%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM437+5 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 11:47:45 EDT 2023 % Result : Theorem 132.47s 18.33s % Output : Proof 132.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM437+5 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.34 % CPULimit : 300 % 0.19/0.34 % WCLimit : 300 % 0.19/0.34 % DateTime : Fri Aug 25 11:31:07 EDT 2023 % 0.19/0.34 % 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 ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.48/1.23 Prover 1: Preprocessing ... % 3.48/1.23 Prover 4: Preprocessing ... % 3.97/1.27 Prover 2: Preprocessing ... % 3.97/1.27 Prover 0: Preprocessing ... % 3.97/1.27 Prover 3: Preprocessing ... % 3.97/1.27 Prover 6: Preprocessing ... % 3.97/1.27 Prover 5: Preprocessing ... % 10.46/2.20 Prover 5: Constructing countermodel ... % 10.46/2.20 Prover 3: Constructing countermodel ... % 10.46/2.21 Prover 1: Constructing countermodel ... % 10.81/2.21 Prover 6: Proving ... % 11.05/2.28 Prover 2: Proving ... % 17.27/3.15 Prover 4: Constructing countermodel ... % 18.18/3.26 Prover 0: Proving ... % 72.05/10.34 Prover 2: stopped % 72.05/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.79/10.44 Prover 7: Preprocessing ... % 73.85/10.58 Prover 7: Constructing countermodel ... % 99.08/13.96 Prover 5: stopped % 99.08/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 99.68/14.04 Prover 8: Preprocessing ... % 100.74/14.15 Prover 8: Warning: ignoring some quantifiers % 100.74/14.15 Prover 8: Constructing countermodel ... % 114.89/16.01 Prover 1: stopped % 115.12/16.03 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.19/16.09 Prover 9: Preprocessing ... % 119.93/16.70 Prover 9: Constructing countermodel ... % 128.40/17.88 Prover 6: stopped % 128.40/17.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 130.13/18.04 Prover 10: Preprocessing ... % 130.27/18.10 Prover 10: Constructing countermodel ... % 132.12/18.32 Prover 10: Found proof (size 35) % 132.12/18.32 Prover 10: proved (423ms) % 132.12/18.33 Prover 9: stopped % 132.12/18.33 Prover 3: stopped % 132.47/18.33 Prover 0: stopped % 132.47/18.33 Prover 8: stopped % 132.47/18.33 Prover 7: stopped % 132.47/18.33 Prover 4: stopped % 132.47/18.33 % 132.47/18.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 132.47/18.33 % 132.47/18.34 % SZS output start Proof for theBenchmark % 132.47/18.34 Assumptions after simplification: % 132.47/18.34 --------------------------------- % 132.47/18.34 % 132.47/18.34 (mArSeq) % 132.55/18.37 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 132.55/18.37 v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 132.55/18.37 | ~ $i(v0) | ~ aSet0(v3) | ~ aInteger0(v1) | ~ aInteger0(v0) | ? [v4: % 132.55/18.37 $i] : ($i(v4) & ( ~ aElementOf0(v4, v3) | ~ sdteqdtlpzmzozddtrp0(v4, v0, % 132.55/18.37 v1) | ~ aInteger0(v4)) & (aElementOf0(v4, v3) | % 132.55/18.37 (sdteqdtlpzmzozddtrp0(v4, v0, v1) & aInteger0(v4))))) & ! [v0: $i] : ! % 132.55/18.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~ % 132.55/18.37 (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 132.55/18.37 ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 132.55/18.37 sdteqdtlpzmzozddtrp0(v3, v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 132.55/18.37 : ! [v3: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ % 132.55/18.37 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 132.55/18.37 aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v3)) & ! [v0: $i] : ! [v1: % 132.55/18.37 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~ % 132.55/18.37 (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 132.55/18.37 ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v3, v0, v1) | ~ aInteger0(v3) | ~ % 132.55/18.37 aInteger0(v1) | ~ aInteger0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! % 132.55/18.37 [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) % 132.55/18.