%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM127+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 : n032.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 13.58s 2.51s % Output : Proof 17.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : COM127+1 : TPTP v8.1.2. Released v6.4.0. % 0.10/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Tue Aug 29 12:53:46 EDT 2023 % 0.10/0.30 % CPUTime : % 0.15/0.50 ________ _____ % 0.15/0.50 ___ __ \_________(_)________________________________ % 0.15/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.50 % 0.15/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.50 (2023-06-19) % 0.15/0.50 % 0.15/0.50 (c) Philipp Rümmer, 2009-2023 % 0.15/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.50 Amanda Stjerna. % 0.15/0.50 Free software under BSD-3-Clause. % 0.15/0.50 % 0.15/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.50 % 0.15/0.51 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.52 Running up to 7 provers in parallel. % 0.15/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.96/1.20 Prover 4: Preprocessing ... % 3.96/1.20 Prover 1: Preprocessing ... % 3.96/1.23 Prover 6: Preprocessing ... % 3.96/1.23 Prover 3: Preprocessing ... % 3.96/1.23 Prover 0: Preprocessing ... % 3.96/1.23 Prover 2: Preprocessing ... % 3.96/1.23 Prover 5: Preprocessing ... % 10.52/2.09 Prover 1: Constructing countermodel ... % 10.96/2.12 Prover 4: Constructing countermodel ... % 11.35/2.15 Prover 6: Proving ... % 11.35/2.19 Prover 3: Constructing countermodel ... % 12.40/2.30 Prover 0: Proving ... % 12.40/2.34 Prover 5: Proving ... % 13.58/2.47 Prover 2: Proving ... % 13.58/2.51 Prover 3: proved (1982ms) % 13.58/2.51 % 13.58/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.58/2.51 % 13.58/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.58/2.51 Prover 2: stopped % 13.58/2.51 Prover 6: stopped % 13.58/2.52 Prover 0: stopped % 13.58/2.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.58/2.52 Prover 5: stopped % 13.58/2.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.58/2.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.58/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.58/2.54 Prover 1: Found proof (size 42) % 13.58/2.54 Prover 1: proved (2018ms) % 13.58/2.54 Prover 4: stopped % 15.22/2.71 Prover 11: Preprocessing ... % 15.22/2.71 Prover 13: Preprocessing ... % 15.60/2.74 Prover 8: Preprocessing ... % 15.76/2.75 Prover 7: Preprocessing ... % 15.76/2.77 Prover 11: stopped % 15.76/2.78 Prover 10: Preprocessing ... % 15.76/2.80 Prover 7: stopped % 15.76/2.81 Prover 13: stopped % 16.29/2.82 Prover 10: stopped % 16.55/2.90 Prover 8: Warning: ignoring some quantifiers % 16.55/2.91 Prover 8: Constructing countermodel ... % 16.55/2.92 Prover 8: stopped % 16.55/2.92 % 16.55/2.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.55/2.92 % 16.55/2.93 % SZS output start Proof for theBenchmark % 16.55/2.94 Assumptions after simplification: % 16.55/2.94 --------------------------------- % 16.55/2.94 % 16.55/2.94 (DIFF-var-abs) % 16.94/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.94/2.98 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.06/2.98 $i(v1) | ~ $i(v0)) % 17.06/2.98 % 17.06/2.98 (DIFF-var-app) % 17.06/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) = % 17.06/2.98 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 17.06/2.98 % 17.06/2.98 (EQ-var) % 17.06/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vvar(v1) = v2) | ~ % 17.06/2.98 (vvar(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 17.06/2.98 % 17.06/2.98 (T-Weak-FreeVar-var) % 17.06/2.