%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM143+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 18:44:36 EDT 2023 % Result : Theorem 13.73s 2.61s % Output : Proof 17.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : COM143+1 : TPTP v8.1.2. Released v6.4.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n022.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 13:09:53 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.19/1.47 Prover 1: Preprocessing ... % 5.19/1.49 Prover 4: Preprocessing ... % 5.19/1.50 Prover 6: Preprocessing ... % 5.19/1.50 Prover 5: Preprocessing ... % 5.19/1.50 Prover 2: Preprocessing ... % 5.19/1.50 Prover 0: Preprocessing ... % 5.19/1.50 Prover 3: Preprocessing ... % 11.58/2.27 Prover 1: Constructing countermodel ... % 11.58/2.28 Prover 6: Proving ... % 11.58/2.30 Prover 4: Constructing countermodel ... % 11.58/2.31 Prover 3: Constructing countermodel ... % 11.58/2.34 Prover 0: Proving ... % 12.41/2.42 Prover 5: Proving ... % 12.86/2.52 Prover 2: Proving ... % 13.73/2.61 Prover 3: proved (1966ms) % 13.73/2.61 % 13.73/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.73/2.61 % 13.73/2.61 Prover 5: stopped % 13.73/2.61 Prover 6: stopped % 13.73/2.61 Prover 0: stopped % 13.73/2.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.73/2.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.73/2.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.73/2.61 Prover 2: stopped % 13.73/2.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.73/2.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.29/2.69 Prover 1: Found proof (size 42) % 14.29/2.69 Prover 1: proved (2053ms) % 14.29/2.69 Prover 4: stopped % 15.36/2.78 Prover 13: Preprocessing ... % 15.36/2.80 Prover 11: Preprocessing ... % 15.36/2.80 Prover 10: Preprocessing ... % 15.36/2.80 Prover 7: Preprocessing ... % 15.36/2.81 Prover 8: Preprocessing ... % 16.07/2.87 Prover 11: stopped % 16.07/2.87 Prover 7: stopped % 16.07/2.87 Prover 10: stopped % 16.07/2.89 Prover 13: stopped % 16.45/2.97 Prover 8: Warning: ignoring some quantifiers % 16.45/2.99 Prover 8: Constructing countermodel ... % 16.45/3.00 Prover 8: stopped % 16.45/3.00 % 16.45/3.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.45/3.00 % 16.45/3.00 % SZS output start Proof for theBenchmark % 16.45/3.01 Assumptions after simplification: % 16.45/3.01 --------------------------------- % 16.45/3.01 % 16.45/3.01 (DIFF-noType-someType) % 16.84/3.03 $i(vnoType) & ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0)) % 16.84/3.03 % 16.84/3.03 (DIFF-var-abs) % 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.84/3.03 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 16.84/3.03 $i(v1) | ~ $i(v0)) % 16.84/3.03 % 16.84/3.03 (DIFF-var-app) % 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) = % 16.84/3.03 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 16.84/3.03 % 16.84/3.03 (EQ-var) % 16.84/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ % 16.84/3.03 (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 16.84/3.03 % 16.84/3.03 (T-Weak-var) % 16.84/3.03 $i(vnoType) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 16.84/3.03 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & vtcheck(v6, % 16.84/3.03 v5, v4) = v7 & vtcheck(v2, v5, v4) = 0 & vlookup(v0, v2) = vnoType & % 16.84/3.03 vbind(v0, v1, v2) = v6 & vvar(v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 16.84/3.03 $i(v2) & $i(v1) & $i(v0)) % 16.84/3.03 % 16.84/3.03 (T-inv) % 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 16.84/3.04 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 16.84/3.04 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 & % 16.84/3.04 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5) % 16.84/3.04 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 16.84/3.04 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 & % 16.84/3.04 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : % 16.84/3.04 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 & % 16.84/3.04 vvar(v4) = v0 & $i(v4)))) % 16.84/3.04 % 16.84/3.04 (T-var) % 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 16.84/3.04 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ~ $i(v2) | ~ $i(v1) % 16.84/3.04 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & vlookup(v1, v0) = % 16.84/3.04 v5 & vsomeType(v2) = v6 & $i(v6) & $i(v5))) % 16.84/3.04 % 16.84/3.04 (lookup2) % 16.84/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.84/3.04 $i] : ! [v6: $i] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ % 16.84/3.04 (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3) | ~ $i(v5) | ~ $i(v4) % 16.84/3.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 16.84/3.04 % 16.84/3.04 (function-axioms) % 16.84/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 16.84/3.05 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 16.84/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.84/3.05 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 16.84/3.05 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 16.84/3.05 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 16.84/3.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 16.84/3.05 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 16.84/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 16.84/3.05 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.84/3.05 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 16.84/3.05 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.84/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.84/3.05 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 16.84/3.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 16.84/3.05 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.84/3.05 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.84/3.05 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 16.84/3.05 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 16.84/3.05 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 16.84/3.05 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 16.84/3.05 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.84/3.05 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.84/3.05 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 16.84/3.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.84/3.05 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 16.84/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 16.84/3.05 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.84/3.05 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 16.84/3.05 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.84/3.05 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 16.84/3.05 % 16.84/3.05 Further assumptions not needed in the proof: % 16.84/3.05 -------------------------------------------- % 16.84/3.05 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, EQ-abs, EQ-app, EQ-arrow, % 16.84/3.05 EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, % 16.84/3.05 T-Context-Duplicate, T-Context-Swap, T-abs, T-app, gensym-is-fresh, getSomeExp0, % 16.84/3.05 getSomeType0, isFreeVar0, isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1, % 16.84/3.05 isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, lookup0, % 16.84/3.05 lookup1, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4, reduce5, % 16.84/3.05 reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5 % 16.84/3.05 % 16.84/3.05 Those formulas are unsatisfiable: % 16.84/3.05 --------------------------------- % 16.84/3.05 % 16.84/3.05 Begin of proof % 16.84/3.05 | % 16.84/3.05 | ALPHA: (DIFF-noType-someType) implies: % 16.84/3.05 | (1) ! [v0: $i] : ( ~ (vsomeType(v0) = vnoType) | ~ $i(v0)) % 16.84/3.05 | % 16.84/3.05 | ALPHA: (T-Weak-var) implies: % 16.84/3.05 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.84/3.05 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & vtcheck(v6, % 16.84/3.05 | v5, v4) = v7 & vtcheck(v2, v5, v4) = 0 & vlookup(v0, v2) = vnoType % 16.84/3.05 | & vbind(v0, v1, v2) = v6 & vvar(v3) = v5 & $i(v6) & $i(v5) & $i(v4) & % 16.84/3.05 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.84/3.05 | % 16.84/3.05 | ALPHA: (function-axioms) implies: % 16.84/3.