TSTP Solution File: NUM500+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:11 EDT 2023
% Result : Theorem 15.55s 3.07s
% Output : Proof 24.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 14:44:33 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.65 ________ _____
% 0.22/0.65 ___ __ \_________(_)________________________________
% 0.22/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.65
% 0.22/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.65 (2023-06-19)
% 0.22/0.65
% 0.22/0.65 (c) Philipp Rümmer, 2009-2023
% 0.22/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.65 Amanda Stjerna.
% 0.22/0.65 Free software under BSD-3-Clause.
% 0.22/0.65
% 0.22/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.65
% 0.22/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.66 Running up to 7 provers in parallel.
% 0.22/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.87/1.39 Prover 1: Preprocessing ...
% 3.87/1.39 Prover 4: Preprocessing ...
% 4.35/1.42 Prover 3: Preprocessing ...
% 4.35/1.42 Prover 0: Preprocessing ...
% 4.35/1.42 Prover 6: Preprocessing ...
% 4.35/1.42 Prover 2: Preprocessing ...
% 4.35/1.42 Prover 5: Preprocessing ...
% 9.65/2.24 Prover 1: Constructing countermodel ...
% 9.65/2.29 Prover 6: Proving ...
% 9.65/2.33 Prover 3: Constructing countermodel ...
% 9.65/2.39 Prover 5: Constructing countermodel ...
% 12.66/2.64 Prover 2: Proving ...
% 13.52/2.72 Prover 4: Constructing countermodel ...
% 14.06/2.82 Prover 0: Proving ...
% 15.55/3.07 Prover 3: proved (2394ms)
% 15.55/3.07
% 15.55/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.55/3.07
% 15.55/3.07 Prover 5: stopped
% 15.55/3.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.55/3.07 Prover 6: stopped
% 15.55/3.08 Prover 0: stopped
% 15.55/3.08 Prover 2: stopped
% 15.55/3.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.55/3.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.55/3.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.55/3.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.65/3.20 Prover 7: Preprocessing ...
% 17.35/3.21 Prover 10: Preprocessing ...
% 17.35/3.22 Prover 8: Preprocessing ...
% 17.35/3.22 Prover 11: Preprocessing ...
% 17.55/3.28 Prover 13: Preprocessing ...
% 18.79/3.41 Prover 10: Constructing countermodel ...
% 19.30/3.47 Prover 8: Warning: ignoring some quantifiers
% 19.35/3.48 Prover 8: Constructing countermodel ...
% 19.60/3.52 Prover 7: Constructing countermodel ...
% 20.48/3.67 Prover 13: Constructing countermodel ...
% 21.01/3.75 Prover 11: Constructing countermodel ...
% 23.77/4.11 Prover 10: Found proof (size 44)
% 23.77/4.11 Prover 10: proved (1030ms)
% 23.77/4.11 Prover 4: stopped
% 23.77/4.11 Prover 13: stopped
% 23.77/4.11 Prover 1: stopped
% 23.77/4.11 Prover 8: stopped
% 23.77/4.12 Prover 7: stopped
% 23.77/4.12 Prover 11: stopped
% 23.77/4.13
% 23.77/4.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.77/4.13
% 24.22/4.13 % SZS output start Proof for theBenchmark
% 24.22/4.14 Assumptions after simplification:
% 24.22/4.14 ---------------------------------
% 24.22/4.14
% 24.22/4.14 (mAddComm)
% 24.22/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 24.22/4.16 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 24.22/4.16 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 24.22/4.16
% 24.22/4.16 (mDefPrime)
% 24.38/4.17 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 24.38/4.17 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 24.38/4.17 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 24.38/4.17 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 24.38/4.17 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 24.38/4.17 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 24.38/4.17 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 24.38/4.17
% 24.38/4.17 (mMulCanc)
% 24.38/4.17 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 24.38/4.17 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) =
% 24.38/4.17 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 24.38/4.17 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : (
% 24.38/4.17 ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & $i(v6) &
% 24.38/4.17 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 =
% 24.38/4.17 v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) |