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 17.06/2.98 $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ~ (v6 = 0) % 17.06/2.98 & vtcheck(v7, v5, v4) = v8 & vtcheck(v2, v5, v4) = 0 & vbind(v0, v1, v2) = % 17.06/2.98 v7 & visFreeVar(v0, v5) = v6 & vvar(v3) = v5 & $i(v7) & $i(v5) & $i(v4) & % 17.06/2.98 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.06/2.98 % 17.06/2.98 (T-inv) % 17.06/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 17.06/2.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 17.06/2.99 ? [v6: $i] : ? [v7: $i] : (varrow(v5, v6) = v1 & vtcheck(v7, v4, v6) = 0 & % 17.06/2.99 vbind(v3, v5, v2) = v7 & vabs(v3, v5, v4) = v0 & $i(v7) & $i(v6) & $i(v5) % 17.06/2.99 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 17.06/2.99 : (varrow(v5, v1) = v6 & vtcheck(v2, v4, v5) = 0 & vtcheck(v2, v3, v6) = 0 & % 17.06/2.99 vapp(v3, v4) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : % 17.06/2.99 (vsomeType(v1) = v3 & $i(v3) & ? [v4: $i] : (vlookup(v4, v2) = v3 & % 17.06/2.99 vvar(v4) = v0 & $i(v4)))) % 17.06/2.99 % 17.06/2.99 (T-var) % 17.06/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.06/2.99 | ~ (vtcheck(v0, v3, v2) = v4) | ~ (vvar(v1) = v3) | ~ $i(v2) | ~ $i(v1) % 17.06/2.99 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & vlookup(v1, v0) = % 17.06/2.99 v5 & vsomeType(v2) = v6 & $i(v6) & $i(v5))) % 17.06/2.99 % 17.06/2.99 (isFreeVar0) % 17.06/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (visFreeVar(v0, % 17.06/2.99 v1) = v3) | ~ (vvar(v2) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (( % 17.06/2.99 ~ (v3 = 0) | v2 = v0) & ( ~ (v2 = v0) | v3 = 0))) % 17.06/2.99 % 17.06/2.99 (lookup2) % 17.06/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.06/2.99 $i] : ! [v6: $i] : (v6 = v4 | v2 = v1 | ~ (vlookup(v2, v5) = v6) | ~ % 17.06/2.99 (vlookup(v2, v3) = v4) | ~ (vbind(v1, v0, v5) = v3) | ~ $i(v5) | ~ $i(v4) % 17.06/2.99 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 17.06/2.99 % 17.06/2.99 (function-axioms) % 17.06/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 17.06/3.00 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 17.06/3.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.06/3.00 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 17.06/3.00 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 17.06/3.00 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 17.06/3.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 17.06/3.00 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 17.06/3.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 17.06/3.00 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.06/3.00 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 17.06/3.00 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.06/3.00 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.06/3.00 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 17.06/3.