TSTP Solution File: RNG123+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG123+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 : n009.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 16.77s 2.91s
% Output : Proof 20.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 02:14:05 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.54/0.62 ________ _____
% 0.54/0.62 ___ __ \_________(_)________________________________
% 0.54/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.62
% 0.54/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.62 (2023-06-19)
% 0.54/0.62
% 0.54/0.62 (c) Philipp Rümmer, 2009-2023
% 0.54/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.62 Amanda Stjerna.
% 0.54/0.62 Free software under BSD-3-Clause.
% 0.54/0.62
% 0.54/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.62
% 0.54/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.64 Running up to 7 provers in parallel.
% 0.67/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.67/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.54/1.15 Prover 1: Preprocessing ...
% 3.54/1.15 Prover 4: Preprocessing ...
% 3.74/1.19 Prover 2: Preprocessing ...
% 3.74/1.19 Prover 0: Preprocessing ...
% 3.74/1.19 Prover 6: Preprocessing ...
% 3.74/1.19 Prover 3: Preprocessing ...
% 3.74/1.19 Prover 5: Preprocessing ...
% 9.24/1.97 Prover 3: Constructing countermodel ...
% 9.72/1.98 Prover 1: Constructing countermodel ...
% 9.72/2.03 Prover 5: Proving ...
% 9.72/2.04 Prover 6: Proving ...
% 10.99/2.22 Prover 2: Proving ...
% 11.60/2.26 Prover 4: Constructing countermodel ...
% 12.77/2.38 Prover 0: Proving ...
% 16.77/2.91 Prover 3: proved (2265ms)
% 16.77/2.91
% 16.77/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.77/2.91
% 16.77/2.91 Prover 6: stopped
% 16.77/2.91 Prover 0: stopped
% 16.77/2.92 Prover 5: stopped
% 16.77/2.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.77/2.94 Prover 2: stopped
% 16.77/2.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.77/2.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.77/2.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.77/2.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.74/3.01 Prover 8: Preprocessing ...
% 17.74/3.03 Prover 13: Preprocessing ...
% 18.01/3.05 Prover 10: Preprocessing ...
% 18.01/3.06 Prover 7: Preprocessing ...
% 18.01/3.07 Prover 11: Preprocessing ...
% 19.12/3.24 Prover 8: Warning: ignoring some quantifiers
% 19.64/3.25 Prover 8: Constructing countermodel ...
% 19.64/3.26 Prover 10: Constructing countermodel ...
% 19.80/3.28 Prover 1: Found proof (size 48)
% 19.80/3.28 Prover 1: proved (2632ms)
% 19.80/3.28 Prover 8: stopped
% 19.80/3.28 Prover 7: Constructing countermodel ...
% 19.80/3.28 Prover 10: stopped
% 19.80/3.29 Prover 4: stopped
% 19.80/3.31 Prover 7: stopped
% 20.09/3.32 Prover 13: Warning: ignoring some quantifiers
% 20.09/3.33 Prover 13: Constructing countermodel ...
% 20.09/3.35 Prover 13: stopped
% 20.27/3.42 Prover 11: Constructing countermodel ...
% 20.62/3.44 Prover 11: stopped
% 20.62/3.44
% 20.62/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.62/3.44
% 20.62/3.45 % SZS output start Proof for theBenchmark
% 20.62/3.45 Assumptions after simplification:
% 20.62/3.45 ---------------------------------
% 20.62/3.45
% 20.62/3.45 (mDefIdeal)
% 20.82/3.48 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ?
% 20.82/3.48 [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2) | ? [v2: $i] : (aElementOf0(v2,
% 20.82/3.48 v0) = 0 & $i(v2) & ( ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 =
% 20.82/3.48 0) & aElementOf0(v4, v0) = v5 & aElementOf0(v3, v0) = 0 &
% 20.82/3.48 sdtpldt0(v2, v3) = v4 & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] :
% 20.82/3.48 ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v4, v0) = v5 & sdtasdt0(v3,
% 20.82/3.48 v2) = v4 & aElement0(v3) = 0 & $i(v4) & $i(v3))))) & ! [v0: $i] : (
% 20.82/3.48 ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i] : ( ~
% 20.82/3.48 (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i] : ! [v3: $i] : !
