%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 9.59s 2.10s % Output : Proof 15.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 09:07:53 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.58/1.07 Prover 4: Preprocessing ... % 2.58/1.07 Prover 1: Preprocessing ... % 2.96/1.12 Prover 2: Preprocessing ... % 2.96/1.12 Prover 6: Preprocessing ... % 2.96/1.12 Prover 0: Preprocessing ... % 2.96/1.12 Prover 5: Preprocessing ... % 2.96/1.12 Prover 3: Preprocessing ... % 5.66/1.53 Prover 1: Constructing countermodel ... % 5.66/1.55 Prover 6: Proving ... % 5.66/1.55 Prover 3: Constructing countermodel ... % 6.75/1.64 Prover 4: Constructing countermodel ... % 6.75/1.65 Prover 5: Constructing countermodel ... % 7.33/1.73 Prover 2: Proving ... % 7.33/1.74 Prover 0: Proving ... % 7.33/1.77 Prover 3: gave up % 7.33/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.76/1.80 Prover 7: Preprocessing ... % 7.76/1.83 Prover 1: gave up % 7.76/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.43/1.88 Prover 8: Preprocessing ... % 8.43/1.97 Prover 7: Constructing countermodel ... % 8.43/2.00 Prover 8: Warning: ignoring some quantifiers % 8.97/2.03 Prover 8: Constructing countermodel ... % 9.59/2.10 Prover 0: proved (1487ms) % 9.59/2.10 % 9.59/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.59/2.10 % 9.59/2.10 Prover 5: stopped % 9.59/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.59/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.59/2.10 Prover 6: stopped % 9.59/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.59/2.11 Prover 2: stopped % 10.20/2.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.20/2.15 Prover 10: Preprocessing ... % 10.20/2.15 Prover 13: Preprocessing ... % 10.20/2.15 Prover 11: Preprocessing ... % 10.20/2.16 Prover 16: Preprocessing ... % 10.67/2.22 Prover 16: Constructing countermodel ... % 10.67/2.22 Prover 10: Constructing countermodel ... % 10.67/2.24 Prover 8: gave up % 10.67/2.25 Prover 13: Constructing countermodel ... % 10.67/2.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.28/2.28 Prover 10: gave up % 11.28/2.29 Prover 19: Preprocessing ... % 11.28/2.30 Prover 11: Constructing countermodel ... % 11.82/2.41 Prover 19: Warning: ignoring some quantifiers % 11.82/2.41 Prover 19: Constructing countermodel ... % 13.48/2.57 Prover 19: gave up % 13.83/2.72 Prover 4: Found proof (size 89) % 13.83/2.72 Prover 4: proved (2099ms) % 13.83/2.72 Prover 16: stopped % 13.83/2.72 Prover 13: stopped % 13.83/2.72 Prover 11: stopped % 13.83/2.72 Prover 7: stopped % 13.83/2.72 % 13.83/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.83/2.72 % 14.58/2.73 % SZS output start Proof for theBenchmark % 14.58/2.73 Assumptions after simplification: % 14.58/2.73 --------------------------------- % 14.58/2.73 % 14.58/2.74 (mAddNeg) % 14.72/2.76 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? % 14.72/2.76 [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 & % 14.72/2.76 sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = % 14.72/2.76 0) | (v4 = sz00 & v3 = sz00)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = % 14.72/2.76 0) | ~ $i(v0) | ? [v1: $i] : (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) % 14.72/2.76 = sz00 & smndt0(v0) = v1 & $i(v1))) % 14.72/2.76 % 14.72/2.76 (mDivisor) % 14.72/2.