% 24.38/4.17 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 24.38/4.17 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 24.38/4.17
% 24.38/4.17 (mPrimDiv)
% 24.38/4.17 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 24.38/4.17 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1,
% 24.38/4.17 v0) & aNaturalNumber0(v1)))
% 24.38/4.17
% 24.38/4.17 (mSortsC_01)
% 24.38/4.17 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 24.38/4.17
% 24.38/4.17 (m__)
% 24.38/4.18 $i(xk) & $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v0 = sz10 | v0 =
% 24.38/4.18 sz00 | ~ (sdtasdt0(v0, v1) = xk) | ~ $i(v1) | ~ $i(v0) | ~
% 24.38/4.18 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : ? [v3: $i] : (
% 24.38/4.18 ~ (v2 = v0) & ~ (v2 = sz10) & sdtasdt0(v2, v3) = v0 & $i(v3) & $i(v2) &
% 24.38/4.18 doDivides0(v2, v0) & aNaturalNumber0(v3) & aNaturalNumber0(v2))) & ! [v0:
% 24.38/4.18 $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xk) | ~ $i(v1) | ~ $i(v0) | ~
% 24.38/4.18 isPrime0(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0:
% 24.38/4.18 $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ doDivides0(v0, xk) | ~
% 24.38/4.18 aNaturalNumber0(v0) | ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & ~ (v1 =
% 24.38/4.18 sz10) & sdtasdt0(v1, v2) = v0 & $i(v2) & $i(v1) & doDivides0(v1, v0) &
% 24.38/4.18 aNaturalNumber0(v2) & aNaturalNumber0(v1))) & ! [v0: $i] : ( ~ $i(v0) |
% 24.38/4.18 ~ isPrime0(v0) | ~ doDivides0(v0, xk) | ~ aNaturalNumber0(v0))
% 24.38/4.18
% 24.38/4.18 (m__1837)
% 24.38/4.18 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 24.38/4.18 aNaturalNumber0(xn)
% 24.38/4.18
% 24.38/4.18 (m__1860)
% 24.38/4.18 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (
% 24.38/4.18 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) =
% 24.38/4.18 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) &
% 24.38/4.18 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~
% 24.38/4.18 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) |
% 24.38/4.18 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) |
% 24.38/4.18 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 24.38/4.18
% 24.38/4.18 (m__2287)
% 24.38/4.18 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ( ~ (xp = xm) & ~ (xp
% 24.38/4.18 = xn) & sdtpldt0(xm, v0) = xp & sdtpldt0(xn, v1) = xp & $i(v1) & $i(v0) &
% 24.38/4.18 sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v1) &
% 24.38/4.18 aNaturalNumber0(v0))
% 24.38/4.18
% 24.38/4.18 (m__2306)
% 24.38/4.18 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 24.38/4.18 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) &
% 24.38/4.18 aNaturalNumber0(xk))
% 24.38/4.18
% 24.38/4.18 (m__2315)
% 24.38/4.18 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 24.38/4.18
% 24.38/4.18 (m__2327)
% 24.38/4.18 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 24.38/4.18
% 24.38/4.18 (function-axioms)
% 24.38/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.38/4.18 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.38/4.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 24.38/4.18 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.38/4.18 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.38/4.18 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.38/4.18 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 24.38/4.18
% 24.38/4.18 Further assumptions not needed in the proof:
% 24.38/4.18 --------------------------------------------
% 24.38/4.18 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDefQuot, mDivAsso,
% 24.38/4.18 mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl,
% 24.38/4.18 mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulComm, mNatSort,
% 24.38/4.18 mSortsB, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit,
% 24.38/4.18 m_MulZero, m__1799, m__1870, m__2075
% 24.38/4.18
% 24.38/4.18 Those formulas are unsatisfiable:
% 24.38/4.18 ---------------------------------
% 24.38/4.18
% 24.38/4.18 Begin of proof
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (mSortsC_01) implies:
% 24.38/4.19 | (1) aNaturalNumber0(sz10)
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (mMulCanc) implies:
% 24.38/4.19 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 =
