessing ... % 5.69/1.44 Prover 3: Preprocessing ... % 5.69/1.45 Prover 2: Preprocessing ... % 10.67/2.12 Prover 3: Constructing countermodel ... % 10.67/2.14 Prover 1: Constructing countermodel ... % 10.67/2.15 Prover 6: Proving ... % 11.69/2.22 Prover 4: Constructing countermodel ... % 11.88/2.31 Prover 0: Proving ... % 12.51/2.33 Prover 5: Proving ... % 13.16/2.46 Prover 2: Proving ... % 15.97/2.78 Prover 6: proved (2150ms) % 15.97/2.78 % 15.97/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.97/2.78 % 15.97/2.78 Prover 3: stopped % 15.97/2.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.97/2.78 Prover 2: stopped % 15.97/2.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.97/2.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.97/2.79 Prover 5: stopped % 15.97/2.79 Prover 0: stopped % 15.97/2.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.97/2.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.34/2.83 Prover 1: Found proof (size 44) % 16.34/2.83 Prover 1: proved (2205ms) % 16.34/2.83 Prover 4: stopped % 17.03/2.94 Prover 7: Preprocessing ... % 17.03/2.94 Prover 8: Preprocessing ... % 17.03/2.96 Prover 13: Preprocessing ... % 17.03/2.96 Prover 10: Preprocessing ... % 17.03/2.97 Prover 11: Preprocessing ... % 17.58/3.03 Prover 10: stopped % 17.58/3.04 Prover 7: stopped % 17.58/3.05 Prover 11: stopped % 17.58/3.08 Prover 13: stopped % 18.62/3.17 Prover 8: Warning: ignoring some quantifiers % 18.62/3.18 Prover 8: Constructing countermodel ... % 18.62/3.19 Prover 8: stopped % 18.62/3.19 % 18.62/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.62/3.19 % 18.62/3.20 % SZS output start Proof for theBenchmark % 18.62/3.20 Assumptions after simplification: % 18.62/3.20 --------------------------------- % 18.62/3.20 % 18.62/3.20 (DIFF-abs-app) % 18.62/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.62/3.23 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~ % 18.62/3.23 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.62/3.23 % 18.62/3.23 (DIFF-var-abs) % 18.62/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 18.62/3.23 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 18.62/3.23 $i(v1) | ~ $i(v0)) % 18.62/3.23 % 18.62/3.23 (EQ-abs) % 18.94/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.94/3.23 $i] : ! [v6: $i] : ( ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, v2) = v6) % 18.94/3.23 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.94/3.23 (v5 = v2 & v4 = v1 & v3 = v0)) % 18.94/3.23 % 18.94/3.23 (T-Strong) % 18.94/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.94/3.23 $i] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ~ % 18.94/3.23 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 18.94/3.23 [v7: any] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 | % 18.94/3.23 v6 = 0))) % 18.94/3.23 % 18.94/3.23 (T-inv) % 18.94/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 18.94/3.24 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 18.94/3.24 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 & % 18.94/3.24 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5) % 18.94/3.24 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 18.94/3.24 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 & % 18.94/3.24 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : % 18.94/3.24 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 & % 18.94/3.24 vvar(v4) = v0 & $i(v4)))) % 18.94/3.24 % 18.94/3.24 (T-subst-abs-1) % 18.94/3.24 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 18.94/3.24 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: int] % 18.94/3.24 : ( ~ (v10 = 0) & vsubst(v2, v3, v8) = v9 & vtcheck(v7, v8, v6) = 0 & % 18.94/3.24 vtcheck(v1, v9, v6) = v10 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0, v1) = v7 % 18.94/3.24 & vabs(v2, v4, v5) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 18.94/3.24 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.94/3.24 % 18.94/3.24 (isFreeVar1) % 18.94/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.94/3.24 any] : ! [v6: any] : ( ~ (visFreeVar(v1, v4) = v5) | ~ (visFreeVar(v1, v2) % 18.94/3.24 = v6) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 18.94/3.24 ~ $i(v1) | ~ $i(v0) | (( ~ (v6 = 0) | (v5 = 0 & ~ (v3 = v1))) & ( ~ (v5 = % 18.94/3.24 0) | v6 = 0 | v3 = v1))) % 18.94/3.24 % 18.94/3.24 (subst3) % 18.94/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.94/3.24 $i] : (v3 = v2 | ~ (vsubst(v1, v0, v2) = v3) | ~ (vabs(v1, v4, v5) = v2) | % 18.94/3.24 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.94/3.24 % 18.94/3.24 (function-axioms) % 18.94/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 18.94/3.25 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 18.94/3.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.94/3.25 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 18.94/3.25 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 18.94/3.25 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 18.94/3.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 18.94/3.25 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 18.94/3.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 18.94/3.25 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.94/3.25 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 18.94/3.25 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.94/3.25 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.94/3.25 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 18.94/3.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 18.94/3.25 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.94/3.25 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 18.94/3.25 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 18.94/3.25 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 18.94/3.25 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 18.94/3.25 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 18.94/3.25 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.94/3.25 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 18.94/3.25 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 18.94/3.25 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.94/3.25 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 18.94/3.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 18.94/3.25 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.94/3.