%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM492+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 : n011.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 11:48:08 EDT 2023 % Result : Theorem 15.01s 2.87s % Output : Proof 28.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM492+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 14:02:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.92/1.23 Prover 4: Preprocessing ... % 3.92/1.23 Prover 1: Preprocessing ... % 3.92/1.30 Prover 3: Preprocessing ... % 3.92/1.30 Prover 0: Preprocessing ... % 3.92/1.30 Prover 5: Preprocessing ... % 3.92/1.30 Prover 6: Preprocessing ... % 3.92/1.31 Prover 2: Preprocessing ... % 12.19/2.43 Prover 3: Constructing countermodel ... % 12.19/2.44 Prover 1: Constructing countermodel ... % 12.19/2.45 Prover 6: Proving ... % 12.90/2.50 Prover 5: Constructing countermodel ... % 15.01/2.85 Prover 3: proved (2207ms) % 15.01/2.85 % 15.01/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.01/2.87 % 15.01/2.88 Prover 5: stopped % 15.01/2.88 Prover 2: Proving ... % 15.01/2.88 Prover 6: stopped % 15.72/2.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.72/2.89 Prover 2: stopped % 15.72/2.89 Prover 4: Constructing countermodel ... % 15.72/2.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.72/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.83/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.54/3.03 Prover 7: Preprocessing ... % 16.54/3.05 Prover 8: Preprocessing ... % 16.54/3.07 Prover 10: Preprocessing ... % 17.21/3.10 Prover 0: Proving ... % 17.21/3.11 Prover 0: stopped % 17.21/3.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.21/3.15 Prover 11: Preprocessing ... % 18.02/3.26 Prover 13: Preprocessing ... % 18.02/3.35 Prover 10: Constructing countermodel ... % 18.02/3.39 Prover 8: Warning: ignoring some quantifiers % 19.74/3.42 Prover 8: Constructing countermodel ... % 19.74/3.43 Prover 7: Constructing countermodel ... % 20.98/3.61 Prover 13: Constructing countermodel ... % 23.16/3.97 Prover 11: Constructing countermodel ... % 27.20/4.50 Prover 10: Found proof (size 53) % 27.20/4.50 Prover 10: proved (1615ms) % 27.20/4.50 Prover 13: stopped % 27.20/4.50 Prover 11: stopped % 27.20/4.50 Prover 4: stopped % 27.20/4.50 Prover 7: stopped % 27.20/4.50 Prover 8: stopped % 27.81/4.56 Prover 1: stopped % 27.81/4.56 % 27.81/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.81/4.56 % 27.81/4.57 % SZS output start Proof for theBenchmark % 28.12/4.58 Assumptions after simplification: % 28.12/4.58 --------------------------------- % 28.12/4.58 % 28.12/4.58 (mDefPrime) % 28.12/4.59 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 28.12/4.59 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 28.12/4.59 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 28.12/4.59 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 28.12/4.59 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 28.12/4.59 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 28.12/4.59 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 28.12/4.59 % 28.12/4.60 (mDivMin) % 28.12/4.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) % 28.12/4.63 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v3) | ~ % 28.12/4.63 doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 28.12/4.63 aNaturalNumber0(v0) | doDivides0(v0, v2)) % 28.12/4.63 % 28.12/4.63 (mMulComm) % 28.12/4.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 28.12/4.63 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.12/4.63 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 28.12/4.63 % 28.12/4.63 (mSortsB_02) % 28.12/4.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 28.12/4.63 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 28.12/4.63 aNaturalNumber0(v2)) % 28.12/4.63 % 28.12/4.63 (mSortsC_01) % 28.12/4.63 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 28.12/4.63 % 28.12/4.63 (m__) % 28.12/4.64 $i(xr) & $i(xp) & $i(xm) & ? [v0: $i] : (sdtasdt0(xr, xm) = v0 & $i(v0) & ~ % 28.12/4.64 doDivides0(xp, v0) & ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) | % 28.12/4.64 ~ aNaturalNumber0(v1))) % 28.12/4.64 % 28.12/4.64 (m__1837) % 28.12/4.64 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 28.12/4.64 aNaturalNumber0(xn) % 28.12/4.64 % 28.12/4.64 (m__1860) % 28.12/4.64 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ( % 28.12/4.64 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = % 28.12/4.64 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) & % 28.12/4.64 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ % 28.12/4.64 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | % 