%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 : Thu Aug 31 11:47:39 EDT 2023 % Result : Theorem 10.35s 2.14s % Output : Proof 16.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n013.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Fri Aug 25 09:58:32 EDT 2023 % 0.14/0.33 % CPUTime : % 0.20/0.55 ________ _____ % 0.20/0.55 ___ __ \_________(_)________________________________ % 0.20/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.55 % 0.20/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.55 (2023-06-19) % 0.20/0.55 % 0.20/0.55 (c) Philipp Rümmer, 2009-2023 % 0.20/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.55 Amanda Stjerna. % 0.20/0.55 Free software under BSD-3-Clause. % 0.20/0.55 % 0.20/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.55 % 0.20/0.55 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.56 Running up to 7 provers in parallel. % 0.20/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.59/1.03 Prover 1: Preprocessing ... % 2.59/1.03 Prover 4: Preprocessing ... % 2.59/1.08 Prover 3: Preprocessing ... % 2.59/1.08 Prover 0: Preprocessing ... % 2.59/1.08 Prover 2: Preprocessing ... % 2.59/1.08 Prover 6: Preprocessing ... % 2.59/1.08 Prover 5: Preprocessing ... % 5.68/1.50 Prover 6: Proving ... % 5.68/1.50 Prover 3: Constructing countermodel ... % 5.68/1.51 Prover 1: Constructing countermodel ... % 6.54/1.57 Prover 4: Constructing countermodel ... % 6.54/1.57 Prover 5: Constructing countermodel ... % 6.54/1.62 Prover 2: Proving ... % 7.32/1.68 Prover 0: Proving ... % 8.41/1.84 Prover 3: gave up % 8.41/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.84/1.88 Prover 7: Preprocessing ... % 9.43/2.11 Prover 7: Constructing countermodel ... % 10.35/2.14 Prover 0: proved (1573ms) % 10.35/2.14 % 10.35/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.35/2.14 % 10.35/2.15 Prover 2: stopped % 10.35/2.15 Prover 6: stopped % 10.35/2.16 Prover 5: stopped % 10.81/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.81/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.81/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.81/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.00/2.19 Prover 8: Preprocessing ... % 11.00/2.20 Prover 11: Preprocessing ... % 11.00/2.20 Prover 13: Preprocessing ... % 11.00/2.20 Prover 10: Preprocessing ... % 11.00/2.21 Prover 1: gave up % 11.00/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.44/2.25 Prover 16: Preprocessing ... % 11.44/2.29 Prover 8: Warning: ignoring some quantifiers % 11.44/2.29 Prover 8: Constructing countermodel ... % 11.44/2.30 Prover 10: Constructing countermodel ... % 12.04/2.32 Prover 16: Constructing countermodel ... % 12.04/2.35 Prover 13: Constructing countermodel ... % 12.51/2.40 Prover 10: gave up % 12.51/2.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.51/2.44 Prover 11: Constructing countermodel ... % 12.51/2.45 Prover 19: Preprocessing ... % 13.75/2.61 Prover 8: gave up % 13.75/2.62 Prover 19: Warning: ignoring some quantifiers % 13.75/2.62 Prover 19: Constructing countermodel ... % 15.16/2.80 Prover 4: Found proof (size 52) % 15.16/2.80 Prover 4: proved (2220ms) % 15.16/2.80 Prover 16: stopped % 15.16/2.80 Prover 13: stopped % 15.16/2.80 Prover 7: stopped % 15.16/2.80 Prover 19: stopped % 15.16/2.80 Prover 11: stopped % 15.16/2.80 % 15.16/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.16/2.80 % 15.16/2.81 % SZS output start Proof for theBenchmark % 15.16/2.81 Assumptions after simplification: % 15.16/2.81 --------------------------------- % 