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 18.94/3.25 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.94/3.25 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 18.94/3.25 % 18.94/3.25 Further assumptions not needed in the proof: % 18.94/3.25 -------------------------------------------- % 18.94/3.25 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-app, EQ-app, % 18.94/3.25 EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, % 18.94/3.25 EQ-var, T-Context-Duplicate, T-Context-Swap, T-Weak, T-Weak-FreeVar, T-abs, % 18.94/3.25 T-app, T-subst-IH-abs, T-var, gensym-is-fresh, getSomeExp0, getSomeType0, % 18.94/3.25 isFreeVar0, isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, % 18.94/3.25 isValue0, isValue1, isValue2, lookup-INV, lookup0, lookup1, lookup2, reduce-INV, % 18.94/3.25 reduce0, reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst-INV, % 18.94/3.25 subst0, subst1, subst2, subst4, subst5 % 18.94/3.25 % 18.94/3.25 Those formulas are unsatisfiable: % 18.94/3.25 --------------------------------- % 18.94/3.25 % 18.94/3.25 Begin of proof % 18.94/3.25 | % 18.94/3.25 | ALPHA: (function-axioms) implies: % 18.94/3.25 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.94/3.25 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | % 18.94/3.25 | ~ (vtcheck(v4, v3, v2) = v0)) % 18.94/3.25 | % 18.94/3.25 | DELTA: instantiating (T-subst-abs-1) with fresh symbols all_57_0, all_57_1, % 18.94/3.25 | all_57_2, all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, % 18.94/3.25 | all_57_9, all_57_10 gives: % 18.94/3.25 | (2) ~ (all_57_0 = 0) & vsubst(all_57_8, all_57_7, all_57_2) = all_57_1 & % 18.94/3.25 | vtcheck(all_57_3, all_57_2, all_57_4) = 0 & vtcheck(all_57_9, all_57_1, % 18.94/3.25 | all_57_4) = all_57_0 & vtcheck(all_57_9, all_57_7, all_57_10) = 0 & % 18.94/3.25 | vbind(all_57_8, all_57_10, all_57_9) = all_57_3 & vabs(all_57_8, % 18.94/3.25 | all_57_6, all_57_5) = all_57_2 & $i(all_57_1) & $i(all_57_2) & % 18.94/3.25 | $i(all_57_3) & $i(all_57_4) & $i(all_57_5) & $i(all_57_6) & % 18.94/3.25 | $i(all_57_7) & $i(all_57_8) & $i(all_57_9) & $i(all_57_10) % 18.94/3.25 | % 18.94/3.25 | ALPHA: (2) implies: % 18.94/3.25 | (3) ~ (all_57_0 = 0) % 18.94/3.25 | (4) $i(all_57_10) % 18.94/3.25 | (5) $i(all_57_9) % 18.94/3.25 | (6) $i(all_57_8) % 18.94/3.25 | (7) $i(all_57_7) % 18.94/3.25 | (8) $i(all_57_6) % 18.94/3.25 | (9) $i(all_57_5) % 18.94/3.25 | (10) $i(all_57_4) % 18.94/3.25 | (11) $i(all_57_3) % 18.94/3.25 | (12) $i(all_57_2) % 18.94/3.25 | (13) $i(all_57_1) % 18.94/3.26 | (14) vabs(all_57_8, all_57_6, all_57_5) = all_57_2 % 18.94/3.26 | (15) vbind(all_57_8, all_57_10, all_57_9) = all_57_3 % 18.94/3.26 | (16) vtcheck(all_57_9, all_57_1, all_57_4) = all_57_0 % 18.94/3.26 | (17) vtcheck(all_57_3, all_57_2, all_57_4) = 0 % 18.94/3.26 | (18) vsubst(all_57_8, all_57_7, all_57_2) = all_57_1 % 18.94/3.26 | % 18.94/3.26 | GROUND_INST: instantiating (T-Strong) with all_57_8, all_57_10, all_57_9, % 18.94/3.26 | all_57_2, all_57_4, all_57_3, simplifying with (4), (5), (6), % 18.94/3.26 | (10), (12), (15), (17) gives: % 18.94/3.26 | (19) ? [v0: any] : ? [v1: any] : (vtcheck(all_57_9, all_57_2, all_57_4) = % 18.94/3.26 | v1 & visFreeVar(all_57_8, all_57_2) = v0 & (v1 = 0 | v0 = 0)) % 18.94/3.26 | % 18.94/3.26 | GROUND_INST: instantiating (T-inv) with all_57_2, all_57_4, all_57_3, % 18.94/3.26 | simplifying with (10), (11), (12), (17) gives: % 18.94/3.26 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.94/3.26 | (varrow(v2, v3) = all_57_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2, % 18.94/3.26 | all_57_3) = v4 & vabs(v0, v2, v1) = all_57_2 & $i(v4) & $i(v3) & % 18.94/3.26 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 18.94/3.26 | : ? [v3: $i] : (varrow(v2, all_57_4) = v3 & vtcheck(all_57_3, v1, v2) % 18.94/3.26 | = 0 & vtcheck(all_57_3, v0, v3) = 0 & vapp(v0, v1) = all_57_2 & % 18.94/3.26 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 18.94/3.26 | (vsomeType(all_57_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 18.94/3.26 | all_57_3) = v0 & vvar(v1) = all_57_2 & $i(v1))) % 18.94/3.26 | % 18.94/3.26 | GROUND_INST: instantiating (subst3) with all_57_7, all_57_8, all_57_2, % 18.94/3.26 | all_57_1, all_57_6, all_57_5, simplifying with (6), (7), (8), % 18.94/3.26 | (9), (12), (13), (14), (18) gives: % 18.94/3.26 | (21) all_57_1 = all_57_2 % 18.94/3.26 | % 18.94/3.26 | DELTA: instantiating (19) with fresh symbols all_65_0, all_65_1 gives: % 18.94/3.26 | (22) vtcheck(all_57_9, all_57_2, all_57_4) = all_65_0 & % 18.94/3.26 | visFreeVar(all_57_8, all_57_2) = all_65_1 & (all_65_0 = 0 | all_65_1 = % 18.94/3.26 | 0) % 18.94/3.26 | % 18.94/3.26 | ALPHA: (22) implies: % 18.94/3.26 | (23) visFreeVar(all_57_8, all_57_2) = all_65_1 % 18.94/3.26 | (24) vtcheck(all_57_9, all_57_2, all_57_4) = all_65_0 % 18.94/3.26 | (25) all_65_0 = 0 | all_65_1 = 0 % 18.94/3.26 | % 18.94/3.26 | REDUCE: (16), (21) imply: % 18.94/3.26 | (26) vtcheck(all_57_9, all_57_2, all_57_4) = all_57_0 % 18.94/3.26 | % 18.94/3.26 | GROUND_INST: instantiating (1) with all_57_0, all_65_0, all_57_4, all_57_2, % 18.94/3.26 | all_57_9, simplifying with (24), (26) gives: % 18.94/3.26 | (27) all_65_0 = all_57_0 % 18.94/3.26 | % 18.94/3.26 | BETA: splitting (25) gives: % 18.94/3.26 | % 18.94/3.26 | Case 1: % 18.94/3.26 | | % 18.94/3.26 | | (28) all_65_0 = 0 % 18.94/3.26 | | % 18.94/3.26 | | COMBINE_EQS: (27), (28) imply: % 18.94/3.26 | | (29) all_57_0 = 0 % 18.94/3.26 | | % 18.94/3.26 | | REDUCE: (3), (29) imply: % 18.94/3.26 | | (30) $false % 19.13/3.27 | | % 19.13/3.27 | | CLOSE: (30) is inconsistent. % 19.13/3.27 | | % 19.13/3.27 | Case 2: % 19.13/3.27 | | % 19.13/3.27 | | (31) all_65_1 = 0 % 19.13/3.27 | | % 19.13/3.27 | | REDUCE: (23), (31) imply: % 19.13/3.27 | | (32) visFreeVar(all_57_8, all_57_2) = 0 % 19.13/3.27 | | % 19.13/3.27 | | BETA: splitting (20) gives: % 19.13/3.27 | | % 19.13/3.27 | | Case 1: % 19.13/3.27 | | | % 19.13/3.27 | | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 19.13/3.27 | | | $i] : (varrow(v2, v3) = all_57_4 & vtcheck(v4, v1, v3) = 0 & % 19.13/3.27 | | | vbind(v0, v2, all_57_3) = v4 & vabs(v0, v2, v1) = all_57_2 & % 19.13/3.27 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.13/3.27 | | | % 19.13/3.27 | | | DELTA: instantiating (33) with fresh symbols all_103_0, all_103_1, % 19.13/3.27 | | | all_103_2, all_103_3, all_103_4 gives: % 19.13/3.27 | | | (34) varrow(all_103_2, all_103_1) = all_57_4 & vtcheck(all_103_0, % 19.13/3.27 | | | all_103_3, all_103_1) = 0 & vbind(all_103_4, all_103_2, % 19.13/3.27 | | | all_57_3) = all_103_0 & vabs(all_103_4, all_103_2, all_103_3) = % 19.13/3.27 | | | all_57_2 & $i(all_103_0) & $i(all_103_1) & $i(all_103_2) & % 19.13/3.27 | | | $i(all_103_3) & $i(all_103_4) % 19.13/3.27 | | | % 19.13/3.27 | | | ALPHA: (34) implies: % 19.13/3.27 | | | (35) $i(all_103_4) % 19.13/3.27 | | | (36) $i(all_103_3) % 19.13/3.27 | | | (37) $i(all_103_2) % 19.13/3.27 | | | (38) $i(all_103_1) % 19.13/3.27 | | | (39) vabs(all_103_4, all_103_2, all_103_3) = all_57_2 % 19.13/3.27 | | | (40) vbind(all_103_4, all_103_2, all_57_3) = all_103_0 % 19.13/3.27 | | | (41) vtcheck(all_103_0, all_103_3, all_103_1) = 0 % 19.13/3.27 | | | % 19.13/3.27 | | | GROUND_INST: instantiating (EQ-abs) with all_57_8, all_57_6, all_57_5, % 19.13/3.27 | | | all_103_4, all_103_2, all_103_3, all_57_2, simplifying with % 19.13/3.27 | | | (6), (8), (9), (14), (35), (36), (37), (39) gives: % 19.13/3.27 | | | (42) all_103_2 = all_57_6 & all_103_3 = all_57_5 & all_103_4 = all_57_8 % 19.13/3.27 | | | % 19.13/3.27 | | | ALPHA: (42) implies: % 19.13/3.27 | | | (43) all_103_4 = all_57_8 % 19.13/3.27 | | | (44) all_103_3 = all_57_5 % 19.13/3.27 | | | (45) all_103_2 = all_57_6 % 19.13/3.27 | | | % 19.13/3.27 | | | GROUND_INST: instantiating (T-Strong) with all_103_4, all_103_2, all_57_3, % 19.13/3.27 | | | all_103_3, all_103_1, all_103_0, simplifying with (11), (35), % 19.13/3.27 | | | (36), (37), (38), (40), (41) gives: % 19.13/3.27 | | | (46) ? [v0: any] : ? [v1: any] : (vtcheck(all_57_3, all_103_3, % 19.13/3.27 | | | all_103_1) = v1 & visFreeVar(all_103_4, all_103_3) = v0 & (v1 % 19.13/3.27 | | | = 0 | v0 = 0)) % 19.13/3.27 | | | % 19.13/3.27 | | | DELTA: instantiating (46) with fresh symbols all_111_0, all_111_1 gives: % 19.13/3.27 | | | (47) vtcheck(all_57_3, all_103_3, all_103_1) = all_111_0 & % 19.13/3.27 | | | visFreeVar(all_103_4, all_103_3) = all_111_1 & (all_111_0 = 0 | % 19.13/3.27 | | | all_111_1 = 0) % 19.13/3.27 | | | % 19.13/3.27 | | | ALPHA: (47) implies: % 19.13/3.27 | | | (48) visFreeVar(all_103_4, all_103_3) = all_111_1 % 19.13/3.27 | | | % 19.13/3.27 | | | REDUCE: (43), (44), (48) imply: % 19.13/3.27 | | | (49) visFreeVar(all_57_8, all_57_5) = all_111_1 % 19.13/3.27 | | | % 19.13/3.27 | | | GROUND_INST: instantiating (isFreeVar1) with all_57_6, all_57_8, all_57_2, % 19.13/3.27 | | | all_57_8, all_57_5, all_111_1, 0, simplifying with (6), (8), % 19.13/3.27 | | | (9), (12), (14), (32), (49) gives: % 19.13/3.27 | | | (50) $false % 19.13/3.27 | | | % 19.13/3.27 | | | CLOSE: (50) is inconsistent. % 19.13/3.27 | | | % 19.13/3.28 | | Case 2: % 19.13/3.28 | | | % 19.13/3.28 | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 19.13/3.28 | | | (varrow(v2, all_57_4) = v3 & vtcheck(all_57_3, v1, v2) = 0 & % 19.13/3.28 | | | vtcheck(all_57_3, v0, v3) = 0 & vapp(v0, v1) = all_57_2 & $i(v3) % 19.13/3.28 | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_57_4) % 19.13/3.28 | | | = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_57_3) = v0 & % 19.13/3.28 | | | vvar(v1) = all_57_2 & $i(v1))) % 19.13/3.28 | | | % 19.13/3.28 | | | BETA: splitting (51) gives: % 19.13/3.28 | | | % 19.13/3.28 | | | Case 1: % 19.13/3.28 | | | | % 19.13/3.28 | | | | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 19.13/3.28 | | | | (varrow(v2, all_57_4) = v3 & vtcheck(all_57_3, v1, v2) = 0 & % 19.13/3.28 | | | | vtcheck(all_57_3, v0, v3) = 0 & vapp(v0, v1) = all_57_2 & % 19.13/3.28 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.13/3.28 | | | | % 19.13/3.28 | | | | DELTA: instantiating (52) with fresh symbols all_103_0, all_103_1, % 19.13/3.28 | | | | all_103_2, all_103_3 gives: % 19.13/3.28 | | | | (53) varrow(all_103_1, all_57_4) = all_103_0 & vtcheck(all_57_3, % 19.13/3.28 | | | | all_103_2, all_103_1) = 0 & vtcheck(all_57_3, all_103_3, % 19.13/3.28 | | | | all_103_0) = 0 & vapp(all_103_3, all_103_2) = all_57_2 & % 19.13/3.28 | | | | $i(all_103_0) & $i(all_103_1) & $i(all_103_2) & $i(all_103_3) % 19.13/3.28 | | | | % 19.13/3.28 | | | | ALPHA: (53) implies: % 19.13/3.28 | | | | (54) $i(all_103_3) % 19.13/3.28 | | | | (55) $i(all_103_2) % 19.13/3.28 | | | | (56) vapp(all_103_3, all_103_2) = all_57_2 % 19.13/3.28 | | | | % 19.13/3.28 | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_57_8, all_57_6, % 19.13/3.28 | | | | all_57_5, all_103_3, all_103_2, all_57_2, simplifying with % 19.13/3.28 | | | | (6), (8), (9), (14), (54), (55), (56) gives: % 19.13/3.28 | | | | (57) $false % 19.13/3.28 | | | | % 19.13/3.28 | | | | CLOSE: (57) is inconsistent. % 19.13/3.28 | | | | % 19.13/3.28 | | | Case 2: % 19.13/3.28 | | | | % 19.13/3.28 | | | | (58) ? [v0: $i] : (vsomeType(all_57_4) = v0 & $i(v0) & ? [v1: $i] : % 19.13/3.28 | | | | (vlookup(v1, all_57_3) = v0 & vvar(v1) = all_57_2 & $i(v1))) % 19.13/3.28 | | | | % 19.13/3.28 | | | | DELTA: instantiating (58) with fresh symbol all_103_0 gives: % 19.13/3.28 | | | | (59) vsomeType(all_57_4) = all_103_0 & $i(all_103_0) & ? [v0: $i] : % 19.13/3.28 | | | | (vlookup(v0, all_57_3) = all_103_0 & vvar(v0) = all_57_2 & % 19.13/3.28 | | | | $i(v0)) % 19.13/3.28 | | | | % 19.13/3.28 | | | | ALPHA: (59) implies: % 19.13/3.28 | | | | (60) ? [v0: $i] : (vlookup(v0, all_57_3) = all_103_0 & vvar(v0) = % 19.13/3.28 | | | | all_57_2 & $i(v0)) % 19.13/3.28 | | | | % 19.13/3.28 | | | | DELTA: instantiating (60) with fresh symbol all_105_0 gives: % 19.13/3.28 | | | | (61) vlookup(all_105_0, all_57_3) = all_103_0 & vvar(all_105_0) = % 19.13/3.28 | | | | all_57_2 & $i(all_105_0) % 19.13/3.28 | | | | % 19.13/3.28 | | | | ALPHA: (61) implies: % 19.13/3.28 | | | | (62) $i(all_105_0) % 19.13/3.28 | | | | (63) vvar(all_105_0) = all_57_2 % 19.13/3.28 | | | | % 19.13/3.28 | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_105_0, all_57_8, % 19.13/3.28 | | | | all_57_6, all_57_5, all_57_2, simplifying with (6), (8), % 19.13/3.28 | | | | (9), (14), (62), (63) gives: % 19.13/3.28 | | | | (64) $false % 19.13/3.28 | | | | % 19.13/3.28 | | | | CLOSE: (64) is inconsistent. % 19.13/3.28 | | | | % 19.13/3.28 | | | End of split % 19.13/3.28 | | | % 19.13/3.28 | | End of split % 19.13/3.28 | | % 19.13/3.28 | End of split % 19.13/3.28 | % 19.13/3.28 End of proof % 19.13/3.28 % SZS output end Proof for theBenchmark % 19.13/3.28 % 19.13/3.28 2678ms %------------------------------------------------------------------------------