% 20.82/3.48 [v4: int] : (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtasdt0(v2,
% 20.82/3.48 v1) = v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) &
% 20.82/3.48 aElement0(v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 20.82/3.48 (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) |
% 20.82/3.48 ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) =
% 20.82/3.48 v5))))))
% 20.82/3.48
% 20.82/3.48 (m__)
% 20.82/3.48 $i(xr) & $i(xI) & ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xr, xI) = v0)
% 20.82/3.48
% 20.82/3.48 (m__2174)
% 20.82/3.49 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 20.82/3.49 slsdtgt0(xa) = v0 & aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & $i(v1) &
% 20.82/3.49 $i(v0))
% 20.82/3.49
% 20.82/3.49 (m__2228)
% 20.82/3.49 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 20.82/3.49 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) &
% 20.82/3.49 $i(v1) & $i(v0) & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 &
% 20.82/3.49 $i(v3)))
% 20.82/3.49
% 20.82/3.49 (m__2666)
% 20.82/3.49 $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 20.82/3.49 [v2: $i] : ? [v3: any] : (iLess0(v1, v2) = v3 & sbrdtbr0(xr) = v1 &
% 20.82/3.49 sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb &
% 20.82/3.49 aElement0(xr) = 0 & aElement0(xq) = 0 & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 |
% 20.82/3.49 xr = sz00))
% 20.82/3.49
% 20.82/3.49 (m__2690)
% 20.82/3.49 $i(xq) & $i(xu) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xI) =
% 20.82/3.49 0 & sdtasdt0(xq, xu) = v0 & smndt0(v0) = v1 & $i(v1) & $i(v0))
% 20.82/3.49
% 20.82/3.49 (m__2699)
% 20.82/3.49 aElementOf0(xb, xI) = 0 & $i(xI) & $i(xb)
% 20.82/3.49
% 20.82/3.49 (m__2718)
% 20.82/3.49 $i(xr) & $i(xq) & $i(xu) & $i(xb) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq,
% 20.82/3.49 xu) = v0 & sdtpldt0(v1, xb) = xr & smndt0(v0) = v1 & $i(v1) & $i(v0))
% 20.82/3.49
% 20.82/3.49 (function-axioms)
% 20.82/3.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 20.82/3.49 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~
% 20.82/3.49 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 20.82/3.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 20.82/3.49 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3,
% 20.82/3.49 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 20.82/3.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) |
% 20.82/3.49 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 20.82/3.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.82/3.49 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0:
% 20.82/3.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.82/3.49 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 20.82/3.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 20.82/3.49 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 20.82/3.49 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.82/3.49 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 20.82/3.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 20.82/3.49 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 20.82/3.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.82/3.49 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] :
% 20.82/3.49 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 20.82/3.49 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.82/3.50 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 20.82/3.50 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1)
% 20.82/3.50 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 20.82/3.50 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0:
% 20.82/3.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 20.82/3.50 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0:
% 20.82/3.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 20.82/3.50 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] :
% 20.82/3.50 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 20.82/3.50 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.82/3.50 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 20.82/3.50 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 20.82/3.50 ~ (aElement0(v2) = v0))
% 20.82/3.50
% 20.82/3.50 Further assumptions not needed in the proof:
% 20.82/3.50 --------------------------------------------
% 20.82/3.50 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 20.82/3.50 mDefDiv, mDefDvs, mDefGCD, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, mDefSSum,
% 20.82/3.50 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 20.82/3.50 mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort,
% 20.82/3.50 mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2091, m__2110,
% 20.82/3.50 m__2129, m__2203, m__2273, m__2383, m__2416, m__2479, m__2612, m__2673
% 20.82/3.50
% 20.82/3.50 Those formulas are unsatisfiable:
% 20.82/3.50 ---------------------------------
% 20.82/3.50
% 20.82/3.50 Begin of proof
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (mDefIdeal) implies:
% 20.82/3.50 | (1) ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & !
% 20.82/3.50 | [v1: $i] : ( ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ( ! [v2: $i]
% 20.82/3.50 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3,
% 20.82/3.50 | v0) = v4) | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ?
