%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM141+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 : n022.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 18:44:35 EDT 2023 % Result : Theorem 11.86s 2.35s % Output : Proof 15.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM141+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 : n022.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 12:48:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.51/0.61 ________ _____ % 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 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 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 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 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.30/1.28 Prover 1: Preprocessing ... % 4.30/1.29 Prover 4: Preprocessing ... % 4.30/1.32 Prover 6: Preprocessing ... % 4.30/1.32 Prover 3: Preprocessing ... % 4.30/1.32 Prover 2: Preprocessing ... % 4.30/1.32 Prover 5: Preprocessing ... % 4.30/1.32 Prover 0: Preprocessing ... % 10.55/2.13 Prover 3: Constructing countermodel ... % 10.55/2.14 Prover 1: Constructing countermodel ... % 10.55/2.15 Prover 6: Proving ... % 11.05/2.21 Prover 0: Proving ... % 11.58/2.28 Prover 4: Constructing countermodel ... % 11.86/2.32 Prover 3: proved (1690ms) % 11.86/2.33 % 11.86/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.86/2.35 % 11.86/2.35 Prover 6: proved (1716ms) % 11.86/2.35 % 11.86/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.86/2.35 % 11.86/2.36 Prover 5: Proving ... % 11.86/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.86/2.36 Prover 0: stopped % 11.86/2.37 Prover 5: stopped % 11.86/2.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.86/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.86/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.32/2.48 Prover 2: Proving ... % 12.32/2.48 Prover 2: stopped % 12.32/2.49 Prover 1: Found proof (size 37) % 12.32/2.49 Prover 1: proved (1855ms) % 12.32/2.49 Prover 4: stopped % 12.32/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.30/2.55 Prover 7: Preprocessing ... % 13.30/2.57 Prover 8: Preprocessing ... % 13.82/2.58 Prover 10: Preprocessing ... % 13.82/2.60 Prover 11: Preprocessing ... % 13.82/2.61 Prover 7: stopped % 13.82/2.64 Prover 10: stopped % 13.82/2.65 Prover 13: Preprocessing ... % 14.55/2.67 Prover 11: stopped % 14.96/2.73 Prover 13: stopped % 14.96/2.77 Prover 8: Warning: ignoring some quantifiers % 14.96/2.78 Prover 8: Constructing countermodel ... % 14.96/2.79 Prover 8: stopped % 14.96/2.79 % 14.96/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.96/2.79 % 14.96/2.80 % SZS output start Proof for theBenchmark % 15.32/2.80 Assumptions after simplification: % 15.32/2.80 --------------------------------- % 15.32/2.80 % 15.32/2.80 (T-Weak-abs) % 15.32/2.83 $i(veabs) & $i(vnoType) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 15.32/2.83 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : % 15.32/2.83 ( ~ (v8 = 0) & vtcheck(v7, v6, v5) = v8 & vtcheck(v2, v6, v5) = 0 & % 15.32/2.83 vlookup(v0, v2) = vnoType & vbind(v0, v1, v2) = v7 & vabs(v3, v4, veabs) = % 15.32/2.83 v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.32/2.83 % 15.32/2.83 (T-Weak-abs-1) % 15.32/2.83 $i(veabs) & $i(vnoType) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.32/2.83 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : % 15.32/2.83 (v8 = 0 | v3 = v0 | ~ (vtcheck(v7, v6, v5) = v8) | ~ (vbind(v0, v1, v2) = % 15.32/2.83 v7) | ~ (vabs(v3, v4, veabs) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 15.32/2.83 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : % 15.32/2.83 (vtcheck(v2, v6, v5) = v10 & vlookup(v0, v2) = v9 & $i(v9) & ( ~ (v10 = 0) | % 15.32/2.83 ~ (v9 = vnoType)))) % 15.32/2.83 % 15.32/2.83 (T-Weak-abs-2) % 15.32/2.83 $i(veabs) & $i(vnoType) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.32/2.83 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 15.32/2.83 (vtcheck(v6, v5, v4) = v7) | ~ (vbind(v0, v1, v2) = v6) | ~ (vabs(v0, v3, % 15.32/2.83 veabs) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 15.32/2.83 | ? [v8: $i] : ? [v9: any] : (vtcheck(v2, v5, v4) = v9 & vlookup(v0, v2) = % 15.32/2.83 v8 & $i(v8) & ( ~ (v9 = 0) | ~ (v8 = vnoType)))) % 15.32/2.83 % 15.32/2.83 (function-axioms) % 15.32/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 15.32/2.84 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 15.32/2.84 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.32/2.84 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 15.32/2.84 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 15.32/2.84 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 15.32/2.