TSTP Solution File: NUM504+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM504+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 : n032.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 11:48:14 EDT 2023
% Result : Theorem 12.61s 2.34s
% Output : Proof 24.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri Aug 25 08:17:57 EDT 2023
% 0.08/0.27 % CPUTime :
% 0.11/0.45 ________ _____
% 0.11/0.45 ___ __ \_________(_)________________________________
% 0.11/0.45 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.11/0.45 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.11/0.45 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.11/0.45
% 0.11/0.45 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.11/0.45 (2023-06-19)
% 0.11/0.45
% 0.11/0.45 (c) Philipp Rümmer, 2009-2023
% 0.11/0.45 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.11/0.45 Amanda Stjerna.
% 0.11/0.45 Free software under BSD-3-Clause.
% 0.11/0.45
% 0.11/0.45 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.11/0.45
% 0.11/0.45 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.11/0.46 Running up to 7 provers in parallel.
% 0.11/0.47 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.11/0.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.11/0.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.11/0.47 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.11/0.47 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.11/0.47 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.11/0.47 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.31/1.03 Prover 1: Preprocessing ...
% 3.31/1.04 Prover 4: Preprocessing ...
% 3.31/1.07 Prover 5: Preprocessing ...
% 3.31/1.07 Prover 0: Preprocessing ...
% 3.31/1.07 Prover 3: Preprocessing ...
% 3.31/1.07 Prover 2: Preprocessing ...
% 3.31/1.07 Prover 6: Preprocessing ...
% 9.62/1.87 Prover 3: Constructing countermodel ...
% 9.62/1.88 Prover 1: Constructing countermodel ...
% 9.62/1.89 Prover 6: Proving ...
% 9.97/1.97 Prover 5: Constructing countermodel ...
% 11.12/2.11 Prover 2: Proving ...
% 11.12/2.18 Prover 4: Constructing countermodel ...
% 11.12/2.30 Prover 0: Proving ...
% 12.61/2.34 Prover 3: proved (1869ms)
% 12.61/2.34
% 12.61/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.61/2.34
% 13.04/2.35 Prover 5: stopped
% 13.04/2.35 Prover 6: stopped
% 13.04/2.36 Prover 2: stopped
% 13.04/2.37 Prover 0: stopped
% 13.04/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.04/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.04/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.04/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.24/2.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.75/2.50 Prover 10: Preprocessing ...
% 13.75/2.51 Prover 7: Preprocessing ...
% 13.75/2.51 Prover 8: Preprocessing ...
% 14.33/2.55 Prover 13: Preprocessing ...
% 14.76/2.58 Prover 11: Preprocessing ...
% 15.56/2.71 Prover 8: Warning: ignoring some quantifiers
% 15.56/2.72 Prover 10: Constructing countermodel ...
% 15.56/2.72 Prover 8: Constructing countermodel ...
% 16.07/2.80 Prover 7: Constructing countermodel ...
% 16.07/2.89 Prover 13: Constructing countermodel ...
% 19.18/3.18 Prover 11: Constructing countermodel ...