% 20.82/3.50 | [v5: int] : ( ~ (v5 = 0) & aElement0(v2) = v5)) & ! [v2: $i]
% 20.82/3.50 | : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (aElementOf0(v3,
% 20.82/3.50 | v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ?
% 20.82/3.50 | [v5: int] : ( ~ (v5 = 0) & aElementOf0(v2, v0) = v5))))))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2174) implies:
% 20.82/3.50 | (2) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 20.82/3.50 | aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2228) implies:
% 20.82/3.50 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xb) = v1 &
% 20.82/3.50 | slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)
% 20.82/3.50 | & ? [v3: $i] : ( ~ (v3 = sz00) & aElementOf0(v3, v2) = 0 & $i(v3)))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2666) implies:
% 20.82/3.50 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (iLess0(v1,
% 20.82/3.50 | v2) = v3 & sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu)
% 20.82/3.50 | = v0 & sdtpldt0(v0, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0
% 20.82/3.50 | & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | xr = sz00))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2690) implies:
% 20.82/3.50 | (5) ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xI) = 0 & sdtasdt0(xq, xu)
% 20.82/3.50 | = v0 & smndt0(v0) = v1 & $i(v1) & $i(v0))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2699) implies:
% 20.82/3.50 | (6) aElementOf0(xb, xI) = 0
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__2718) implies:
% 20.82/3.50 | (7) $i(xb)
% 20.82/3.50 | (8) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xu) = v0 & sdtpldt0(v1, xb) =
% 20.82/3.50 | xr & smndt0(v0) = v1 & $i(v1) & $i(v0))
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (m__) implies:
% 20.82/3.50 | (9) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xr, xI) = v0)
% 20.82/3.50 |
% 20.82/3.50 | ALPHA: (function-axioms) implies:
% 20.82/3.51 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 20.82/3.51 | v1) | ~ (smndt0(v2) = v0))
% 20.82/3.51 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 20.82/3.51 | = v1) | ~ (slsdtgt0(v2) = v0))
% 20.82/3.51 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.82/3.51 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 20.82/3.51 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 20.82/3.51 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 20.82/3.51 | (aElementOf0(v3, v2) = v0))
% 20.82/3.51 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.82/3.51 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (9) with fresh symbol all_34_0 gives:
% 20.82/3.51 | (15) ~ (all_34_0 = 0) & aElementOf0(xr, xI) = all_34_0
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (15) implies:
% 20.82/3.51 | (16) ~ (all_34_0 = 0)
% 20.82/3.51 | (17) aElementOf0(xr, xI) = all_34_0
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (8) with fresh symbols all_40_0, all_40_1 gives:
% 20.82/3.51 | (18) sdtasdt0(xq, xu) = all_40_1 & sdtpldt0(all_40_0, xb) = xr &
% 20.82/3.51 | smndt0(all_40_1) = all_40_0 & $i(all_40_0) & $i(all_40_1)
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (18) implies:
% 20.82/3.51 | (19) smndt0(all_40_1) = all_40_0
% 20.82/3.51 | (20) sdtpldt0(all_40_0, xb) = xr
% 20.82/3.51 | (21) sdtasdt0(xq, xu) = all_40_1
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (5) with fresh symbols all_42_0, all_42_1 gives:
% 20.82/3.51 | (22) aElementOf0(all_42_0, xI) = 0 & sdtasdt0(xq, xu) = all_42_1 &
% 20.82/3.51 | smndt0(all_42_1) = all_42_0 & $i(all_42_0) & $i(all_42_1)
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (22) implies:
% 20.82/3.51 | (23) $i(all_42_0)
% 20.82/3.51 | (24) smndt0(all_42_1) = all_42_0
% 20.82/3.51 | (25) sdtasdt0(xq, xu) = all_42_1
% 20.82/3.51 | (26) aElementOf0(all_42_0, xI) = 0
