TSTP Solution File: RNG125+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 13:58:01 EDT 2023
% Result : Theorem 18.47s 3.25s
% Output : Proof 25.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 01:44:56 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.59/0.60 ________ _____
% 0.59/0.60 ___ __ \_________(_)________________________________
% 0.59/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.60 (2023-06-19)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2023
% 0.59/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.60 Amanda Stjerna.
% 0.59/0.60 Free software under BSD-3-Clause.
% 0.59/0.60
% 0.59/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.61 Running up to 7 provers in parallel.
% 0.63/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.63/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.63/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.63/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.63/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.63/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.63/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.58/1.25 Prover 1: Preprocessing ...
% 3.58/1.25 Prover 4: Preprocessing ...
% 3.58/1.29 Prover 6: Preprocessing ...
% 3.58/1.29 Prover 5: Preprocessing ...
% 3.58/1.30 Prover 2: Preprocessing ...
% 3.58/1.30 Prover 0: Preprocessing ...
% 3.58/1.30 Prover 3: Preprocessing ...
% 11.51/2.38 Prover 1: Constructing countermodel ...
% 12.22/2.39 Prover 3: Constructing countermodel ...
% 12.22/2.39 Prover 5: Proving ...
% 12.47/2.43 Prover 6: Proving ...
% 13.17/2.55 Prover 2: Proving ...
% 13.80/2.61 Prover 4: Constructing countermodel ...
% 13.80/2.62 Prover 0: Proving ...
% 18.47/3.24 Prover 3: proved (2617ms)
% 18.47/3.24
% 18.47/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.47/3.25
% 18.47/3.25 Prover 6: stopped
% 18.47/3.25 Prover 0: stopped
% 18.47/3.26 Prover 5: stopped
% 18.47/3.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.47/3.26 Prover 2: stopped
% 18.47/3.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.47/3.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.47/3.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.47/3.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.32/3.35 Prover 7: Preprocessing ...
% 19.32/3.35 Prover 8: Preprocessing ...
% 20.08/3.41 Prover 13: Preprocessing ...
% 20.08/3.42 Prover 10: Preprocessing ...
% 20.08/3.45 Prover 11: Preprocessing ...
% 20.95/3.55 Prover 7: Constructing countermodel ...
% 21.71/3.64 Prover 8: Warning: ignoring some quantifiers
% 21.71/3.66 Prover 8: Constructing countermodel ...
% 21.71/3.69 Prover 13: Warning: ignoring some quantifiers
% 22.40/3.74 Prover 13: Constructing countermodel ...
% 22.40/3.76 Prover 10: Constructing countermodel ...
% 23.00/3.79 Prover 1: Found proof (size 139)
% 23.00/3.79 Prover 1: proved (3172ms)
% 23.00/3.79 Prover 8: stopped
% 23.00/3.80 Prover 10: stopped
% 23.00/3.80 Prover 13: stopped
% 23.00/3.80 Prover 4: stopped
% 23.00/3.80 Prover 7: stopped
% 23.95/4.01 Prover 11: Constructing countermodel ...
% 23.95/4.03 Prover 11: stopped
% 23.95/4.03
% 23.95/4.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.95/4.03
% 23.95/4.07 % SZS output start Proof for theBenchmark
% 23.95/4.07 Assumptions after simplification:
% 23.95/4.07 ---------------------------------
% 23.95/4.07
% 23.95/4.07 (mAddComm)
% 24.36/4.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 24.36/4.11 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 24.36/4.11 (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 24.36/4.11 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 24.36/4.11
% 24.36/4.12 (mDefDvs)
% 24.36/4.12 ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2:
% 24.36/4.12 any] : ( ~ (doDivides0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ?