15.16/2.81 % 15.16/2.81 (mAddComm) % 15.71/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 15.71/2.84 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 15.71/2.84 (sdtpldt0(v0, v1) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) & % 15.71/2.84 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : ! % 15.71/2.84 [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] % 15.71/2.84 : ? [v4: any] : ? [v5: $i] : (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 & % 15.71/2.84 aInteger0(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 15.71/2.84 % 15.71/2.84 (mAddNeg) % 15.71/2.84 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? % 15.71/2.84 [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 & % 15.71/2.84 sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = % 15.71/2.84 0) | (v4 = sz00 & v3 = sz00)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = % 15.71/2.84 0) | ~ $i(v0) | ? [v1: $i] : (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) % 15.71/2.84 = sz00 & smndt0(v0) = v1 & $i(v1))) % 15.71/2.84 % 15.71/2.84 (mIntPlus) % 15.71/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 15.71/2.84 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 15.71/2.84 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 15.71/2.84 | ~ (v3 = 0) | v5 = 0))) % 15.71/2.84 % 15.71/2.84 (mIntZero) % 15.71/2.84 aInteger0(sz00) = 0 & $i(sz00) % 15.71/2.84 % 15.71/2.84 (mMulMinOne) % 15.71/2.85 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 15.71/2.85 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 15.71/2.85 : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & aInteger0(v1) = % 15.71/2.85 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: % 15.71/2.85 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] % 15.71/2.85 : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & % 15.71/2.85 aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = % 15.71/2.85 v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ % 15.71/2.85 $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 % 15.71/2.85 & sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 % 15.71/2.85 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ (aInteger0(v1) = % 15.71/2.85 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) % 15.71/2.85 = v2 & smndt0(v1) = v2 & $i(v2)))) % 15.71/2.85 % 15.71/2.85 (mMulZero) % 15.71/2.85 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ % 15.71/2.85 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz00, v0) = v3 & % 15.71/2.85 aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & % 15.71/2.85 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ? [v2: % 15.71/2.85 any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & aInteger0(v0) = v2 & % 15.71/2.85 $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0: $i] : ( ~ % 15.71/2.85 (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) = sz00 & % 15.71/2.85 sdtasdt0(sz00, v0) = sz00)) % 15.71/2.85 % 15.71/2.85 (m__) % 15.71/2.85 $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( % 15.71/2.85 ~ (v3 = 0) & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v3 & % 15.71/2.85 aDivisorOf0(xq, v1) = v2 & sdtpldt0(xa, v0) = v1 & smndt0(xa) = v0 & $i(v1) % 15.71/2.85 & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5: % 15.71/2.85 int] : ( ~ (v5 = 0) & aInteger0(v4) = v5)) & ! [v4: $i] : ( ~ % 15.71/2.85 (aInteger0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 = v1) & % 15.71/2.85 sdtasdt0(xq, v4) = v5 & $i(v5)))) % 15.71/2.85 % 15.71/2.85 (m__671) % 15.71/2.85 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) & % 15.71/2.85 $i(sz00) % 15.71/2.85 % 15.71/2.85 (function-axioms) % 15.71/2.