TSTP Solution File: NUM448+5 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------