% 24.36/4.12 [v4: any] : (aDivisorOf0(v1, v0) = v3 & aElement0(v1) = v4 & ( ~ (v3 =
% 24.36/4.12 0) | (v4 = 0 & v2 = 0)))) & ! [v1: $i] : ( ~ (doDivides0(v1, v0)
% 24.36/4.12 = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v1, v0)
% 24.36/4.12 = v3 & aElement0(v1) = v2 & ( ~ (v2 = 0) | v3 = 0)))))
% 24.36/4.12
% 24.36/4.12 (mEucSort)
% 24.36/4.12 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) |
% 24.36/4.12 ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 24.36/4.12 aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.36/4.12
% 24.36/4.12 (mMulComm)
% 24.36/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 24.36/4.12 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 24.36/4.12 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 24.36/4.12 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 24.36/4.12
% 24.36/4.12 (mSortsB)
% 24.36/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 24.36/4.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.36/4.13 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 24.36/4.13 | ~ (v3 = 0) | v5 = 0)))
% 24.36/4.13
% 24.36/4.13 (mSortsB_02)
% 24.36/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 24.36/4.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.36/4.13 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 24.36/4.13 | ~ (v3 = 0) | v5 = 0)))
% 24.36/4.13
% 24.36/4.13 (m__2091)
% 24.36/4.13 aElement0(xb) = 0 & aElement0(xa) = 0 & $i(xb) & $i(xa)
% 24.36/4.13
% 24.36/4.13 (m__2273)
% 24.36/4.13 $i(xu) & $i(xI) & $i(sz00) & ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0
% 24.36/4.13 & aElementOf0(xu, xI) = 0 & $i(v0) & ! [v1: $i] : (v1 = sz00 | ~
% 24.36/4.13 (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~
% 24.36/4.13 (v3 = 0) & iLess0(v2, v0) = v3 & sbrdtbr0(v1) = v2 & $i(v2))))
% 24.36/4.13
% 24.36/4.13 (m__2383)
% 24.36/4.13 $i(xu) & $i(xb) & $i(xa) & ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb)
% 24.36/4.13 = v1 & aDivisorOf0(xu, xa) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.36/4.13
% 24.36/4.13 (m__2416)
% 24.36/4.13 $i(xu) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 24.36/4.13 $i] : (sdtasdt0(xb, v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu
% 24.36/4.13 & aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 24.36/4.13
% 24.36/4.13 (m__2479)
% 24.36/4.13 doDivides0(xu, xa) = 0 & $i(xu) & $i(xa)
% 24.36/4.13
% 24.36/4.13 (m__2612)
% 24.36/4.13 doDivides0(xu, xb) = 0 & $i(xu) & $i(xb)
% 24.36/4.13
% 24.36/4.13 (function-axioms)
% 24.36/4.14 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 24.36/4.14 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~
% 24.36/4.14 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.36/4.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 24.36/4.14 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3,
% 24.36/4.14 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 24.36/4.14 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) |
% 24.36/4.14 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.36/4.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.36/4.14 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0:
% 24.36/4.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.36/4.14 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 24.36/4.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.36/4.14 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 24.36/4.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.36/4.14 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.36/4.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 24.36/4.14 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.36/4.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.36/4.14 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] :
% 24.36/4.14 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 24.36/4.14 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.36/4.14 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 24.36/4.14 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1)
% 24.36/4.14 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 24.36/4.14 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0:
% 24.36/4.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 24.36/4.14 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0:
% 24.36/4.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 24.36/4.14 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] :