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | % 14.72/2.77 v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | ~ (sdtasdt0(v1, v3) = v0) | ~ % 14.72/2.77 (aInteger0(v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : (( % 14.72/2.77 ~ (v4 = 0) & aInteger0(v3) = v4) | ( ~ (v4 = 0) & aInteger0(v1) = v4))) % 14.72/2.77 & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | v1 = sz00 % 14.72/2.77 | ~ (aDivisorOf0(v1, v0) = v2) | ~ (aInteger0(v3) = 0) | ~ (aInteger0(v0) % 14.72/2.77 = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : (( ~ (v4 = v0) & % 14.72/2.77 sdtasdt0(v1, v3) = v4 & $i(v4)) | ( ~ (v4 = 0) & aInteger0(v1) = v4))) & % 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aInteger0(v1) = v2) | % 14.72/2.77 ~ (aInteger0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 14.72/2.77 & aDivisorOf0(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.72/2.77 (v1 = sz00 | ~ (sdtasdt0(v1, v2) = v0) | ~ (aInteger0(v1) = 0) | ~ % 14.72/2.77 (aInteger0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 14.72/2.77 ((v3 = 0 & aDivisorOf0(v1, v0) = 0) | ( ~ (v3 = 0) & aInteger0(v2) = v3))) & % 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (aInteger0(v2) = 0) % 14.72/2.77 | ~ (aInteger0(v1) = 0) | ~ (aInteger0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 14.72/2.77 ~ $i(v0) | ? [v3: any] : ((v3 = 0 & aDivisorOf0(v1, v0) = 0) | ( ~ (v3 = % 14.72/2.77 v0) & sdtasdt0(v1, v2) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : % 14.72/2.77 ! [v2: MultipleValueBool] : ( ~ (aInteger0(v1) = v2) | ~ (aInteger0(v0) = 0) % 14.72/2.77 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? % 14.72/2.77 [v6: $i] : ($i(v4) & ((v6 = v0 & v5 = 0 & sdtasdt0(v1, v4) = v0 & % 14.72/2.77 aInteger0(v4) = 0) | ( ~ (v3 = 0) & aDivisorOf0(v1, v0) = v3)))) & ! % 14.72/2.77 [v0: $i] : ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) = 0) | ~ (aInteger0(v0) = % 14.72/2.77 0) | ~ $i(v1) | ~ $i(v0) | aInteger0(v1) = 0) & ! [v0: $i] : ! [v1: % 14.72/2.77 $i] : ( ~ (aDivisorOf0(v1, v0) = 0) | ~ (aInteger0(v0) = 0) | ~ $i(v1) | % 14.72/2.77 ~ $i(v0) | ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & aInteger0(v2) = 0 & % 14.72/2.77 $i(v2))) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (aInteger0(v0) = % 14.72/2.77 0) | ~ (aInteger0(sz00) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 14.72/2.77 aDivisorOf0(sz00, v0) = v2)) & ! [v0: $i] : ( ~ (aDivisorOf0(sz00, v0) = % 14.72/2.77 0) | ~ (aInteger0(v0) = 0) | ~ $i(v0)) % 14.72/2.77 % 14.72/2.77 (mEquMod) % 14.72/2.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 14.72/2.77 : ! [v5: any] : (v2 = sz00 | ~ (aDivisorOf0(v2, v4) = v5) | ~ (sdtpldt0(v0, % 14.72/2.77 v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.72/2.77 ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 14.72/2.77 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v9 & aInteger0(v2) = v8 & aInteger0(v1) % 14.72/2.77 = v7 & aInteger0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | (( % 14.72/2.77 ~ (v9 = 0) | v5 = 0) & ( ~ (v5 = 0) | v9 = 0))))) & ! [v0: $i] : ! % 14.72/2.77 [v1: $i] : ! [v2: $i] : ! [v3: any] : (v2 = sz00 | ~ % 14.72/2.77 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.72/2.77 | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 14.72/2.77 ? [v9: any] : (aDivisorOf0(v2, v8) = v9 & sdtpldt0(v0, v7) = v8 & smndt0(v1) % 14.72/2.77 = v7 & aInteger0(v2) = v6 & aInteger0(v1) = v5 & aInteger0(v0) = v4 & % 14.72/2.77 $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v9 = 0) % 14.72/2.77 | v3 = 0) & ( ~ (v3 = 0) | v9 = 0))))) % 14.72/2.77 % 14.72/2.77 (mIntNeg) % 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 14.72/2.77 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 % 14.72/2.77 = 0))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 14.72/2.77 : (smndt0(v0) = v1 & aInteger0(v1) = 0 & $i(v1))) % 14.72/2.77 % 14.72/2.77 (mIntZero) % 14.72/2.77 aInteger0(sz00) = 0 & $i(sz00) % 14.72/2.77 % 14.72/2.77 (mMulMinOne) % 14.72/2.78 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 14.72/2.78 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 14.72/2.78 : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & aInteger0(v1) = % 14.72/2.78 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: % 14.72/2.78 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] % 14.72/2.78 : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & % 14.72/2.78 aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = % 14.72/2.78 v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ % 14.72/2.78 $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 % 14.72/2.78 & sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 % 14.72/2.78 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ (aInteger0(v1) = % 14.72/2.78 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) % 14.72/2.78 = v2 & smndt0(v1) = v2 & $i(v2)))) % 14.72/2.78 % 14.72/2.78 (mMulZero) % 14.72/2.78 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ % 14.72/2.78 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz00, v0) = v3 & % 14.72/2.78 aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & % 14.72/2.78 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ? [v2: % 14.72/2.78 any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & aInteger0(v0) = v2 & % 14.72/2.78 $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0: $i] : ( ~ % 14.72/2.78 (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) = sz00 & % 14.72/2.78 sdtasdt0(sz00, v0) = sz00)) % 14.72/2.78 % 14.72/2.78 (m__) % 14.72/2.78 $i(xq) & $i(xa) & ? [v0: int] : ( ~ (v0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, % 14.72/2.78 xq) = v0) % 14.72/2.78 % 14.72/2.78 (m__671) % 14.72/2.78 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) & % 14.72/2.78 $i(sz00) % 14.72/2.78 % 14.72/2.78 (function-axioms) % 14.72/2.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.72/2.78 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 14.72/2.78 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 14.72/2.78 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.72/2.78 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] : % 14.72/2.78 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 14.72/2.78 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.72/2.78 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.72/2.78 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | % 14.72/2.78 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.72/2.78 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ % 14.72/2.78 (aInteger0(v2) = v0)) % 14.72/2.78 % 14.72/2.78 Further assumptions not needed in the proof: % 14.72/2.78 -------------------------------------------- % 14.72/2.78 mAddAsso, mAddComm, mAddZero, mDistrib, mIntMult, mIntOne, mIntPlus, mIntegers, % 14.72/2.78 mMulAsso, mMulComm, mMulOne, mZeroDiv % 14.72/2.78 % 14.72/2.78 Those formulas are unsatisfiable: % 14.72/2.78 --------------------------------- % 14.72/2.78 % 14.72/2.78 Begin of proof % 14.72/2.78 | % 14.72/2.78 | ALPHA: (mIntZero) implies: % 14.72/2.78 | (1) aInteger0(sz00) = 0 % 14.72/2.78 | % 14.72/2.78 | ALPHA: (mIntNeg) implies: % 14.72/2.79 | (2) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.72/2.79 | (smndt0(v0) = v1 & aInteger0(v1) = 0 & $i(v1))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mAddNeg) implies: % 14.72/2.79 | (3) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.72/2.79 | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00 & smndt0(v0) = v1 % 14.72/2.79 | & $i(v1))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mMulZero) implies: % 14.72/2.79 | (4) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) % 14.72/2.79 | = sz00 & sdtasdt0(sz00, v0) = sz00)) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mMulMinOne) implies: % 14.72/2.79 | (5) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 14.72/2.79 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 14.72/2.79 | : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & % 14.72/2.79 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & % 14.72/2.79 | v4 = v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, % 14.72/2.79 | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: % 14.72/2.79 | $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) = % 14.72/2.79 | v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! % 