%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM448+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 : n026.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 11:47:49 EDT 2023 % Result : Theorem 25.46s 4.22s % Output : Proof 26.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM448+5 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n026.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 10:18:02 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.17/1.39 Prover 4: Preprocessing ... % 4.17/1.39 Prover 1: Preprocessing ... % 4.17/1.44 Prover 3: Preprocessing ... % 4.17/1.44 Prover 6: Preprocessing ... % 4.17/1.44 Prover 2: Preprocessing ... % 4.17/1.44 Prover 5: Preprocessing ... % 4.17/1.44 Prover 0: Preprocessing ... % 12.27/2.47 Prover 1: Constructing countermodel ... % 12.27/2.52 Prover 3: Constructing countermodel ... % 12.27/2.53 Prover 6: Proving ... % 12.27/2.54 Prover 5: Proving ... % 13.25/2.61 Prover 2: Proving ... % 17.27/3.18 Prover 4: Constructing countermodel ... % 17.27/3.18 Prover 0: Proving ... % 25.46/4.22 Prover 1: Found proof (size 146) % 25.46/4.22 Prover 1: proved (3569ms) % 25.46/4.22 Prover 3: stopped % 25.46/4.22 Prover 5: stopped % 25.46/4.22 Prover 2: stopped % 25.46/4.22 Prover 4: stopped % 25.46/4.22 Prover 0: stopped % 25.46/4.22 Prover 6: stopped % 25.46/4.22 % 25.46/4.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.46/4.23 % 25.59/4.24 % SZS output start Proof for theBenchmark % 25.59/4.24 Assumptions after simplification: % 25.59/4.24 --------------------------------- % 25.59/4.24 % 25.59/4.24 (mIntNeg) % 25.59/4.27 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] : % 25.59/4.27 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 % 25.59/4.27 = 0))) % 25.59/4.27 % 25.59/4.27 (mIntOne) % 25.59/4.27 aInteger0(sz10) = 0 & $i(sz10) % 25.59/4.27 % 25.59/4.27 (mMulMinOne) % 25.59/4.27 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 25.59/4.27 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 25.59/4.27 : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) = % 25.59/4.27 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2))))) % 25.59/4.27 % 25.59/4.27 (mPrimeDivisor) % 25.59/4.27 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 25.59/4.27 (aInteger0(v1) = 0) | ~ $i(v1) | ((v1 = v0 | v1 = sz10 | ? [v2: $i] : % 25.59/4.27 (isPrime0(v2) = 0 & aDivisorOf0(v2, v1) = 0 & $i(v2))) & ( ! [v2: $i] % 25.59/4.27 : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 25.59/4.27 aDivisorOf0(v2, v1) = v3)) | ( ~ (v1 = v0) & ~ (v1 = sz10)))))) % 25.59/4.27 % 25.59/4.27 (m__) % 25.59/4.29 $i(cS2076) & $i(xS) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 25.59/4.29 [v2: $i] : ( ~ (v1 = cS2076) & stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & % 25.59/4.29 aSet0(v1) = 0 & aSet0(v0) = 0 & smndt0(sz10) = v2 & $i(v2) & $i(v1) & $i(v0) % 25.59/4.29 & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | ~ % 25.59/4.29 $i(v3) | ? [v5: any] : ? [v6: any] : (aElementOf0(v3, v0) = v6 & % 25.59/4.29 aInteger0(v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] : ! [v4: % 25.59/4.29 int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] % 25.59/4.29 : ( ~ (v5 = 0) & aInteger0(v3) = v5) | ! [v5: $i] : ( ~ (aElementOf0(v5, % 25.59/4.29 xS) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & aElementOf0(v3, % 25.59/4.29 v5) = v6))) & ! [v3: $i] : ! [v4: any] : ( ~ (aElementOf0(v3, v0) % 25.59/4.29 = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & aInteger0(v3) = v5) | % 25.59/4.29 (( ? [v5: $i] : ( ~ (v5 = sz00) & isPrime0(v5) = 0 & aDivisorOf0(v5, v3) = % 25.59/4.29 0 & aInteger0(v5) = 0 & $i(v5) & ? [v6: $i] : (sdtasdt0(v5, v6) = % 25.59/4.29 v3 & aInteger0(v6) = 0 & $i(v6))) | ( ~ (v4 = 0) & ! [v5: $i] : ( % 25.59/4.29 ~ (aElementOf0(v5, xS) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 25.59/4.29 0) & aElementOf0(v3, v5) = v6)))) & ( ! [v5: $i] : ( ~ % 25.59/4.29 (isPrime0(v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: int] : ( ~ % 25.59/4.29 (v7 = 0) & aDivisorOf0(v5, v3) = v7 & aInteger0(v5) = v6 & ( ~ (v6 % 25.59/4.29 = 0) | v5 = sz00 | ! [v8: $i] : ( ~ (sdtasdt0(v5, v8) = v3) | % 25.59/4.29 ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & aInteger0(v8) = % 25.59/4.29 v9))))) | (v4 = 0 & ? [v5: $i] : (aElementOf0(v5, xS) = 0 & % 25.59/4.29 aElementOf0(v3, v5) = 0 & $i(v5)))))) & ! [v3: $i] : ( ~ % 25.59/4.29 (aElementOf0(v3, v1) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 25.59/4.29 aElementOf0(v3, v0) = v4 & aInteger0(v3) = 0)) & ! [v3: $i] : ( ~ % 25.59/4.29 (aElementOf0(v3, v0) = 0) | ~ $i(v3) | (aInteger0(v3) = 0 & ? [v4: $i] : % 25.59/4.29 (aElementOf0(v4, xS) = 0 & aElementOf0(v3, v4) = 0 & $i(v4)))) & ? [v3: % 25.59/4.29 $i] : ? [v4: any] : (aElementOf0(v3, v1) = v4 & $i(v3) & ((v4 = 0 & ~ % 25.59/4.29 (v3 = v2) & ~ (v3 = sz10)) | ( ~ (v4 = 0) & (v3 = v2 | v3 = sz10))))) % 25.59/4.29 % 25.59/4.29 (function-axioms) % 25.59/4.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 25.59/4.30 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 25.59/4.30 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 25.59/4.30 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) % 25.59/4.30 | ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.59/4.30 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtslmnbsdt0(v3, v2) = v1) | ~ % 25.59/4.30 (sdtslmnbsdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 25.59/4.30 [v3: $i] : (v1 = v0 | ~ (sdtbsmnsldt0(v3, v2) = v1) | ~ (sdtbsmnsldt0(v3, % 25.59/4.30 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 25.59/4.30 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ % 25.59/4.30 (aSubsetOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.59/4.30 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.59/4.30 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: % 25.59/4.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.59/4.30 : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & % 25.59/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.59/4.30 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 25.59/4.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 25.59/4.30 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.59/4.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~ % 25.59/4.30 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.59/4.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isClosed0(v2) = v1) | ~ % 25.59/4.30 (isClosed0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.59/4.30 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isOpen0(v2) = v1) | ~ % 25.59/4.30 (isOpen0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 25.59/4.30 ~ (stldt0(v2) = v1) | ~ (stldt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.59/4.30 [v2: $i] : (v1 = v0 | ~ (sbsmnsldt0(v2) = v1) | ~ (sbsmnsldt0(v2) = v0)) & % 25.59/4.30 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 25.59/4.30 v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] % 25.59/4.30 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) % 25.59/4.30 | ~ (isPrime0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 25.59/4.30 v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 25.59/4.