% 24.36/4.14 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 24.36/4.14 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.36/4.14 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 24.36/4.14 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 24.36/4.14 ~ (aElement0(v2) = v0))
% 24.36/4.14
% 24.36/4.14 Further assumptions not needed in the proof:
% 24.36/4.14 --------------------------------------------
% 24.36/4.14 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv,
% 24.36/4.14 mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, mDefSSum,
% 24.36/4.14 mDivision, mEOfElem, mElmSort, mIdeInt, mIdeSum, mMulAsso, mMulMnOne, mMulUnit,
% 24.36/4.14 mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsC, mSortsC_01,
% 24.36/4.14 mSortsU, mUnNeZr, m__, m__2110, m__2129, m__2174, m__2203, m__2228
% 24.36/4.14
% 24.36/4.14 Those formulas are unsatisfiable:
% 24.36/4.14 ---------------------------------
% 24.36/4.14
% 24.36/4.14 Begin of proof
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (mEucSort) implies:
% 24.36/4.15 | (1) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 24.36/4.15 | $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 24.36/4.15 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2091) implies:
% 24.36/4.15 | (2) aElement0(xa) = 0
% 24.36/4.15 | (3) aElement0(xb) = 0
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2273) implies:
% 24.36/4.15 | (4) ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & aElementOf0(xu, xI)
% 24.36/4.15 | = 0 & $i(v0) & ! [v1: $i] : (v1 = sz00 | ~ (aElementOf0(v1, xI) =
% 24.36/4.15 | 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 24.36/4.15 | iLess0(v2, v0) = v3 & sbrdtbr0(v1) = v2 & $i(v2))))
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2383) implies:
% 24.36/4.15 | (5) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb) = v1 &
% 24.36/4.15 | aDivisorOf0(xu, xa) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2416) implies:
% 24.36/4.15 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xb,
% 24.36/4.15 | v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu &
% 24.36/4.15 | aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 24.36/4.15 | $i(v0))
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2479) implies:
% 24.36/4.15 | (7) $i(xa)
% 24.36/4.15 | (8) doDivides0(xu, xa) = 0
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (m__2612) implies:
% 24.36/4.15 | (9) $i(xb)
% 24.36/4.15 | (10) $i(xu)
% 24.36/4.15 | (11) doDivides0(xu, xb) = 0
% 24.36/4.15 |
% 24.36/4.15 | ALPHA: (function-axioms) implies:
% 24.36/4.16 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.36/4.16 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 24.36/4.16 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.36/4.16 | : ! [v3: $i] : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~
% 24.36/4.16 | (aDivisorOf0(v3, v2) = v0))
% 24.36/4.16 |
% 24.36/4.16 | DELTA: instantiating (5) with fresh symbols all_34_0, all_34_1 gives:
% 24.36/4.16 | (14) aDivisorOf0(xu, xb) = all_34_0 & aDivisorOf0(xu, xa) = all_34_1 & ( ~
% 24.36/4.16 | (all_34_0 = 0) | ~ (all_34_1 = 0))
% 24.36/4.16 |
% 24.36/4.16 | ALPHA: (14) implies:
% 24.36/4.16 | (15) aDivisorOf0(xu, xa) = all_34_1
% 24.36/4.16 | (16) aDivisorOf0(xu, xb) = all_34_0
% 24.36/4.16 | (17) ~ (all_34_0 = 0) | ~ (all_34_1 = 0)
% 24.36/4.16 |
% 24.36/4.16 | DELTA: instantiating (6) with fresh symbols all_40_0, all_40_1, all_40_2,
% 24.36/4.16 | all_40_3 gives:
% 24.36/4.16 | (18) sdtasdt0(xb, all_40_2) = all_40_0 & sdtasdt0(xa, all_40_3) = all_40_1
% 24.36/4.16 | & sdtpldt0(all_40_1, all_40_0) = xu & aElement0(all_40_2) = 0 &
% 24.36/4.16 | aElement0(all_40_3) = 0 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) &
% 24.36/4.16 | $i(all_40_3)
% 24.36/4.16 |
% 24.36/4.16 | ALPHA: (18) implies:
% 24.36/4.16 | (19) $i(all_40_3)
% 24.36/4.16 | (20) $i(all_40_2)
% 24.36/4.16 | (21) $i(all_40_1)
% 24.36/4.16 | (22) $i(all_40_0)
% 24.36/4.16 | (23) aElement0(all_40_3) = 0
% 24.36/4.16 | (24) aElement0(all_40_2) = 0
% 24.36/4.16 | (25) sdtpldt0(all_40_1, all_40_0) = xu
% 24.36/4.16 | (26) sdtasdt0(xa, all_40_3) = all_40_1
% 24.36/4.16 | (27) sdtasdt0(xb, all_40_2) = all_40_0
% 24.36/4.16 |
% 24.36/4.16 | DELTA: instantiating (4) with fresh symbol all_44_0 gives:
% 24.36/4.16 | (28) ~ (xu = sz00) & sbrdtbr0(xu) = all_44_0 & aElementOf0(xu, xI) = 0 &
% 24.36/4.16 | $i(all_44_0) & ! [v0: $i] : (v0 = sz00 | ~ (aElementOf0(v0, xI) = 0)
% 24.36/4.16 | | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & iLess0(v1,