14.72/2.79 | [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3: % 14.72/2.79 | any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & % 14.72/2.79 | sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( % 14.72/2.79 | ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ % 14.72/2.79 | (aInteger0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = % 14.72/2.79 | v2 & sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2)))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mDivisor) implies: % 14.72/2.79 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: MultipleValueBool] : ( ~ % 14.72/2.79 | (aInteger0(v1) = v2) | ~ (aInteger0(v0) = 0) | ~ $i(v1) | ~ $i(v0) % 14.72/2.79 | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ($i(v4) & % 14.72/2.79 | ((v6 = v0 & v5 = 0 & sdtasdt0(v1, v4) = v0 & aInteger0(v4) = 0) | ( % 14.72/2.79 | ~ (v3 = 0) & aDivisorOf0(v1, v0) = v3)))) % 14.72/2.79 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 14.72/2.79 | (aInteger0(v2) = 0) | ~ (aInteger0(v1) = 0) | ~ (aInteger0(v0) = 0) % 14.72/2.79 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ((v3 = 0 & % 14.72/2.79 | aDivisorOf0(v1, v0) = 0) | ( ~ (v3 = v0) & sdtasdt0(v1, v2) = v3 % 14.72/2.79 | & $i(v3)))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (mEquMod) implies: % 14.72/2.79 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : (v2 = sz00 | % 14.72/2.79 | ~ (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 14.72/2.79 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 14.72/2.79 | ? [v8: $i] : ? [v9: any] : (aDivisorOf0(v2, v8) = v9 & sdtpldt0(v0, % 14.72/2.79 | v7) = v8 & smndt0(v1) = v7 & aInteger0(v2) = v6 & aInteger0(v1) = % 14.72/2.79 | v5 & aInteger0(v0) = v4 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 14.72/2.79 | 0) | ~ (v4 = 0) | (( ~ (v9 = 0) | v3 = 0) & ( ~ (v3 = 0) | v9 % 14.72/2.79 | = 0))))) % 14.72/2.79 | % 14.72/2.79 | ALPHA: (m__671) implies: % 14.72/2.79 | (9) ~ (xq = sz00) % 14.72/2.79 | (10) $i(sz00) % 14.72/2.79 | (11) aInteger0(xa) = 0 % 14.72/2.79 | (12) aInteger0(xq) = 0 % 14.72/2.79 | % 14.72/2.79 | ALPHA: (m__) implies: % 14.72/2.79 | (13) $i(xa) % 14.72/2.79 | (14) $i(xq) % 14.72/2.80 | (15) ? [v0: int] : ( ~ (v0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v0) % 14.72/2.80 | % 14.72/2.80 | ALPHA: (function-axioms) implies: % 14.72/2.80 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.72/2.80 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 14.72/2.80 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 14.72/2.80 | v1) | ~ (smndt0(v2) = v0)) % 14.72/2.80 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.72/2.80 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.72/2.80 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.72/2.80 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 14.72/2.80 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.72/2.80 | : ! [v3: $i] : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ % 14.72/2.80 | (aDivisorOf0(v3, v2) = v0)) % 14.72/2.80 | % 14.72/2.80 | DELTA: instantiating (15) with fresh symbol all_19_0 gives: % 14.72/2.80 | (21) ~ (all_19_0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = all_19_0 % 14.72/2.80 | % 14.72/2.80 | ALPHA: (21) implies: % 14.72/2.80 | (22) ~ (all_19_0 = 0) % 14.72/2.80 | (23) sdteqdtlpzmzozddtrp0(xa, xa, xq) = all_19_0 % 14.72/2.80 | % 14.72/2.80 | DELTA: instantiating (5) with fresh symbol all_21_0 gives: % 14.72/2.80 | (24) smndt0(sz10) = all_21_0 & $i(all_21_0) & ! [v0: $i] : ! [v1: $i] : ( % 14.72/2.80 | ~ (sdtasdt0(v0, all_21_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 14.72/2.80 | $i] : ? [v4: $i] : (sdtasdt0(all_21_0, v0) = v3 & smndt0(v0) = v4 % 14.72/2.80 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.72/2.80 | (sdtasdt0(all_21_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 14.72/2.80 