TSTP Solution File: NUM529+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM529+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 : n013.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 11:48:24 EDT 2023
% Result : Theorem 25.35s 4.13s
% Output : Proof 40.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM529+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 14:51:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.60/1.20 Prover 4: Preprocessing ...
% 3.60/1.20 Prover 1: Preprocessing ...
% 3.86/1.24 Prover 0: Preprocessing ...
% 3.86/1.24 Prover 2: Preprocessing ...
% 3.86/1.25 Prover 3: Preprocessing ...
% 3.86/1.25 Prover 5: Preprocessing ...
% 3.86/1.25 Prover 6: Preprocessing ...
% 9.02/1.96 Prover 1: Constructing countermodel ...
% 9.28/2.02 Prover 6: Proving ...
% 9.28/2.02 Prover 3: Constructing countermodel ...
% 10.14/2.16 Prover 5: Constructing countermodel ...
% 11.37/2.36 Prover 2: Proving ...
% 12.28/2.42 Prover 4: Constructing countermodel ...
% 13.77/2.60 Prover 0: Proving ...
% 25.35/4.13 Prover 0: proved (3487ms)
% 25.35/4.13
% 25.35/4.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.35/4.13
% 25.35/4.13 Prover 3: stopped
% 25.35/4.14 Prover 5: stopped
% 25.35/4.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.35/4.14 Prover 6: stopped
% 25.35/4.15 Prover 2: stopped
% 25.35/4.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.35/4.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.35/4.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.35/4.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.07/4.25 Prover 8: Preprocessing ...
% 26.71/4.29 Prover 13: Preprocessing ...
% 26.71/4.30 Prover 10: Preprocessing ...
% 26.71/4.30 Prover 11: Preprocessing ...
% 26.71/4.31 Prover 7: Preprocessing ...
% 26.71/4.41 Prover 8: Warning: ignoring some quantifiers
% 26.71/4.43 Prover 8: Constructing countermodel ...
% 26.71/4.43 Prover 10: Constructing countermodel ...
% 26.71/4.47 Prover 7: Constructing countermodel ...
% 26.71/4.47 Prover 13: Constructing countermodel ...
% 28.97/4.62 Prover 11: Constructing countermodel ...
% 39.73/6.01 Prover 10: Found proof (size 68)
% 39.73/6.01 Prover 10: proved (1869ms)
% 39.73/6.01 Prover 7: stopped
% 39.73/6.01 Prover 11: stopped
% 39.73/6.01 Prover 13: stopped
% 39.73/6.01 Prover 8: stopped
% 39.73/6.01 Prover 1: stopped
% 39.73/6.01 Prover 4: stopped
% 39.73/6.01
% 39.73/6.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.73/6.01
% 39.73/6.02 % SZS output start Proof for theBenchmark
% 39.73/6.02 Assumptions after simplification:
% 39.73/6.02 ---------------------------------
% 39.73/6.02
% 39.73/6.02 (mAddComm)
% 39.73/6.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 39.73/6.05 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 39.73/6.05 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 39.73/6.05
% 39.73/6.05 (mDefDiv)
% 39.73/6.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 39.73/6.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 39.73/6.05 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0:
% 39.73/6.05 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 39.73/6.05 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0,
% 39.73/6.05 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 39.73/6.05
% 39.73/6.05 (mDefLE)
% 39.73/6.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 39.73/6.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 39.73/6.05 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 39.73/6.05 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 39.73/6.05 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 39.73/6.05 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 39.73/6.05
% 39.73/6.05 (mDefPrime)
% 40.02/6.06 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 40.02/6.06 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 40.02/6.06 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 40.02/6.06 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 40.02/6.06 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 40.02/6.06 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 40.02/6.06 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 40.02/6.06
% 40.02/6.06 (mDefQuot)
% 40.02/6.06 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 40.02/6.06 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 40.02/6.06 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 40.02/6.06 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 40.02/6.06 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~