% 24.36/4.16 | all_44_0) = v2 & sbrdtbr0(v0) = v1 & $i(v1)))
% 24.36/4.16 |
% 24.36/4.16 | ALPHA: (28) implies:
% 24.36/4.16 | (29) ~ (xu = sz00)
% 24.36/4.16 | (30) sbrdtbr0(xu) = all_44_0
% 24.36/4.16 |
% 24.36/4.17 | GROUND_INST: instantiating (mDefDvs) with xa, simplifying with (2), (7) gives:
% 24.36/4.17 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~ $i(v0)
% 24.36/4.17 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xa) = v2 &
% 24.36/4.17 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 24.36/4.17 | $i] : ( ~ (doDivides0(v0, xa) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.36/4.17 | [v2: any] : (aDivisorOf0(v0, xa) = v2 & aElement0(v0) = v1 & ( ~ (v1
% 24.36/4.17 | = 0) | v2 = 0)))
% 24.36/4.17 |
% 24.36/4.17 | ALPHA: (31) implies:
% 24.36/4.17 | (32) ! [v0: $i] : ( ~ (doDivides0(v0, xa) = 0) | ~ $i(v0) | ? [v1: any]
% 24.36/4.17 | : ? [v2: any] : (aDivisorOf0(v0, xa) = v2 & aElement0(v0) = v1 & (
% 24.36/4.17 | ~ (v1 = 0) | v2 = 0)))
% 24.36/4.17 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~ $i(v0)
% 24.36/4.17 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xa) = v2 &
% 24.36/4.17 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 24.36/4.17 |
% 24.36/4.17 | GROUND_INST: instantiating (mDefDvs) with xb, simplifying with (3), (9) gives:
% 24.36/4.17 | (34) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xb) = v1) | ~ $i(v0)
% 24.36/4.17 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xb) = v2 &
% 24.36/4.17 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 24.36/4.17 | $i] : ( ~ (doDivides0(v0, xb) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.36/4.17 | [v2: any] : (aDivisorOf0(v0, xb) = v2 & aElement0(v0) = v1 & ( ~ (v1
% 24.36/4.17 | = 0) | v2 = 0)))
% 24.36/4.17 |
% 24.36/4.17 | ALPHA: (34) implies:
% 24.36/4.17 | (35) ! [v0: $i] : ( ~ (doDivides0(v0, xb) = 0) | ~ $i(v0) | ? [v1: any]
% 24.36/4.17 | : ? [v2: any] : (aDivisorOf0(v0, xb) = v2 & aElement0(v0) = v1 & (
% 24.36/4.17 | ~ (v1 = 0) | v2 = 0)))
% 24.36/4.17 | (36) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xb) = v1) | ~ $i(v0)
% 24.36/4.17 | | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v0, xb) = v2 &
% 24.36/4.17 | aElement0(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 24.36/4.17 |
% 24.36/4.17 | GROUND_INST: instantiating (mAddComm) with all_40_1, all_40_0, xu, simplifying
% 24.36/4.18 | with (21), (22), (25) gives:
% 24.36/4.18 | (37) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_40_0,
% 24.36/4.18 | all_40_1) = v2 & aElement0(all_40_0) = v1 & aElement0(all_40_1) =
% 24.36/4.18 | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xu))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (mSortsB) with all_40_1, all_40_0, xu, simplifying
% 24.36/4.18 | with (21), (22), (25) gives:
% 24.36/4.18 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_40_0) = v1
% 24.36/4.18 | & aElement0(all_40_1) = v0 & aElement0(xu) = v2 & ( ~ (v1 = 0) | ~
% 24.36/4.18 | (v0 = 0) | v2 = 0))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (mMulComm) with xa, all_40_3, all_40_1, simplifying
% 24.36/4.18 | with (7), (19), (26) gives:
% 24.36/4.18 | (39) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_40_3, xa) =
% 24.36/4.18 | v2 & aElement0(all_40_3) = v1 & aElement0(xa) = v0 & $i(v2) & ( ~
% 24.36/4.18 | (v1 = 0) | ~ (v0 = 0) | v2 = all_40_1))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (mSortsB_02) with xa, all_40_3, all_40_1,
% 24.36/4.18 | simplifying with (7), (19), (26) gives:
% 24.36/4.18 | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_40_1) = v2
% 24.36/4.18 | & aElement0(all_40_3) = v1 & aElement0(xa) = v0 & ( ~ (v1 = 0) | ~
% 24.36/4.18 | (v0 = 0) | v2 = 0))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (mMulComm) with xb, all_40_2, all_40_0, simplifying
% 24.36/4.18 | with (9), (20), (27) gives:
% 24.36/4.18 | (41) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_40_2, xb) =
% 24.36/4.18 | v2 & aElement0(all_40_2) = v1 & aElement0(xb) = v0 & $i(v2) & ( ~
% 24.36/4.18 | (v1 = 0) | ~ (v0 = 0) | v2 = all_40_0))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (mSortsB_02) with xb, all_40_2, all_40_0,
% 24.36/4.18 | simplifying with (9), (20), (27) gives:
% 24.36/4.18 | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_40_0) = v2
% 24.36/4.18 | & aElement0(all_40_2) = v1 & aElement0(xb) = v0 & ( ~ (v1 = 0) | ~
% 24.36/4.18 | (v0 = 0) | v2 = 0))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (1) with xu, all_44_0, simplifying with (10), (30)