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | % 132.55/18.37 aSet0(v2)) % 132.55/18.37 % 132.55/18.37 (mEquModRef) % 132.55/18.38 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 132.55/18.38 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 132.55/18.38 % 132.55/18.38 (mIntZero) % 132.55/18.38 $i(sz00) & aInteger0(sz00) % 132.55/18.38 % 132.55/18.38 (m__) % 132.55/18.38 $i(xS) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sbsmnsldt0(xS) % 132.55/18.38 = v0 & smndt0(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & % 132.55/18.38 aSet0(v0) & ~ isOpen0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 132.55/18.39 [v6: $i] : ! [v7: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = % 132.55/18.39 v4) | ~ (sdtasdt0(v3, v7) = v6) | ~ (sdtpldt0(v5, v2) = v6) | ~ % 132.55/18.39 $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ aInteger0(v7) | ~ aInteger0(v5) | ~ % 132.55/18.39 aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 132.55/18.39 $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) % 132.55/18.39 | ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, % 132.55/18.39 v4) | ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, v1, v3)) & ! [v3: $i] % 132.55/18.39 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 132.55/18.39 (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ (sdtpldt0(v5, v2) = v6) | ~ % 132.55/18.39 $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ aInteger0(v3) | % 132.55/18.39 aDivisorOf0(v3, v6)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 132.55/18.39 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.39 (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | % 132.55/18.39 ~ aInteger0(v3) | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 132.55/18.39 $i] : ! [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) % 132.55/18.39 | ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, % 132.55/18.39 v4) | ~ aInteger0(v3) | ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) & % 132.55/18.39 $i(v6) & aInteger0(v7))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 132.55/18.39 [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.39 (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 132.55/18.39 sdteqdtlpzmzozddtrp0(v5, v1, v3) | ~ aInteger0(v5) | ~ aInteger0(v3) | % 132.55/18.39 aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 132.55/18.39 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.39 (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) | % 132.55/18.39 ~ aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : % 132.55/18.39 ! [v4: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.39 $i(v3) | ~ aSubsetOf0(v4, v0) | ~ aInteger0(v3)) & ! [v3: $i] : ! [v4: % 132.55/18.39 $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ $i(v3) | % 132.55/18.39 ~ aInteger0(v3) | aSet0(v4)) & ! [v3: $i] : ! [v4: $i] : (v3 = sz00 | ~ % 132.55/18.39 (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ $i(v3) | ~ aInteger0(v3) | ? % 132.55/18.39 [v5: $i] : ($i(v5) & aElementOf0(v5, v4) & ~ aElementOf0(v5, v0))) & ! % 132.55/18.39 [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, xS) | % 132.55/18.39 ~ aElementOf0(v3, v4) | ~ aInteger0(v3) | aElementOf0(v3, v0)) & ! [v3: % 132.55/18.39 $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aInteger0(v3)) & ! [v3: $i] : % 132.55/18.39 ( ~ $i(v3) | ~ aElementOf0(v3, v0) | ? [v4: $i] : ($i(v4) & % 132.55/18.39 aElementOf0(v4, xS) & aElementOf0(v3, v4)))) % 