% 40.02/6.06 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 40.02/6.06 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~
% 40.02/6.06 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 40.02/6.06 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 40.02/6.06 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 40.02/6.06 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 40.02/6.06
% 40.02/6.06 (mIH_03)
% 40.02/6.06 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 40.02/6.06 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 40.02/6.06 iLess0(v0, v1))
% 40.02/6.06
% 40.02/6.06 (mMonAdd)
% 40.02/6.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.02/6.06 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 40.02/6.06 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 40.02/6.06 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 =
% 40.02/6.06 v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 &
% 40.02/6.06 sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v4, v5) &
% 40.02/6.06 sdtlseqdt0(v3, v6)))
% 40.02/6.06
% 40.02/6.06 (mMulComm)
% 40.02/6.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 40.02/6.06 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 40.02/6.06 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 40.02/6.06
% 40.02/6.06 (mSortsC_01)
% 40.02/6.07 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 40.02/6.07
% 40.02/6.07 (m_MulZero)
% 40.02/6.07 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) =
% 40.02/6.07 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : (
% 40.02/6.07 ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 40.02/6.07 sdtasdt0(v0, sz00) = sz00)
% 40.02/6.07
% 40.02/6.07 (m__2963)
% 40.02/6.07 $i(xn) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 40.02/6.07 [v4: $i] : (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) |
% 40.02/6.07 ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ $i(v2) | ~
% 40.02/6.07 $i(v1) | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~
% 40.02/6.07 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 40.02/6.07
% 40.02/6.07 (m__2987)
% 40.02/6.07 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) &
% 40.02/6.07 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn)
% 40.02/6.07
% 40.02/6.07 (m__3014)
% 40.02/6.07 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1
% 40.02/6.07 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0))
% 40.02/6.07
% 40.02/6.07 (m__3025)
% 40.02/6.07 $i(xp) & isPrime0(xp)
% 40.02/6.07
% 40.02/6.07 (m__3046)
% 40.02/6.07 $i(xp) & $i(xn) & ? [v0: $i] : (sdtasdt0(xn, xn) = v0 & $i(v0) &
% 40.02/6.07 doDivides0(xp, v0) & doDivides0(xp, xn))
% 40.02/6.07
% 40.02/6.07 (m__3059)
% 40.02/6.07 sdtsldt0(xn, xp) = xq & $i(xq) & $i(xp) & $i(xn)
% 40.02/6.07
% 40.02/6.07 (m__3082)
% 40.02/6.07 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xq) = v1
% 40.02/6.07 & sdtasdt0(xp, v1) = v0 & sdtasdt0(xm, xm) = v0 & $i(v1) & $i(v0))
% 40.02/6.07
% 40.02/6.07 (m__3124)
% 40.02/6.07 ~ (xm = xn) & $i(xm) & $i(xn) & sdtlseqdt0(xm, xn)
% 40.02/6.07
% 40.02/6.07 (function-axioms)
% 40.02/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.02/6.07 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 40.02/6.07 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 40.02/6.07 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 40.02/6.07 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 40.02/6.07 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.02/6.07 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 40.02/6.07
% 40.02/6.07 Further assumptions not needed in the proof:
% 40.02/6.07 --------------------------------------------
% 40.02/6.07 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDivAsso, mDivLE, mDivMin, mDivSum,
% 40.02/6.07 mDivTrans, mIH, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonMul, mMonMul2,
% 40.02/6.07 mMulAsso, mMulCanc, mNatSort, mPDP, mPrimDiv, mSortsB, mSortsB_02, mSortsC,
% 40.02/6.07 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m__
% 40.02/6.07
% 40.02/6.07 Those formulas are unsatisfiable:
% 40.02/6.07 ---------------------------------
% 40.02/6.07
% 40.02/6.07 Begin of proof
% 40.02/6.07 |
% 40.02/6.08 | ALPHA: (mSortsC_01) implies:
% 40.02/6.08 | (1) aNaturalNumber0(sz10)