% 24.36/4.18 | gives:
% 24.36/4.18 | (43) xu = sz00 | ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_44_0) =
% 24.36/4.18 | v1 & aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.36/4.18 |
% 24.36/4.18 | GROUND_INST: instantiating (35) with xu, simplifying with (10), (11) gives:
% 24.36/4.18 | (44) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb) = v1 &
% 24.36/4.19 | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.36/4.19 |
% 24.36/4.19 | GROUND_INST: instantiating (36) with xu, 0, simplifying with (10), (11) gives:
% 24.36/4.19 | (45) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb) = v0 &
% 24.36/4.19 | aElement0(xu) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 24.36/4.19 |
% 24.36/4.19 | GROUND_INST: instantiating (32) with xu, simplifying with (8), (10) gives:
% 24.36/4.19 | (46) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v1 &
% 24.36/4.19 | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.36/4.19 |
% 24.36/4.19 | GROUND_INST: instantiating (33) with xu, 0, simplifying with (8), (10) gives:
% 24.36/4.19 | (47) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v0 &
% 24.36/4.19 | aElement0(xu) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 24.36/4.19 |
% 24.36/4.19 | DELTA: instantiating (42) with fresh symbols all_121_0, all_121_1, all_121_2
% 24.36/4.19 | gives:
% 24.36/4.19 | (48) aElement0(all_40_0) = all_121_0 & aElement0(all_40_2) = all_121_1 &
% 24.36/4.19 | aElement0(xb) = all_121_2 & ( ~ (all_121_1 = 0) | ~ (all_121_2 = 0) |
% 24.36/4.19 | all_121_0 = 0)
% 24.36/4.19 |
% 24.36/4.19 | ALPHA: (48) implies:
% 24.36/4.19 | (49) aElement0(xb) = all_121_2
% 24.36/4.19 | (50) aElement0(all_40_2) = all_121_1
% 24.36/4.19 | (51) aElement0(all_40_0) = all_121_0
% 24.36/4.19 | (52) ~ (all_121_1 = 0) | ~ (all_121_2 = 0) | all_121_0 = 0
% 24.36/4.19 |
% 24.36/4.19 | DELTA: instantiating (40) with fresh symbols all_123_0, all_123_1, all_123_2
% 24.36/4.19 | gives:
% 24.36/4.19 | (53) aElement0(all_40_1) = all_123_0 & aElement0(all_40_3) = all_123_1 &
% 24.36/4.19 | aElement0(xa) = all_123_2 & ( ~ (all_123_1 = 0) | ~ (all_123_2 = 0) |
% 24.36/4.19 | all_123_0 = 0)
% 24.36/4.19 |
% 24.36/4.19 | ALPHA: (53) implies:
% 24.36/4.19 | (54) aElement0(xa) = all_123_2
% 24.36/4.19 | (55) aElement0(all_40_3) = all_123_1
% 24.36/4.19 | (56) aElement0(all_40_1) = all_123_0
% 24.36/4.19 | (57) ~ (all_123_1 = 0) | ~ (all_123_2 = 0) | all_123_0 = 0
% 24.36/4.19 |
% 24.36/4.19 | DELTA: instantiating (38) with fresh symbols all_125_0, all_125_1, all_125_2
% 24.36/4.19 | gives:
% 24.36/4.19 | (58) aElement0(all_40_0) = all_125_1 & aElement0(all_40_1) = all_125_2 &
% 24.36/4.19 | aElement0(xu) = all_125_0 & ( ~ (all_125_1 = 0) | ~ (all_125_2 = 0) |
% 24.36/4.19 | all_125_0 = 0)
% 24.36/4.19 |
% 24.36/4.19 | ALPHA: (58) implies:
% 24.36/4.19 | (59) aElement0(xu) = all_125_0
% 24.36/4.19 | (60) aElement0(all_40_1) = all_125_2
% 24.36/4.19 | (61) aElement0(all_40_0) = all_125_1
% 24.36/4.19 | (62) ~ (all_125_1 = 0) | ~ (all_125_2 = 0) | all_125_0 = 0
% 24.36/4.19 |
% 24.36/4.19 | DELTA: instantiating (41) with fresh symbols all_127_0, all_127_1, all_127_2
% 24.36/4.19 | gives:
% 24.36/4.19 | (63) sdtasdt0(all_40_2, xb) = all_127_0 & aElement0(all_40_2) = all_127_1 &
% 24.36/4.19 | aElement0(xb) = all_127_2 & $i(all_127_0) & ( ~ (all_127_1 = 0) | ~
% 24.36/4.19 | (all_127_2 = 0) | all_127_0 = all_40_0)
% 24.36/4.19 |
% 24.36/4.19 | ALPHA: (63) implies:
% 24.36/4.19 | (64) aElement0(xb) = all_127_2
% 24.36/4.19 | (65) aElement0(all_40_2) = all_127_1
% 24.36/4.19 |
% 24.36/4.19 | DELTA: instantiating (37) with fresh symbols all_129_0, all_129_1, all_129_2
% 24.36/4.19 | gives:
% 24.36/4.20 | (66) sdtpldt0(all_40_0, all_40_1) = all_129_0 & aElement0(all_40_0) =
% 24.36/4.20 | all_129_1 & aElement0(all_40_1) = all_129_2 & $i(all_129_0) & ( ~
% 24.36/4.20 | (all_129_1 = 0) | ~ (all_129_2 = 0) | all_129_0 = xu)
% 24.36/4.20 |
% 24.36/4.20 | ALPHA: (66) implies:
% 24.36/4.20 | (67) aElement0(all_40_1) = all_129_2
% 24.36/4.20 | (68) aElement0(all_40_0) = all_129_1
% 24.36/4.20 |
% 24.36/4.20 | DELTA: instantiating (39) with fresh symbols all_131_0, all_131_1, all_131_2
% 24.36/4.20 | gives:
% 24.90/4.20 | (69) sdtasdt0(all_40_3, xa) = all_131_0 & aElement0(all_40_3) = all_131_1 &
% 24.90/4.20 | aElement0(xa) = all_131_2 & $i(all_131_0) & ( ~ (all_131_1 = 0) | ~
% 24.90/4.20 | (all_131_2 = 0) | all_131_0 = all_40_1)
% 24.90/4.20 |
% 24.90/4.20 | ALPHA: (69) implies:
% 24.90/4.20 | (70) aElement0(xa) = all_131_2
% 24.90/4.20 | (71) aElement0(all_40_3) = all_131_1
% 24.90/4.20 |
% 24.90/4.20 | DELTA: instantiating (45) with fresh symbols all_133_0, all_133_1 gives:
% 24.90/4.20 | (72) aDivisorOf0(xu, xb) = all_133_1 & aElement0(xu) = all_133_0 & ( ~
% 24.90/4.20 | (all_133_1 = 0) | all_133_0 = 0)
% 24.90/4.20 |
% 24.90/4.20 | ALPHA: (72) implies:
% 24.90/4.20 | (73) aElement0(xu) = all_133_0
% 24.90/4.20 |
% 24.90/4.20 | DELTA: instantiating (44) with fresh symbols all_135_0, all_135_1 gives:
% 24.90/4.20 | (74) aDivisorOf0(xu, xb) = all_135_0 & aElement0(xu) = all_135_1 & ( ~
% 24.90/4.20 | (all_135_1 = 0) | all_135_0 = 0)
% 24.90/4.20 |
% 24.90/4.20 | ALPHA: (74) implies:
% 24.90/4.20 | (75) aElement0(xu) = all_135_1
% 24.90/4.20 | (76) aDivisorOf0(xu, xb) = all_135_0
% 24.90/4.20 | (77) ~ (all_135_1 = 0) | all_135_0 = 0
% 24.90/4.20 |
% 24.90/4.20 | DELTA: instantiating (47) with fresh symbols all_137_0, all_137_1 gives:
% 24.90/4.20 | (78) aDivisorOf0(xu, xa) = all_137_1 & aElement0(xu) = all_137_0 & ( ~
% 24.90/4.20 | (all_137_1 = 0) | all_137_0 = 0)
% 24.90/4.20 |
% 24.90/4.20 | ALPHA: (78) implies:
% 24.90/4.20 | (79) aElement0(xu) = all_137_0
% 24.90/4.20 | (80) aDivisorOf0(xu, xa) = all_137_1
% 24.90/4.20 |
% 24.90/4.20 | DELTA: instantiating (46) with fresh symbols all_139_0, all_139_1 gives:
% 24.90/4.20 | (81) aDivisorOf0(xu, xa) = all_139_0 & aElement0(xu) = all_139_1 & ( ~
% 24.90/4.20 | (all_139_1 = 0) | all_139_0 = 0)
% 24.90/4.20 |
% 24.90/4.20 | ALPHA: (81) implies:
% 24.90/4.20 | (82) aElement0(xu) = all_139_1
% 24.90/4.20 | (83) aDivisorOf0(xu, xa) = all_139_0
% 24.90/4.20 | (84) ~ (all_139_1 = 0) | all_139_0 = 0
% 24.90/4.20 |
% 24.90/4.20 | BETA: splitting (43) gives:
% 24.90/4.20 |
% 24.90/4.20 | Case 1:
% 24.90/4.20 | |
% 24.90/4.20 | | (85) xu = sz00
% 24.90/4.20 | |
% 24.90/4.20 | | REDUCE: (29), (85) imply:
% 24.90/4.20 | | (86) $false
% 24.90/4.20 | |
% 24.90/4.20 | | CLOSE: (86) is inconsistent.
% 24.90/4.20 | |
% 24.90/4.20 | Case 2:
% 24.90/4.20 | |
% 24.90/4.21 | | (87) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_44_0) = v1 &
% 24.90/4.21 | | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.90/4.21 | |
% 24.90/4.21 | | DELTA: instantiating (87) with fresh symbols all_150_0, all_150_1 gives:
% 24.90/4.21 | | (88) aNaturalNumber0(all_44_0) = all_150_0 & aElement0(xu) = all_150_1 &
% 24.90/4.21 | | ( ~ (all_150_1 = 0) | all_150_0 = 0)
% 24.90/4.21 | |
% 24.90/4.21 | | ALPHA: (88) implies:
% 24.90/4.21 | | (89) aElement0(xu) = all_150_1
% 24.90/4.21 | |
% 24.90/4.21 | | GROUND_INST: instantiating (12) with 0, all_131_2, xa, simplifying with (2),
% 24.90/4.21 | | (70) gives:
% 24.90/4.21 | | (90) all_131_2 = 0
% 24.90/4.21 | |
% 24.90/4.21 | | GROUND_INST: instantiating (12) with all_123_2, all_131_2, xa, simplifying
% 24.90/4.21 | | with (54), (70) gives:
% 24.90/4.21 | | (91) all_131_2 = all_123_2
% 24.90/4.21 | |
% 24.90/4.21 | | GROUND_INST: instantiating (12) with 0, all_127_2, xb, simplifying with (3),
% 24.90/4.21 | | (64) gives:
% 24.90/4.21 | | (92) all_127_2 = 0
% 24.90/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_121_2, all_127_2, xb, simplifying
% 24.98/4.21 | | with (49), (64) gives:
% 24.98/4.21 | | (93) all_127_2 = all_121_2
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_125_0, all_135_1, xu, simplifying
% 24.98/4.21 | | with (59), (75) gives:
% 24.98/4.21 | | (94) all_135_1 = all_125_0
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_139_1, all_150_1, xu, simplifying
% 24.98/4.21 | | with (82), (89) gives:
% 24.98/4.21 | | (95) all_150_1 = all_139_1
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_137_0, all_150_1, xu, simplifying
% 24.98/4.21 | | with (79), (89) gives:
% 24.98/4.21 | | (96) all_150_1 = all_137_0
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_135_1, all_150_1, xu, simplifying
% 24.98/4.21 | | with (75), (89) gives:
% 24.98/4.21 | | (97) all_150_1 = all_135_1
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_133_0, all_150_1, xu, simplifying
% 24.98/4.21 | | with (73), (89) gives:
% 24.98/4.21 | | (98) all_150_1 = all_133_0
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with 0, all_131_1, all_40_3, simplifying
% 24.98/4.21 | | with (23), (71) gives:
% 24.98/4.21 | | (99) all_131_1 = 0
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_123_1, all_131_1, all_40_3,
% 24.98/4.21 | | simplifying with (55), (71) gives:
% 24.98/4.21 | | (100) all_131_1 = all_123_1