% 24.38/4.19 | sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 24.38/4.19 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 24.38/4.19 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (mDefPrime) implies:
% 24.38/4.19 | (3) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (mPrimDiv) implies:
% 24.38/4.19 | (4) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 24.38/4.19 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 24.38/4.19 | doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__1837) implies:
% 24.38/4.19 | (5) aNaturalNumber0(xm)
% 24.38/4.19 | (6) aNaturalNumber0(xp)
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__1860) implies:
% 24.38/4.19 | (7) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) &
% 24.38/4.19 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) &
% 24.38/4.19 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: $i]
% 24.38/4.19 | : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = xp) |
% 24.38/4.19 | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~
% 24.38/4.19 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~
% 24.38/4.19 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__2287) implies:
% 24.38/4.19 | (8) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = xm) & ~ (xp = xn) & sdtpldt0(xm,
% 24.38/4.19 | v0) = xp & sdtpldt0(xn, v1) = xp & $i(v1) & $i(v0) & sdtlseqdt0(xm,
% 24.38/4.19 | xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v1) &
% 24.38/4.19 | aNaturalNumber0(v0))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__2306) implies:
% 24.38/4.19 | (9) $i(xm)
% 24.38/4.19 | (10) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 &
% 24.38/4.19 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__2327) implies:
% 24.38/4.19 | (11) ~ (xk = sz00)
% 24.38/4.19 | (12) ~ (xk = sz10)
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (m__) implies:
% 24.38/4.19 | (13) $i(xk)
% 24.38/4.19 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v0, xk) |
% 24.38/4.19 | ~ aNaturalNumber0(v0))
% 24.38/4.19 |
% 24.38/4.19 | ALPHA: (function-axioms) implies:
% 24.38/4.19 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.38/4.19 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.38/4.19 |
% 24.38/4.20 | DELTA: instantiating (10) with fresh symbol all_41_0 gives:
% 24.38/4.20 | (16) sdtsldt0(all_41_0, xp) = xk & sdtasdt0(xp, xk) = all_41_0 &
% 24.38/4.20 | sdtasdt0(xn, xm) = all_41_0 & $i(all_41_0) & aNaturalNumber0(xk)
% 24.38/4.20 |
% 24.38/4.20 | ALPHA: (16) implies:
% 24.38/4.20 | (17) aNaturalNumber0(xk)
% 24.38/4.20 | (18) sdtasdt0(xn, xm) = all_41_0
% 24.38/4.20 | (19) sdtasdt0(xp, xk) = all_41_0
% 24.38/4.20 |
% 24.38/4.20 | DELTA: instantiating (8) with fresh symbols all_43_0, all_43_1 gives:
% 24.38/4.20 | (20) ~ (xp = xm) & ~ (xp = xn) & sdtpldt0(xm, all_43_1) = xp &
% 24.38/4.20 | sdtpldt0(xn, all_43_0) = xp & $i(all_43_0) & $i(all_43_1) &
% 24.38/4.20 | sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(all_43_0) &
% 24.38/4.20 | aNaturalNumber0(all_43_1)
% 24.38/4.20 |
% 24.38/4.20 | ALPHA: (20) implies:
% 24.38/4.20 | (21) aNaturalNumber0(all_43_1)
% 24.38/4.20 | (22) $i(all_43_1)
% 24.38/4.20 | (23) sdtpldt0(xm, all_43_1) = xp
% 24.38/4.20 |
% 24.38/4.20 | DELTA: instantiating (7) with fresh symbols all_45_0, all_45_1 gives:
% 24.38/4.20 | (24) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_45_0) = all_45_1 &
% 24.38/4.20 | sdtasdt0(xn, xm) = all_45_1 & $i(all_45_0) & $i(all_45_1) &
% 24.38/4.20 | isPrime0(xp) & doDivides0(xp, all_45_1) & aNaturalNumber0(all_45_0) &
% 24.38/4.20 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1)
% 24.38/4.20 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 24.38/4.20 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 24.38/4.20 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 24.38/4.20 |
% 24.38/4.20 | ALPHA: (24) implies:
% 24.38/4.20 | (25) ~ (xp = sz00)
% 24.38/4.20 | (26) aNaturalNumber0(all_45_0)
% 24.38/4.20 | (27) $i(all_45_0)
% 24.38/4.20 | (28) sdtasdt0(xn, xm) = all_45_1
% 24.38/4.20 | (29) sdtasdt0(xp, all_45_0) = all_45_1
% 24.38/4.20 |
% 24.38/4.20 | BETA: splitting (3) gives:
% 24.38/4.20 |
% 24.38/4.20 | Case 1:
% 24.38/4.20 | |
% 24.38/4.20 | | (30) ~ aNaturalNumber0(sz10)
% 24.38/4.20 | |
% 24.38/4.20 | | PRED_UNIFY: (1), (30) imply:
% 24.38/4.20 | | (31) $false
% 24.38/4.20 | |
% 24.38/4.20 | | CLOSE: (31) is inconsistent.