% 24.18/3.87 Prover 10: Found proof (size 54)
% 24.18/3.87 Prover 10: proved (1517ms)
% 24.18/3.87 Prover 7: stopped
% 24.18/3.87 Prover 4: stopped
% 24.18/3.87 Prover 1: stopped
% 24.18/3.87 Prover 13: stopped
% 24.18/3.88 Prover 8: stopped
% 24.18/3.88 Prover 11: stopped
% 24.18/3.88
% 24.18/3.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.18/3.88
% 24.18/3.88 % SZS output start Proof for theBenchmark
% 24.18/3.89 Assumptions after simplification:
% 24.18/3.89 ---------------------------------
% 24.18/3.89
% 24.18/3.89 (mAddComm)
% 24.18/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 24.18/3.91 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 24.18/3.91 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 24.18/3.91
% 24.18/3.91 (mDefPrime)
% 24.18/3.91 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 24.18/3.91 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 24.18/3.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 24.18/3.91 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 24.18/3.91 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 24.18/3.91 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 24.18/3.91 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 24.18/3.91
% 24.18/3.91 (mLEAsym)
% 24.18/3.91 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 24.18/3.91 sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~
% 24.18/3.91 aNaturalNumber0(v0))
% 24.18/3.91
% 24.18/3.91 (mMulComm)
% 24.18/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 24.18/3.91 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 24.18/3.91 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 24.18/3.91
% 24.18/3.91 (mSortsB_02)
% 24.18/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 24.18/3.92 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 24.18/3.92 aNaturalNumber0(v2))
% 24.18/3.92
% 24.18/3.92 (mSortsC_01)
% 24.18/3.92 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 24.18/3.92
% 24.18/3.92 (m__1837)
% 24.18/3.92 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 24.18/3.92 aNaturalNumber0(xn)
% 24.18/3.92
% 24.18/3.92 (m__1860)
% 24.18/3.92 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (
% 24.18/3.92 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) =
% 24.18/3.92 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) &
% 24.18/3.92 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~
% 24.18/3.92 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) |
% 24.18/3.92 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) |
% 24.18/3.92 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 24.18/3.92
% 24.18/3.92 (m__2287)
% 24.18/3.92 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ( ~ (xp = xm) & ~ (xp
% 24.18/3.92 = xn) & sdtpldt0(xm, v0) = xp & sdtpldt0(xn, v1) = xp & $i(v1) & $i(v0) &
% 24.18/3.92 sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v1) &
% 24.18/3.92 aNaturalNumber0(v0))
% 24.18/3.92
% 24.18/3.92 (m__2306)
% 24.69/3.92 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 24.69/3.92 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) &
% 24.69/3.92 aNaturalNumber0(xk))
% 24.69/3.92
% 24.69/3.92 (m__2342)
% 24.69/3.92 $i(xr) & $i(xk) & $i(sz10) & $i(sz00) & ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr
% 24.69/3.92 = sz00) & sdtasdt0(xr, v0) = xk & $i(v0) & isPrime0(xr) & doDivides0(xr,
% 24.69/3.92 xk) & aNaturalNumber0(v0) & aNaturalNumber0(xr) & ! [v1: $i] : ! [v2:
% 24.69/3.92 $i] : (v1 = xr | v1 = sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~
% 24.69/3.92 $i(v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] :
% 24.69/3.92 (v1 = xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~
% 24.69/3.92 aNaturalNumber0(v1)))
% 24.69/3.92
% 24.69/3.92 (m__2362)
% 24.69/3.92 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 24.69/3.92 (sdtasdt0(xr, v1) = v0 & sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk &
% 24.69/3.92 $i(v2) & $i(v1) & $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) &