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 17.06/3.00 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 17.06/3.00 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 17.06/3.00 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 17.06/3.00 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 17.06/3.00 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 17.06/3.00 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 17.06/3.00 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 17.06/3.00 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 17.06/3.00 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 17.06/3.00 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.06/3.00 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 17.06/3.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 17.06/3.00 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.06/3.00 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 17.06/3.00 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 17.06/3.00 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 17.06/3.00 % 17.06/3.00 Further assumptions not needed in the proof: % 17.06/3.00 -------------------------------------------- % 17.06/3.00 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, EQ-abs, % 17.06/3.00 EQ-app, EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, % 17.06/3.00 EQ-someType, T-Context-Duplicate, T-Context-Swap, T-Strong, T-Weak, T-abs, % 17.06/3.00 T-app, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar1, isFreeVar2, % 17.06/3.00 isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2, % 17.06/3.00 lookup-INV, lookup0, lookup1, reduce-INV, reduce0, reduce1, reduce2, reduce3, % 17.06/3.00 reduce4, reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, % 17.06/3.00 subst5 % 17.06/3.00 % 17.06/3.00 Those formulas are unsatisfiable: % 17.06/3.00 --------------------------------- % 17.06/3.00 % 17.06/3.00 Begin of proof % 17.06/3.00 | % 17.06/3.00 | ALPHA: (function-axioms) implies: % 17.06/3.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) % 17.06/3.01 | = v1) | ~ (vsomeType(v2) = v0)) % 17.06/3.01 | % 17.06/3.01 | DELTA: instantiating (T-Weak-FreeVar-var) with fresh symbols all_55_0, % 17.06/3.01 | all_55_1, all_55_2, all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, % 17.06/3.01 | all_55_8 gives: % 17.06/3.01 | (2) ~ (all_55_0 = 0) & ~ (all_55_2 = 0) & vtcheck(all_55_1, all_55_3, % 17.06/3.01 | all_55_4) = all_55_0 & vtcheck(all_55_6, all_55_3, all_55_4) = 0 & % 17.06/3.01 | vbind(all_55_8, all_55_7, all_55_6) = all_55_1 & visFreeVar(all_55_8, % 17.06/3.01 | all_55_3) = all_55_2 & vvar(all_55_5) = all_55_3 & $i(all_55_1) & % 17.06/3.01 | $i(all_55_3) & $i(all_55_4) & $i(all_55_5) & $i(all_55_6) & % 17.06/3.01 | $i(all_55_7) & $i(all_55_8) % 17.06/3.01 | % 17.06/3.01 | ALPHA: (2) implies: % 17.06/3.01 | (3) ~ (all_55_2 = 0) % 17.06/3.01 | (4) ~ (all_55_0 = 0) % 17.06/3.01 | (5) $i(all_55_8) % 17.06/3.01 | (6) $i(all_55_7) % 17.06/3.01 | (7) $i(all_55_6) % 17.06/3.01 | (8) $i(all_55_5) % 17.06/3.01 | (9) $i(all_55_4) % 17.06/3.01 | (10) $i(all_55_3) % 17.06/3.01 | (11) $i(all_55_1) % 17.06/3.01 | (12) vvar(all_55_5) = all_55_3 % 17.06/3.01 | (13) visFreeVar(all_55_8, all_55_3) = all_55_2 % 17.06/3.01 | (14) vbind(all_55_8, all_55_7, all_55_6) = all_55_1 % 17.06/3.01 | (15) vtcheck(all_55_6, all_55_3, all_55_4) = 0 % 17.06/3.01 | (16) vtcheck(all_55_1, all_55_3, all_55_4) = all_55_0 % 17.06/3.01 | % 17.06/3.01 | GROUND_INST: instantiating (isFreeVar0) with all_55_8, all_55_3, all_55_5, % 17.06/3.01 | all_55_2, simplifying with (5), (8), (10), (12), (13) gives: % 17.06/3.01 | (17) ( ~ (all_55_2 = 0) | all_55_5 = all_55_8) & ( ~ (all_55_5 = all_55_8) % 17.06/3.01 | | all_55_2 = 0) % 17.06/3.01 | % 17.06/3.01 | ALPHA: (17) implies: % 17.06/3.01 | (18) ~ (all_55_5 = all_55_8) | all_55_2 = 0 % 17.06/3.01 | % 17.06/3.01 | GROUND_INST: instantiating (T-inv) with all_55_3, all_55_4, all_55_6, % 17.06/3.01 | simplifying with (7), (9), (10), (15) gives: % 17.06/3.02 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.06/3.02 | (varrow(v2, v3) = all_55_4 & vtcheck(v4, v1, v3) = 0 & vbind(v0, v2, % 17.06/3.02 | all_55_6) = v4 & vabs(v0, v2, v1) = all_55_3 & $i(v4) & $i(v3) & % 17.06/3.02 | $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 17.06/3.02 | : ? [v3: $i] : (varrow(v2, all_55_4) = v3 & vtcheck(all_55_6, v1, v2) % 17.06/3.02 | = 0 & vtcheck(all_55_6, v0, v3) = 0 & vapp(v0, v1) = all_55_3 & % 17.06/3.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 17.06/3.02 | (vsomeType(all_55_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 17.06/3.02 | all_55_6) = v0 & vvar(v1) = all_55_3 & $i(v1))) % 17.06/3.02 | % 17.06/3.02 | GROUND_INST: instantiating (T-var) with all_55_1, all_55_5, all_55_4, % 17.06/3.02 | all_55_3, all_55_0, simplifying with (8), (9), (11), (12), (16) % 17.06/3.02 | gives: % 17.06/3.02 | (20) all_55_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 17.06/3.02 | vlookup(all_55_5, all_55_1) = v0 & vsomeType(all_55_4) = v1 & $i(v1) % 17.06/3.02 | & $i(v0)) % 17.06/3.02 | % 17.06/3.02 | BETA: splitting (20) gives: % 17.06/3.02 | % 17.06/3.02 | Case 1: % 17.06/3.02 | | % 17.06/3.02 | | (21) all_55_0 = 0 % 17.06/3.02 | | % 17.06/3.02 | | REDUCE: (4), (21) imply: % 17.06/3.02 | | (22) $false % 17.06/3.02 | | % 17.06/3.02 | | CLOSE: (22) is inconsistent. % 17.06/3.02 | | % 17.06/3.02 | Case 2: % 17.06/3.02 | | % 17.06/3.02 | | (23) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & vlookup(all_55_5, % 17.06/3.02 | | all_55_1) = v0 & vsomeType(all_55_4) = v1 & $i(v1) & $i(v0)) % 17.06/3.02 | | % 17.06/3.02 | | DELTA: instantiating (23) with fresh symbols all_64_0, all_64_1 gives: % 17.06/3.02 | | (24) ~ (all_64_0 = all_64_1) & vlookup(all_55_5, all_55_1) = all_64_1 & % 17.06/3.02 | | vsomeType(all_55_4) = all_64_0 & $i(all_64_0) & $i(all_64_1) % 17.06/3.02 | | % 17.06/3.02 | | ALPHA: (24) implies: % 17.06/3.02 | | (25) ~ (all_64_0 = all_64_1) % 17.06/3.02 | | (26) $i(all_64_1) % 17.06/3.02 | | (27) vsomeType(all_55_4) = all_64_0 % 17.06/3.02 | | (28) vlookup(all_55_5, all_55_1) = all_64_1 % 17.06/3.02 | | % 17.06/3.02 | | BETA: splitting (18) gives: % 17.06/3.02 | | % 17.06/3.02 | | Case 1: % 17.06/3.02 | | | % 17.06/3.02 | | | (29) ~ (all_55_5 = all_55_8) % 17.06/3.02 | | | % 17.06/3.02 | | | BETA: splitting (19) gives: % 17.06/3.02 | | | % 17.06/3.02 | | | Case 1: % 17.06/3.02 | | | | % 17.06/3.02 | | | | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 17.06/3.02 | | | | $i] : (varrow(v2, v3) = all_55_4 & vtcheck(v4, v1, v3) = 0 & % 17.06/3.02 | | | | vbind(v0, v2, all_55_6) = v4 & vabs(v0, v2, v1) = all_55_3 & % 17.06/3.02 | | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.06/3.02 | | | | % 17.06/3.02 | | | | DELTA: instantiating (30) with fresh symbols all_89_0, all_89_1, % 17.06/3.02 | | | | all_89_2, all_89_3, all_89_4 gives: % 17.30/3.02 | | | | (31) varrow(all_89_2, all_89_1) = all_55_4 & vtcheck(all_89_0, % 17.30/3.03 | | | | all_89_3, all_89_1) = 