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 25.59/4.30 ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 25.59/4.30 % 25.59/4.30 Further assumptions not needed in the proof: % 25.59/4.30 -------------------------------------------- % 25.59/4.30 mAddAsso, mAddComm, mAddNeg, mAddZero, mArSeq, mArSeqClosed, mClosed, % 25.59/4.30 mComplement, mDistrib, mDivisor, mElements, mEquMod, mEquModMul, mEquModRef, % 25.59/4.30 mEquModSym, mEquModTrn, mFinSet, mIntMult, mIntPlus, mIntZero, mIntegers, % 25.59/4.30 mInterOpen, mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, mOpen, mPrime, % 25.59/4.30 mSets, mSubset, mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, % 25.59/4.30 mZeroDiv, m__2046 % 25.59/4.30 % 25.59/4.30 Those formulas are unsatisfiable: % 25.59/4.30 --------------------------------- % 25.59/4.30 % 25.59/4.30 Begin of proof % 25.59/4.30 | % 25.59/4.30 | ALPHA: (mIntOne) implies: % 25.59/4.30 | (1) aInteger0(sz10) = 0 % 25.59/4.30 | % 25.59/4.30 | ALPHA: (mMulMinOne) implies: % 25.59/4.30 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 25.59/4.30 | ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] % 25.59/4.30 | : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & % 25.59/4.30 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & % 25.59/4.30 | v4 = v2))))) % 25.59/4.30 | % 25.59/4.30 | ALPHA: (mPrimeDivisor) implies: % 25.59/4.30 | (3) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 25.59/4.30 | (aInteger0(v1) = 0) | ~ $i(v1) | ((v1 = v0 | v1 = sz10 | ? [v2: % 25.59/4.30 | $i] : (isPrime0(v2) = 0 & aDivisorOf0(v2, v1) = 0 & $i(v2))) % 25.59/4.30 | & ( ! [v2: $i] : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) | ? [v3: % 25.59/4.30 | int] : ( ~ (v3 = 0) & aDivisorOf0(v2, v1) = v3)) | ( ~ (v1 % 25.59/4.30 | = v0) & ~ (v1 = sz10)))))) % 25.59/4.30 | % 25.59/4.30 | ALPHA: (m__) implies: % 25.59/4.30 | (4) $i(sz10) % 25.59/4.31 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = cS2076) & % 25.59/4.31 | stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 & aSet0(v1) = 0 & aSet0(v0) = 0 % 25.59/4.31 | & smndt0(sz10) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 25.59/4.31 | [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v1) = v4) | ~ $i(v3) | ? % 25.59/4.31 | [v5: any] : ? [v6: any] : (aElementOf0(v3, v0) = v6 & % 25.59/4.31 | aInteger0(v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] : ! % 25.59/4.31 | [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? % 25.59/4.31 | [v5: int] : ( ~ (v5 = 0) & aInteger0(v3) = v5) | ! [v5: $i] : ( ~ % 25.59/4.31 | (aElementOf0(v5, xS) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 25.59/4.31 | 0) & aElementOf0(v3, v5) = v6))) & ! [v3: $i] : ! [v4: any] % 25.59/4.31 | : ( ~ (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 % 25.59/4.31 | = 0) & aInteger0(v3) = v5) | (( ? [v5: $i] : ( ~ (v5 = sz00) & % 25.59/4.31 | isPrime0(v5) = 0 & aDivisorOf0(v5, v3) = 0 & aInteger0(v5) = % 25.59/4.31 | 0 & $i(v5) & ? [v6: $i] : (sdtasdt0(v5, v6) = v3 & % 25.59/4.31 | aInteger0(v6) = 0 & $i(v6))) | ( ~ (v4 = 0) & ! [v5: $i] : % 25.59/4.31 | ( ~ (aElementOf0(v5, xS) = 0) | ~ $i(v5) | ? [v6: int] : ( % 25.59/4.31 | ~ (v6 = 0) & aElementOf0(v3, v5) = v6)))) & ( ! [v5: $i] % 25.59/4.31 | : ( ~ (isPrime0(v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: % 25.59/4.31 | int] : ( ~ (v7 = 0) & aDivisorOf0(v5, v3) = v7 & % 25.59/4.31 | aInteger0(v5) = v6 & ( ~ (v6 = 0) | v5 = sz00 | ! [v8: $i] % 25.59/4.31 | : ( ~ (sdtasdt0(v5, v8) = v3) | ~ $i(v8) | ? [v9: int] % 25.59/4.31 | : ( ~ (v9 = 0) & aInteger0(v8) = v9))))) | (v4 = 0 & ? % 25.59/4.31 | [v5: $i] : (aElementOf0(v5, xS) = 0 & aElementOf0(v3, v5) = 0 % 25.59/4.31 | & $i(v5)))))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v1) = 0) % 25.59/4.31 | | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v3, v0) = % 25.59/4.31 | v4 & aInteger0(v3) = 0)) & ! [v3: $i] : ( ~ (aElementOf0(v3, v0) % 25.59/4.31 | = 0) | ~ $i(v3) | (aInteger0(v3) = 0 & ? [v4: $i] : % 25.59/4.31 | (aElementOf0(v4, xS) = 0 & aElementOf0(v3, v4) = 0 & $i(v4)))) & % 25.59/4.31 | ? [v3: $i] : ? [v4: any] : (aElementOf0(v3, v1) = v4 & $i(v3) & ((v4 % 25.59/4.31 | = 0 & ~ (v3 = v2) & ~ (v3 = sz10)) | ( ~ (v4 = 0) & (v3 = v2 % 25.59/4.31 | | v3 = sz10))))) % 25.59/4.31 | % 25.59/4.31 | ALPHA: (function-axioms) implies: % 25.59/4.31 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 25.59/4.31 | (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 25.59/4.31 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 25.59/4.31 | v1) | ~ (smndt0(v2) = v0)) % 25.59/4.31 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 25.59/4.31 | ! [v3: $i] : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~ % 25.59/4.31 | (aDivisorOf0(v3, v2) = v0)) % 25.59/4.31 | % 25.59/4.31 | DELTA: instantiating (2) with fresh symbol all_36_0 gives: % 25.59/4.32 | (9) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: $i] : ! [v1: $i] : ( % 25.59/4.32 | ~ (sdtasdt0(all_36_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 25.59/4.32 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_36_0) = v4 & smndt0(v0) = v3 % 25.59/4.32 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & % 25.59/4.32 | v3 = v1)))) % 25.59/4.32 | % 25.59/4.32 | ALPHA: (9) implies: % 25.59/4.32 | (10) smndt0(sz10) = all_36_0 % 25.59/4.32 | % 25.59/4.32 | DELTA: instantiating (3) with fresh symbol all_39_0 gives: % 25.59/4.32 | (11) smndt0(sz10) = all_39_0 & $i(all_39_0) & ! [v0: $i] : ( ~ % 25.59/4.32 | (aInteger0(v0) = 0) | ~ $i(v0) | ((v0 = all_39_0 | v0 = sz10 | ? % 25.59/4.32 | [v1: $i] : (isPrime0(v1) = 0 & aDivisorOf0(v1, v0) = 0 & % 25.59/4.32 | $i(v1))) & ( ! [v1: $i] : ( ~ (isPrime0(v1) = 0) | ~ $i(v1) | % 25.59/4.32 | ? [v2: int] : ( ~ (v2 = 0) & aDivisorOf0(v1, v0) = v2)) | ( ~ % 25.59/4.32 | (v0 = all_39_0) & ~ (v0 = sz10))))) % 26.03/4.32 | % 26.03/4.32 | ALPHA: (11) implies: % 26.03/4.32 | (12) $i(all_39_0) % 26.03/4.32 | (13) smndt0(sz10) = all_39_0 % 26.03/4.32 | (14) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ((v0 = all_39_0 | % 26.03/4.32 | v0 = sz10 | ? [v1: $i] : (isPrime0(v1) = 0 & aDivisorOf0(v1, % 26.03/4.32 | v0) = 0 & $i(v1))) & ( ! [v1: $i] : ( ~ (isPrime0(v1) = 0) | % 26.03/4.32 | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & aDivisorOf0(v1, v0) % 26.03/4.32 | = v2)) | ( ~ (v0 = all_39_0) & ~ (v0 = sz10))))) % 26.03/4.32 | % 26.03/4.32 | DELTA: instantiating (5) with fresh symbols all_42_0, all_42_1, all_42_2 % 26.03/4.32 | gives: % 26.03/4.33 | (15) ~ (all_42_1 = cS2076) & stldt0(all_42_2) = all_42_1 & sbsmnsldt0(xS) % 26.03/4.33 | = all_42_2 & aSet0(all_42_1) = 0 & aSet0(all_42_2) = 0 & smndt0(sz10) % 26.03/4.33 | = all_42_0 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & ! [v0: $i] % 26.03/4.33 | : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_42_1) = v1) | ~ % 26.03/4.33 | $i(v0) | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, all_42_2) = % 26.03/4.33 | v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : % 26.03/4.33 | ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_42_2) = v1) | ~ % 26.03/4.33 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | ! [v2: % 26.03/4.33 | $i] : ( ~ (aElementOf0(v2, xS) = 0) | ~ $i(v2) | ? [v3: int] : ( % 26.03/4.33 | ~ (v3 = 0) & aElementOf0(v0, v2) = v3))) & ! [v0: $i] : ! [v1: % 26.03/4.33 | any] : ( ~ (aElementOf0(v0, all_42_2) = v1) | ~ $i(v0) | ? [v2: % 26.03/4.33 | int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | (( ? [v2: $i] : ( ~ % 26.03/4.33 | (v2 = sz00) & isPrime0(v2) = 0 & aDivisorOf0(v2, v0) = 0 & % 26.03/4.33 | aInteger0(v2) = 0 & $i(v2) & ? [v3: $i] : (sdtasdt0(v2, v3) = % 26.03/4.33 | v0 & aInteger0(v3) = 0 & $i(v3))) | ( ~ (v1 = 0) & ! [v2: % 26.03/4.33 | $i] : ( ~ (aElementOf0(v2, xS) = 0) | ~ $i(v2) | ? [v3: % 26.03/4.33 | int] : ( ~ (v3 = 0) & aElementOf0(v0, v2) = v3)))) & ( ! % 26.03/4.33 | [v2: $i] : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) | ? [v3: any] : % 26.03/4.33 | ? [v4: int] : ( ~ (v4 = 0) & aDivisorOf0(v2, v0) = v4 & % 26.03/4.33 | aInteger0(v2) = v3 & ( ~ (v3 = 0) | v2 = sz00 | ! [v5: $i] % 26.03/4.33 | : ( ~ (sdtasdt0(v2, v5) = v0) | ~ $i(v5) | ? [v6: int] : % 26.03/4.33 | ( ~ (v6 = 0) & aInteger0(v5) = v6))))) | (v1 = 0 & ? % 26.03/4.33 | [v2: $i] : (aElementOf0(v2, xS) = 0 & aElementOf0(v0, v2) = 0 % 26.03/4.33 | & $i(v2)))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, all_42_1) % 26.03/4.33 | = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, % 26.03/4.33 | all_42_2) = v1 & aInteger0(v0) = 0)) & ! [v0: $i] : ( ~ % 26.03/4.33 | (aElementOf0(v0, all_42_2) = 0) | ~ $i(v0) | (aInteger0(v0) = 0 & % 26.03/4.33 | ? [v1: $i] : (aElementOf0(v1, xS) = 0 & aElementOf0(v0, v1) = 0 & % 26.03/4.33 | $i(v1)))) & ? [v0: $i] : ? [v1: any] : (aElementOf0(v0, % 26.03/4.33 | all_42_1) = v1 & $i(v0) & ((v1 = 0 & ~ (v0 = all_42_0) & ~ (v0 = % 26.03/4.33 | sz10)) | ( ~ (v1 = 0) & (v0 = all_42_0 | v0 = sz10)))) % 26.03/4.33 | % 26.03/4.33 | ALPHA: (15) implies: % 26.03/4.33 | (16) smndt0(sz10) = all_42_0 % 26.03/4.33 | (17) ! [v0: $i] : ( ~ (aElementOf0(v0, all_42_1) = 0) | ~ $i(v0) | ? % 26.03/4.33 | [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, all_42_2) = v1 & % 26.03/4.33 | aInteger0(v0) = 0)) % 26.03/4.33 | (18) ! [v0: $i] : ! [v1: any] : ( ~ (aElementOf0(v0, all_42_2) = v1) | ~ % 26.03/4.33 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = v2) | (( ? % 26.03/4.33 | [v2: $i] : ( ~ (v2 = sz00) & isPrime0(v2) = 0 & aDivisorOf0(v2, % 26.03/4.33 | v0) = 0 & aInteger0(v2) = 0 & $i(v2) & ? [v3: $i] : % 26.03/4.33 | (sdtasdt0(v2, v3) = v0 & aInteger0(v3) = 0 & $i(v3))) | ( ~ % 26.03/4.33 | (v1 = 0) & ! [v2: $i] : ( ~ (aElementOf0(v2, xS) = 0) | ~ % 26.03/4.33 | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, v2) = % 26.03/4.33 | v3)))) & ( ! [v2: $i] : ( ~ (isPrime0(v2) = 0) | ~ $i(v2) % 26.03/4.33 | | ? [v3: any] : ? [v4: int] : ( ~ (v4 = 0) & aDivisorOf0(v2, % 26.03/4.33 | v0) = v4 & aInteger0(v2) = v3 & ( ~ (v3 = 0) | v2 = sz00 | % 26.03/4.33 | ! [v5: $i] : ( ~ (sdtasdt0(v2, v5) = v0) | ~ $i(v5) | ? % 26.03/4.33 | [v6: int] : ( ~ (v6 = 0) & aInteger0(v5) = v6))))) | (v1 % 26.03/4.33 | = 0 & ? [v2: $i] : (aElementOf0(v2, xS) = 0 & aElementOf0(v0, % 26.03/4.33 | v2) = 0 & $i(v2)))))) % 26.03/4.33 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_42_2) = % 26.03/4.33 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aInteger0(v0) = % 26.03/4.33 | v2) | ! [v2: $i] : ( ~ (aElementOf0(v2, xS) = 0) | ~ $i(v2) | ? % 26.03/4.33 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, v2) = v3))) % 26.03/4.34 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aElementOf0(v0, all_42_1) = % 26.03/4.34 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aElementOf0(v0, % 26.03/4.34 | all_42_2) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 26.03/4.34 | (21) ? [v0: $i] : ? [v1: any] : (aElementOf0(v0, all_42_1) = v1 & $i(v0) % 26.03/4.34 | & ((v1 = 0 & ~ (v0 = all_42_0) & ~ (v0 = sz10)) | ( ~ (v1 = 0) & % 26.03/4.34 | (v0 = all_42_0 | v0 = sz10)))) % 26.03/4.34 | % 26.03/4.34 | DELTA: instantiating (21) with fresh symbols all_45_0, all_45_1 gives: % 26.03/4.34 | (22) aElementOf0(all_45_1, all_42_1) = all_45_0 & $i(all_45_1) & ((all_45_0 % 26.03/4.34 | = 0 & ~ (all_45_1 = all_42_0) & ~ (all_45_1 = sz10)) | ( ~ % 26.03/4.34 | (all_45_0 = 0) & (all_45_1 = all_42_0 | all_45_1 = sz10))) % 26.03/4.34 | % 26.03/4.34 | ALPHA: (22) implies: % 26.03/4.34 | (23) $i(all_45_1) % 26.03/4.34 | (24) aElementOf0(all_45_1, all_42_1) = all_45_0 % 26.03/4.34 | (25) (all_45_0 = 0 & ~ (all_45_1 = all_42_0) & ~ (all_45_1 = sz10)) | ( ~ % 26.03/4.34 | (all_45_0 = 0) & (all_45_1 = all_42_0 | all_45_1 = sz10)) % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (7) with all_39_0, all_42_0, sz10, simplifying with % 26.03/4.34 | (13), (16) gives: % 26.03/4.34 | (26) all_42_0 = all_39_0 % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (7) with all_36_0, all_42_0, sz10, simplifying with % 26.03/4.34 | (10), (16) gives: % 26.03/4.34 | (27) all_42_0 = all_36_0 % 26.03/4.34 | % 26.03/4.34 | COMBINE_EQS: (26), (27) imply: % 26.03/4.34 | (28) all_39_0 = all_36_0 % 26.03/4.34 | % 26.03/4.34 | SIMP: (28) implies: % 26.03/4.34 | (29) all_39_0 = all_36_0 % 26.03/4.34 | % 26.03/4.34 | REDUCE: (12), (29) imply: % 26.03/4.34 | (30) $i(all_36_0) % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (14) with sz10, simplifying with (1), (4) gives: % 26.03/4.34 | (31) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 26.03/4.34 | (v1 = 0) & aDivisorOf0(v0, sz10) = v1)) % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (mIntNeg) with sz10, all_36_0, simplifying with % 26.03/4.34 | (4), (10) gives: % 26.03/4.34 | (32) ? [v0: any] : ? [v1: any] : (aInteger0(all_36_0) = v1 & % 26.03/4.34 | aInteger0(sz10) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (20) with all_45_1, all_45_0, simplifying with % 26.03/4.34 | (23), (24) gives: % 26.03/4.34 | (33) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : (aElementOf0(all_45_1, % 26.03/4.34 | all_42_2) = v1 & aInteger0(all_45_1) = v0 & ( ~ (v0 = 0) | v1 = % 26.03/4.34 | 0)) % 26.03/4.34 | % 26.03/4.34 | DELTA: instantiating (32) with fresh