% 24.69/3.92 aNaturalNumber0(v1))
% 24.69/3.92
% 24.69/3.92 (m__2414)
% 24.69/3.93 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 24.69/3.93 ? [v3: $i] : ? [v4: $i] : ( ~ (v2 = v1) & ~ (v1 = v0) & sdtasdt0(xp, xk) =
% 24.69/3.93 v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v3) = v2 &
% 24.69/3.93 sdtpldt0(v0, v4) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 24.69/3.93 sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, v1) & aNaturalNumber0(v4) &
% 24.69/3.93 aNaturalNumber0(v3))
% 24.69/3.93
% 24.69/3.93 (function-axioms)
% 24.69/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.69/3.93 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.69/3.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 24.69/3.93 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.69/3.93 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.69/3.93 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.69/3.93 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 24.69/3.93
% 24.69/3.93 Further assumptions not needed in the proof:
% 24.69/3.93 --------------------------------------------
% 24.69/3.93 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDefQuot, mDivAsso,
% 24.69/3.93 mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLENTr, mLERefl, mLETotal,
% 24.69/3.93 mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, mPrimDiv,
% 24.69/3.93 mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__,
% 24.69/3.93 m__1799, m__1870, m__2075, m__2315, m__2327, m__2389
% 24.69/3.93
% 24.69/3.93 Those formulas are unsatisfiable:
% 24.69/3.93 ---------------------------------
% 24.69/3.93
% 24.69/3.93 Begin of proof
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (mSortsC_01) implies:
% 24.69/3.93 | (1) aNaturalNumber0(sz10)
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (mDefPrime) implies:
% 24.69/3.93 | (2) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (m__1837) implies:
% 24.69/3.93 | (3) aNaturalNumber0(xm)
% 24.69/3.93 | (4) aNaturalNumber0(xp)
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (m__1860) implies:
% 24.69/3.93 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) &
% 24.69/3.93 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) &
% 24.69/3.93 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: $i]
% 24.69/3.93 | : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = xp) |
% 24.69/3.93 | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~
% 24.69/3.93 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~
% 24.69/3.93 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (m__2287) implies:
% 24.69/3.93 | (6) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = xm) & ~ (xp = xn) & sdtpldt0(xm,
% 24.69/3.93 | v0) = xp & sdtpldt0(xn, v1) = xp & $i(v1) & $i(v0) & sdtlseqdt0(xm,
% 24.69/3.93 | xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(v1) &
% 24.69/3.93 | aNaturalNumber0(v0))
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (m__2306) implies:
% 24.69/3.93 | (7) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 &
% 24.69/3.93 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk))
% 24.69/3.93 |
% 24.69/3.93 | ALPHA: (m__2342) implies:
% 24.69/3.94 | (8) ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, v0) = xk
% 24.69/3.94 | & $i(v0) & isPrime0(xr) & doDivides0(xr, xk) & aNaturalNumber0(v0) &
% 24.69/3.94 | aNaturalNumber0(xr) & ! [v1: $i] : ! [v2: $i] : (v1 = xr | v1 =
% 24.69/3.94 | sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~ $i(v1) | ~
% 24.69/3.94 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] : (v1 =
% 24.69/3.94 | xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~
% 24.69/3.94 | aNaturalNumber0(v1)))
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (m__2362) implies:
% 24.69/3.94 | (9) $i(xr)
% 24.69/3.94 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, v1) = v0 &
% 24.69/3.94 | sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk & $i(v2) & $i(v1) &
% 24.69/3.94 | $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) &