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (2) with fresh symbols all_44_0, all_44_1 gives:
% 20.82/3.51 | (27) slsdtgt0(xb) = all_44_0 & slsdtgt0(xa) = all_44_1 & aIdeal0(xI) = 0 &
% 20.82/3.51 | sdtpldt1(all_44_1, all_44_0) = xI & $i(all_44_0) & $i(all_44_1)
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (27) implies:
% 20.82/3.51 | (28) sdtpldt1(all_44_1, all_44_0) = xI
% 20.82/3.51 | (29) aIdeal0(xI) = 0
% 20.82/3.51 | (30) slsdtgt0(xa) = all_44_1
% 20.82/3.51 | (31) slsdtgt0(xb) = all_44_0
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (3) with fresh symbols all_48_0, all_48_1, all_48_2
% 20.82/3.51 | gives:
% 20.82/3.51 | (32) slsdtgt0(xb) = all_48_1 & slsdtgt0(xa) = all_48_2 & sdtpldt1(all_48_2,
% 20.82/3.51 | all_48_1) = all_48_0 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 20.82/3.51 | ? [v0: $i] : ( ~ (v0 = sz00) & aElementOf0(v0, all_48_0) = 0 & $i(v0))
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (32) implies:
% 20.82/3.51 | (33) $i(all_48_0)
% 20.82/3.51 | (34) sdtpldt1(all_48_2, all_48_1) = all_48_0
% 20.82/3.51 | (35) slsdtgt0(xa) = all_48_2
% 20.82/3.51 | (36) slsdtgt0(xb) = all_48_1
% 20.82/3.51 |
% 20.82/3.51 | DELTA: instantiating (4) with fresh symbols all_58_0, all_58_1, all_58_2,
% 20.82/3.51 | all_58_3 gives:
% 20.82/3.51 | (37) iLess0(all_58_2, all_58_1) = all_58_0 & sbrdtbr0(xr) = all_58_2 &
% 20.82/3.51 | sbrdtbr0(xu) = all_58_1 & sdtasdt0(xq, xu) = all_58_3 &
% 20.82/3.51 | sdtpldt0(all_58_3, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 &
% 20.82/3.51 | $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & (all_58_0 = 0 | xr =
% 20.82/3.51 | sz00)
% 20.82/3.51 |
% 20.82/3.51 | ALPHA: (37) implies:
% 20.82/3.51 | (38) sdtasdt0(xq, xu) = all_58_3
% 20.82/3.51 |
% 20.82/3.52 | GROUND_INST: instantiating (12) with all_42_1, all_58_3, xu, xq, simplifying
% 20.82/3.52 | with (25), (38) gives:
% 20.82/3.52 | (39) all_58_3 = all_42_1
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (12) with all_40_1, all_58_3, xu, xq, simplifying
% 20.82/3.52 | with (21), (38) gives:
% 20.82/3.52 | (40) all_58_3 = all_40_1
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (11) with all_44_1, all_48_2, xa, simplifying with
% 20.82/3.52 | (30), (35) gives:
% 20.82/3.52 | (41) all_48_2 = all_44_1
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (11) with all_44_0, all_48_1, xb, simplifying with
% 20.82/3.52 | (31), (36) gives:
% 20.82/3.52 | (42) all_48_1 = all_44_0
% 20.82/3.52 |
% 20.82/3.52 | COMBINE_EQS: (39), (40) imply:
% 20.82/3.52 | (43) all_42_1 = all_40_1
% 20.82/3.52 |
% 20.82/3.52 | REDUCE: (34), (41), (42) imply:
% 20.82/3.52 | (44) sdtpldt1(all_44_1, all_44_0) = all_48_0
% 20.82/3.52 |
% 20.82/3.52 | REDUCE: (24), (43) imply:
% 20.82/3.52 | (45) smndt0(all_40_1) = all_42_0
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (10) with all_40_0, all_42_0, all_40_1, simplifying
% 20.82/3.52 | with (19), (45) gives:
% 20.82/3.52 | (46) all_42_0 = all_40_0
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (14) with xI, all_48_0, all_44_0, all_44_1,
% 20.82/3.52 | simplifying with (28), (44) gives:
% 20.82/3.52 | (47) all_48_0 = xI
% 20.82/3.52 |
% 20.82/3.52 | REDUCE: (26), (46) imply:
% 20.82/3.52 | (48) aElementOf0(all_40_0, xI) = 0
% 20.82/3.52 |
% 20.82/3.52 | REDUCE: (33), (47) imply:
% 20.82/3.52 | (49) $i(xI)
% 20.82/3.52 |
% 20.82/3.52 | REDUCE: (23), (46) imply:
% 20.82/3.52 | (50) $i(all_40_0)
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (1) with xI, simplifying with (29), (49) gives:
% 20.82/3.52 | (51) aSet0(xI) = 0 & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~
% 20.82/3.52 | $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 20.82/3.52 | (aElementOf0(v2, xI) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~
% 20.82/3.52 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElement0(v1) = v4)) & !