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_21_0) = v4 & smndt0(v0) = v3 % 14.72/2.80 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = % 14.72/2.80 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 14.72/2.80 | (sdtasdt0(v0, all_21_0) = v4 & sdtasdt0(all_21_0, v0) = v3 & % 14.72/2.80 | aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ % 14.72/2.80 | $i(v0) | ? [v1: $i] : (sdtasdt0(v0, all_21_0) = v1 & % 14.72/2.80 | sdtasdt0(all_21_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) % 14.72/2.80 | % 14.72/2.80 | ALPHA: (24) implies: % 14.72/2.80 | (25) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 14.72/2.80 | (sdtasdt0(v0, all_21_0) = v1 & sdtasdt0(all_21_0, v0) = v1 & % 14.72/2.80 | smndt0(v0) = v1 & $i(v1))) % 14.72/2.80 | % 14.72/2.80 | GROUND_INST: instantiating (25) with xa, simplifying with (11), (13) gives: % 14.72/2.80 | (26) ? [v0: $i] : (sdtasdt0(all_21_0, xa) = v0 & sdtasdt0(xa, all_21_0) = % 14.72/2.80 | v0 & smndt0(xa) = v0 & $i(v0)) % 14.72/2.80 | % 14.72/2.80 | GROUND_INST: instantiating (3) with xa, simplifying with (11), (13) gives: % 14.72/2.80 | (27) ? [v0: $i] : (sdtpldt0(v0, xa) = sz00 & sdtpldt0(xa, v0) = sz00 & % 14.72/2.80 | smndt0(xa) = v0 & $i(v0)) % 14.72/2.80 | % 14.72/2.80 | GROUND_INST: instantiating (2) with xa, simplifying with (11), (13) gives: % 14.72/2.80 | (28) ? [v0: $i] : (smndt0(xa) = v0 & aInteger0(v0) = 0 & $i(v0)) % 14.72/2.80 | % 14.72/2.81 | GROUND_INST: instantiating (6) with sz00, xq, 0, simplifying with (1), (10), % 14.72/2.81 | (12), (14) gives: % 14.72/2.81 | (29) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ($i(v1) & % 14.72/2.81 | ((v3 = sz00 & v2 = 0 & sdtasdt0(xq, v1) = sz00 & aInteger0(v1) = 0) % 14.72/2.81 | | ( ~ (v0 = 0) & aDivisorOf0(xq, sz00) = v0))) % 14.72/2.81 | % 14.72/2.81 | GROUND_INST: instantiating (7) with sz00, xq, sz00, simplifying with (1), % 14.72/2.81 | (10), (12), (14) gives: % 14.72/2.81 | (30) xq = sz00 | ? [v0: any] : ((v0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~ % 14.72/2.81 | (v0 = sz00) & sdtasdt0(xq, sz00) = v0 & $i(v0))) % 14.72/2.81 | % 14.72/2.81 | GROUND_INST: instantiating (4) with xq, simplifying with (12), (14) gives: % 14.72/2.81 | (31) sdtasdt0(xq, sz00) = sz00 & sdtasdt0(sz00, xq) = sz00 % 14.72/2.81 | % 14.72/2.81 | ALPHA: (31) implies: % 14.72/2.81 | (32) sdtasdt0(xq, sz00) = sz00 % 14.72/2.81 | % 14.72/2.81 | GROUND_INST: instantiating (8) with xa, xa, xq, all_19_0, simplifying with % 14.72/2.81 | (13), (14), (23) gives: % 14.72/2.81 | (33) xq = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : % 14.72/2.81 | ? [v4: $i] : ? [v5: any] : (aDivisorOf0(xq, v4) = v5 & sdtpldt0(xa, % 14.72/2.81 | v3) = v4 & smndt0(xa) = v3 & aInteger0(xq) = v2 & aInteger0(xa) = % 14.72/2.81 | v1 & aInteger0(xa) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 14.72/2.81 | 0) | ~ (v0 = 0) | (( ~ (v5 = 0) | all_19_0 = 0) & ( ~ (all_19_0 % 14.72/2.81 | = 0) | v5 = 0)))) % 14.72/2.81 | % 14.72/2.81 | DELTA: instantiating (28) with fresh symbol all_44_0 gives: % 14.72/2.81 | (34) smndt0(xa) = all_44_0 & aInteger0(all_44_0) = 0 & $i(all_44_0) % 14.72/2.81 | % 14.72/2.81 | ALPHA: (34) implies: % 14.72/2.81 | (35) smndt0(xa) = all_44_0 % 14.72/2.81 | % 14.72/2.81 | DELTA: instantiating (27) with fresh symbol all_52_0 gives: % 14.72/2.81 | (36) sdtpldt0(all_52_0, xa) = sz00 & sdtpldt0(xa, all_52_0) = sz00 & % 14.72/2.81 | smndt0(xa) = all_52_0 & $i(all_52_0) % 14.72/2.81 | % 14.72/2.81 | ALPHA: (36) implies: % 14.72/2.81 | (37) smndt0(xa) = all_52_0 % 14.72/2.81 | (38) sdtpldt0(xa, all_52_0) = sz00 % 14.72/2.81 | % 14.72/2.81 | DELTA: instantiating (26) with fresh symbol all_56_0 gives: % 14.72/2.81 | (39) sdtasdt0(all_21_0, xa) = all_56_0 & sdtasdt0(xa, all_21_0) = all_56_0 % 14.72/2.81 | & smndt0(xa) = all_56_0 & $i(all_56_0) % 14.72/2.81 | % 14.72/2.81 | ALPHA: (39) implies: % 