% 24.38/4.20 | |
% 24.38/4.20 | Case 2:
% 24.38/4.20 | |
% 24.38/4.20 | |
% 24.38/4.20 | | GROUND_INST: instantiating (15) with all_41_0, all_45_1, xm, xn, simplifying
% 24.38/4.20 | | with (18), (28) gives:
% 24.38/4.20 | | (32) all_45_1 = all_41_0
% 24.38/4.20 | |
% 24.38/4.20 | | REDUCE: (29), (32) imply:
% 24.38/4.20 | | (33) sdtasdt0(xp, all_45_0) = all_41_0
% 24.38/4.20 | |
% 24.38/4.20 | | GROUND_INST: instantiating (4) with all_45_0, simplifying with (26), (27)
% 24.38/4.20 | | gives:
% 24.38/4.20 | | (34) all_45_0 = sz10 | all_45_0 = sz00 | ? [v0: $i] : ($i(v0) &
% 24.38/4.20 | | isPrime0(v0) & doDivides0(v0, all_45_0) & aNaturalNumber0(v0))
% 24.38/4.20 | |
% 24.38/4.20 | | GROUND_INST: instantiating (mAddComm) with xm, all_43_1, xp, simplifying
% 24.38/4.20 | | with (5), (9), (21), (22), (23) gives:
% 24.38/4.20 | | (35) sdtpldt0(all_43_1, xm) = xp & $i(xp)
% 24.38/4.20 | |
% 24.38/4.20 | | ALPHA: (35) implies:
% 24.38/4.20 | | (36) $i(xp)
% 24.38/4.20 | |
% 24.38/4.21 | | GROUND_INST: instantiating (2) with xp, xk, all_45_0, all_41_0, simplifying
% 24.38/4.21 | | with (6), (13), (17), (19), (26), (27), (33), (36) gives:
% 24.38/4.21 | | (37) all_45_0 = xk | xp = sz00
% 24.38/4.21 | |
% 24.38/4.21 | | BETA: splitting (37) gives:
% 24.38/4.21 | |
% 24.38/4.21 | | Case 1:
% 24.38/4.21 | | |
% 24.38/4.21 | | | (38) xp = sz00
% 24.38/4.21 | | |
% 24.38/4.21 | | | REDUCE: (25), (38) imply:
% 24.38/4.21 | | | (39) $false
% 24.38/4.21 | | |
% 24.38/4.21 | | | CLOSE: (39) is inconsistent.
% 24.38/4.21 | | |
% 24.38/4.21 | | Case 2:
% 24.38/4.21 | | |
% 24.38/4.21 | | | (40) all_45_0 = xk
% 24.38/4.21 | | |
% 24.38/4.21 | | | BETA: splitting (34) gives:
% 24.38/4.21 | | |
% 24.38/4.21 | | | Case 1:
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | (41) all_45_0 = sz00
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | COMBINE_EQS: (40), (41) imply:
% 24.38/4.21 | | | | (42) xk = sz00
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | REDUCE: (11), (42) imply:
% 24.38/4.21 | | | | (43) $false
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | CLOSE: (43) is inconsistent.
% 24.38/4.21 | | | |
% 24.38/4.21 | | | Case 2:
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | (44) all_45_0 = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 24.38/4.21 | | | | doDivides0(v0, all_45_0) & aNaturalNumber0(v0))
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | BETA: splitting (44) gives:
% 24.38/4.21 | | | |
% 24.38/4.21 | | | | Case 1:
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | (45) all_45_0 = sz10
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | COMBINE_EQS: (40), (45) imply:
% 24.38/4.21 | | | | | (46) xk = sz10
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | REDUCE: (12), (46) imply:
% 24.38/4.21 | | | | | (47) $false
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | CLOSE: (47) is inconsistent.
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | Case 2:
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | (48) ? [v0: $i] : ($i(v0) & isPrime0(v0) & doDivides0(v0,
% 24.38/4.21 | | | | | all_45_0) & aNaturalNumber0(v0))
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | DELTA: instantiating (48) with fresh symbol all_142_0 gives:
% 24.38/4.21 | | | | | (49) $i(all_142_0) & isPrime0(all_142_0) & doDivides0(all_142_0,
% 24.38/4.21 | | | | | all_45_0) & aNaturalNumber0(all_142_0)
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | ALPHA: (49) implies:
% 24.38/4.21 | | | | | (50) aNaturalNumber0(all_142_0)
% 24.38/4.21 | | | | | (51) doDivides0(all_142_0, all_45_0)
% 24.38/4.21 | | | | | (52) isPrime0(all_142_0)
% 24.38/4.21 | | | | | (53) $i(all_142_0)
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | REDUCE: (40), (51) imply:
% 24.38/4.21 | | | | | (54) doDivides0(all_142_0, xk)
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | GROUND_INST: instantiating (14) with all_142_0, simplifying with (50),
% 24.38/4.21 | | | | | (52), (53), (54) gives:
% 24.38/4.21 | | | | | (55) $false
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | | CLOSE: (55) is inconsistent.
% 24.38/4.21 | | | | |
% 24.38/4.21 | | | | End of split
% 24.38/4.21 | | | |
% 24.38/4.21 | | | End of split
% 24.38/4.21 | | |
% 24.38/4.21 | | End of split
% 24.38/4.21 | |
% 24.38/4.21 | End of split
% 24.38/4.21 |
% 24.38/4.21 End of proof
% 24.38/4.21 % SZS output end Proof for theBenchmark
% 24.38/4.21
% 24.38/4.21 3561ms
%------------------------------------------------------------------------------