symbols all_65_0, all_65_1 gives: % 26.03/4.34 | (34) aInteger0(all_36_0) = all_65_0 & aInteger0(sz10) = all_65_1 & ( ~ % 26.03/4.34 | (all_65_1 = 0) | all_65_0 = 0) % 26.03/4.34 | % 26.03/4.34 | ALPHA: (34) implies: % 26.03/4.34 | (35) aInteger0(sz10) = all_65_1 % 26.03/4.34 | (36) aInteger0(all_36_0) = all_65_0 % 26.03/4.34 | (37) ~ (all_65_1 = 0) | all_65_0 = 0 % 26.03/4.34 | % 26.03/4.34 | GROUND_INST: instantiating (6) with 0, all_65_1, sz10, simplifying with (1), % 26.03/4.34 | (35) gives: % 26.03/4.34 | (38) all_65_1 = 0 % 26.03/4.34 | % 26.03/4.34 | BETA: splitting (37) gives: % 26.03/4.34 | % 26.03/4.34 | Case 1: % 26.03/4.34 | | % 26.03/4.34 | | (39) ~ (all_65_1 = 0) % 26.03/4.34 | | % 26.03/4.34 | | REDUCE: (38), (39) imply: % 26.03/4.34 | | (40) $false % 26.03/4.35 | | % 26.03/4.35 | | CLOSE: (40) is inconsistent. % 26.03/4.35 | | % 26.03/4.35 | Case 2: % 26.03/4.35 | | % 26.03/4.35 | | (41) all_65_0 = 0 % 26.03/4.35 | | % 26.03/4.35 | | REDUCE: (36), (41) imply: % 26.03/4.35 | | (42) aInteger0(all_36_0) = 0 % 26.03/4.35 | | % 26.03/4.35 | | GROUND_INST: instantiating (14) with all_36_0, simplifying with (30), (42) % 26.03/4.35 | | gives: % 26.03/4.35 | | (43) (all_39_0 = all_36_0 | all_36_0 = sz10 | ? [v0: $i] : (isPrime0(v0) % 26.03/4.35 | | = 0 & aDivisorOf0(v0, all_36_0) = 0 & $i(v0))) & ( ! [v0: $i] : % 26.03/4.35 | | ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.35 | | aDivisorOf0(v0, all_36_0) = v1)) | ( ~ (all_39_0 = all_36_0) & % 26.03/4.35 | | ~ (all_36_0 = sz10))) % 26.03/4.35 | | % 26.03/4.35 | | ALPHA: (43) implies: % 26.03/4.35 | | (44) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( % 26.03/4.35 | | ~ (v1 = 0) & aDivisorOf0(v0, all_36_0) = v1)) | ( ~ (all_39_0 = % 26.03/4.35 | | all_36_0) & ~ (all_36_0 = sz10)) % 26.03/4.35 | | % 26.03/4.35 | | BETA: splitting (44) gives: % 26.03/4.35 | | % 26.03/4.35 | | Case 1: % 26.03/4.35 | | | % 26.03/4.35 | | | (45) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: int] : % 26.03/4.35 | | | ( ~ (v1 = 0) & aDivisorOf0(v0, all_36_0) = v1)) % 26.03/4.35 | | | % 26.03/4.35 | | | BETA: splitting (25) gives: % 26.03/4.35 | | | % 26.03/4.35 | | | Case 1: % 26.03/4.35 | | | | % 26.03/4.35 | | | | (46) all_45_0 = 0 & ~ (all_45_1 = all_42_0) & ~ (all_45_1 = sz10) % 26.03/4.35 | | | | % 26.03/4.35 | | | | ALPHA: (46) implies: % 26.03/4.35 | | | | (47) all_45_0 = 0 % 26.03/4.35 | | | | (48) ~ (all_45_1 = sz10) % 26.03/4.35 | | | | (49) ~ (all_45_1 = all_42_0) % 26.03/4.35 | | | | % 26.03/4.35 | | | | REDUCE: (27), (49) imply: % 26.03/4.35 | | | | (50) ~ (all_45_1 = all_36_0) % 26.03/4.35 | | | | % 26.03/4.35 | | | | REDUCE: (24), (47) imply: % 26.03/4.35 | | | | (51) aElementOf0(all_45_1, all_42_1) = 0 % 26.03/4.35 | | | | % 26.03/4.35 | | | | GROUND_INST: instantiating (17) with all_45_1, simplifying with (23), % 26.03/4.35 | | | | (51) gives: % 26.03/4.35 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(all_45_1, all_42_2) = % 26.03/4.35 | | | | v0 & aInteger0(all_45_1) = 0) % 26.03/4.35 | | | | % 26.03/4.35 | | | | DELTA: instantiating (52) with fresh symbol all_101_0 gives: % 26.03/4.35 | | | | (53) ~ (all_101_0 = 0) & aElementOf0(all_45_1, all_42_2) = all_101_0 % 26.03/4.35 | | | | & aInteger0(all_45_1) = 0 % 26.03/4.35 | | | | % 26.03/4.35 | | | | ALPHA: (53) implies: % 26.03/4.35 | | | | (54) ~ (all_101_0 = 0) % 26.03/4.35 | | | | (55) aInteger0(all_45_1) = 0 % 26.03/4.35 | | | | (56) aElementOf0(all_45_1, all_42_2) = all_101_0 % 26.03/4.35 | | | | % 26.03/4.35 | | | | GROUND_INST: instantiating (14) with all_45_1, simplifying with (23), % 26.03/4.35 | | | | (55) gives: % 26.03/4.35 | | | | (57) (all_45_1 = all_39_0 | all_45_1 = sz10 | ? [v0: $i] : % 26.03/4.35 | | | | (isPrime0(v0) = 0 & aDivisorOf0(v0, all_45_1) = 0 & $i(v0))) & % 26.03/4.35 | | | | ( ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: int] % 26.03/4.35 | | | | : ( ~ (v1 = 0) & aDivisorOf0(v0, all_45_1) = v1)) | ( ~ % 26.03/4.35 | | | | (all_45_1 = all_39_0) & ~ (all_45_1 = sz10))) % 26.03/4.35 | | | | % 26.03/4.35 | | | | ALPHA: (57) implies: % 26.03/4.35 | | | | (58) all_45_1 = all_39_0 | all_45_1 = sz10 | ? [v0: $i] : % 26.03/4.35 | | | | (isPrime0(v0) = 0 & aDivisorOf0(v0, all_45_1) = 0 & $i(v0)) % 26.03/4.35 | | | | % 26.03/4.35 | | | | GROUND_INST: instantiating (19) with all_45_1, all_101_0, simplifying % 26.03/4.35 | | | | with (23), (56) gives: % 26.03/4.35 | | | | (59) all_101_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 26.03/4.35 | | | | aInteger0(all_45_1) = v0) | ! [v0: $i] : ( ~ (aElementOf0(v0, % 26.03/4.35 | | | | xS) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.35 | | | | aElementOf0(all_45_1, v0) = v1)) % 26.03/4.35 | | | | % 26.03/4.35 | | | | GROUND_INST: instantiating (18) with all_45_1, all_101_0, simplifying % 26.03/4.35 | | | | with (23), (56) gives: % 26.03/4.36 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_45_1) = v0) | (( ? % 26.03/4.36 | | | | [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.36 | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & $i(v0) % 26.03/4.36 | | | | & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 & % 26.03/4.36 | | | | aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_101_0 = 0) & ! % 26.03/4.36 | | | | [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ $i(v0) | ? % 26.03/4.36 | | | | [v1: int] : ( ~ (v1 = 0) & aElementOf0(all_45_1, v0) = % 26.03/4.36 | | | | v1)))) & ( ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ % 26.03/4.36 | | | | $i(v0) | ? [v1: any] : ? [v2: int] : ( ~ (v2 = 0) & % 26.03/4.36 | | | | aDivisorOf0(v0, all_45_1) = v2 & aInteger0(v0) = v1 & ( % 26.03/4.36 | | | | ~ (v1 = 0) | v0 = sz00 | ! [v3: $i] : ( ~ % 26.03/4.36 | | | | (sdtasdt0(v0, v3) = all_45_1) | ~ $i(v3) | ? [v4: % 26.03/4.36 | | | | int] : ( ~ (v4 = 0) & aInteger0(v3) = v4))))) | % 26.03/4.36 | | | | (all_101_0 = 0 & ? [v0: $i] : (aElementOf0(v0, xS) = 0 & % 26.03/4.36 | | | | aElementOf0(all_45_1, v0) = 0 & $i(v0))))) % 26.03/4.36 | | | | % 26.03/4.36 | | | | BETA: splitting (60) gives: % 26.03/4.36 | | | | % 26.03/4.36 | | | | Case 1: % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_45_1) = v0) % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | BETA: splitting (59) gives: % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | Case 1: % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | (62) all_101_0 = 0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | REDUCE: (54), (62) imply: % 26.03/4.36 | | | | | | (63) $false % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | CLOSE: (63) is inconsistent. % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | Case 2: % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | DELTA: instantiating (61) with fresh symbol all_119_0 gives: % 26.03/4.36 | | | | | | (64) ~ (all_119_0 = 0) & aInteger0(all_45_1) = all_119_0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | ALPHA: (64) implies: % 26.03/4.36 | | | | | | (65) ~ (all_119_0 = 0) % 26.03/4.36 | | | | | | (66) aInteger0(all_45_1) = all_119_0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | GROUND_INST: instantiating (6) with 0, all_119_0, all_45_1, % 26.03/4.36 | | | | | | simplifying with (55), (66) gives: % 26.03/4.36 | | | | | | (67) all_119_0 = 0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | REDUCE: (65), (67) imply: % 26.03/4.36 | | | | | | (68) $false % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | CLOSE: (68) is inconsistent. % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | End of split % 26.03/4.36 | | | | | % 26.03/4.36 | | | | Case 2: % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | (69) ( ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.36 | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & $i(v0) % 26.03/4.36 | | | | | & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 & % 26.03/4.36 | | | | | aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_101_0 = 0) & ! % 26.03/4.36 | | | | | [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ $i(v0) | ? % 26.03/4.36 | | | | | [v1: int] : ( ~ (v1 = 0) & aElementOf0(all_45_1, v0) = % 26.03/4.36 | | | | | v1)))) & ( ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ % 26.03/4.36 | | | | | $i(v0) | ? [v1: any] : ? [v2: int] : ( ~ (v2 = 0) & % 26.03/4.36 | | | | | aDivisorOf0(v0, all_45_1) = v2 & aInteger0(v0) = v1 & ( % 26.03/4.36 | | | | | ~ (v1 = 0) | v0 = sz00 | ! [v3: $i] : ( ~ % 26.03/4.36 | | | | | (sdtasdt0(v0, v3) = all_45_1) | ~ $i(v3) | ? [v4: % 26.03/4.36 | | | | | int] : ( ~ (v4 = 0) & aInteger0(v3) = v4))))) | % 26.03/4.36 | | | | | (all_101_0 = 0 & ? [v0: $i] : (aElementOf0(v0, xS) = 0 & % 26.03/4.36 | | | | | aElementOf0(all_45_1, v0) = 0 & $i(v0)))) % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | ALPHA: (69) implies: % 26.03/4.36 | | | | | (70) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.36 | | | | | any] : ? [v2: int] : ( ~ (v2 = 0) & aDivisorOf0(v0, % 26.03/4.36 | | | | | all_45_1) = v2 & aInteger0(v0) = v1 & ( ~ (v1 = 0) | v0 % 26.03/4.36 | | | | | = sz00 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = all_45_1) % 26.03/4.36 | | | | | | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 26.03/4.36 | | | | | aInteger0(v3) = v4))))) | (all_101_0 = 0 & ? [v0: % 26.03/4.36 | | | | | $i] : (aElementOf0(v0, xS) = 0 & aElementOf0(all_45_1, v0) % 26.03/4.36 | | | | | = 0 & $i(v0))) % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | BETA: splitting (58) gives: % 26.03/4.36 | | | | | % 26.03/4.36 | | | | | Case 1: % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | (71) all_45_1 = all_39_0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | COMBINE_EQS: (29), (71) imply: % 26.03/4.36 | | | | | | (72) all_45_1 = all_36_0 % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | REDUCE: (50), (72) imply: % 26.03/4.36 | | | | | | (73) $false % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | CLOSE: (73) is inconsistent. % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | Case 2: % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | (74) all_45_1 = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & % 26.03/4.36 | | | | | | aDivisorOf0(v0, all_45_1) = 0 & $i(v0)) % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | BETA: splitting (70) gives: % 26.03/4.36 | | | | | | % 26.03/4.36 | | | | | | Case 1: % 26.03/4.36 | | | | | | | % 26.03/4.37 | | | | | | | (75) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.37 | | | | | | | any] : ? [v2: int] : ( ~ (v2 = 0) & aDivisorOf0(v0, % 26.03/4.37 | | | | | | | all_45_1) = v2 & aInteger0(v0) = v1 & ( ~ (v1 = 0) | % 26.03/4.37 | | | | | | | v0 = sz00 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = % 26.03/4.37 | | | | | | | all_45_1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = % 26.03/4.37 | | | | | | | 0) & aInteger0(v3) = v4))))) % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | BETA: splitting (74) gives: % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | Case 1: % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | (76) all_45_1 = sz10 % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | REDUCE: (48), (76) imply: % 26.03/4.37 | | | | | | | | (77) $false % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | CLOSE: (77) is inconsistent. % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | Case 2: % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | (78) ? [v0: $i] : (isPrime0(v0) = 0 & aDivisorOf0(v0, % 26.03/4.37 | | | | | | | | all_45_1) = 0 & $i(v0)) % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | DELTA: instantiating (78) with fresh symbol all_130_0 gives: % 26.03/4.37 | | | | | | | | (79) isPrime0(all_130_0) = 0 & aDivisorOf0(all_130_0, % 26.03/4.37 | | | | | | | | all_45_1) = 0 & $i(all_130_0) % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | ALPHA: (79) implies: % 26.03/4.37 | | | | | | | | (80) $i(all_130_0) % 26.03/4.37 | | | | | | | | (81) aDivisorOf0(all_130_0, all_45_1) = 0 % 26.03/4.37 | | | | | | | | (82) isPrime0(all_130_0) = 0 % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | GROUND_INST: instantiating (75) with all_130_0, simplifying with % 26.03/4.37 | | | | | | | | (80), (82) gives: % 26.03/4.37 | | | | | | | | (83) ? [v0: any] : ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.37 | | | | | | | | aDivisorOf0(all_130_0, all_45_1) = v1 & % 26.03/4.37 | | | | | | | | aInteger0(all_130_0) = v0 & ( ~ (v0 = 0) | all_130_0 = % 26.03/4.37 | | | | | | | | sz00 | ! [v2: $i] : ( ~ (sdtasdt0(all_130_0, v2) = % 26.03/4.37 | | | | | | | | all_45_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = % 26.03/4.37 | | | | | | | | 0) & aInteger0(v2) = v3)))) % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | DELTA: instantiating (83) with fresh symbols all_152_0, % 26.03/4.37 | | | | | | | | all_152_1 gives: % 26.03/4.37 | | | | | | | | (84) ~ (all_152_0 = 0) & aDivisorOf0(all_130_0, all_45_1) = % 26.03/4.37 | | | | | | | | all_152_0 & aInteger0(all_130_0) = all_152_1 & ( ~ % 26.03/4.37 | | | | | | | | (all_152_1 = 0) | all_130_0 = sz00 | ! [v0: $i] : ( ~ % 26.03/4.37 | | | | | | | | (sdtasdt0(all_130_0, v0) = all_45_1) | ~ $i(v0) | % 26.03/4.37 | | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1))) % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | ALPHA: (84) implies: % 26.03/4.37 | | | | | | | | (85) ~ (all_152_0 = 0) % 26.03/4.37 | | | | | | | | (86) aDivisorOf0(all_130_0, all_45_1) = all_152_0 % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | GROUND_INST: instantiating (8) with 0, all_152_0, all_45_1, % 26.03/4.37 | | | | | | | | all_130_0, simplifying with (81), (86) gives: % 