% 20.82/3.52 | [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 20.82/3.52 | (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v0, v1) = v2) | ~
% 20.82/3.52 | $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v1, xI) =
% 20.82/3.52 | v4))))
% 20.82/3.52 |
% 20.82/3.52 | ALPHA: (51) implies:
% 20.82/3.52 | (52) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i]
% 20.82/3.52 | : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) =
% 20.82/3.52 | v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v4: int] :
% 20.82/3.52 | ( ~ (v4 = 0) & aElement0(v1) = v4)) & ! [v1: $i] : ! [v2: $i]
% 20.82/3.52 | : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~
% 20.82/3.52 | (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 20.82/3.52 | 0) & aElementOf0(v1, xI) = v4))))
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (52) with all_40_0, simplifying with (48), (50)
% 20.82/3.52 | gives:
% 20.82/3.52 | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 20.82/3.52 | (aElementOf0(v1, xI) = v2) | ~ (sdtasdt0(v0, all_40_0) = v1) | ~
% 20.82/3.52 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aElement0(v0) = v3)) & !
% 20.82/3.52 | [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1,
% 20.82/3.52 | xI) = v2) | ~ (sdtpldt0(all_40_0, v0) = v1) | ~ $i(v0) | ?
% 20.82/3.52 | [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3))
% 20.82/3.52 |
% 20.82/3.52 | ALPHA: (53) implies:
% 20.82/3.52 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 20.82/3.52 | (aElementOf0(v1, xI) = v2) | ~ (sdtpldt0(all_40_0, v0) = v1) | ~
% 20.82/3.52 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v0, xI) = v3))
% 20.82/3.52 |
% 20.82/3.52 | GROUND_INST: instantiating (54) with xb, xr, all_34_0, simplifying with (7),
% 20.82/3.52 | (17), (20) gives:
% 20.82/3.52 | (55) all_34_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xI) = v0)
% 20.82/3.52 |
% 20.82/3.52 | BETA: splitting (55) gives:
% 20.82/3.52 |
% 20.82/3.53 | Case 1:
% 20.82/3.53 | |
% 20.82/3.53 | | (56) all_34_0 = 0
% 20.82/3.53 | |
% 20.82/3.53 | | REDUCE: (16), (56) imply:
% 20.82/3.53 | | (57) $false
% 20.82/3.53 | |
% 20.82/3.53 | | CLOSE: (57) is inconsistent.
% 20.82/3.53 | |
% 20.82/3.53 | Case 2:
% 20.82/3.53 | |
% 20.82/3.53 | | (58) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xb, xI) = v0)
% 20.82/3.53 | |
% 20.82/3.53 | | DELTA: instantiating (58) with fresh symbol all_203_0 gives:
% 20.82/3.53 | | (59) ~ (all_203_0 = 0) & aElementOf0(xb, xI) = all_203_0
% 20.82/3.53 | |
% 20.82/3.53 | | ALPHA: (59) implies:
% 20.82/3.53 | | (60) ~ (all_203_0 = 0)
% 20.82/3.53 | | (61) aElementOf0(xb, xI) = all_203_0
% 20.82/3.53 | |
% 20.82/3.53 | | GROUND_INST: instantiating (13) with 0, all_203_0, xI, xb, simplifying with
% 20.82/3.53 | | (6), (61) gives:
% 20.82/3.53 | | (62) all_203_0 = 0
% 20.82/3.53 | |
% 20.82/3.53 | | REDUCE: (60), (62) imply:
% 20.82/3.53 | | (63) $false
% 20.82/3.53 | |
% 20.82/3.53 | | CLOSE: (63) is inconsistent.
% 20.82/3.53 | |
% 20.82/3.53 | End of split
% 20.82/3.53 |
% 20.82/3.53 End of proof
% 20.82/3.53 % SZS output end Proof for theBenchmark
% 20.82/3.53
% 20.82/3.53 2903ms
%------------------------------------------------------------------------------