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m_MulZero) implies:
% 40.02/6.08 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) |
% 40.02/6.08 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (mDefLE) implies:
% 40.02/6.08 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 40.02/6.08 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 40.02/6.08 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (mDefDiv) implies:
% 40.02/6.08 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 40.02/6.08 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 40.02/6.08 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (mDefQuot) implies:
% 40.02/6.08 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 =
% 40.02/6.08 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 40.02/6.08 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 40.02/6.08 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~
% 40.02/6.08 | aNaturalNumber0(v0))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (mDefPrime) implies:
% 40.02/6.08 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__2987) implies:
% 40.02/6.08 | (7) ~ (xn = sz00)
% 40.02/6.08 | (8) ~ (xm = sz00)
% 40.02/6.08 | (9) ~ (xp = sz00)
% 40.02/6.08 | (10) aNaturalNumber0(xn)
% 40.02/6.08 | (11) aNaturalNumber0(xm)
% 40.02/6.08 | (12) aNaturalNumber0(xp)
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__2963) implies:
% 40.02/6.08 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 40.02/6.08 | (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~
% 40.02/6.08 | (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ $i(v2) |
% 40.02/6.08 | ~ $i(v1) | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~
% 40.02/6.08 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 40.02/6.08 | aNaturalNumber0(v0))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3014) implies:
% 40.02/6.08 | (14) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm)
% 40.02/6.08 | = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3025) implies:
% 40.02/6.08 | (15) isPrime0(xp)
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3046) implies:
% 40.02/6.08 | (16) ? [v0: $i] : (sdtasdt0(xn, xn) = v0 & $i(v0) & doDivides0(xp, v0) &
% 40.02/6.08 | doDivides0(xp, xn))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3059) implies:
% 40.02/6.08 | (17) sdtsldt0(xn, xp) = xq
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3082) implies:
% 40.02/6.08 | (18) $i(xp)
% 40.02/6.08 | (19) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xq) = v1 & sdtasdt0(xp, v1)
% 40.02/6.08 | = v0 & sdtasdt0(xm, xm) = v0 & $i(v1) & $i(v0))
% 40.02/6.08 |
% 40.02/6.08 | ALPHA: (m__3124) implies:
% 40.02/6.09 | (20) ~ (xm = xn)
% 40.02/6.09 | (21) sdtlseqdt0(xm, xn)
% 40.02/6.09 | (22) $i(xn)
% 40.02/6.09 | (23) $i(xm)
% 40.02/6.09 |
% 40.02/6.09 | ALPHA: (function-axioms) implies:
% 40.02/6.09 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.02/6.09 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 40.02/6.09 |
% 40.02/6.09 | DELTA: instantiating (16) with fresh symbol all_40_0 gives:
% 40.02/6.09 | (25) sdtasdt0(xn, xn) = all_40_0 & $i(all_40_0) & doDivides0(xp, all_40_0)
% 40.02/6.09 | & doDivides0(xp, xn)
% 40.02/6.09 |
% 40.02/6.09 | ALPHA: (25) implies:
% 40.02/6.09 | (26) doDivides0(xp, xn)
% 40.02/6.09 |
% 40.02/6.09 | DELTA: instantiating (19) with fresh symbols all_42_0, all_42_1 gives:
% 40.02/6.09 | (27) sdtasdt0(xq, xq) = all_42_0 & sdtasdt0(xp, all_42_0) = all_42_1 &
% 40.02/6.09 | sdtasdt0(xm, xm) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 40.02/6.09 |
% 40.02/6.09 | ALPHA: (27) implies:
% 40.02/6.09 | (28) sdtasdt0(xm, xm) = all_42_1
% 40.02/6.09 | (29) sdtasdt0(xp, all_42_0) = all_42_1
% 40.02/6.09 | (30) sdtasdt0(xq, xq) = all_42_0
% 40.02/6.09 |
% 40.02/6.09 | DELTA: instantiating (14) with fresh symbols all_44_0, all_44_1 gives:
% 40.02/6.09 | (31) sdtasdt0(xp, all_44_1) = all_44_0 & sdtasdt0(xm, xm) = all_44_1 &
% 40.02/6.09 | sdtasdt0(xn, xn) = all_44_0 & $i(all_44_0) & $i(all_44_1)
% 40.02/6.09 |
% 40.02/6.09 | ALPHA: (31) implies:
% 40.02/6.09 | (32) sdtasdt0(xm, xm) = all_44_1
% 40.02/6.09 |
% 40.02/6.09 | BETA: splitting (6) gives:
% 40.02/6.09 |
% 40.02/6.09 | Case 1:
% 40.02/6.09 | |
% 40.02/6.09 | | (33) ~ aNaturalNumber0(sz10)
% 40.02/6.09 | |
% 40.02/6.09 | | PRED_UNIFY: (1), (33) imply:
% 40.02/6.09 | | (34) $false
% 40.02/6.09 | |
% 40.02/6.09 | | CLOSE: (34) is inconsistent.