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with 0, all_127_1, all_40_2, simplifying
% 24.98/4.21 | | with (24), (65) gives:
% 24.98/4.21 | | (101) all_127_1 = 0
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_121_1, all_127_1, all_40_2,
% 24.98/4.21 | | simplifying with (50), (65) gives:
% 24.98/4.21 | | (102) all_127_1 = all_121_1
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_125_2, all_129_2, all_40_1,
% 24.98/4.21 | | simplifying with (60), (67) gives:
% 24.98/4.21 | | (103) all_129_2 = all_125_2
% 24.98/4.21 | |
% 24.98/4.21 | | GROUND_INST: instantiating (12) with all_123_0, all_129_2, all_40_1,
% 24.98/4.21 | | simplifying with (56), (67) gives:
% 24.98/4.22 | | (104) all_129_2 = all_123_0
% 24.98/4.22 | |
% 24.98/4.22 | | GROUND_INST: instantiating (12) with all_125_1, all_129_1, all_40_0,
% 24.98/4.22 | | simplifying with (61), (68) gives:
% 24.98/4.22 | | (105) all_129_1 = all_125_1
% 24.98/4.22 | |
% 24.98/4.22 | | GROUND_INST: instantiating (12) with all_121_0, all_129_1, all_40_0,
% 24.98/4.22 | | simplifying with (51), (68) gives:
% 24.98/4.22 | | (106) all_129_1 = all_121_0
% 24.98/4.22 | |
% 24.98/4.22 | | GROUND_INST: instantiating (13) with all_34_1, all_139_0, xa, xu,
% 24.98/4.22 | | simplifying with (15), (83) gives:
% 24.98/4.22 | | (107) all_139_0 = all_34_1
% 24.98/4.22 | |
% 24.98/4.22 | | GROUND_INST: instantiating (13) with all_137_1, all_139_0, xa, xu,
% 24.98/4.22 | | simplifying with (80), (83) gives:
% 24.98/4.22 | | (108) all_139_0 = all_137_1
% 24.98/4.22 | |
% 24.98/4.22 | | GROUND_INST: instantiating (13) with all_34_0, all_135_0, xb, xu,
% 24.98/4.22 | | simplifying with (16), (76) gives:
% 24.98/4.22 | | (109) all_135_0 = all_34_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (95), (97) imply:
% 24.98/4.22 | | (110) all_139_1 = all_135_1
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (95), (96) imply:
% 24.98/4.22 | | (111) all_139_1 = all_137_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (95), (98) imply:
% 24.98/4.22 | | (112) all_139_1 = all_133_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (107), (108) imply:
% 24.98/4.22 | | (113) all_137_1 = all_34_1
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (111), (112) imply:
% 24.98/4.22 | | (114) all_137_0 = all_133_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (110), (111) imply:
% 24.98/4.22 | | (115) all_137_0 = all_135_1
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (114), (115) imply:
% 24.98/4.22 | | (116) all_135_1 = all_133_0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (116) implies:
% 24.98/4.22 | | (117) all_135_1 = all_133_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (94), (117) imply:
% 24.98/4.22 | | (118) all_133_0 = all_125_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (99), (100) imply:
% 24.98/4.22 | | (119) all_123_1 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (119) implies:
% 24.98/4.22 | | (120) all_123_1 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (90), (91) imply:
% 24.98/4.22 | | (121) all_123_2 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (121) implies:
% 24.98/4.22 | | (122) all_123_2 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (105), (106) imply:
% 24.98/4.22 | | (123) all_125_1 = all_121_0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (123) implies:
% 24.98/4.22 | | (124) all_125_1 = all_121_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (103), (104) imply:
% 24.98/4.22 | | (125) all_125_2 = all_123_0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (125) implies:
% 24.98/4.22 | | (126) all_125_2 = all_123_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (101), (102) imply:
% 24.98/4.22 | | (127) all_121_1 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (92), (93) imply:
% 24.98/4.22 | | (128) all_121_2 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | SIMP: (128) implies:
% 24.98/4.22 | | (129) all_121_2 = 0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (114), (118) imply:
% 24.98/4.22 | | (130) all_137_0 = all_125_0
% 24.98/4.22 | |
% 24.98/4.22 | | COMBINE_EQS: (111), (130) imply:
% 24.98/4.22 | | (131) all_139_1 = all_125_0
% 24.98/4.22 | |
% 24.98/4.22 | | BETA: splitting (52) gives:
% 24.98/4.22 | |
% 24.98/4.22 | | Case 1:
% 24.98/4.22 | | |
% 24.98/4.22 | | | (132) ~ (all_121_1 = 0)
% 24.98/4.22 | | |
% 24.98/4.22 | | | REDUCE: (127), (132) imply:
% 24.98/4.22 | | | (133) $false
% 24.98/4.22 | | |
% 24.98/4.22 | | | CLOSE: (133) is inconsistent.