% 24.69/3.94 | aNaturalNumber0(v1))
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (m__2414) implies:
% 24.69/3.94 | (11) $i(xm)
% 24.69/3.94 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.69/3.94 | ( ~ (v2 = v1) & ~ (v1 = v0) & sdtasdt0(xp, xk) = v2 & sdtasdt0(xp,
% 24.69/3.94 | xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v3) = v2 &
% 24.69/3.94 | sdtpldt0(v0, v4) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 24.69/3.94 | sdtlseqdt0(v1, v2) & sdtlseqdt0(v0, v1) & aNaturalNumber0(v4) &
% 24.69/3.94 | aNaturalNumber0(v3))
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (function-axioms) implies:
% 24.69/3.94 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.69/3.94 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.69/3.94 |
% 24.69/3.94 | DELTA: instantiating (7) with fresh symbol all_42_0 gives:
% 24.69/3.94 | (14) sdtsldt0(all_42_0, xp) = xk & sdtasdt0(xp, xk) = all_42_0 &
% 24.69/3.94 | sdtasdt0(xn, xm) = all_42_0 & $i(all_42_0) & aNaturalNumber0(xk)
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (14) implies:
% 24.69/3.94 | (15) sdtasdt0(xn, xm) = all_42_0
% 24.69/3.94 | (16) sdtasdt0(xp, xk) = all_42_0
% 24.69/3.94 |
% 24.69/3.94 | DELTA: instantiating (10) with fresh symbols all_44_0, all_44_1, all_44_2
% 24.69/3.94 | gives:
% 24.69/3.94 | (17) sdtasdt0(xr, all_44_1) = all_44_2 & sdtasdt0(xn, xm) = all_44_2 &
% 24.69/3.94 | sdtpldt0(xr, all_44_0) = xk & $i(all_44_0) & $i(all_44_1) &
% 24.69/3.94 | $i(all_44_2) & doDivides0(xr, all_44_2) & aNaturalNumber0(all_44_0) &
% 24.69/3.94 | aNaturalNumber0(all_44_1)
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (17) implies:
% 24.69/3.94 | (18) aNaturalNumber0(all_44_1)
% 24.69/3.94 | (19) $i(all_44_1)
% 24.69/3.94 | (20) sdtasdt0(xn, xm) = all_44_2
% 24.69/3.94 | (21) sdtasdt0(xr, all_44_1) = all_44_2
% 24.69/3.94 |
% 24.69/3.94 | DELTA: instantiating (6) with fresh symbols all_46_0, all_46_1 gives:
% 24.69/3.94 | (22) ~ (xp = xm) & ~ (xp = xn) & sdtpldt0(xm, all_46_1) = xp &
% 24.69/3.94 | sdtpldt0(xn, all_46_0) = xp & $i(all_46_0) & $i(all_46_1) &
% 24.69/3.94 | sdtlseqdt0(xm, xp) & sdtlseqdt0(xn, xp) & aNaturalNumber0(all_46_0) &
% 24.69/3.94 | aNaturalNumber0(all_46_1)
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (22) implies:
% 24.69/3.94 | (23) aNaturalNumber0(all_46_1)
% 24.69/3.94 | (24) $i(all_46_1)
% 24.69/3.94 | (25) sdtpldt0(xm, all_46_1) = xp
% 24.69/3.94 |
% 24.69/3.94 | DELTA: instantiating (12) with fresh symbols all_48_0, all_48_1, all_48_2,
% 24.69/3.94 | all_48_3, all_48_4 gives:
% 24.69/3.94 | (26) ~ (all_48_2 = all_48_3) & ~ (all_48_3 = all_48_4) & sdtasdt0(xp, xk)
% 24.69/3.94 | = all_48_2 & sdtasdt0(xp, xm) = all_48_3 & sdtasdt0(xn, xm) = all_48_4
% 24.69/3.94 | & sdtpldt0(all_48_3, all_48_1) = all_48_2 & sdtpldt0(all_48_4,
% 24.69/3.94 | all_48_0) = all_48_3 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 24.69/3.94 | $i(all_48_3) & $i(all_48_4) & sdtlseqdt0(all_48_3, all_48_2) &
% 24.69/3.94 | sdtlseqdt0(all_48_4, all_48_3) & aNaturalNumber0(all_48_0) &
% 24.69/3.94 | aNaturalNumber0(all_48_1)
% 24.69/3.94 |
% 24.69/3.94 | ALPHA: (26) implies:
% 24.69/3.94 | (27) ~ (all_48_3 = all_48_4)
% 24.69/3.95 | (28) aNaturalNumber0(all_48_1)
% 24.69/3.95 | (29) aNaturalNumber0(all_48_0)
% 24.69/3.95 | (30) sdtlseqdt0(all_48_4, all_48_3)
% 24.69/3.95 | (31) sdtlseqdt0(all_48_3, all_48_2)
% 24.69/3.95 | (32) $i(all_48_1)
% 24.69/3.95 | (33) $i(all_48_0)
% 24.69/3.95 | (34) sdtpldt0(all_48_4, all_48_0) = all_48_3
% 24.69/3.95 | (35) sdtpldt0(all_48_3, all_48_1) = all_48_2
% 24.69/3.95 | (36) sdtasdt0(xn, xm) = all_48_4
% 24.69/3.95 | (37) sdtasdt0(xp, xm) = all_48_3
% 24.69/3.95 | (38) sdtasdt0(xp, xk) = all_48_2
% 24.69/3.95 |
% 24.69/3.95 | DELTA: instantiating (8) with fresh symbol all_50_0 gives:
% 24.69/3.95 | (39) ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, all_50_0) = xk &
% 24.69/3.95 | $i(all_50_0) & isPrime0(xr) & doDivides0(xr, xk) &
% 24.69/3.95 | aNaturalNumber0(all_50_0) & aNaturalNumber0(xr) & ! [v0: $i] : !