132.55/18.39 % 132.55/18.39 (m__1750) % 132.55/18.39 $i(xS) & $i(cS1395) & $i(sz00) & aSet0(xS) & ! [v0: $i] : ! [v1: $i] : ! % 132.55/18.39 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, % 132.55/18.39 v0) | ~ aElementOf0(v0, xS) | ? [v3: $i] : ? [v4: $i] : ( ~ (v3 = sz00) % 132.55/18.39 & szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4 & $i(v4) & $i(v3) & aSubsetOf0(v4, % 132.55/18.39 v0) & aSet0(v4) & aInteger0(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 132.55/18.39 $i] : ( ~ (sdtasdt0(v3, v7) = v6) | ~ (sdtpldt0(v5, v2) = v6) | ~ % 132.55/18.39 $i(v7) | ~ $i(v5) | ~ aInteger0(v7) | ~ aInteger0(v5) | % 132.55/18.39 aElementOf0(v5, v4)) & ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) % 132.55/18.39 = v6) | ~ $i(v5) | ~ aElementOf0(v5, v4) | sdteqdtlpzmzozddtrp0(v5, % 132.55/18.39 v1, v3)) & ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | % 132.55/18.39 ~ $i(v5) | ~ aElementOf0(v5, v4) | aDivisorOf0(v3, v6)) & ! [v5: $i] : % 132.55/18.39 ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ aElementOf0(v5, % 132.55/18.39 v4) | aInteger0(v5)) & ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, % 132.55/18.39 v2) = v6) | ~ $i(v5) | ~ aElementOf0(v5, v4) | ? [v7: $i] : % 132.55/18.39 (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) & aInteger0(v7))) & ! [v5: $i] % 132.55/18.39 : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ % 132.55/18.39 sdteqdtlpzmzozddtrp0(v5, v1, v3) | ~ aInteger0(v5) | aElementOf0(v5, % 132.55/18.39 v4)) & ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ % 132.55/18.39 $i(v5) | ~ aDivisorOf0(v3, v6) | ~ aInteger0(v5) | aElementOf0(v5, % 132.55/18.39 v4)) & ! [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v4) | % 132.55/18.39 aElementOf0(v5, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 132.55/18.39 $i(v0) | ~ aElementOf0(v1, v0) | ~ aElementOf0(v0, xS) | aElementOf0(v1, % 132.55/18.39 cS1395)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 132.55/18.39 aElementOf0(v1, cS1395) | ~ aElementOf0(v0, xS) | aInteger0(v1)) & ! [v0: % 132.55/18.39 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xS) | ~ % 132.55/18.39 aInteger0(v1) | aElementOf0(v1, cS1395)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 132.55/18.39 aElementOf0(v0, xS) | isOpen0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 132.55/18.39 aElementOf0(v0, xS) | aSubsetOf0(v0, cS1395)) & ! [v0: $i] : ( ~ $i(v0) | % 132.55/18.39 ~ aElementOf0(v0, xS) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 132.55/18.39 aElementOf0(v0, xS) | aSet0(cS1395)) % 132.55/18.39 % 132.55/18.39 Further assumptions not needed in the proof: % 132.55/18.39 -------------------------------------------- % 132.55/18.39 mAddAsso, mAddComm, mAddNeg, mAddZero, mClosed, mComplement, mDistrib, mDivisor, % 132.55/18.39 mElements, mEquMod, mEquModMul, mEquModSym, mEquModTrn, mFinSet, mIntMult, % 132.55/18.39 mIntNeg, mIntOne, mIntPlus, mIntegers, mIntersection, mMulAsso, mMulComm, % 132.55/18.39 mMulMinOne, mMulOne, mMulZero, mOpen, mPrime, mPrimeDivisor, mSets, mSubset, % 132.55/18.39 mUnion, mUnionSet, mZeroDiv % 132.55/18.39 % 132.55/18.39 Those formulas are unsatisfiable: % 132.55/18.39 --------------------------------- % 132.55/18.39 % 132.55/18.39 Begin of proof % 132.55/18.39 | % 132.55/18.39 | ALPHA: (mIntZero) implies: % 132.55/18.39 | (1) aInteger0(sz00) % 132.55/18.39 | % 132.55/18.39 | ALPHA: (mEquModRef) implies: % 132.55/18.40 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 132.55/18.40 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1)) % 132.55/18.40 | % 132.55/18.40 | ALPHA: (mArSeq) implies: % 132.55/18.40 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = sz00 | ~ % 132.55/18.40 | (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 132.55/18.40 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aInteger0(v1) | ~ % 132.55/18.40 | aInteger0(v0) | aInteger0(v3)) % 132.55/18.40 | % 132.55/18.40 | ALPHA: (m__1750) implies: % 132.55/18.40 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ % 132.55/18.40 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | ~ aElementOf0(v0, xS) % 132.55/18.40 | | ? [v3: $i] : ? [v4: $i] : ( ~ (v3 = sz00) & % 132.55/18.40 | szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4 & $i(v4) & $i(v3) & % 132.55/18.40 | aSubsetOf0(v4, v0) & aSet0(v4) & aInteger0(v3) & ! [v5: $i] : ! % 132.55/18.40 | [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(v3, v7) = v6) | ~ % 132.55/18.40 | (sdtpldt0(v5, v2) = v6) | ~ $i(v7) | ~ $i(v5) | ~ % 132.55/18.40 | aInteger0(v7) | ~ aInteger0(v5) | aElementOf0(v5, v4)) & ! [v5: % 132.55/18.40 | $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ % 132.55/18.40 | aElementOf0(v5, v4) | sdteqdtlpzmzozddtrp0(v5, v1, v3)) & ! [v5: % 132.55/18.40 | $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ % 132.55/18.40 | aElementOf0(v5, v4) | aDivisorOf0(v3, v6)) & ! [v5: $i] : ! % 132.55/18.40 | [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ % 132.55/18.40 | aElementOf0(v5, v4) | aInteger0(v5)) & ! [v5: $i] : ! [v6: $i] % 132.55/18.40 | : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ aElementOf0(v5, v4) % 132.55/18.40 | | ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) & % 132.55/18.40 | aInteger0(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, % 132.55/18.40 | v2) = v6) | ~ $i(v5) | ~ sdteqdtlpzmzozddtrp0(v5, v1, v3) | % 132.55/18.40 | ~ aInteger0(v5) | aElementOf0(v5, v4)) & ! [v5: $i] : ! [v6: % 132.55/18.40 | $i] : ( ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ % 132.55/18.40 | aDivisorOf0(v3, v6) | ~ aInteger0(v5) | aElementOf0(v5, v4)) & % 132.55/18.40 | ! [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v4) | aElementOf0(v5, % 132.55/18.40 | v0)))) % 132.55/18.40 | % 132.55/18.40 | ALPHA: (m__) implies: % 132.55/18.40 | (5) $i(sz00) % 132.55/18.41 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sbsmnsldt0(xS) = v0 & % 132.55/18.41 | smndt0(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & % 132.55/18.41 | aSet0(v0) & ~ isOpen0(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 132.55/18.41 | : ! [v6: $i] : ! [v7: $i] : (v3 = sz00 | ~ % 132.55/18.41 | (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ (sdtasdt0(v3, v7) = v6) % 132.55/18.41 | | ~ (sdtpldt0(v5, v2) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | % 132.55/18.41 | ~ aInteger0(v7) | ~ aInteger0(v5) | ~ aInteger0(v3) | % 132.55/18.41 | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 132.55/18.41 | [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.41 | (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 132.55/18.41 | aElementOf0(v5, v4) | ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, % 132.55/18.41 | v1, v3)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 132.55/18.41 | : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.41 | (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 132.55/18.41 | aElementOf0(v5, v4) | ~ aInteger0(v3) | aDivisorOf0(v3, v6)) & ! % 132.55/18.41 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 132.55/18.41 | (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ (sdtpldt0(v5, v2) = v6) % 132.55/18.41 | | ~ $i(v5) | ~ $i(v3) | ~ aElementOf0(v5, v4) | ~ aInteger0(v3) % 132.55/18.41 | | aInteger0(v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 132.55/18.41 | [v6: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.41 | (sdtpldt0(v5, v2) = v6) | ~ $i(v5) | ~ $i(v3) | ~ % 132.55/18.41 | aElementOf0(v5, v4) | ~ aInteger0(v3) | ? [v7: $i] : % 132.55/18.41 | (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) & aInteger0(v7))) & ! % 132.55/18.41 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 132.55/18.41 | (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ (sdtpldt0(v5, v2) = v6) % 132.55/18.41 | | ~ $i(v5) | ~ $i(v3) | ~ sdteqdtlpzmzozddtrp0(v5, v1, v3) | ~ % 132.55/18.41 | aInteger0(v5) | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: % 132.55/18.41 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = sz00 | ~ % 132.55/18.41 | (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ (sdtpldt0(v5, v2) = v6) % 132.55/18.41 | | ~ $i(v5) | ~ $i(v3) | ~ aDivisorOf0(v3, v6) | ~ aInteger0(v5) % 132.55/18.41 | | ~ aInteger0(v3) | aElementOf0(v5, v4)) & ! [v3: $i] : ! [v4: % 132.55/18.41 | $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.41 | $i(v3) | ~ aSubsetOf0(v4, v0) | ~ aInteger0(v3)) & ! [v3: $i] : % 132.55/18.41 | ! [v4: $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | % 132.55/18.41 | ~ $i(v3) | ~ aInteger0(v3) | aSet0(v4)) & ! [v3: $i] : ! [v4: % 132.55/18.41 | $i] : (v3 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | ~ % 132.55/18.41 | $i(v3) | ~ aInteger0(v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 132.55/18.41 | v4) & ~ aElementOf0(v5, v0))) & ! [v3: $i] : ! [v4: $i] : ( % 132.55/18.41 | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, xS) | ~ aElementOf0(v3, % 132.55/18.41 | v4) | ~ aInteger0(v3) | aElementOf0(v3, v0)) & ! [v3: $i] : ( ~ % 132.55/18.41 | $i(v3) | ~ aElementOf0(v3, v0) | aInteger0(v3)) & ! [v3: $i] : ( % 132.55/18.41 | ~ $i(v3) | ~ aElementOf0(v3, v0) | ? [v4: $i] : ($i(v4) & % 132.55/18.41 | aElementOf0(v4, xS) & aElementOf0(v3, v4)))) % 132.55/18.41 | % 132.55/18.41 | DELTA: instantiating (6) with fresh symbols all_38_0, all_38_1, all_38_2 % 132.55/18.41 | gives: % 132.55/18.42 | (7) sbsmnsldt0(xS) = all_38_2 & smndt0(all_38_1) = all_38_0 & $i(all_38_0) % 132.55/18.42 | & $i(all_38_1) & $i(all_38_2) & aElementOf0(all_38_1, all_38_2) & % 132.55/18.42 | aSet0(all_38_2) & ~ isOpen0(all_38_2) & ! [v0: $i] : ! [v1: $i] : ! % 132.55/18.42 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ (sdtasdt0(v0, v4) = % 132.55/18.42 | v3) | ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 132.55/18.42 | $i(v0) | ~ aInteger0(v4) | ~ aInteger0(v2) | ~ aInteger0(v0) | % 132.55/18.42 | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 132.55/18.42 | [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) % 132.55/18.42 | | ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 132.55/18.42 | aElementOf0(v2, v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v2, % 132.55/18.42 | all_38_1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 132.55/18.42 | $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | % 132.55/18.42 | ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 132.55/18.42 | aElementOf0(v2, v1) | ~ aInteger0(v0) | aDivisorOf0(v0, v3)) & ! % 132.55/18.42 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ (sdtpldt0(v2, % 132.55/18.42 | all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) % 132.55/18.42 | | ~ aInteger0(v0) | aInteger0(v2)) & ! [v0: $i] : ! [v1: $i] : ! % 132.55/18.42 | [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ (sdtpldt0(v2, % 132.55/18.42 | all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) % 132.55/18.42 | | ~ aInteger0(v0) | ? [v4: $i] : (sdtasdt0(v0, v4) = v3 & $i(v4) & % 132.55/18.42 | $i(v3) & aInteger0(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 132.55/18.42 | : ! [v3: $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = % 132.55/18.42 | v1) | ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 132.55/18.42 | sdteqdtlpzmzozddtrp0(v2, all_38_1, v0) | ~ aInteger0(v2) | ~ % 132.55/18.42 | aInteger0(v0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! % 132.55/18.42 | [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ (sdtpldt0(v2, % 132.55/18.42 | all_38_0) = v3) | ~ $i(v2) | ~ $i(v0) | ~ aDivisorOf0(v0, v3) % 132.55/18.42 | | ~ aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v2, v1)) & ! % 132.55/18.42 | [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ $i(v0) | ~ % 132.55/18.42 | aSubsetOf0(v1, all_38_2) | ~ aInteger0(v0)) & ! [v0: $i] : ! [v1: % 132.55/18.42 | $i] : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | % 132.55/18.42 | ~ $i(v0) | ~ aInteger0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 132.55/18.42 | : (v0 = sz00 | ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ % 132.55/18.42 | $i(v0) | ~ aInteger0(v0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2, % 132.55/18.42 | v1) & ~ aElementOf0(v2, all_38_2))) & ! [v0: $i] : ! [v1: $i] % 132.55/18.42 | : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xS) | ~ aElementOf0(v0, % 132.55/18.42 | v1) | ~ aInteger0(v0) | aElementOf0(v0, all_38_2)) & ! [v0: $i] : % 132.55/18.42 | ( ~ $i(v0) | ~ aElementOf0(v0, all_38_2) | aInteger0(v0)) & ! [v0: % 132.55/18.42 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_38_2) | ? [v1: $i] : % 132.55/18.42 | ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) % 132.55/18.42 | % 132.55/18.42 | ALPHA: (7) implies: % 132.55/18.42 | (8) aElementOf0(all_38_1, all_38_2) % 132.55/18.42 | (9) $i(all_38_1) % 132.55/18.42 | (10) smndt0(all_38_1) = all_38_0 % 132.55/18.42 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_38_2) | ? [v1: $i] % 132.55/18.42 | : ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) % 132.55/18.42 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_38_2) | % 132.55/18.42 | aInteger0(v0)) % 132.55/18.42 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 132.55/18.42 | aElementOf0(v1, xS) | ~ aElementOf0(v0, v1) | ~ aInteger0(v0) | % 132.55/18.42 | aElementOf0(v0, all_38_2)) % 132.55/18.42 | (14) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ % 132.55/18.42 | (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | ~ $i(v0) | ~ % 132.55/18.42 | aInteger0(v0) | ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ % 132.55/18.42 | aElementOf0(v2, all_38_2))) % 132.55/18.42 | % 132.55/18.42 | GROUND_INST: instantiating (12) with all_38_1, simplifying with (8), (9) % 132.55/18.42 | gives: % 132.55/18.42 | (15) aInteger0(all_38_1) % 132.55/18.42 | % 132.55/18.42 | GROUND_INST: instantiating (11) with all_38_1, simplifying with (8), (9) % 132.55/18.42 | gives: % 132.55/18.42 | (16) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & aElementOf0(all_38_1, % 132.55/18.42 | v0)) % 132.55/18.42 | % 132.55/18.42 | DELTA: instantiating (16) with fresh symbol all_51_0 gives: % 132.55/18.42 | (17) $i(all_51_0) & aElementOf0(all_51_0, xS) & aElementOf0(all_38_1, % 132.55/18.42 | all_51_0) % 132.55/18.42 | % 132.55/18.42 | ALPHA: (17) implies: % 132.55/18.42 | (18) aElementOf0(all_38_1, all_51_0) % 132.55/18.42 | (19) aElementOf0(all_51_0, xS) % 132.55/18.42 | (20) $i(all_51_0) % 132.55/18.42 | % 132.55/18.43 | GROUND_INST: instantiating (4) with all_51_0, all_38_1, all_38_0, simplifying % 132.55/18.43 | with (9), (10), (18), (19), (20) gives: % 132.55/18.43 | (21) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = sz00) & % 132.55/18.43 | szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1 & $i(v1) & $i(v0) & % 132.55/18.43 | aSubsetOf0(v1, all_51_0) & aSet0(v1) & aInteger0(v0) & ! [v2: $i] : % 132.55/18.43 | ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) = v3) | ~ % 132.55/18.43 | (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 132.55/18.43 | aInteger0(v4) | ~ aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: % 132.55/18.43 | $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) % 132.55/18.43 | | ~ aElementOf0(v2, v1) | sdteqdtlpzmzozddtrp0(v2, all_38_1, v0)) % 132.55/18.43 | & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) | ~ % 132.55/18.43 | $i(v2) | ~ aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) & ! [v2: % 132.55/18.43 | $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) % 132.55/18.43 | | ~ aElementOf0(v2, v1) | aInteger0(v2)) & ! [v2: $i] : ! [v3: % 132.55/18.43 | $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ % 132.55/18.43 | aElementOf0(v2, v1) | ? [v4: $i] : (sdtasdt0(v0, v4) = v3 & % 132.55/18.43 | $i(v4) & $i(v3) & aInteger0(v4))) & ! [v2: $i] : ! [v3: $i] : % 132.55/18.43 | ( ~ (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ % 132.55/18.43 | sdteqdtlpzmzozddtrp0(v2, all_38_1, v0) | ~ aInteger0(v2) | % 132.55/18.43 | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 132.55/18.43 | (sdtpldt0(v2, all_38_0) = v3) | ~ $i(v2) | ~ aDivisorOf0(v0, v3) % 132.55/18.43 | | ~ aInteger0(v2) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 132.55/18.43 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, all_51_0))) % 132.55/18.43 | % 132.55/18.43 | DELTA: instantiating (21) with fresh symbols all_61_0, all_61_1 gives: % 132.55/18.43 | (22) ~ (all_61_1 = sz00) & szAzrzSzezqlpdtcmdtrp0(all_38_1, all_61_1) = % 132.55/18.43 | all_61_0 & $i(all_61_0) & $i(all_61_1) & aSubsetOf0(all_61_0, % 132.55/18.43 | all_51_0) & aSet0(all_61_0) & aInteger0(all_61_1) & ! [v0: $i] : ! % 132.55/18.43 | [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(all_61_1, v2) = v1) | ~ % 132.55/18.43 | (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 132.55/18.43 | aInteger0(v2) | ~ aInteger0(v0) | aElementOf0(v0, all_61_0)) & ! % 132.55/18.43 | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v0) % 132.55/18.43 | | ~ aElementOf0(v0, all_61_0) | sdteqdtlpzmzozddtrp0(v0, all_38_1, % 132.55/18.43 | all_61_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, % 132.55/18.43 | all_38_0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_61_0) | % 132.55/18.43 | aDivisorOf0(all_61_1, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 132.55/18.43 | (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 132.55/18.43 | all_61_0) | aInteger0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 132.55/18.43 | (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 132.55/18.43 | all_61_0) | ? [v2: $i] : (sdtasdt0(all_61_1, v2) = v1 & $i(v2) & % 132.55/18.43 | $i(v1) & aInteger0(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 132.55/18.43 | (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v0) | ~ % 132.55/18.43 | sdteqdtlpzmzozddtrp0(v0, all_38_1, all_61_1) | ~ aInteger0(v0) | % 132.55/18.43 | aElementOf0(v0, all_61_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 132.55/18.43 | (sdtpldt0(v0, all_38_0) = v1) | ~ $i(v0) | ~ aDivisorOf0(all_61_1, % 132.55/18.43 | v1) | ~ aInteger0(v0) | aElementOf0(v0, all_61_0)) & ! [v0: $i] % 132.55/18.43 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_61_0) | aElementOf0(v0, % 132.55/18.43 | all_51_0)) % 132.55/18.43 | % 132.55/18.43 | ALPHA: (22) implies: % 132.55/18.43 | (23) ~ (all_61_1 = sz00) % 132.55/18.43 | (24) aInteger0(all_61_1) % 132.55/18.43 | (25) $i(all_61_1) % 132.55/18.43 | (26) $i(all_61_0) % 132.55/18.43 | (27) szAzrzSzezqlpdtcmdtrp0(all_38_1, all_61_1) = all_61_0 % 132.55/18.43 | (28) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_61_0) | % 132.55/18.43 | aElementOf0(v0, all_51_0)) % 132.55/18.43 | % 132.55/18.43 | GROUND_INST: instantiating (2) with sz00, all_61_1, simplifying with (1), (5), % 132.55/18.43 | (24), (25) gives: % 132.55/18.43 | (29) all_61_1 = sz00 | sdteqdtlpzmzozddtrp0(sz00, sz00, all_61_1) % 132.55/18.43 | % 132.55/18.43 | GROUND_INST: instantiating (14) with all_61_1, all_61_0, simplifying with % 132.55/18.43 | (24), (25), (27) gives: % 132.55/18.44 | (30) all_61_1 = sz00 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_61_0) & % 132.55/18.44 | ~ aElementOf0(v0, all_38_2)) % 132.55/18.44 | % 132.55/18.44 | BETA: splitting (30) gives: % 132.55/18.44 | % 132.55/18.44 | Case 1: % 132.55/18.44 | | % 132.55/18.44 | | (31) all_61_1 = sz00 % 132.55/18.44 | | % 132.55/18.44 | | REDUCE: (23), (31) imply: % 132.55/18.44 | | (32) $false % 132.55/18.44 | | % 132.55/18.44 | | CLOSE: (32) is inconsistent. % 132.55/18.44 | | % 132.55/18.44 | Case 2: % 132.55/18.44 | | % 132.55/18.44 | | (33) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_61_0) & ~ % 132.55/18.44 | | aElementOf0(v0, all_38_2)) % 132.55/18.44 | | % 132.55/18.44 | | DELTA: instantiating (33) with fresh symbol all_91_0 gives: % 132.55/18.44 | | (34) $i(all_91_0) & aElementOf0(all_91_0, all_61_0) & ~ % 132.55/18.44 | | aElementOf0(all_91_0, all_38_2) % 132.55/18.44 | | % 132.55/18.44 | | ALPHA: (34) implies: % 132.55/18.44 | | (35) ~ aElementOf0(all_91_0, all_38_2) % 132.55/18.44 | | (36) aElementOf0(all_91_0, all_61_0) % 132.55/18.44 | | (37) $i(all_91_0) % 132.55/18.44 | | % 132.55/18.44 | | BETA: splitting (29) gives: % 132.55/18.44 | | % 132.55/18.44 | | Case 1: % 132.55/18.44 | | | % 132.55/18.44 | | | % 132.55/18.44 | | | GROUND_INST: instantiating (3) with all_38_1, all_61_1, all_61_0, % 132.55/18.44 | | | all_91_0, simplifying with (9), (15), (24), (25), (26), (27), % 132.55/18.44 | | | (36), (37) gives: % 132.55/18.44 | | | (38) all_61_1 = sz00 | aInteger0(all_91_0) % 132.55/18.44 | | | % 132.55/18.44 | | | GROUND_INST: instantiating (28) with all_91_0, simplifying with (36), (37) % 132.55/18.44 | | | gives: % 132.55/18.44 | | | (39) aElementOf0(all_91_0, all_51_0) % 132.55/18.44 | | | % 132.55/18.44 | | | BETA: splitting (38) gives: % 132.55/18.44 | | | % 132.55/18.44 | | | Case 1: % 132.55/18.44 | | | | % 132.55/18.44 | | | | (40) aInteger0(all_91_0) % 132.55/18.44 | | | | % 132.55/18.44 | | | | GROUND_INST: instantiating (13) with all_91_0, all_51_0, simplifying % 132.55/18.44 | | | | with (19), (20), (35), (37), (39), (40) gives: % 132.55/18.44 | | | | (41) $false % 132.55/18.44 | | | | % 132.55/18.44 | | | | CLOSE: (41) is inconsistent. % 132.55/18.44 | | | | % 132.55/18.44 | | | Case 2: % 132.55/18.44 | | | | % 132.55/18.44 | | | | (42) all_61_1 = sz00 % 132.55/18.44 | | | | % 132.55/18.44 | | | | REDUCE: (23), (42) imply: % 132.55/18.44 | | | | (43) $false % 132.55/18.44 | | | | % 132.55/18.44 | | | | CLOSE: (43) is inconsistent. % 132.55/18.44 | | | | % 132.55/18.44 | | | End of split % 132.55/18.44 | | | % 132.55/18.44 | | Case 2: % 132.55/18.44 | | | % 132.55/18.44 | | | (44) all_61_1 = sz00 % 132.55/18.44 | | | % 132.55/18.44 | | | REDUCE: (23), (44) imply: % 132.55/18.44 | | | (45) $false % 132.55/18.44 | | | % 132.55/18.44 | | | CLOSE: (45) is inconsistent. % 132.55/18.44 | | | % 132.55/18.44 | | End of split % 132.55/18.44 | | % 132.55/18.44 | End of split % 132.55/18.44 | % 132.55/18.44 End of proof % 132.55/18.44 % SZS output end Proof for theBenchmark % 132.55/18.44 % 132.55/18.44 17836ms %------------------------------------------------------------------------------