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.71/2.86 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 15.71/2.86 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 15.71/2.86 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.71/2.86 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] : % 15.71/2.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 15.71/2.86 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.71/2.86 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.71/2.86 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | % 15.71/2.86 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.71/2.86 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ % 15.71/2.86 (aInteger0(v2) = v0)) % 15.71/2.86 % 15.71/2.86 Further assumptions not needed in the proof: % 15.71/2.86 -------------------------------------------- % 15.71/2.86 mAddAsso, mAddZero, mDistrib, mDivisor, mEquMod, mIntMult, mIntNeg, mIntOne, % 15.71/2.86 mIntegers, mMulAsso, mMulComm, mMulOne, mZeroDiv % 15.71/2.86 % 15.71/2.86 Those formulas are unsatisfiable: % 15.71/2.86 --------------------------------- % 15.71/2.86 % 15.71/2.86 Begin of proof % 15.71/2.86 | % 15.71/2.86 | ALPHA: (mIntZero) implies: % 15.71/2.86 | (1) aInteger0(sz00) = 0 % 15.71/2.86 | % 15.71/2.86 | ALPHA: (mAddComm) implies: % 15.71/2.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 15.71/2.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 15.71/2.86 | (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & % 15.71/2.86 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 15.71/2.86 | % 15.71/2.86 | ALPHA: (mAddNeg) implies: % 15.71/2.86 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: % 15.71/2.86 | any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 & % 15.71/2.86 | sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ % 15.71/2.86 | (v2 = 0) | (v4 = sz00 & v3 = sz00)))) % 15.71/2.86 | % 15.71/2.86 | ALPHA: (mMulZero) implies: % 15.71/2.86 | (4) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) % 15.71/2.86 | = sz00 & sdtasdt0(sz00, v0) = sz00)) % 15.71/2.86 | % 15.71/2.86 | ALPHA: (mMulMinOne) implies: % 15.71/2.87 | (5) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 15.71/2.87 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 15.71/2.87 | : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & % 15.71/2.87 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & % 15.71/2.87 | v4 = v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, % 15.71/2.87 | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: % 15.71/2.87 | $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) = % 15.71/2.87 | v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! % 15.71/2.87 | [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3: % 15.71/2.87 | any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & % 15.71/2.87 | sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( % 15.71/2.87 | ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ % 15.71/2.87 | (aInteger0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = % 15.71/2.87 | v2 & sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2)))) % 15.71/2.87 | % 15.71/2.87 | ALPHA: (m__671) implies: % 15.71/2.87 | (6) $i(sz00) % 15.71/2.87 | (7) aInteger0(xa) = 0 % 15.71/2.87 | (8) aInteger0(xq) = 0 % 15.71/2.87 | % 15.71/2.87 | ALPHA: (m__) implies: % 15.71/2.87 | (9) $i(xa) % 