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) % 16.84/3.05 | = v1) | ~ (vsomeType(v2) = v0)) % 16.84/3.05 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.84/3.05 | (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0)) % 16.84/3.05 | % 16.84/3.05 | DELTA: instantiating (2) with fresh symbols all_53_0, all_53_1, all_53_2, % 16.84/3.05 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7 gives: % 16.84/3.05 | (5) ~ (all_53_0 = 0) & vtcheck(all_53_1, all_53_2, all_53_3) = all_53_0 & % 16.84/3.05 | vtcheck(all_53_5, all_53_2, all_53_3) = 0 & vlookup(all_53_7, all_53_5) % 16.84/3.05 | = vnoType & vbind(all_53_7, all_53_6, all_53_5) = all_53_1 & % 16.84/3.05 | vvar(all_53_4) = all_53_2 & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) % 16.84/3.05 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) % 16.84/3.05 | % 16.84/3.05 | ALPHA: (5) implies: % 16.84/3.05 | (6) ~ (all_53_0 = 0) % 16.84/3.05 | (7) $i(all_53_7) % 16.84/3.05 | (8) $i(all_53_6) % 16.84/3.05 | (9) $i(all_53_5) % 16.84/3.05 | (10) $i(all_53_4) % 16.84/3.05 | (11) $i(all_53_3) % 16.84/3.05 | (12) $i(all_53_2) % 16.84/3.05 | (13) $i(all_53_1) % 16.84/3.05 | (14) vvar(all_53_4) = all_53_2 % 16.84/3.05 | (15) vbind(all_53_7, all_53_6, all_53_5) = all_53_1 % 16.84/3.05 | (16) vlookup(all_53_7, all_53_5) = vnoType % 16.84/3.06 | (17) vtcheck(all_53_5, all_53_2, all_53_3) = 0 % 16.84/3.06 | (18) vtcheck(all_53_1, all_53_2, all_53_3) = all_53_0 % 16.84/3.06 | % 16.84/3.06 | GROUND_INST: instantiating (T-inv) with all_53_2, all_53_3, all_53_5, % 16.84/3.06 | simplifying with (9), (11), (12), (17) gives: % 16.84/3.06 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.84/3.06 | (varrow(v2, v3) = all_53_3 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2, % 16.84/3.06 | all_53_5) = v4 & vabs(v0, v2, v1) = all_53_2 & $i(v4) & $i(v3) & % 16.84/3.06 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 16.84/3.06 | : ? [v3: $i] : (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2) % 16.84/3.06 | = 0 & vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 & % 16.84/3.06 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 16.84/3.06 | (vsomeType(all_53_3) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 16.84/3.06 | all_53_5) = v0 & vvar(v1) = all_53_2 & $i(v1))) % 16.84/3.06 | % 16.84/3.06 | GROUND_INST: instantiating (T-var) with all_53_1, all_53_4, all_53_3, % 16.84/3.06 | all_53_2, all_53_0, simplifying with (10), (11), (13), (14), (18) % 16.84/3.06 | gives: % 16.84/3.06 | (20) all_53_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 16.84/3.06 | vlookup(all_53_4, all_53_1) = v0 & vsomeType(all_53_3) = v1 & $i(v1) % 16.84/3.06 | & $i(v0)) % 16.84/3.06 | % 16.84/3.06 | BETA: splitting (20) gives: % 16.84/3.06 | % 16.84/3.06 | Case 1: % 16.84/3.06 | | % 16.84/3.06 | | (21) all_53_0 = 0 % 16.84/3.06 | | % 16.84/3.06 | | REDUCE: (6), (21) imply: % 16.84/3.06 | | (22) $false % 16.84/3.06 | | % 16.84/3.06 | | CLOSE: (22) is inconsistent. % 16.84/3.06 | | % 16.84/3.06 | Case 2: % 16.84/3.06 | | % 16.84/3.06 | | (23) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & vlookup(all_53_4, % 16.84/3.06 | | all_53_1) = v0 & vsomeType(all_53_3) = v1 & $i(v1) & $i(v0)) % 16.84/3.06 | | % 16.84/3.06 | | DELTA: instantiating (23) with fresh symbols all_62_0, all_62_1 gives: % 16.84/3.06 | | (24) ~ (all_62_0 = all_62_1) & vlookup(all_53_4, all_53_1) = all_62_1 & % 16.84/3.06 | | vsomeType(all_53_3) = all_62_0 & $i(all_62_0) & $i(all_62_1) % 16.84/3.06 | | % 16.84/3.06 | | ALPHA: (24) implies: % 16.84/3.06 | | (25) ~ (all_62_0 = all_62_1) % 16.84/3.06 | | (26) $i(all_62_1) % 16.84/3.06 | | (27) vsomeType(all_53_3) = all_62_0 % 16.84/3.06 | | (28) vlookup(all_53_4, all_53_1) = all_62_1 % 16.84/3.06 | | % 16.84/3.06 | | BETA: splitting (19) gives: % 16.84/3.06 | | % 16.84/3.06 | | Case 1: % 16.84/3.06 | | | % 16.84/3.06 | | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 16.84/3.06 | | | $i] : (varrow(v2, v3) = all_53_3 & vtcheck(v4, v1, v3) = 0 & % 16.84/3.06 | | | vbind(v0, v2, all_53_5) = v4 & vabs(v0, v2, v1) = all_53_2 & % 16.84/3.06 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.84/3.06 | | | % 16.84/3.06 | | | DELTA: instantiating (29) with fresh symbols all_70_0, all_70_1, all_70_2, % 16.84/3.06 | | | all_70_3, all_70_4 gives: % 16.84/3.06 | | | (30) varrow(all_70_2, all_70_1) = all_53_3 & vtcheck(all_70_0, % 16.84/3.06 | | | all_70_3, all_70_1) = 0 & vbind(all_70_4, all_70_2, all_53_5) = % 16.84/3.06 | | | all_70_0 & vabs(all_70_4, all_70_2, all_70_3) = all_53_2 & % 16.84/3.06 | | | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) & % 16.84/3.06 | | | $i(all_70_4) % 16.84/3.06 | | | % 16.84/3.06 | | | ALPHA: (30) implies: % 16.84/3.06 | | | (31) $i(all_70_4) % 16.84/3.06 | | | (32) $i(all_70_3) % 16.84/3.07 | | | (33) $i(all_70_2) % 16.84/3.07 | | | (34) vabs(all_70_4, all_70_2, all_70_3) = all_53_2 % 16.84/3.07 | | | % 16.84/3.07 | | | GROUND_INST: instantiating (DIFF-var-abs) with all_53_4, all_70_4, % 16.84/3.07 | | | all_70_2, all_70_3, all_53_2, simplifying with (10), (14), % 16.84/3.07 | | | (31), (32), (33), (34) gives: % 16.84/3.07 | | | (35) $false % 16.84/3.07 | | | % 16.84/3.07 | | | CLOSE: (35) is inconsistent. % 16.84/3.07 | | | % 16.84/3.07 | | Case 2: % 16.84/3.07 | | | % 16.84/3.07 | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 16.84/3.07 | | | (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2) = 0 & % 16.84/3.07 | | | vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 & $i(v3) % 16.84/3.07 | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : (vsomeType(all_53_3) % 16.84/3.07 | | | = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, all_53_5) = v0 & % 16.84/3.07 | | | vvar(v1) = all_53_2 & $i(v1))) % 16.84/3.07 | | | % 16.84/3.07 | | | BETA: splitting (36) gives: % 16.84/3.07 | | | % 16.84/3.07 | | | Case 1: % 16.84/3.07 | | | | % 16.84/3.07 | | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 16.84/3.07 | | | | (varrow(v2, all_53_3) = v3 & vtcheck(all_53_5, v1, v2) = 0 & % 16.84/3.07 | | | | vtcheck(all_53_5, v0, v3) = 0 & vapp(v0, v1) = all_53_2 & % 16.84/3.07 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.84/3.07 | | | | % 16.84/3.07 | | | | DELTA: instantiating (37) with fresh symbols all_70_0, all_70_1, % 16.84/3.07 | | | | all_70_2, all_70_3 gives: % 16.84/3.07 | | | | (38) varrow(all_70_1, all_53_3) = all_70_0 & vtcheck(all_53_5, % 16.84/3.07 | | | | all_70_2, all_70_1) = 0 & vtcheck(all_53_5, all_70_3, % 16.84/3.07 | | | | all_70_0) = 0 & vapp(all_70_3, all_70_2) = all_53_2 & % 16.84/3.07 | | | | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) % 16.84/3.07 | | | | % 16.84/3.07 | | | | ALPHA: (38) implies: % 16.84/3.07 | | | | (39) $i(all_70_3) % 16.84/3.07 | | | | (40) $i(all_70_2) % 16.84/3.07 | | | | (41) vapp(all_70_3, all_70_2) = all_53_2 % 16.84/3.07 | | | | % 16.84/3.07 | | | | GROUND_INST: instantiating (DIFF-var-app) with all_53_4, all_70_3, % 16.84/3.07 | | | | all_70_2, all_53_2, simplifying with (10), (14), (39), % 16.84/3.07 | | | | (40), (41) gives: % 16.84/3.07 | | | | (42) $false % 16.84/3.07 | | | | % 16.84/3.07 | | | | CLOSE: (42) is inconsistent. % 16.84/3.07 | | | | % 16.84/3.07 | | | Case 2: % 16.84/3.07 | | | | % 16.84/3.07 | | | | (43) ? [v0: $i] : (vsomeType(all_53_3) = v0 & $i(v0) & ? [v1: $i] : % 16.84/3.07 | | | | (vlookup(v1, all_53_5) = v0 & vvar(v1) = all_53_2 & $i(v1))) % 16.84/3.07 | | | | % 16.84/3.07 | | | | DELTA: instantiating (43) with fresh symbol all_70_0 gives: % 16.84/3.07 | | | | (44) vsomeType(all_53_3) = all_70_0 & $i(all_70_0) & ? [v0: $i] : % 16.84/3.07 | | | | (vlookup(v0, all_53_5) = all_70_0 & vvar(v0) = all_53_2 & % 16.84/3.07 | | | | $i(v0)) % 16.84/3.07 | | | | % 16.84/3.07 | | | | ALPHA: (44) implies: % 16.84/3.07 | | | | (45) vsomeType(all_53_3) = all_70_0 % 16.84/3.07 | | | | (46) ? [v0: $i] : (vlookup(v0, all_53_5) = all_70_0 & vvar(v0) = % 16.84/3.07 | | | | all_53_2 & $i(v0)) % 16.84/3.07 | | | | % 16.84/3.07 | | | | DELTA: instantiating (46) with fresh symbol all_72_0 gives: % 16.84/3.07 | | | | (47) vlookup(all_72_0, all_53_5) = all_70_0 & vvar(all_72_0) = % 16.84/3.07 | | | | all_53_2 & $i(all_72_0) % 16.84/3.07 | | | | % 16.84/3.07 | | | | ALPHA: (47) implies: % 16.84/3.07 | | | | (48) $i(all_72_0) % 16.84/3.07 | | | | (49) vvar(all_72_0) = all_53_2 % 16.84/3.07 | | | | (50) vlookup(all_72_0, all_53_5) = all_70_0 % 16.84/3.07 | | | | % 16.84/3.07 | | | | GROUND_INST: instantiating (3) with all_62_0, all_70_0, all_53_3, % 16.84/3.07 | | | | simplifying with (27), (45) gives: % 16.84/3.07 | | | | (51) all_70_0 = all_62_0 % 16.84/3.07 | | | | % 16.84/3.07 | | | | REDUCE: (50), (51) imply: % 16.84/3.07 | | | | (52) vlookup(all_72_0, all_53_5) = all_62_0 % 16.84/3.07 | | | | % 16.84/3.07 | | | | GROUND_INST: instantiating (EQ-var) with all_53_4, all_72_0, all_53_2, % 16.84/3.07 | | | | simplifying with (10), (14), (48), (49) gives: % 16.84/3.07 | | | | (53) all_72_0 = all_53_4 % 16.84/3.07 | | | | % 16.84/3.08 | | | | REDUCE: (52), (53) imply: % 16.84/3.08 | | | | (54) vlookup(all_53_4, all_53_5) = all_62_0 % 16.84/3.08 | | | | % 16.84/3.08 | | | | GROUND_INST: instantiating (lookup2) with all_53_6, all_53_7, all_53_4, % 16.84/3.08 | | | | all_53_1, all_62_1, all_53_5, all_62_0, simplifying with % 16.84/3.08 | | | | (7), (8), (9), (10), (13), (15), (26), (28), (54) gives: % 16.84/3.08 | | | | (55) all_62_0 = all_62_1 | all_53_4 = all_53_7 % 16.84/3.08 | | | | % 16.84/3.08 | | | | BETA: splitting (55) gives: % 16.84/3.08 | | | | % 16.84/3.08 | | | | Case 1: % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | (56) all_62_0 = all_62_1 % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | REDUCE: (25), (56) imply: % 16.84/3.08 | | | | | (57) $false % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | CLOSE: (57) is inconsistent. % 16.84/3.08 | | | | | % 16.84/3.08 | | | | Case 2: % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | (58) all_53_4 = all_53_7 % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | REDUCE: (54), (58) imply: % 16.84/3.08 | | | | | (59) vlookup(all_53_7, all_53_5) = all_62_0 % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | GROUND_INST: instantiating (4) with vnoType, all_62_0, all_53_5, % 16.84/3.08 | | | | | all_53_7, simplifying with (16), (59) gives: % 16.84/3.08 | | | | | (60) all_62_0 = vnoType % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | REDUCE: (27), (60) imply: % 16.84/3.08 | | | | | (61) vsomeType(all_53_3) = vnoType % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | GROUND_INST: instantiating (1) with all_53_3, simplifying with (11), % 16.84/3.08 | | | | | (61) gives: % 16.84/3.08 | | | | | (62) $false % 16.84/3.08 | | | | | % 16.84/3.08 | | | | | CLOSE: (62) is inconsistent. % 16.84/3.08 | | | | | % 16.84/3.08 | | | | End of split % 16.84/3.08 | | | | % 17.13/3.08 | | | End of split % 17.13/3.08 | | | % 17.13/3.08 | | End of split % 17.13/3.08 | | % 17.13/3.08 | End of split % 17.13/3.08 | % 17.13/3.08 End of proof % 17.13/3.08 % SZS output end Proof for theBenchmark % 17.13/3.08 % 17.13/3.08 2460ms %------------------------------------------------------------------------------