26.03/4.37 | | | | | | | | (87) all_152_0 = 0 % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | REDUCE: (85), (87) imply: % 26.03/4.37 | | | | | | | | (88) $false % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | | CLOSE: (88) is inconsistent. % 26.03/4.37 | | | | | | | | % 26.03/4.37 | | | | | | | End of split % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | Case 2: % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | (89) all_101_0 = 0 & ? [v0: $i] : (aElementOf0(v0, xS) = 0 & % 26.03/4.37 | | | | | | | aElementOf0(all_45_1, v0) = 0 & $i(v0)) % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | ALPHA: (89) implies: % 26.03/4.37 | | | | | | | (90) all_101_0 = 0 % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | REDUCE: (54), (90) imply: % 26.03/4.37 | | | | | | | (91) $false % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | | CLOSE: (91) is inconsistent. % 26.03/4.37 | | | | | | | % 26.03/4.37 | | | | | | End of split % 26.03/4.37 | | | | | | % 26.03/4.37 | | | | | End of split % 26.03/4.37 | | | | | % 26.03/4.37 | | | | End of split % 26.03/4.37 | | | | % 26.03/4.37 | | | Case 2: % 26.03/4.37 | | | | % 26.03/4.37 | | | | (92) ~ (all_45_0 = 0) & (all_45_1 = all_42_0 | all_45_1 = sz10) % 26.03/4.37 | | | | % 26.03/4.37 | | | | ALPHA: (92) implies: % 26.03/4.37 | | | | (93) ~ (all_45_0 = 0) % 26.03/4.37 | | | | (94) all_45_1 = all_42_0 | all_45_1 = sz10 % 26.03/4.37 | | | | % 26.03/4.37 | | | | BETA: splitting (33) gives: % 26.03/4.37 | | | | % 26.03/4.37 | | | | Case 1: % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | (95) all_45_0 = 0 % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | REDUCE: (93), (95) imply: % 26.03/4.37 | | | | | (96) $false % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | CLOSE: (96) is inconsistent. % 26.03/4.37 | | | | | % 26.03/4.37 | | | | Case 2: % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | (97) ? [v0: any] : ? [v1: any] : (aElementOf0(all_45_1, all_42_2) % 26.03/4.37 | | | | | = v1 & aInteger0(all_45_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | DELTA: instantiating (97) with fresh symbols all_100_0, all_100_1 % 26.03/4.37 | | | | | gives: % 26.03/4.37 | | | | | (98) aElementOf0(all_45_1, all_42_2) = all_100_0 & % 26.03/4.37 | | | | | aInteger0(all_45_1) = all_100_1 & ( ~ (all_100_1 = 0) | % 26.03/4.37 | | | | | all_100_0 = 0) % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | ALPHA: (98) implies: % 26.03/4.37 | | | | | (99) aInteger0(all_45_1) = all_100_1 % 26.03/4.37 | | | | | (100) aElementOf0(all_45_1, all_42_2) = all_100_0 % 26.03/4.37 | | | | | (101) ~ (all_100_1 = 0) | all_100_0 = 0 % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | GROUND_INST: instantiating (18) with all_45_1, all_100_0, simplifying % 26.03/4.37 | | | | | with (23), (100) gives: % 26.03/4.37 | | | | | (102) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_45_1) = v0) | (( % 26.03/4.37 | | | | | ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.37 | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.37 | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 & % 26.03/4.37 | | | | | aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_100_0 = 0) & % 26.03/4.37 | | | | | ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ $i(v0) % 26.03/4.37 | | | | | | ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(all_45_1, % 26.03/4.37 | | | | | v0) = v1)))) & ( ! [v0: $i] : ( ~ (isPrime0(v0) = % 26.03/4.37 | | | | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: int] : ( ~ % 26.03/4.37 | | | | | (v2 = 0) & aDivisorOf0(v0, all_45_1) = v2 & % 26.03/4.37 | | | | | aInteger0(v0) = v1 & ( ~ (v1 = 0) | v0 = sz00 | ! % 26.03/4.37 | | | | | [v3: $i] : ( ~ (sdtasdt0(v0, v3) = all_45_1) | ~ % 26.03/4.37 | | | | | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 26.03/4.37 | | | | | aInteger0(v3) = v4))))) | (all_100_0 = 0 & ? % 26.03/4.37 | | | | | [v0: $i] : (aElementOf0(v0, xS) = 0 & % 26.03/4.37 | | | | | aElementOf0(all_45_1, v0) = 0 & $i(v0))))) % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | BETA: splitting (94) gives: % 26.03/4.37 | | | | | % 26.03/4.37 | | | | | Case 1: % 26.03/4.37 | | | | | | % 26.03/4.37 | | | | | | (103) all_45_1 = all_42_0 % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | COMBINE_EQS: (27), (103) imply: % 26.03/4.38 | | | | | | (104) all_45_1 = all_36_0 % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | REDUCE: (99), (104) imply: % 26.03/4.38 | | | | | | (105) aInteger0(all_36_0) = all_100_1 % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | GROUND_INST: instantiating (6) with 0, all_100_1, all_36_0, % 26.03/4.38 | | | | | | simplifying with (42), (105) gives: % 26.03/4.38 | | | | | | (106) all_100_1 = 0 % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | BETA: splitting (101) gives: % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | Case 1: % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | (107) ~ (all_100_1 = 0) % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | REDUCE: (106), (107) imply: % 26.03/4.38 | | | | | | | (108) $false % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | CLOSE: (108) is inconsistent. % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | Case 2: % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | (109) all_100_0 = 0 % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | BETA: splitting (102) gives: % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | | Case 1: % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | (110) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_45_1) = v0) % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | DELTA: instantiating (110) with fresh symbol all_266_0 gives: % 26.03/4.38 | | | | | | | | (111) ~ (all_266_0 = 0) & aInteger0(all_45_1) = all_266_0 % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | ALPHA: (111) implies: % 26.03/4.38 | | | | | | | | (112) ~ (all_266_0 = 0) % 26.03/4.38 | | | | | | | | (113) aInteger0(all_45_1) = all_266_0 % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | REDUCE: (104), (113) imply: % 26.03/4.38 | | | | | | | | (114) aInteger0(all_36_0) = all_266_0 % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_266_0, all_36_0, % 26.03/4.38 | | | | | | | | simplifying with (42), (114) gives: % 26.03/4.38 | | | | | | | | (115) all_266_0 = 0 % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | REDUCE: (112), (115) imply: % 26.03/4.38 | | | | | | | | (116) $false % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | CLOSE: (116) is inconsistent. % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | Case 2: % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | (117) ( ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.38 | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.38 | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 % 26.03/4.38 | | | | | | | | & aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_100_0 = % 26.03/4.38 | | | | | | | | 0) & ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) % 26.03/4.38 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.38 | | | | | | | | aElementOf0(all_45_1, v0) = v1)))) & ( ! [v0: % 26.03/4.38 | | | | | | | | $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.38 | | | | | | | | any] : ? [v2: int] : ( ~ (v2 = 0) & % 26.03/4.38 | | | | | | | | aDivisorOf0(v0, all_45_1) = v2 & aInteger0(v0) = % 26.03/4.38 | | | | | | | | v1 & ( ~ (v1 = 0) | v0 = sz00 | ! [v3: $i] : ( ~ % 26.03/4.38 | | | | | | | | (sdtasdt0(v0, v3) = all_45_1) | ~ $i(v3) | % 26.03/4.38 | | | | | | | | ? [v4: int] : ( ~ (v4 = 0) & aInteger0(v3) = % 26.03/4.38 | | | | | | | | v4))))) | (all_100_0 = 0 & ? [v0: $i] : % 26.03/4.38 | | | | | | | | (aElementOf0(v0, xS) = 0 & aElementOf0(all_45_1, % 26.03/4.38 | | | | | | | | v0) = 0 & $i(v0)))) % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | ALPHA: (117) implies: % 26.03/4.38 | | | | | | | | (118) ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.38 | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.38 | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 & % 26.03/4.38 | | | | | | | | aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_100_0 = 0) % 26.03/4.38 | | | | | | | | & ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ % 26.03/4.38 | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.38 | | | | | | | | aElementOf0(all_45_1, v0) = v1))) % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | BETA: splitting (118) gives: % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | | Case 1: % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | (119) ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.38 | | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.38 | | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 % 26.03/4.38 | | | | | | | | | & aInteger0(v1) = 0 & $i(v1))) % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | DELTA: instantiating (119) with fresh symbol all_268_0 gives: % 26.03/4.38 | | | | | | | | | (120) ~ (all_268_0 = sz00) & isPrime0(all_268_0) = 0 & % 26.03/4.38 | | | | | | | | | aDivisorOf0(all_268_0, all_45_1) = 0 & % 26.03/4.38 | | | | | | | | | aInteger0(all_268_0) = 0 & $i(all_268_0) & ? [v0: % 26.03/4.38 | | | | | | | | | $i] : (sdtasdt0(all_268_0, v0) = all_45_1 & % 26.03/4.38 | | | | | | | | | aInteger0(v0) = 0 & $i(v0)) % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | ALPHA: (120) implies: % 26.03/4.38 | | | | | | | | | (121) $i(all_268_0) % 26.03/4.38 | | | | | | | | | (122) aDivisorOf0(all_268_0, all_45_1) = 0 % 26.03/4.38 | | | | | | | | | (123) isPrime0(all_268_0) = 0 % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | REDUCE: (104), (122) imply: % 26.03/4.38 | | | | | | | | | (124) aDivisorOf0(all_268_0, all_36_0) = 0 % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | GROUND_INST: instantiating (45) with all_268_0, simplifying % 26.03/4.38 | | | | | | | | | with (121), (123) gives: % 26.03/4.38 | | | | | | | | | (125) ? [v0: int] : ( ~ (v0 = 0) & aDivisorOf0(all_268_0, % 26.03/4.38 | | | | | | | | | all_36_0) = v0) % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | DELTA: instantiating (125) with fresh symbol all_284_0 gives: % 26.03/4.38 | | | | | | | | | (126) ~ (all_284_0 = 0) & aDivisorOf0(all_268_0, all_36_0) % 26.03/4.38 | | | | | | | | | = all_284_0 % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | ALPHA: (126) implies: % 26.03/4.38 | | | | | | | | | (127) ~ (all_284_0 = 0) % 26.03/4.38 | | | | | | | | | (128) aDivisorOf0(all_268_0, all_36_0) = all_284_0 % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_284_0, all_36_0, % 26.03/4.38 | | | | | | | | | all_268_0, simplifying with (124), (128) gives: % 26.03/4.38 | | | | | | | | | (129) all_284_0 = 0 % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | REDUCE: (127), (129) imply: % 26.03/4.38 | | | | | | | | | (130) $false % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | CLOSE: (130) is inconsistent. % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | Case 2: % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | (131) ~ (all_100_0 = 0) & ! [v0: $i] : ( ~ % 26.03/4.38 | | | | | | | | | (aElementOf0(v0, xS) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.38 | | | | | | | | | int] : ( ~ (v1 = 0) & aElementOf0(all_45_1, v0) = % 26.03/4.38 | | | | | | | | | v1)) % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | ALPHA: (131) implies: % 26.03/4.38 | | | | | | | | | (132) ~ (all_100_0 = 0) % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | REDUCE: (109), (132) imply: % 26.03/4.38 | | | | | | | | | (133) $false % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | | CLOSE: (133) is inconsistent. % 26.03/4.38 | | | | | | | | | % 26.03/4.38 | | | | | | | | End of split % 26.03/4.38 | | | | | | | | % 26.03/4.38 | | | | | | | End of split % 26.03/4.38 | | | | | | | % 26.03/4.38 | | | | | | End of split % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | Case 2: % 26.03/4.38 | | | | | | % 26.03/4.38 | | | | | | (134) all_45_1 = sz10 % 26.03/4.38 | | | | | | % 26.03/4.39 | | | | | | REDUCE: (99), (134) imply: % 26.03/4.39 | | | | | | (135) aInteger0(sz10) = all_100_1 % 26.03/4.39 | | | | | | % 26.03/4.39 | | | | | | GROUND_INST: instantiating (6) with 0, all_100_1, sz10, simplifying % 26.03/4.39 | | | | | | with (1), (135) gives: % 26.03/4.39 | | | | | | (136) all_100_1 = 0 % 26.03/4.39 | | | | | | % 26.03/4.39 | | | | | | BETA: splitting (101) gives: % 26.03/4.39 | | | | | | % 26.03/4.39 | | | | | | Case 1: % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | (137) ~ (all_100_1 = 0) % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | REDUCE: (136), (137) imply: % 26.03/4.39 | | | | | | | (138) $false % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | CLOSE: (138) is inconsistent. % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | Case 2: % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | (139) all_100_0 = 0 % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | BETA: splitting (102) gives: % 26.03/4.39 | | | | | | | % 26.03/4.39 | | | | | | | Case 1: % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | (140) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_45_1) = v0) % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | DELTA: instantiating (140) with fresh symbol all_266_0 gives: % 26.03/4.39 | | | | | | | | (141) ~ (all_266_0 = 0) & aInteger0(all_45_1) = all_266_0 % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | ALPHA: (141) implies: % 26.03/4.39 | | | | | | | | (142) ~ (all_266_0 = 0) % 26.03/4.39 | | | | | | | | (143) aInteger0(all_45_1) = all_266_0 % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | REDUCE: (134), (143) imply: % 26.03/4.39 | | | | | | | | (144) aInteger0(sz10) = all_266_0 % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | GROUND_INST: instantiating (6) with 0, all_266_0, sz10, % 26.03/4.39 | | | | | | | | simplifying with (1), (144) gives: % 26.03/4.39 | | | | | | | | (145) all_266_0 = 0 % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | REDUCE: (142), (145) imply: % 26.03/4.39 | | | | | | | | (146) $false % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | CLOSE: (146) is inconsistent. % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | Case 2: % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | (147) ( ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.39 | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.39 | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 % 26.03/4.39 | | | | | | | | & aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_100_0 = % 26.03/4.39 | | | | | | | | 0) & ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) % 26.03/4.39 | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.39 | | | | | | | | aElementOf0(all_45_1, v0) = v1)))) & ( ! [v0: % 26.03/4.39 | | | | | | | | $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.39 | | | | | | | | any] : ? [v2: int] : ( ~ (v2 = 0) & % 26.03/4.39 | | | | | | | | aDivisorOf0(v0, all_45_1) = v2 & aInteger0(v0) = % 26.03/4.39 | | | | | | | | v1 & ( ~ (v1 = 0) | v0 = sz00 | ! [v3: $i] : ( ~ % 26.03/4.39 | | | | | | | | (sdtasdt0(v0, v3) = all_45_1) | ~ $i(v3) | % 26.03/4.39 | | | | | | | | ? [v4: int] : ( ~ (v4 = 0) & aInteger0(v3) = % 26.03/4.39 | | | | | | | | v4))))) | (all_100_0 = 0 & ? [v0: $i] : % 26.03/4.39 | | | | | | | | (aElementOf0(v0, xS) = 0 & aElementOf0(all_45_1, % 26.03/4.39 | | | | | | | | v0) = 0 & $i(v0)))) % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | ALPHA: (147) implies: % 26.03/4.39 | | | | | | | | (148) ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.39 | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.39 | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 & % 26.03/4.39 | | | | | | | | aInteger0(v1) = 0 & $i(v1))) | ( ~ (all_100_0 = 0) % 26.03/4.39 | | | | | | | | & ! [v0: $i] : ( ~ (aElementOf0(v0, xS) = 0) | ~ % 26.03/4.39 | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.03/4.39 | | | | | | | | aElementOf0(all_45_1, v0) = v1))) % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | BETA: splitting (148) gives: % 26.03/4.39 | | | | | | | | % 26.03/4.39 | | | | | | | | Case 1: % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | (149) ? [v0: $i] : ( ~ (v0 = sz00) & isPrime0(v0) = 0 & % 26.03/4.39 | | | | | | | | | aDivisorOf0(v0, all_45_1) = 0 & aInteger0(v0) = 0 & % 26.03/4.39 | | | | | | | | | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = all_45_1 % 26.03/4.39 | | | | | | | | | & aInteger0(v1) = 0 & $i(v1))) % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | DELTA: instantiating (149) with fresh symbol all_268_0 gives: % 26.03/4.39 | | | | | | | | | (150) ~ (all_268_0 = sz00) & isPrime0(all_268_0) = 0 & % 26.03/4.39 | | | | | | | | | aDivisorOf0(all_268_0, all_45_1) = 0 & % 26.03/4.39 | | | | | | | | | aInteger0(all_268_0) = 0 & $i(all_268_0) & ? [v0: % 26.03/4.39 | | | | | | | | | $i] : (sdtasdt0(all_268_0, v0) = all_45_1 & % 26.03/4.39 | | | | | | | | | aInteger0(v0) = 0 & $i(v0)) % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | ALPHA: (150) implies: % 26.03/4.39 | | | | | | | | | (151) $i(all_268_0) % 26.03/4.39 | | | | | | | | | (152) aDivisorOf0(all_268_0, all_45_1) = 0 % 26.03/4.39 | | | | | | | | | (153) isPrime0(all_268_0) = 0 % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | REDUCE: (134), (152) imply: % 26.03/4.39 | | | | | | | | | (154) aDivisorOf0(all_268_0, sz10) = 0 % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | GROUND_INST: instantiating (31) with all_268_0, simplifying % 26.03/4.39 | | | | | | | | | with (151), (153) gives: % 26.03/4.39 | | | | | | | | | (155) ? [v0: int] : ( ~ (v0 = 0) & aDivisorOf0(all_268_0, % 26.03/4.39 | | | | | | | | | sz10) = v0) % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | DELTA: instantiating (155) with fresh symbol all_282_0 gives: % 26.03/4.39 | | | | | | | | | (156) ~ (all_282_0 = 0) & aDivisorOf0(all_268_0, sz10) = % 26.03/4.39 | | | | | | | | | all_282_0 % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | ALPHA: (156) implies: % 26.03/4.39 | | | | | | | | | (157) ~ (all_282_0 = 0) % 26.03/4.39 | | | | | | | | | (158) aDivisorOf0(all_268_0, sz10) = all_282_0 % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_282_0, sz10, % 26.03/4.39 | | | | | | | | | all_268_0, simplifying with (154), (158) gives: % 26.03/4.39 | | | | | | | | | (159) all_282_0 = 0 % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | REDUCE: (157), (159) imply: % 26.03/4.39 | | | | | | | | | (160) $false % 26.03/4.39 | | | | | | | | | % 26.03/4.39 | | | | | | | | | CLOSE: (160) is inconsistent. % 26.03/4.39 | | | | | | | | | % 26.03/4.40 | | | | | | | | Case 2: % 26.03/4.40 | | | | | | | | | % 26.03/4.40 | | | | | | | | | (161) ~ (all_100_0 = 0) & ! [v0: $i] : ( ~ % 26.03/4.40 | | | | | | | | | (aElementOf0(v0, xS) = 0) | ~ $i(v0) | ? [v1: % 26.03/4.40 | | | | | | | | | int] : ( ~ (v1 = 0) & aElementOf0(all_45_1, v0) = % 26.03/4.40 | | | | | | | | | v1)) % 26.03/4.40 | | | | | | | | | % 26.03/4.40 | | | | | | | | | ALPHA: (161) implies: % 26.03/4.40 | | | | | | | | | (162) ~ (all_100_0 = 0) % 26.03/4.40 | | | | | | | | | % 26.03/4.40 | | | | | | | | | REDUCE: (139), (162) imply: % 26.03/4.40 | | | | | | | | | (163) $false % 26.03/4.40 | | | | | | | | | % 26.03/4.40 | | | | | | | | | CLOSE: (163) is inconsistent. % 26.03/4.40 | | | | | | | | | % 26.03/4.40 | | | | | | | | End of split % 26.03/4.40 | | | | | | | | % 26.03/4.40 | | | | | | | End of split % 26.03/4.40 | | | | | | | % 26.03/4.40 | | | | | | End of split % 26.03/4.40 | | | | | | % 26.03/4.40 | | | | | End of split % 26.03/4.40 | | | | | % 26.03/4.40 | | | | End of split % 26.03/4.40 | | | | % 26.03/4.40 | | | End of split % 26.03/4.40 | | | % 26.03/4.40 | | Case 2: % 26.03/4.40 | | | % 26.03/4.40 | | | (164) ~ (all_39_0 = all_36_0) & ~ (all_36_0 = sz10) % 26.03/4.40 | | | % 26.03/4.40 | | | ALPHA: (164) implies: % 26.03/4.40 | | | (165) ~ (all_39_0 = all_36_0) % 26.03/4.40 | | | % 26.03/4.40 | | | REDUCE: (29), (165) imply: % 26.03/4.40 | | | (166) $false % 26.03/4.40 | | | % 26.03/4.40 | | | CLOSE: (166) is inconsistent. % 26.03/4.40 | | | % 26.03/4.40 | | End of split % 26.03/4.40 | | % 26.03/4.40 | End of split % 26.03/4.40 | % 26.03/4.40 End of proof % 26.03/4.40 % SZS output end Proof for theBenchmark % 26.03/4.40 % 26.03/4.40 3774ms %------------------------------------------------------------------------------