% 40.02/6.09 | |
% 40.02/6.09 | Case 2:
% 40.02/6.09 | |
% 40.02/6.09 | |
% 40.02/6.09 | | GROUND_INST: instantiating (24) with all_42_1, all_44_1, xm, xm, simplifying
% 40.02/6.09 | | with (28), (32) gives:
% 40.02/6.09 | | (35) all_44_1 = all_42_1
% 40.02/6.09 | |
% 40.02/6.09 | | GROUND_INST: instantiating (mIH_03) with xm, xn, simplifying with (10),
% 40.02/6.09 | | (11), (21), (22), (23) gives:
% 40.02/6.09 | | (36) xm = xn | iLess0(xm, xn)
% 40.02/6.09 | |
% 40.02/6.09 | | GROUND_INST: instantiating (3) with xm, xn, simplifying with (10), (11),
% 40.02/6.09 | | (21), (22), (23) gives:
% 40.02/6.09 | | (37) ? [v0: $i] : (sdtpldt0(xm, v0) = xn & $i(v0) & aNaturalNumber0(v0))
% 40.02/6.09 | |
% 40.02/6.09 | | GROUND_INST: instantiating (4) with xp, xn, simplifying with (10), (12),
% 40.02/6.09 | | (18), (22), (26) gives:
% 40.02/6.09 | | (38) ? [v0: $i] : (sdtasdt0(xp, v0) = xn & $i(v0) & aNaturalNumber0(v0))
% 40.02/6.09 | |
% 40.02/6.09 | | DELTA: instantiating (38) with fresh symbol all_64_0 gives:
% 40.02/6.09 | | (39) sdtasdt0(xp, all_64_0) = xn & $i(all_64_0) &
% 40.02/6.09 | | aNaturalNumber0(all_64_0)
% 40.02/6.09 | |
% 40.02/6.09 | | ALPHA: (39) implies:
% 40.02/6.10 | | (40) aNaturalNumber0(all_64_0)
% 40.02/6.10 | | (41) $i(all_64_0)
% 40.02/6.10 | | (42) sdtasdt0(xp, all_64_0) = xn
% 40.02/6.10 | |
% 40.02/6.10 | | DELTA: instantiating (37) with fresh symbol all_66_0 gives:
% 40.02/6.10 | | (43) sdtpldt0(xm, all_66_0) = xn & $i(all_66_0) &
% 40.02/6.10 | | aNaturalNumber0(all_66_0)
% 40.02/6.10 | |
% 40.02/6.10 | | ALPHA: (43) implies:
% 40.02/6.10 | | (44) aNaturalNumber0(all_66_0)
% 40.02/6.10 | | (45) $i(all_66_0)
% 40.02/6.10 | | (46) sdtpldt0(xm, all_66_0) = xn
% 40.02/6.10 | |
% 40.02/6.10 | | BETA: splitting (36) gives:
% 40.02/6.10 | |
% 40.02/6.10 | | Case 1:
% 40.02/6.10 | | |
% 40.02/6.10 | | | (47) iLess0(xm, xn)
% 40.02/6.10 | | |
% 40.02/6.10 | | | GROUND_INST: instantiating (mMonAdd) with xm, xn, all_66_0, xn,
% 40.02/6.10 | | | simplifying with (10), (11), (21), (22), (23), (44), (45),
% 40.02/6.10 | | | (46) gives:
% 40.02/6.10 | | | (48) xm = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn)
% 40.02/6.10 | | | & ~ (v1 = v0) & sdtpldt0(all_66_0, xm) = v0 &
% 40.02/6.10 | | | sdtpldt0(all_66_0, xn) = v1 & sdtpldt0(xn, all_66_0) = v2 &
% 40.02/6.10 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn,
% 40.02/6.10 | | | v2))
% 40.02/6.10 | | |
% 40.02/6.10 | | | GROUND_INST: instantiating (mAddComm) with xm, all_66_0, xn, simplifying
% 40.02/6.10 | | | with (11), (23), (44), (45), (46) gives:
% 40.02/6.10 | | | (49) sdtpldt0(all_66_0, xm) = xn & $i(xn)
% 40.02/6.10 | | |
% 40.02/6.10 | | | GROUND_INST: instantiating (5) with xp, xn, xq, all_64_0, simplifying with
% 40.02/6.10 | | | (10), (12), (17), (18), (22), (26), (40), (41), (42) gives:
% 40.02/6.10 | | | (50) all_64_0 = xq | xp = sz00
% 40.02/6.10 | | |
% 40.02/6.10 | | | GROUND_INST: instantiating (mMulComm) with xp, all_64_0, xn, simplifying
% 40.02/6.10 | | | with (12), (18), (40), (41), (42) gives:
% 40.02/6.10 | | | (51) sdtasdt0(all_64_0, xp) = xn & $i(xn)
% 40.02/6.10 | | |
% 40.02/6.10 | | | ALPHA: (51) implies:
% 40.02/6.10 | | | (52) sdtasdt0(all_64_0, xp) = xn
% 40.02/6.10 | | |
% 40.02/6.10 | | | BETA: splitting (50) gives:
% 40.02/6.10 | | |
% 40.02/6.10 | | | Case 1:
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | (53) xp = sz00
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | REDUCE: (9), (53) imply:
% 40.02/6.10 | | | | (54) $false
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | CLOSE: (54) is inconsistent.