% 24.69/3.95 | [v1: $i] : (v0 = xr | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xr) | ~
% 24.69/3.95 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 24.69/3.95 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~
% 24.69/3.95 | $i(v0) | ~ doDivides0(v0, xr) | ~ aNaturalNumber0(v0))
% 24.69/3.95 |
% 24.69/3.95 | ALPHA: (39) implies:
% 24.69/3.95 | (40) aNaturalNumber0(xr)
% 24.69/3.95 |
% 24.69/3.95 | DELTA: instantiating (5) with fresh symbols all_53_0, all_53_1 gives:
% 24.69/3.95 | (41) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_53_0) = all_53_1 &
% 24.69/3.95 | sdtasdt0(xn, xm) = all_53_1 & $i(all_53_0) & $i(all_53_1) &
% 24.69/3.95 | isPrime0(xp) & doDivides0(xp, all_53_1) & aNaturalNumber0(all_53_0) &
% 24.69/3.95 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1)
% 24.69/3.95 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 24.69/3.95 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 24.69/3.95 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 24.69/3.95 |
% 24.69/3.95 | ALPHA: (41) implies:
% 24.69/3.95 | (42) sdtasdt0(xn, xm) = all_53_1
% 24.69/3.95 |
% 24.69/3.95 | BETA: splitting (2) gives:
% 24.69/3.95 |
% 24.69/3.95 | Case 1:
% 24.69/3.95 | |
% 24.69/3.95 | | (43) ~ aNaturalNumber0(sz10)
% 24.69/3.95 | |
% 24.69/3.95 | | PRED_UNIFY: (1), (43) imply:
% 24.69/3.95 | | (44) $false
% 24.69/3.95 | |
% 24.69/3.95 | | CLOSE: (44) is inconsistent.
% 24.69/3.95 | |
% 24.69/3.95 | Case 2:
% 24.69/3.95 | |
% 24.69/3.95 | |
% 24.69/3.95 | | GROUND_INST: instantiating (13) with all_44_2, all_48_4, xm, xn, simplifying
% 24.69/3.95 | | with (20), (36) gives:
% 24.69/3.95 | | (45) all_48_4 = all_44_2
% 24.69/3.95 | |
% 24.69/3.95 | | GROUND_INST: instantiating (13) with all_48_4, all_53_1, xm, xn, simplifying
% 24.69/3.95 | | with (36), (42) gives:
% 24.69/3.95 | | (46) all_53_1 = all_48_4
% 24.69/3.95 | |
% 24.69/3.95 | | GROUND_INST: instantiating (13) with all_42_0, all_53_1, xm, xn, simplifying
% 24.69/3.95 | | with (15), (42) gives:
% 24.69/3.95 | | (47) all_53_1 = all_42_0
% 24.69/3.95 | |
% 24.69/3.95 | | GROUND_INST: instantiating (13) with all_42_0, all_48_2, xk, xp, simplifying
% 24.69/3.95 | | with (16), (38) gives:
% 24.69/3.95 | | (48) all_48_2 = all_42_0
% 24.69/3.95 | |
% 24.69/3.95 | | COMBINE_EQS: (46), (47) imply:
% 24.69/3.95 | | (49) all_48_4 = all_42_0
% 24.69/3.95 | |
% 24.69/3.95 | | SIMP: (49) implies:
% 24.69/3.95 | | (50) all_48_4 = all_42_0
% 24.69/3.95 | |
% 24.69/3.95 | | COMBINE_EQS: (45), (50) imply:
% 24.69/3.95 | | (51) all_44_2 = all_42_0
% 24.69/3.95 | |
% 24.69/3.95 | | REDUCE: (27), (50) imply:
% 24.69/3.95 | | (52) ~ (all_48_3 = all_42_0)
% 24.69/3.95 | |
% 24.69/3.96 | | REDUCE: (21), (51) imply:
% 24.69/3.96 | | (53) sdtasdt0(xr, all_44_1) = all_42_0
% 24.69/3.96 | |
% 24.69/3.96 | | REDUCE: (35), (48) imply:
% 24.69/3.96 | | (54) sdtpldt0(all_48_3, all_48_1) = all_42_0
% 24.69/3.96 | |
% 24.69/3.96 | | REDUCE: (34), (50) imply:
% 24.69/3.96 | | (55) sdtpldt0(all_42_0, all_48_0) = all_48_3
% 24.69/3.96 | |
% 24.69/3.96 | | REDUCE: (31), (48) imply:
% 24.69/3.96 | | (56) sdtlseqdt0(all_48_3, all_42_0)
% 24.69/3.96 | |
% 24.69/3.96 | | REDUCE: (30), (50) imply:
% 24.69/3.96 | | (57) sdtlseqdt0(all_42_0, all_48_3)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mAddComm) with xm, all_46_1, xp, simplifying
% 24.69/3.96 | | with (3), (11), (23), (24), (25) gives:
% 24.69/3.96 | | (58) sdtpldt0(all_46_1, xm) = xp & $i(xp)
% 24.69/3.96 | |
% 24.69/3.96 | | ALPHA: (58) implies:
% 24.69/3.96 | | (59) $i(xp)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mSortsB_02) with xp, xm, all_48_3, simplifying
% 24.69/3.96 | | with (3), (4), (11), (37), (59) gives:
% 24.69/3.96 | | (60) aNaturalNumber0(all_48_3)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mSortsB_02) with xr, all_44_1, all_42_0,
% 24.69/3.96 | | simplifying with (9), (18), (19), (40), (53) gives:
% 24.69/3.96 | | (61) aNaturalNumber0(all_42_0)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mMulComm) with xr, all_44_1, all_42_0,
% 24.69/3.96 | | simplifying with (9), (18), (19), (40), (53) gives:
% 24.69/3.96 | | (62) sdtasdt0(all_44_1, xr) = all_42_0 & $i(all_42_0)
% 24.69/3.96 | |
% 24.69/3.96 | | ALPHA: (62) implies:
% 24.69/3.96 | | (63) $i(all_42_0)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mAddComm) with all_42_0, all_48_0, all_48_3,
% 24.69/3.96 | | simplifying with (29), (33), (55), (61), (63) gives:
% 24.69/3.96 | | (64) sdtpldt0(all_48_0, all_42_0) = all_48_3 & $i(all_48_3)
% 24.69/3.96 | |
% 24.69/3.96 | | ALPHA: (64) implies:
% 24.69/3.96 | | (65) $i(all_48_3)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mAddComm) with all_48_3, all_48_1, all_42_0,
% 24.69/3.96 | | simplifying with (28), (32), (54), (60), (65) gives:
% 24.69/3.96 | | (66) sdtpldt0(all_48_1, all_48_3) = all_42_0 & $i(all_42_0)
% 24.69/3.96 | |
% 24.69/3.96 | | GROUND_INST: instantiating (mLEAsym) with all_42_0, all_48_3, simplifying
% 24.69/3.96 | | with (56), (57), (60), (61), (63), (65) gives:
% 24.69/3.96 | | (67) all_48_3 = all_42_0
% 24.69/3.96 | |
% 24.69/3.96 | | REDUCE: (52), (67) imply:
% 24.69/3.96 | | (68) $false
% 24.69/3.96 | |
% 24.69/3.96 | | CLOSE: (68) is inconsistent.
% 24.69/3.96 | |
% 24.69/3.96 | End of split
% 24.69/3.96 |
% 24.69/3.96 End of proof
% 24.69/3.96 % SZS output end Proof for theBenchmark
% 24.69/3.96
% 24.69/3.96 3515ms
%------------------------------------------------------------------------------