0 & vbind(all_89_4, all_89_2, all_55_6) % 17.30/3.03 | | | | = all_89_0 & vabs(all_89_4, all_89_2, all_89_3) = all_55_3 & % 17.30/3.03 | | | | $i(all_89_0) & $i(all_89_1) & $i(all_89_2) & $i(all_89_3) & % 17.30/3.03 | | | | $i(all_89_4) % 17.30/3.03 | | | | % 17.30/3.03 | | | | ALPHA: (31) implies: % 17.30/3.03 | | | | (32) $i(all_89_4) % 17.30/3.03 | | | | (33) $i(all_89_3) % 17.30/3.03 | | | | (34) $i(all_89_2) % 17.30/3.03 | | | | (35) vabs(all_89_4, all_89_2, all_89_3) = all_55_3 % 17.30/3.03 | | | | % 17.30/3.03 | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_55_5, all_89_4, % 17.30/3.03 | | | | all_89_2, all_89_3, all_55_3, simplifying with (8), (12), % 17.30/3.03 | | | | (32), (33), (34), (35) gives: % 17.30/3.03 | | | | (36) $false % 17.30/3.03 | | | | % 17.30/3.03 | | | | CLOSE: (36) is inconsistent. % 17.30/3.03 | | | | % 17.30/3.03 | | | Case 2: % 17.30/3.03 | | | | % 17.30/3.03 | | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.30/3.03 | | | | (varrow(v2, all_55_4) = v3 & vtcheck(all_55_6, v1, v2) = 0 & % 17.30/3.03 | | | | vtcheck(all_55_6, v0, v3) = 0 & vapp(v0, v1) = all_55_3 & % 17.30/3.03 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 17.30/3.03 | | | | (vsomeType(all_55_4) = v0 & $i(v0) & ? [v1: $i] : (vlookup(v1, % 17.30/3.03 | | | | all_55_6) = v0 & vvar(v1) = all_55_3 & $i(v1))) % 17.30/3.03 | | | | % 17.30/3.03 | | | | BETA: splitting (37) gives: % 17.30/3.03 | | | | % 17.30/3.03 | | | | Case 1: % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.30/3.03 | | | | | (varrow(v2, all_55_4) = v3 & vtcheck(all_55_6, v1, v2) = 0 & % 17.30/3.03 | | | | | vtcheck(all_55_6, v0, v3) = 0 & vapp(v0, v1) = all_55_3 & % 17.30/3.03 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | DELTA: instantiating (38) with fresh symbols all_89_0, all_89_1, % 17.30/3.03 | | | | | all_89_2, all_89_3 gives: % 17.30/3.03 | | | | | (39) varrow(all_89_1, all_55_4) = all_89_0 & vtcheck(all_55_6, % 17.30/3.03 | | | | | all_89_2, all_89_1) = 0 & vtcheck(all_55_6, all_89_3, % 17.30/3.03 | | | | | all_89_0) = 0 & vapp(all_89_3, all_89_2) = all_55_3 & % 17.30/3.03 | | | | | $i(all_89_0) & $i(all_89_1) & $i(all_89_2) & $i(all_89_3) % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | ALPHA: (39) implies: % 17.30/3.03 | | | | | (40) $i(all_89_3) % 17.30/3.03 | | | | | (41) $i(all_89_2) % 17.30/3.03 | | | | | (42) vapp(all_89_3, all_89_2) = all_55_3 % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | GROUND_INST: instantiating (DIFF-var-app) with all_55_5, all_89_3, % 17.30/3.03 | | | | | all_89_2, all_55_3, simplifying with (8), (12), (40), % 17.30/3.03 | | | | | (41), (42) gives: % 17.30/3.03 | | | | | (43) $false % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | CLOSE: (43) is inconsistent. % 17.30/3.03 | | | | | % 17.30/3.03 | | | | Case 2: % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | (44) ? [v0: $i] : (vsomeType(all_55_4) = v0 & $i(v0) & ? [v1: $i] % 17.30/3.03 | | | | | : (vlookup(v1, all_55_6) = v0 & vvar(v1) = all_55_3 & % 17.30/3.03 | | | | | $i(v1))) % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | DELTA: instantiating (44) with fresh symbol all_89_0 gives: % 17.30/3.03 | | | | | (45) vsomeType(all_55_4) = all_89_0 & $i(all_89_0) & ? [v0: $i] : % 17.30/3.03 | | | | | (vlookup(v0, all_55_6) = all_89_0 & vvar(v0) = all_55_3 & % 17.30/3.03 | | | | | $i(v0)) % 17.30/3.03 | | | | | % 17.30/3.03 | | | | | ALPHA: (45) implies: % 17.30/3.04 | | | | | (46) vsomeType(all_55_4) = all_89_0 % 17.30/3.04 | | | | | (47) ? [v0: $i] : (vlookup(v0, all_55_6) = all_89_0 & vvar(v0) = % 17.30/3.04 | | | | | all_55_3 & $i(v0)) % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | DELTA: instantiating (47) with fresh symbol all_91_0 gives: % 17.30/3.04 | | | | | (48) vlookup(all_91_0, all_55_6) = all_89_0 & vvar(all_91_0) = % 17.30/3.04 | | | | | all_55_3 & $i(all_91_0) % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | ALPHA: (48) implies: % 17.30/3.04 | | | | | (49) $i(all_91_0) % 17.30/3.04 | | | | | (50) vvar(all_91_0) = all_55_3 % 17.30/3.04 | | | | | (51) vlookup(all_91_0, all_55_6) = all_89_0 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | GROUND_INST: instantiating (1) with all_64_0, all_89_0, all_55_4, % 17.30/3.04 | | | | | simplifying with (27), (46) gives: % 17.30/3.04 | | | | | (52) all_89_0 = all_64_0 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | REDUCE: (51), (52) imply: % 17.30/3.04 | | | | | (53) vlookup(all_91_0, all_55_6) = all_64_0 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | GROUND_INST: instantiating (EQ-var) with all_55_5, all_91_0, all_55_3, % 17.30/3.04 | | | | | simplifying with (8), (12), (49), (50) gives: % 17.30/3.04 | | | | | (54) all_91_0 = all_55_5 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | REDUCE: (53), (54) imply: % 17.30/3.04 | | | | | (55) vlookup(all_55_5, all_55_6) = all_64_0 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | GROUND_INST: instantiating (lookup2) with all_55_7, all_55_8, % 17.30/3.04 | | | | | all_55_5, all_55_1, all_64_1, all_55_6, all_64_0, % 17.30/3.04 | | | | | simplifying with (5), (6), (7), (8), (11), (14), (26), % 17.30/3.04 | | | | | (28), (55) gives: % 17.30/3.04 | | | | | (56) all_64_0 = all_64_1 | all_55_5 = all_55_8 % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | BETA: splitting (56) gives: % 17.30/3.04 | | | | | % 17.30/3.04 | | | | | Case 1: % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | (57) all_64_0 = all_64_1 % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | REDUCE: (25), (57) imply: % 17.30/3.04 | | | | | | (58) $false % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | CLOSE: (58) is inconsistent. % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | Case 2: % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | (59) all_55_5 = all_55_8 % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | REDUCE: (29), (59) imply: % 17.30/3.04 | | | | | | (60) $false % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | | CLOSE: (60) is inconsistent. % 17.30/3.04 | | | | | | % 17.30/3.04 | | | | | End of split % 17.30/3.04 | | | | | % 17.30/3.04 | | | | End of split % 17.30/3.04 | | | | % 17.30/3.04 | | | End of split % 17.30/3.04 | | | % 17.30/3.04 | | Case 2: % 17.30/3.04 | | | % 17.30/3.04 | | | (61) all_55_2 = 0 % 17.30/3.04 | | | % 17.30/3.04 | | | REDUCE: (3), (61) imply: % 17.30/3.04 | | | (62) $false % 17.30/3.04 | | | % 17.30/3.04 | | | CLOSE: (62) is inconsistent. % 17.30/3.04 | | | % 17.30/3.04 | | End of split % 17.30/3.04 | | % 17.30/3.04 | End of split % 17.30/3.04 | % 17.30/3.04 End of proof % 17.30/3.04 % SZS output end Proof for theBenchmark % 17.30/3.04 % 17.30/3.04 2536ms %------------------------------------------------------------------------------