% 40.02/6.10 | | | |
% 40.02/6.10 | | | Case 2:
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | (55) all_64_0 = xq
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | REDUCE: (52), (55) imply:
% 40.02/6.10 | | | | (56) sdtasdt0(xq, xp) = xn
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | REDUCE: (41), (55) imply:
% 40.02/6.10 | | | | (57) $i(xq)
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | REDUCE: (40), (55) imply:
% 40.02/6.10 | | | | (58) aNaturalNumber0(xq)
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | BETA: splitting (48) gives:
% 40.02/6.10 | | | |
% 40.02/6.10 | | | | Case 1:
% 40.02/6.10 | | | | |
% 40.02/6.10 | | | | | (59) xm = xn
% 40.02/6.10 | | | | |
% 40.02/6.10 | | | | | REDUCE: (20), (59) imply:
% 40.02/6.10 | | | | | (60) $false
% 40.02/6.10 | | | | |
% 40.02/6.10 | | | | | CLOSE: (60) is inconsistent.
% 40.02/6.10 | | | | |
% 40.02/6.10 | | | | Case 2:
% 40.02/6.10 | | | | |
% 40.02/6.10 | | | | |
% 40.02/6.11 | | | | | GROUND_INST: instantiating (13) with xm, xq, xp, all_42_0, all_42_1,
% 40.02/6.11 | | | | | simplifying with (11), (12), (15), (18), (23), (28),
% 40.02/6.11 | | | | | (29), (30), (47), (57), (58) gives:
% 40.02/6.11 | | | | | (61) xq = sz00 | xp = sz00 | xm = sz00
% 40.02/6.11 | | | | |
% 40.02/6.11 | | | | | BETA: splitting (61) gives:
% 40.02/6.11 | | | | |
% 40.02/6.11 | | | | | Case 1:
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | (62) xq = sz00
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | REDUCE: (56), (62) imply:
% 40.02/6.11 | | | | | | (63) sdtasdt0(sz00, xp) = xn
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | GROUND_INST: instantiating (2) with xp, xn, simplifying with (12),
% 40.02/6.11 | | | | | | (18), (63) gives:
% 40.02/6.11 | | | | | | (64) xn = sz00
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | REDUCE: (7), (64) imply:
% 40.02/6.11 | | | | | | (65) $false
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | CLOSE: (65) is inconsistent.
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | Case 2:
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | (66) xp = sz00 | xm = sz00
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | BETA: splitting (66) gives:
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | | Case 1:
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | (67) xp = sz00
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | REDUCE: (9), (67) imply:
% 40.02/6.11 | | | | | | | (68) $false
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | CLOSE: (68) is inconsistent.
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | Case 2:
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | (69) xm = sz00
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | REDUCE: (8), (69) imply:
% 40.02/6.11 | | | | | | | (70) $false
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | | CLOSE: (70) is inconsistent.
% 40.02/6.11 | | | | | | |
% 40.02/6.11 | | | | | | End of split
% 40.02/6.11 | | | | | |
% 40.02/6.11 | | | | | End of split
% 40.02/6.11 | | | | |
% 40.02/6.11 | | | | End of split
% 40.02/6.11 | | | |
% 40.02/6.11 | | | End of split
% 40.02/6.11 | | |
% 40.02/6.11 | | Case 2:
% 40.02/6.11 | | |
% 40.02/6.11 | | | (71) xm = xn
% 40.02/6.11 | | |
% 40.02/6.11 | | | REDUCE: (20), (71) imply:
% 40.02/6.11 | | | (72) $false
% 40.02/6.11 | | |
% 40.02/6.11 | | | CLOSE: (72) is inconsistent.
% 40.02/6.11 | | |
% 40.02/6.11 | | End of split
% 40.02/6.11 | |
% 40.02/6.11 | End of split
% 40.02/6.11 |
% 40.02/6.11 End of proof
% 40.02/6.11 % SZS output end Proof for theBenchmark
% 40.02/6.11
% 40.02/6.11 5500ms
%------------------------------------------------------------------------------