% 24.98/4.22 | | |
% 24.98/4.22 | | Case 2:
% 24.98/4.22 | | |
% 24.98/4.22 | | | (134) ~ (all_121_2 = 0) | all_121_0 = 0
% 24.98/4.22 | | |
% 24.98/4.22 | | | BETA: splitting (57) gives:
% 24.98/4.22 | | |
% 24.98/4.22 | | | Case 1:
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | (135) ~ (all_123_1 = 0)
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | REDUCE: (120), (135) imply:
% 24.98/4.22 | | | | (136) $false
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | CLOSE: (136) is inconsistent.
% 24.98/4.22 | | | |
% 24.98/4.22 | | | Case 2:
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | (137) ~ (all_123_2 = 0) | all_123_0 = 0
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | BETA: splitting (134) gives:
% 24.98/4.22 | | | |
% 24.98/4.22 | | | | Case 1:
% 24.98/4.22 | | | | |
% 24.98/4.22 | | | | | (138) ~ (all_121_2 = 0)
% 25.05/4.22 | | | | |
% 25.05/4.22 | | | | | REDUCE: (129), (138) imply:
% 25.05/4.22 | | | | | (139) $false
% 25.05/4.22 | | | | |
% 25.05/4.23 | | | | | CLOSE: (139) is inconsistent.
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | Case 2:
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | | (140) all_121_0 = 0
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | | COMBINE_EQS: (124), (140) imply:
% 25.05/4.23 | | | | | (141) all_125_1 = 0
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | | BETA: splitting (137) gives:
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | | Case 1:
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | (142) ~ (all_123_2 = 0)
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | REDUCE: (122), (142) imply:
% 25.05/4.23 | | | | | | (143) $false
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | CLOSE: (143) is inconsistent.
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | Case 2:
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | (144) all_123_0 = 0
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | COMBINE_EQS: (126), (144) imply:
% 25.05/4.23 | | | | | | (145) all_125_2 = 0
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | BETA: splitting (62) gives:
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | | Case 1:
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | (146) ~ (all_125_1 = 0)
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | REDUCE: (141), (146) imply:
% 25.05/4.23 | | | | | | | (147) $false
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | CLOSE: (147) is inconsistent.
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | Case 2:
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | (148) ~ (all_125_2 = 0) | all_125_0 = 0
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | BETA: splitting (148) gives:
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | | Case 1:
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | (149) ~ (all_125_2 = 0)
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | REDUCE: (145), (149) imply:
% 25.05/4.23 | | | | | | | | (150) $false
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | CLOSE: (150) is inconsistent.
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | Case 2:
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | (151) all_125_0 = 0
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | COMBINE_EQS: (94), (151) imply:
% 25.05/4.23 | | | | | | | | (152) all_135_1 = 0
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | COMBINE_EQS: (131), (151) imply:
% 25.05/4.23 | | | | | | | | (153) all_139_1 = 0
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | BETA: splitting (77) gives:
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | | Case 1:
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | (154) ~ (all_135_1 = 0)
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | REDUCE: (152), (154) imply:
% 25.05/4.23 | | | | | | | | | (155) $false
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | CLOSE: (155) is inconsistent.
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | Case 2:
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | (156) all_135_0 = 0
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | COMBINE_EQS: (109), (156) imply:
% 25.05/4.23 | | | | | | | | | (157) all_34_0 = 0
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | BETA: splitting (17) gives:
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | | Case 1:
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | (158) ~ (all_34_0 = 0)
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | REDUCE: (157), (158) imply:
% 25.05/4.23 | | | | | | | | | | (159) $false
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | CLOSE: (159) is inconsistent.
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | Case 2:
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | (160) ~ (all_34_1 = 0)
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | BETA: splitting (84) gives:
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | Case 1:
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | (161) ~ (all_139_1 = 0)
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | REDUCE: (153), (161) imply:
% 25.05/4.23 | | | | | | | | | | | (162) $false
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | Case 2:
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | (163) all_139_0 = 0
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | COMBINE_EQS: (107), (163) imply:
% 25.05/4.23 | | | | | | | | | | | (164) all_34_1 = 0
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | REDUCE: (160), (164) imply:
% 25.05/4.23 | | | | | | | | | | | (165) $false
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 25.05/4.23 | | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | | End of split
% 25.05/4.23 | | | | | | | | | |
% 25.05/4.23 | | | | | | | | | End of split
% 25.05/4.23 | | | | | | | | |
% 25.05/4.23 | | | | | | | | End of split
% 25.05/4.23 | | | | | | | |
% 25.05/4.23 | | | | | | | End of split
% 25.05/4.23 | | | | | | |
% 25.05/4.23 | | | | | | End of split
% 25.05/4.23 | | | | | |
% 25.05/4.23 | | | | | End of split
% 25.05/4.23 | | | | |
% 25.05/4.23 | | | | End of split
% 25.05/4.23 | | | |
% 25.05/4.23 | | | End of split
% 25.05/4.23 | | |
% 25.05/4.23 | | End of split
% 25.05/4.23 | |
% 25.05/4.23 | End of split
% 25.05/4.23 |
% 25.05/4.23 End of proof
% 25.05/4.23 % SZS output end Proof for theBenchmark
% 25.05/4.23
% 25.05/4.23 3632ms
%------------------------------------------------------------------------------