15.71/2.87 | (10) $i(xq) % 15.71/2.87 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) % 15.71/2.87 | & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v3 & % 15.71/2.87 | aDivisorOf0(xq, v1) = v2 & sdtpldt0(xa, v0) = v1 & smndt0(xa) = v0 & % 15.71/2.87 | $i(v1) & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~ % 15.71/2.87 | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aInteger0(v4) = v5)) & ! % 15.71/2.87 | [v4: $i] : ( ~ (aInteger0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ % 15.71/2.87 | (v5 = v1) & sdtasdt0(xq, v4) = v5 & $i(v5)))) % 15.71/2.87 | % 15.71/2.87 | ALPHA: (function-axioms) implies: % 15.71/2.87 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.71/2.87 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 15.71/2.87 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.71/2.87 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.71/2.87 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.71/2.87 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 15.71/2.87 | % 15.71/2.87 | DELTA: instantiating (11) with fresh symbols all_19_0, all_19_1, all_19_2, % 15.71/2.87 | all_19_3 gives: % 15.71/2.87 | (15) ~ (all_19_0 = 0) & ~ (all_19_1 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, % 15.71/2.87 | xq) = all_19_0 & aDivisorOf0(xq, all_19_2) = all_19_1 & sdtpldt0(xa, % 15.71/2.87 | all_19_3) = all_19_2 & smndt0(xa) = all_19_3 & $i(all_19_2) & % 15.71/2.87 | $i(all_19_3) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_19_2) | ~ % 15.71/2.87 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)) & ! % 15.71/2.87 | [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 15.71/2.87 | (v1 = all_19_2) & sdtasdt0(xq, v0) = v1 & $i(v1))) % 15.71/2.87 | % 15.71/2.87 | ALPHA: (15) implies: % 15.71/2.87 | (16) $i(all_19_3) % 15.71/2.88 | (17) smndt0(xa) = all_19_3 % 15.71/2.88 | (18) sdtpldt0(xa, all_19_3) = all_19_2 % 15.71/2.88 | (19) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 15.71/2.88 | (v1 = all_19_2) & sdtasdt0(xq, v0) = v1 & $i(v1))) % 15.71/2.88 | % 15.71/2.88 | DELTA: instantiating (5) with fresh symbol all_22_0 gives: % 15.71/2.88 | (20) smndt0(sz10) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1: $i] : ( % 15.71/2.88 | ~ (sdtasdt0(v0, all_22_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 15.71/2.88 | $i] : ? [v4: $i] : (sdtasdt0(all_22_0, v0) = v3 & smndt0(v0) = v4 % 15.71/2.88 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.71/2.88 | (sdtasdt0(all_22_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 15.71/2.88 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_22_0) = v4 & smndt0(v0) = v3 % 15.71/2.88 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = % 15.71/2.88 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 15.71/2.88 | (sdtasdt0(v0, all_22_0) = v4 & sdtasdt0(all_22_0, v0) = v3 & % 15.71/2.88 | aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ % 15.71/2.88 | $i(v0) | ? [v1: $i] : (sdtasdt0(v0, all_22_0) = v1 & % 15.71/2.88 | sdtasdt0(all_22_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) % 15.71/2.88 | % 15.71/2.88 | ALPHA: (20) implies: % 15.71/2.88 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? % 15.71/2.88 | [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v0, all_22_0) = v4 % 15.71/2.88 | & sdtasdt0(all_22_0, v0) = v3 & aInteger0(v0) = v2 & $i(v4) & % 15.71/2.88 | $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & v3 = v1)))) % 15.71/2.88 | % 15.71/2.88 | GROUND_INST: instantiating (19) with sz00, simplifying with (1), (6) gives: % 15.71/2.88 | (22) ? [v0: any] : ( ~ (v0 = all_19_2) & sdtasdt0(xq, sz00) = v0 & $i(v0)) % 15.71/2.88 | % 15.71/2.88 | GROUND_INST: instantiating (4) with xq, simplifying with (8), (10) gives: % 15.71/2.88 | (23) sdtasdt0(xq, sz00) = sz00 & sdtasdt0(sz00, xq) = sz00 % 15.71/2.88 | % 15.71/2.88 | ALPHA: (23) implies: % 15.71/2.88 | (24) sdtasdt0(xq, sz00) = sz00 % 15.71/2.88 | % 15.71/2.88 | GROUND_INST: instantiating (21) with xa, all_19_3, simplifying with (9), (17) % 15.71/2.88 | gives: % 15.71/2.88 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(all_22_0, xa) = % 15.71/2.88 | v1 & sdtasdt0(xa, all_22_0) = v2 & aInteger0(xa) = v0 & $i(v2) & % 15.71/2.88 | $i(v1) & ( ~ (v0 = 0) | (v2 = all_19_3 & v1 = all_19_3))) % 15.71/2.88 | % 15.71/2.88 | GROUND_INST: instantiating (3) with xa, all_19_3, simplifying with (9), (17) % 15.71/2.88 | gives: % 15.71/2.89 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (sdtpldt0(all_19_3, xa) = % 15.71/2.89 | v2 & sdtpldt0(xa, all_19_3) = v1 & aInteger0(xa) = v0 & $i(v2) & % 15.71/2.89 | $i(v1) & ( ~ (v0 = 0) | (v2 = sz00 & v1 = sz00))) % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (2) with xa, all_19_3, all_19_2, simplifying with % 15.71/2.89 | (9), (16), (18) gives: % 15.71/2.89 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_19_3, xa) = % 15.71/2.89 | v2 & aInteger0(all_19_3) = v1 & aInteger0(xa) = v0 & $i(v2) & ( ~ % 15.71/2.89 | (v1 = 0) | ~ (v0 = 0) | v2 = all_19_2)) % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (mIntPlus) with xa, all_19_3, all_19_2, simplifying % 15.71/2.89 | with (9), (16), (18) gives: % 15.71/2.89 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_19_2) = v2 % 15.71/2.89 | & aInteger0(all_19_3) = v1 & aInteger0(xa) = v0 & ( ~ (v1 = 0) | ~ % 15.71/2.89 | (v0 = 0) | v2 = 0)) % 15.71/2.89 | % 15.71/2.89 | DELTA: instantiating (22) with fresh symbol all_45_0 gives: % 15.71/2.89 | (29) ~ (all_45_0 = all_19_2) & sdtasdt0(xq, sz00) = all_45_0 & % 15.71/2.89 | $i(all_45_0) % 15.71/2.89 | % 15.71/2.89 | ALPHA: (29) implies: % 15.71/2.89 | (30) ~ (all_45_0 = all_19_2) % 15.71/2.89 | (31) sdtasdt0(xq, sz00) = all_45_0 % 15.71/2.89 | % 15.71/2.89 | DELTA: instantiating (28) with fresh symbols all_75_0, all_75_1, all_75_2 % 15.71/2.89 | gives: % 15.71/2.89 | (32) aInteger0(all_19_2) = all_75_0 & aInteger0(all_19_3) = all_75_1 & % 15.71/2.89 | aInteger0(xa) = all_75_2 & ( ~ (all_75_1 = 0) | ~ (all_75_2 = 0) | % 15.71/2.89 | all_75_0 = 0) % 15.71/2.89 | % 15.71/2.89 | ALPHA: (32) implies: % 15.71/2.89 | (33) aInteger0(xa) = all_75_2 % 15.71/2.89 | % 15.71/2.89 | DELTA: instantiating (27) with fresh symbols all_103_0, all_103_1, all_103_2 % 15.71/2.89 | gives: % 15.71/2.89 | (34) sdtpldt0(all_19_3, xa) = all_103_0 & aInteger0(all_19_3) = all_103_1 & % 15.71/2.89 | aInteger0(xa) = all_103_2 & $i(all_103_0) & ( ~ (all_103_1 = 0) | ~ % 15.71/2.89 | (all_103_2 = 0) | all_103_0 = all_19_2) % 15.71/2.89 | % 15.71/2.89 | ALPHA: (34) implies: % 15.71/2.89 | (35) aInteger0(xa) = all_103_2 % 15.71/2.89 | % 15.71/2.89 | DELTA: instantiating (26) with fresh symbols all_115_0, all_115_1, all_115_2 % 15.71/2.89 | gives: % 15.71/2.89 | (36) sdtpldt0(all_19_3, xa) = all_115_0 & sdtpldt0(xa, all_19_3) = % 15.71/2.89 | all_115_1 & aInteger0(xa) = all_115_2 & $i(all_115_0) & $i(all_115_1) % 15.71/2.89 | & ( ~ (all_115_2 = 0) | (all_115_0 = sz00 & all_115_1 = sz00)) % 15.71/2.89 | % 15.71/2.89 | ALPHA: (36) implies: % 15.71/2.89 | (37) aInteger0(xa) = all_115_2 % 15.71/2.89 | (38) sdtpldt0(xa, all_19_3) = all_115_1 % 15.71/2.89 | (39) ~ (all_115_2 = 0) | (all_115_0 = sz00 & all_115_1 = sz00) % 15.71/2.89 | % 15.71/2.89 | DELTA: instantiating (25) with fresh symbols all_119_0, all_119_1, all_119_2 % 15.71/2.89 | gives: % 15.71/2.89 | (40) sdtasdt0(all_22_0, xa) = all_119_1 & sdtasdt0(xa, all_22_0) = % 15.71/2.89 | all_119_0 & aInteger0(xa) = all_119_2 & $i(all_119_0) & $i(all_119_1) % 15.71/2.89 | & ( ~ (all_119_2 = 0) | (all_119_0 = all_19_3 & all_119_1 = all_19_3)) % 15.71/2.89 | % 15.71/2.89 | ALPHA: (40) implies: % 15.71/2.89 | (41) aInteger0(xa) = all_119_2 % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (12) with 0, all_103_2, xa, simplifying with (7), % 15.71/2.89 | (35) gives: % 15.71/2.89 | (42) all_103_2 = 0 % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (12) with all_103_2, all_115_2, xa, simplifying % 15.71/2.89 | with (35), (37) gives: % 15.71/2.89 | (43) all_115_2 = all_103_2 % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (12) with all_115_2, all_119_2, xa, simplifying % 15.71/2.89 | with (37), (41) gives: % 15.71/2.89 | (44) all_119_2 = all_115_2 % 15.71/2.89 | % 15.71/2.89 | GROUND_INST: instantiating (12) with all_75_2, all_119_2, xa, simplifying with % 15.71/2.89 | (33), (41) gives: % 15.71/2.89 | (45) all_119_2 = all_75_2 % 15.71/2.89 | % 15.71/2.90 | GROUND_INST: instantiating (13) with all_19_2, all_115_1, all_19_3, xa, % 15.71/2.90 | simplifying with (18), (38) gives: % 15.71/2.90 | (46) all_115_1 = all_19_2 % 15.71/2.90 | % 15.71/2.90 | GROUND_INST: instantiating (14) with sz00, all_45_0, sz00, xq, simplifying % 15.71/2.90 | with (24), (31) gives: % 15.71/2.90 | (47) all_45_0 = sz00 % 15.71/2.90 | % 15.71/2.90 | COMBINE_EQS: (44), (45) imply: % 15.71/2.90 | (48) all_115_2 = all_75_2 % 15.71/2.90 | % 15.71/2.90 | SIMP: (48) implies: % 15.71/2.90 | (49) all_115_2 = all_75_2 % 15.71/2.90 | % 15.71/2.90 | COMBINE_EQS: (43), (49) imply: % 15.71/2.90 | (50) all_103_2 = all_75_2 % 15.71/2.90 | % 15.71/2.90 | SIMP: (50) implies: % 15.71/2.90 | (51) all_103_2 = all_75_2 % 15.71/2.90 | % 15.71/2.90 | COMBINE_EQS: (42), (51) imply: % 15.71/2.90 | (52) all_75_2 = 0 % 15.71/2.90 | % 15.71/2.90 | COMBINE_EQS: (49), (52) imply: % 15.71/2.90 | (53) all_115_2 = 0 % 15.71/2.90 | % 15.71/2.90 | REDUCE: (30), (47) imply: % 15.71/2.90 | (54) ~ (all_19_2 = sz00) % 15.71/2.90 | % 15.71/2.90 | SIMP: (54) implies: % 15.71/2.90 | (55) ~ (all_19_2 = sz00) % 15.71/2.90 | % 15.71/2.90 | BETA: splitting (39) gives: % 15.71/2.90 | % 15.71/2.90 | Case 1: % 15.71/2.90 | | % 15.71/2.90 | | (56) ~ (all_115_2 = 0) % 15.71/2.90 | | % 15.71/2.90 | | REDUCE: (53), (56) imply: % 15.71/2.90 | | (57) $false % 16.13/2.90 | | % 16.13/2.90 | | CLOSE: (57) is inconsistent. % 16.13/2.90 | | % 16.13/2.90 | Case 2: % 16.13/2.90 | | % 16.13/2.90 | | (58) all_115_0 = sz00 & all_115_1 = sz00 % 16.13/2.90 | | % 16.13/2.90 | | ALPHA: (58) implies: % 16.13/2.90 | | (59) all_115_1 = sz00 % 16.13/2.90 | | % 16.13/2.90 | | COMBINE_EQS: (46), (59) imply: % 16.13/2.90 | | (60) all_19_2 = sz00 % 16.13/2.90 | | % 16.13/2.90 | | SIMP: (60) implies: % 16.13/2.90 | | (61) all_19_2 = sz00 % 16.13/2.90 | | % 16.13/2.90 | | REDUCE: (55), (61) imply: % 16.13/2.90 | | (62) $false % 16.13/2.90 | | % 16.13/2.90 | | CLOSE: (62) is inconsistent. % 16.13/2.90 | | % 16.13/2.90 | End of split % 16.13/2.90 | % 16.13/2.90 End of proof % 16.13/2.90 % SZS output end Proof for theBenchmark % 16.13/2.90 % 16.13/2.90 2347ms %------------------------------------------------------------------------------