%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------