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 15.32/2.84 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 15.32/2.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 15.32/2.84 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.32/2.84 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 15.32/2.84 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.32/2.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.32/2.84 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 15.32/2.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 15.32/2.84 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.32/2.84 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.32/2.84 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 15.32/2.84 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 15.32/2.84 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 15.32/2.84 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 15.32/2.84 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.32/2.84 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.32/2.84 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 15.32/2.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.32/2.84 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 15.32/2.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 15.32/2.84 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.32/2.84 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 15.32/2.84 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.32/2.85 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 15.32/2.85 % 15.32/2.85 Further assumptions not needed in the proof: % 15.32/2.85 -------------------------------------------- % 15.32/2.85 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, % 15.32/2.85 DIFF-var-abs, DIFF-var-app, EQ-abs, EQ-app, EQ-arrow, EQ-bind, EQ-empty, % 15.32/2.85 EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Context-Duplicate, % 15.32/2.85 T-Context-Swap, T-Weak-abs-IH, T-abs, T-app, T-inv, T-var, gensym-is-fresh, % 15.32/2.85 getSomeExp0, getSomeType0, isFreeVar0, isFreeVar1, isFreeVar2, isSomeExp0, % 15.32/2.85 isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, % 15.32/2.85 lookup0, lookup1, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3, % 15.32/2.85 reduce4, reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, % 15.32/2.85 subst5 % 15.32/2.85 % 15.32/2.85 Those formulas are unsatisfiable: % 15.32/2.85 --------------------------------- % 15.32/2.85 % 15.32/2.85 Begin of proof % 15.32/2.85 | % 15.32/2.85 | ALPHA: (T-Weak-abs-1) implies: % 15.32/2.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.32/2.85 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | v3 = % 15.32/2.85 | v0 | ~ (vtcheck(v7, v6, v5) = v8) | ~ (vbind(v0, v1, v2) = v7) | ~ % 15.32/2.85 | (vabs(v3, v4, veabs) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 15.32/2.85 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : % 15.32/2.85 | (vtcheck(v2, v6, v5) = v10 & vlookup(v0, v2) = v9 & $i(v9) & ( ~ (v10 % 15.32/2.85 | = 0) | ~ (v9 = vnoType)))) % 15.32/2.85 | % 15.32/2.85 | ALPHA: (T-Weak-abs-2) implies: % 15.32/2.