14.72/2.81 | (40) smndt0(xa) = all_56_0 % 14.72/2.81 | % 14.72/2.81 | DELTA: instantiating (29) with fresh symbols all_78_0, all_78_1, all_78_2, % 14.72/2.81 | all_78_3 gives: % 14.72/2.81 | (41) $i(all_78_2) & ((all_78_0 = sz00 & all_78_1 = 0 & sdtasdt0(xq, % 14.72/2.81 | all_78_2) = sz00 & aInteger0(all_78_2) = 0) | ( ~ (all_78_3 = 0) % 14.72/2.81 | & aDivisorOf0(xq, sz00) = all_78_3)) % 14.72/2.81 | % 14.72/2.81 | ALPHA: (41) implies: % 14.72/2.81 | (42) (all_78_0 = sz00 & all_78_1 = 0 & sdtasdt0(xq, all_78_2) = sz00 & % 14.72/2.81 | aInteger0(all_78_2) = 0) | ( ~ (all_78_3 = 0) & aDivisorOf0(xq, % 14.72/2.81 | sz00) = all_78_3) % 14.72/2.81 | % 14.72/2.81 | BETA: splitting (30) gives: % 14.72/2.81 | % 14.72/2.81 | Case 1: % 14.72/2.81 | | % 14.72/2.81 | | (43) xq = sz00 % 14.72/2.81 | | % 14.72/2.81 | | REDUCE: (9), (43) imply: % 14.72/2.81 | | (44) $false % 14.72/2.81 | | % 14.72/2.81 | | CLOSE: (44) is inconsistent. % 14.72/2.81 | | % 14.72/2.81 | Case 2: % 14.72/2.81 | | % 14.72/2.82 | | (45) ? [v0: any] : ((v0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~ (v0 = % 14.72/2.82 | | sz00) & sdtasdt0(xq, sz00) = v0 & $i(v0))) % 14.72/2.82 | | % 14.72/2.82 | | DELTA: instantiating (45) with fresh symbol all_125_0 gives: % 14.72/2.82 | | (46) (all_125_0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~ (all_125_0 = sz00) % 14.72/2.82 | | & sdtasdt0(xq, sz00) = all_125_0 & $i(all_125_0)) % 14.72/2.82 | | % 14.72/2.82 | | BETA: splitting (46) gives: % 14.72/2.82 | | % 14.72/2.82 | | Case 1: % 14.72/2.82 | | | % 14.72/2.82 | | | (47) all_125_0 = 0 & aDivisorOf0(xq, sz00) = 0 % 14.72/2.82 | | | % 14.72/2.82 | | | ALPHA: (47) implies: % 14.72/2.82 | | | (48) aDivisorOf0(xq, sz00) = 0 % 14.72/2.82 | | | % 14.72/2.82 | | | BETA: splitting (33) gives: % 14.72/2.82 | | | % 14.72/2.82 | | | Case 1: % 14.72/2.82 | | | | % 14.72/2.82 | | | | (49) xq = sz00 % 14.72/2.82 | | | | % 14.72/2.82 | | | | REDUCE: (9), (49) imply: % 14.72/2.82 | | | | (50) $false % 14.72/2.82 | | | | % 14.72/2.82 | | | | CLOSE: (50) is inconsistent. % 14.72/2.82 | | | | % 14.72/2.82 | | | Case 2: % 14.72/2.82 | | | | % 14.72/2.82 | | | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 14.72/2.82 | | | | [v4: $i] : ? [v5: any] : (aDivisorOf0(xq, v4) = v5 & % 14.72/2.82 | | | | sdtpldt0(xa, v3) = v4 & smndt0(xa) = v3 & aInteger0(xq) = v2 & % 14.72/2.82 | | | | aInteger0(xa) = v1 & aInteger0(xa) = v0 & $i(v4) & $i(v3) & ( % 14.72/2.82 | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v5 = 0) | % 14.72/2.82 | | | | all_19_0 = 0) & ( ~ (all_19_0 = 0) | v5 = 0)))) % 14.72/2.82 | | | | % 14.72/2.82 | | | | DELTA: instantiating (51) with fresh symbols all_165_0, all_165_1, % 14.72/2.82 | | | | all_165_2, all_165_3, all_165_4, all_165_5 gives: % 14.72/2.82 | | | | (52) aDivisorOf0(xq, all_165_1) = all_165_0 & sdtpldt0(xa, all_165_2) % 14.72/2.82 | | | | = all_165_1 & smndt0(xa) = all_165_2 & aInteger0(xq) = all_165_3 % 14.72/2.82 | | | | & aInteger0(xa) = all_165_4 & aInteger0(xa) = all_165_5 & % 14.72/2.82 | | | | $i(all_165_1) & $i(all_165_2) & ( ~ (all_165_3 = 0) | ~ % 14.72/2.82 | | | | (all_165_4 = 0) | ~ (all_165_5 = 0) | (( ~ (all_165_0 = 0) | % 14.72/2.82 | | | | all_19_0 = 0) & ( ~ (all_19_0 = 0) | all_165_0 = 0))) % 14.72/2.82 | | | | % 14.72/2.82 | | | | ALPHA: (52) implies: % 14.72/2.82 | | | | (53) aInteger0(xa) = all_165_5 % 14.72/2.82 | | | | (54) aInteger0(xa) = all_165_4 % 14.72/2.82 | | | | (55) aInteger0(xq) = all_165_3 % 14.72/2.82 | | | | (56) smndt0(xa) = all_165_2 % 14.72/2.82 | | | | (57) sdtpldt0(xa, all_165_2) = all_165_1 % 14.72/2.82 | | | | (58) aDivisorOf0(xq, all_165_1) = all_165_0 % 14.72/2.82 | | | | (59) ~ (all_165_3 = 0) | ~ (all_165_4 = 0) | ~ (all_165_5 = 0) | % 14.72/2.82 | | | | (( ~ (all_165_0 = 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0) | % 14.72/2.82 | | | | all_165_0 = 0)) % 14.72/2.82 | | | | % 14.72/2.82 | | | | BETA: splitting (42) gives: % 14.72/2.82 | | | | % 14.72/2.82 | | | | Case 1: % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with 0, all_165_4, xa, simplifying % 14.72/2.82 | | | | | with (11), (54) gives: % 14.72/2.82 | | | | | (60) all_165_4 = 0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with all_165_5, all_165_4, xa, % 14.72/2.82 | | | | | simplifying with (53), (54) gives: % 14.72/2.82 | | | | | (61) all_165_4 = all_165_5 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with 0, all_165_3, xq, simplifying % 14.72/2.82 | | | | | with (12), (55) gives: % 14.72/2.82 | | | | | (62) all_165_3 = 0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_44_0, all_56_0, xa, % 14.72/2.82 | | | | | simplifying with (35), (40) gives: % 14.72/2.82 | | | | | (63) all_56_0 = all_44_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_56_0, all_165_2, xa, % 14.72/2.82 | | | | | simplifying with (40), (56) gives: % 14.72/2.82 | | | | | (64) all_165_2 = all_56_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_52_0, all_165_2, xa, % 14.72/2.82 | | | | | simplifying with (37), (56) gives: % 14.72/2.82 | | | | | (65) all_165_2 = all_52_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | COMBINE_EQS: (64), (65) imply: % 14.72/2.82 | | | | | (66) all_56_0 = all_52_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | SIMP: (66) implies: % 14.72/2.82 | | | | | (67) all_56_0 = all_52_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | COMBINE_EQS: (60), (61) imply: % 14.72/2.82 | | | | | (68) all_165_5 = 0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | COMBINE_EQS: (63), (67) imply: % 14.72/2.82 | | | | | (69) all_52_0 = all_44_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | COMBINE_EQS: (65), (69) imply: % 14.72/2.82 | | | | | (70) all_165_2 = all_44_0 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | REDUCE: (57), (70) imply: % 14.72/2.82 | | | | | (71) sdtpldt0(xa, all_44_0) = all_165_1 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | REDUCE: (38), (69) imply: % 14.72/2.82 | | | | | (72) sdtpldt0(xa, all_44_0) = sz00 % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | BETA: splitting (59) gives: % 14.72/2.82 | | | | | % 14.72/2.82 | | | | | Case 1: % 14.72/2.82 | | | | | | % 14.72/2.82 | | | | | | (73) ~ (all_165_3 = 0) % 14.72/2.82 | | | | | | % 14.72/2.82 | | | | | | REDUCE: (62), (73) imply: % 14.72/2.82 | | | | | | (74) $false % 14.72/2.82 | | | | | | % 14.72/2.82 | | | | | | CLOSE: (74) is inconsistent. % 14.72/2.82 | | | | | | % 14.72/2.82 | | | | | Case 2: % 14.72/2.82 | | | | | | % 15.07/2.82 | | | | | | (75) ~ (all_165_4 = 0) | ~ (all_165_5 = 0) | (( ~ (all_165_0 = % 15.07/2.82 | | | | | | 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0) | all_165_0 = % 15.07/2.82 | | | | | | 0)) % 15.07/2.82 | | | | | | % 15.07/2.82 | | | | | | BETA: splitting (75) gives: % 15.07/2.82 | | | | | | % 15.07/2.82 | | | | | | Case 1: % 15.07/2.82 | | | | | | | % 15.07/2.82 | | | | | | | (76) ~ (all_165_4 = 0) % 15.07/2.82 | | | | | | | % 15.07/2.82 | | | | | | | REDUCE: (60), (76) imply: % 15.07/2.83 | | | | | | | (77) $false % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | | CLOSE: (77) is inconsistent. % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | Case 2: % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | | (78) ~ (all_165_5 = 0) | (( ~ (all_165_0 = 0) | all_19_0 = 0) % 15.07/2.83 | | | | | | | & ( ~ (all_19_0 = 0) | all_165_0 = 0)) % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | | BETA: splitting (78) gives: % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | | Case 1: % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | (79) ~ (all_165_5 = 0) % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | REDUCE: (68), (79) imply: % 15.07/2.83 | | | | | | | | (80) $false % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | CLOSE: (80) is inconsistent. % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | Case 2: % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | (81) ( ~ (all_165_0 = 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0) % 15.07/2.83 | | | | | | | | | all_165_0 = 0) % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | ALPHA: (81) implies: % 15.07/2.83 | | | | | | | | (82) ~ (all_165_0 = 0) | all_19_0 = 0 % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | BETA: splitting (82) gives: % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | | Case 1: % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | (83) ~ (all_165_0 = 0) % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | GROUND_INST: instantiating (18) with sz00, all_165_1, all_44_0, % 15.07/2.83 | | | | | | | | | xa, simplifying with (71), (72) gives: % 15.07/2.83 | | | | | | | | | (84) all_165_1 = sz00 % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | REDUCE: (58), (84) imply: % 15.07/2.83 | | | | | | | | | (85) aDivisorOf0(xq, sz00) = all_165_0 % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_165_0, sz00, xq, % 15.07/2.83 | | | | | | | | | simplifying with (48), (85) gives: % 15.07/2.83 | | | | | | | | | (86) all_165_0 = 0 % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | REDUCE: (83), (86) imply: % 15.07/2.83 | | | | | | | | | (87) $false % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | CLOSE: (87) is inconsistent. % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | Case 2: % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | (88) all_19_0 = 0 % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | REDUCE: (22), (88) imply: % 15.07/2.83 | | | | | | | | | (89) $false % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | | CLOSE: (89) is inconsistent. % 15.07/2.83 | | | | | | | | | % 15.07/2.83 | | | | | | | | End of split % 15.07/2.83 | | | | | | | | % 15.07/2.83 | | | | | | | End of split % 15.07/2.83 | | | | | | | % 15.07/2.83 | | | | | | End of split % 15.07/2.83 | | | | | | % 15.07/2.83 | | | | | End of split % 15.07/2.83 | | | | | % 15.07/2.83 | | | | Case 2: % 15.07/2.83 | | | | | % 15.07/2.83 | | | | | (90) ~ (all_78_3 = 0) & aDivisorOf0(xq, sz00) = all_78_3 % 15.07/2.83 | | | | | % 15.07/2.83 | | | | | ALPHA: (90) implies: % 15.07/2.83 | | | | | (91) ~ (all_78_3 = 0) % 15.07/2.83 | | | | | (92) aDivisorOf0(xq, sz00) = all_78_3 % 15.07/2.83 | | | | | % 15.07/2.83 | | | | | GROUND_INST: instantiating (20) with 0, all_78_3, sz00, xq, % 15.07/2.83 | | | | | simplifying with (48), (92) gives: % 15.07/2.83 | | | | | (93) all_78_3 = 0 % 15.07/2.83 | | | | | % 15.07/2.83 | | | | | REDUCE: (91), (93) imply: % 15.07/2.83 | | | | | (94) $false % 15.07/2.83 | | | | | % 15.07/2.83 | | | | | CLOSE: (94) is inconsistent. % 15.07/2.83 | | | | | % 15.07/2.83 | | | | End of split % 15.07/2.83 | | | | % 15.07/2.83 | | | End of split % 15.07/2.83 | | | % 15.07/2.83 | | Case 2: % 15.07/2.83 | | | % 15.07/2.83 | | | (95) ~ (all_125_0 = sz00) & sdtasdt0(xq, sz00) = all_125_0 & % 15.07/2.83 | | | $i(all_125_0) % 15.07/2.83 | | | % 15.07/2.83 | | | ALPHA: (95) implies: % 15.07/2.83 | | | (96) ~ (all_125_0 = sz00) % 15.07/2.83 | | | (97) sdtasdt0(xq, sz00) = all_125_0 % 15.07/2.83 | | | % 15.07/2.83 | | | GROUND_INST: instantiating (19) with sz00, all_125_0, sz00, xq, % 15.07/2.83 | | | simplifying with (32), (97) gives: % 15.07/2.83 | | | (98) all_125_0 = sz00 % 15.07/2.83 | | | % 15.07/2.83 | | | REDUCE: (96), (98) imply: % 15.07/2.83 | | | (99) $false % 15.07/2.83 | | | % 15.07/2.83 | | | CLOSE: (99) is inconsistent. % 15.07/2.83 | | | % 15.07/2.83 | | End of split % 15.07/2.83 | | % 15.07/2.83 | End of split % 15.07/2.83 | % 15.07/2.83 End of proof % 15.07/2.83 % SZS output end Proof for theBenchmark % 15.07/2.83 % 15.07/2.83 2235ms %------------------------------------------------------------------------------