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.32/2.85 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vtcheck(v6, v5, % 15.32/2.85 | v4) = v7) | ~ (vbind(v0, v1, v2) = v6) | ~ (vabs(v0, v3, veabs) % 15.32/2.85 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.32/2.85 | ? [v8: $i] : ? [v9: any] : (vtcheck(v2, v5, v4) = v9 & vlookup(v0, % 15.32/2.85 | v2) = v8 & $i(v8) & ( ~ (v9 = 0) | ~ (v8 = vnoType)))) % 15.32/2.85 | % 15.32/2.85 | ALPHA: (T-Weak-abs) implies: % 15.32/2.85 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.32/2.85 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 15.32/2.85 | vtcheck(v7, v6, v5) = v8 & vtcheck(v2, v6, v5) = 0 & vlookup(v0, v2) % 15.32/2.85 | = vnoType & vbind(v0, v1, v2) = v7 & vabs(v3, v4, veabs) = v6 & % 15.32/2.85 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 15.32/2.85 | $i(v0)) % 15.32/2.86 | % 15.32/2.86 | ALPHA: (function-axioms) implies: % 15.32/2.86 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.32/2.86 | (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) % 15.32/2.86 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.32/2.86 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | % 15.32/2.86 | ~ (vtcheck(v4, v3, v2) = v0)) % 15.32/2.86 | % 15.32/2.86 | DELTA: instantiating (3) with fresh symbols all_56_0, all_56_1, all_56_2, % 15.32/2.86 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8 gives: % 15.32/2.86 | (6) ~ (all_56_0 = 0) & vtcheck(all_56_1, all_56_2, all_56_3) = all_56_0 & % 15.32/2.86 | vtcheck(all_56_6, all_56_2, all_56_3) = 0 & vlookup(all_56_8, all_56_6) % 15.32/2.86 | = vnoType & vbind(all_56_8, all_56_7, all_56_6) = all_56_1 & % 15.32/2.86 | vabs(all_56_5, all_56_4, veabs) = all_56_2 & $i(all_56_1) & % 15.32/2.86 | $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & $i(all_56_5) & % 15.32/2.86 | $i(all_56_6) & $i(all_56_7) & $i(all_56_8) % 15.32/2.86 | % 15.32/2.86 | ALPHA: (6) implies: % 15.32/2.86 | (7) ~ (all_56_0 = 0) % 15.32/2.86 | (8) $i(all_56_8) % 15.32/2.86 | (9) $i(all_56_7) % 15.32/2.86 | (10) $i(all_56_6) % 15.32/2.86 | (11) $i(all_56_5) % 15.32/2.86 | (12) $i(all_56_4) % 15.32/2.86 | (13) $i(all_56_3) % 15.32/2.86 | (14) vabs(all_56_5, all_56_4, veabs) = all_56_2 % 15.32/2.86 | (15) vbind(all_56_8, all_56_7, all_56_6) = all_56_1 % 15.32/2.86 | (16) vlookup(all_56_8, all_56_6) = vnoType % 15.32/2.86 | (17) vtcheck(all_56_6, all_56_2, all_56_3) = 0 % 15.32/2.86 | (18) vtcheck(all_56_1, all_56_2, all_56_3) = all_56_0 % 15.32/2.86 | % 15.32/2.86 | GROUND_INST: instantiating (1) with all_56_8, all_56_7, all_56_6, all_56_5, % 15.32/2.86 | all_56_4, all_56_3, all_56_2, all_56_1, all_56_0, simplifying % 15.32/2.86 | with (8), (9), (10), (11), (12), (13), (14), (15), (18) gives: % 15.32/2.87 | (19) all_56_0 = 0 | all_56_5 = all_56_8 | ? [v0: $i] : ? [v1: any] : % 15.32/2.87 | (vtcheck(all_56_6, all_56_2, all_56_3) = v1 & vlookup(all_56_8, % 15.32/2.87 | all_56_6) = v0 & $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType))) % 15.32/2.87 | % 15.32/2.87 | BETA: splitting (19) gives: % 15.32/2.87 | % 15.32/2.87 | Case 1: % 15.32/2.87 | | % 15.32/2.87 | | (20) all_56_0 = 0 % 15.32/2.87 | | % 15.32/2.87 | | REDUCE: (7), (20) imply: % 15.32/2.87 | | (21) $false % 15.32/2.87 | | % 15.32/2.87 | | CLOSE: (21) is inconsistent. % 15.32/2.87 | | % 15.32/2.87 | Case 2: % 15.32/2.87 | | % 15.63/2.87 | | (22) all_56_5 = all_56_8 | ? [v0: $i] : ? [v1: any] : % 15.63/2.87 | | (vtcheck(all_56_6, all_56_2, all_56_3) = v1 & vlookup(all_56_8, % 15.63/2.87 | | all_56_6) = v0 & $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType))) % 15.63/2.87 | | % 15.63/2.87 | | BETA: splitting (22) gives: % 15.63/2.87 | | % 15.63/2.87 | | Case 1: % 15.63/2.87 | | | % 15.63/2.87 | | | (23) all_56_5 = all_56_8 % 15.63/2.87 | | | % 15.63/2.87 | | | REDUCE: (14), (23) imply: % 15.63/2.87 | | | (24) vabs(all_56_8, all_56_4, veabs) = all_56_2 % 15.63/2.87 | | | % 15.63/2.87 | | | GROUND_INST: instantiating (2) with all_56_8, all_56_7, all_56_6, % 15.63/2.87 | | | all_56_4, all_56_3, all_56_2, all_56_1, all_56_0, simplifying % 15.63/2.87 | | | with (8), (9), (10), (12), (13), (15), (18), (24) gives: % 15.63/2.87 | | | (25) all_56_0 = 0 | ? [v0: $i] : ? [v1: any] : (vtcheck(all_56_6, % 15.63/2.87 | | | all_56_2, all_56_3) = v1 & vlookup(all_56_8, all_56_6) = v0 & % 15.63/2.87 | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType))) % 15.63/2.87 | | | % 15.63/2.87 | | | BETA: splitting (25) gives: % 15.63/2.87 | | | % 15.63/2.87 | | | Case 1: % 15.63/2.87 | | | | % 15.63/2.87 | | | | (26) all_56_0 = 0 % 15.63/2.87 | | | | % 15.63/2.87 | | | | REDUCE: (7), (26) imply: % 15.63/2.87 | | | | (27) $false % 15.63/2.87 | | | | % 15.63/2.87 | | | | CLOSE: (27) is inconsistent. % 15.63/2.87 | | | | % 15.63/2.87 | | | Case 2: % 15.63/2.87 | | | | % 15.63/2.87 | | | | (28) ? [v0: $i] : ? [v1: any] : (vtcheck(all_56_6, all_56_2, % 15.63/2.87 | | | | all_56_3) = v1 & vlookup(all_56_8, all_56_6) = v0 & $i(v0) & % 15.63/2.87 | | | | ( ~ (v1 = 0) | ~ (v0 = vnoType))) % 15.63/2.87 | | | | % 15.63/2.87 | | | | DELTA: instantiating (28) with fresh symbols all_81_0, all_81_1 gives: % 15.63/2.87 | | | | (29) vtcheck(all_56_6, all_56_2, all_56_3) = all_81_0 & % 15.63/2.87 | | | | vlookup(all_56_8, all_56_6) = all_81_1 & $i(all_81_1) & ( ~ % 15.63/2.87 | | | | (all_81_0 = 0) | ~ (all_81_1 = vnoType)) % 15.63/2.87 | | | | % 15.63/2.87 | | | | REF_CLOSE: (4), (5), (16), (17), (29) are inconsistent by sub-proof #1. % 15.63/2.87 | | | | % 15.63/2.87 | | | End of split % 15.63/2.87 | | | % 15.63/2.87 | | Case 2: % 15.63/2.87 | | | % 15.63/2.88 | | | (30) ? [v0: $i] : ? [v1: any] : (vtcheck(all_56_6, all_56_2, % 15.63/2.88 | | | all_56_3) = v1 & vlookup(all_56_8, all_56_6) = v0 & $i(v0) & ( % 15.63/2.88 | | | ~ (v1 = 0) | ~ (v0 = vnoType))) % 15.63/2.88 | | | % 15.63/2.88 | | | DELTA: instantiating (30) with fresh symbols all_81_0, all_81_1 gives: % 15.63/2.88 | | | (31) vtcheck(all_56_6, all_56_2, all_56_3) = all_81_0 & % 15.63/2.88 | | | vlookup(all_56_8, all_56_6) = all_81_1 & $i(all_81_1) & ( ~ % 15.63/2.88 | | | (all_81_0 = 0) | ~ (all_81_1 = vnoType)) % 15.63/2.88 | | | % 15.63/2.88 | | | REF_CLOSE: (4), (5), (16), (17), (31) are inconsistent by sub-proof #1. % 15.63/2.88 | | | % 15.63/2.88 | | End of split % 15.63/2.88 | | % 15.63/2.88 | End of split % 15.63/2.88 | % 15.63/2.88 End of proof % 15.63/2.88 % 15.63/2.88 Sub-proof #1 shows that the following formulas are inconsistent: % 15.63/2.88 ---------------------------------------------------------------- % 15.63/2.88 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.63/2.88 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ % 15.63/2.88 (vtcheck(v4, v3, v2) = v0)) % 15.63/2.88 (2) vlookup(all_56_8, all_56_6) = vnoType % 15.63/2.88 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.63/2.88 (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) % 15.63/2.88 (4) vtcheck(all_56_6, all_56_2, all_56_3) = all_81_0 & vlookup(all_56_8, % 15.63/2.88 all_56_6) = all_81_1 & $i(all_81_1) & ( ~ (all_81_0 = 0) | ~ (all_81_1 % 15.63/2.88 = vnoType)) % 15.63/2.88 (5) vtcheck(all_56_6, all_56_2, all_56_3) = 0 % 15.63/2.88 % 15.63/2.88 Begin of proof % 15.63/2.88 | % 15.63/2.88 | ALPHA: (4) implies: % 15.63/2.88 | (6) vlookup(all_56_8, all_56_6) = all_81_1 % 15.63/2.88 | (7) vtcheck(all_56_6, all_56_2, all_56_3) = all_81_0 % 15.63/2.88 | (8) ~ (all_81_0 = 0) | ~ (all_81_1 = vnoType) % 15.63/2.88 | % 15.63/2.88 | GROUND_INST: instantiating (3) with vnoType, all_81_1, all_56_6, all_56_8, % 15.63/2.88 | simplifying with (2), (6) gives: % 15.63/2.88 | (9) all_81_1 = vnoType % 15.63/2.88 | % 15.63/2.88 | GROUND_INST: instantiating (1) with 0, all_81_0, all_56_3, all_56_2, all_56_6, % 15.63/2.88 | simplifying with (5), (7) gives: % 15.63/2.88 | (10) all_81_0 = 0 % 15.63/2.88 | % 15.63/2.88 | BETA: splitting (8) gives: % 15.63/2.88 | % 15.63/2.88 | Case 1: % 15.63/2.88 | | % 15.63/2.88 | | (11) ~ (all_81_1 = vnoType) % 15.63/2.88 | | % 15.63/2.88 | | REDUCE: (9), (11) imply: % 15.63/2.88 | | (12) $false % 15.63/2.88 | | % 15.63/2.88 | | CLOSE: (12) is inconsistent. % 15.63/2.88 | | % 15.63/2.88 | Case 2: % 15.63/2.88 | | % 15.63/2.88 | | (13) ~ (all_81_0 = 0) % 15.63/2.88 | | % 15.63/2.88 | | REDUCE: (10), (13) imply: % 15.63/2.88 | | (14) $false % 15.63/2.88 | | % 15.63/2.88 | | CLOSE: (14) is inconsistent. % 15.63/2.88 | | % 15.63/2.88 | End of split % 15.63/2.88 | % 15.63/2.88 End of proof % 15.63/2.88 % SZS output end Proof for theBenchmark % 15.63/2.88 % 15.63/2.88 2273ms %------------------------------------------------------------------------------