28.12/4.64 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) | % 28.12/4.64 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 28.12/4.64 % 28.12/4.64 (m__1883) % 28.12/4.64 sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & $i(xr) & $i(xp) & $i(xn) & % 28.12/4.65 aNaturalNumber0(xr) % 28.12/4.65 % 28.12/4.65 (m__1951) % 28.12/4.65 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 28.12/4.65 (sdtasdt0(xr, xm) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & % 28.12/4.65 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 28.12/4.65 % 28.12/4.65 (m__1978) % 28.12/4.65 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 28.12/4.65 (sdtmndt0(v2, v0) = v1 & sdtasdt0(xr, xm) = v1 & sdtasdt0(xp, xm) = v0 & % 28.12/4.65 sdtasdt0(xn, xm) = v2 & sdtpldt0(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 28.12/4.65 % 28.12/4.65 (m__2001) % 28.12/4.65 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 28.12/4.65 $i] : (sdtasdt0(xp, v3) = v0 & sdtasdt0(xp, v2) = v1 & sdtasdt0(xp, xm) = v1 % 28.12/4.65 & sdtasdt0(xn, xm) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & doDivides0(xp, % 28.12/4.65 v1) & aNaturalNumber0(v3) & aNaturalNumber0(v2)) % 28.12/4.65 % 28.12/4.65 (function-axioms) % 28.12/4.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.12/4.66 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 28.12/4.66 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 28.12/4.66 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.12/4.66 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 28.12/4.66 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.12/4.66 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 28.12/4.66 % 28.12/4.66 Further assumptions not needed in the proof: % 28.12/4.66 -------------------------------------------- % 28.12/4.66 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefQuot, % 28.12/4.66 mDivAsso, mDivLE, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, % 28.12/4.66 mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, % 28.12/4.66 mPrimDiv, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, % 28.12/4.66 m__1799, m__1870, m__1894, m__1924 % 28.12/4.66 % 28.12/4.66 Those formulas are unsatisfiable: % 28.12/4.66 --------------------------------- % 28.12/4.66 % 28.12/4.66 Begin of proof % 28.12/4.66 | % 28.12/4.66 | ALPHA: (mSortsC_01) implies: % 28.12/4.66 | (1) aNaturalNumber0(sz10) % 28.12/4.66 | % 28.12/4.66 | ALPHA: (mDefPrime) implies: % 28.12/4.66 | (2) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 28.12/4.66 | % 28.12/4.66 | ALPHA: (m__1837) implies: % 28.12/4.66 | (3) aNaturalNumber0(xm) % 28.12/4.66 | (4) aNaturalNumber0(xp) % 28.12/4.66 | % 28.12/4.66 | ALPHA: (m__1860) implies: % 28.12/4.67 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) & % 28.12/4.67 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) & % 28.12/4.67 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: $i] % 28.12/4.67 | : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = xp) | % 28.12/4.67 | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~ % 28.12/4.67 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ % 28.12/4.67 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 28.12/4.67 | % 28.12/4.67 | ALPHA: (m__1883) implies: % 28.12/4.67 | (6) aNaturalNumber0(xr) % 28.12/4.67 | % 28.12/4.67 | ALPHA: (m__1951) implies: % 28.12/4.67 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, xm) = v2 & % 28.12/4.67 | sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v2) = v0 % 28.12/4.67 | & $i(v2) & $i(v1) & $i(v0)) % 28.12/4.67 | % 28.12/4.67 | ALPHA: (m__1978) implies: % 28.12/4.67 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v2, v0) = v1 & % 28.12/4.67 | sdtasdt0(xr, xm) = v1 & sdtasdt0(xp, xm) = v0 & sdtasdt0(xn, xm) = v2 % 28.12/4.67 | & sdtpldt0(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 28.12/4.67 | % 28.12/4.67 | ALPHA: (m__2001) implies: % 28.12/4.67 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xp, % 28.12/4.67 | v3) = v0 & sdtasdt0(xp, v2) = v1 & sdtasdt0(xp, xm) = v1 & % 28.12/4.67 | sdtasdt0(xn, xm) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 28.12/4.67 | doDivides0(xp, v1) & aNaturalNumber0(v3) & aNaturalNumber0(v2)) % 28.12/4.67 | % 28.12/4.67 | ALPHA: (m__) implies: % 28.12/4.67 | (10) $i(xm) % 28.12/4.68 | (11) $i(xp) % 28.12/4.68 | (12) $i(xr) % 28.12/4.68 | (13) ? [v0: $i] : (sdtasdt0(xr, xm) = v0 & $i(v0) & ~ doDivides0(xp, v0) % 28.12/4.68 | & ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) | ~ % 28.12/4.68 | aNaturalNumber0(v1))) % 28.12/4.68 | % 28.12/4.68 | ALPHA: (function-axioms) implies: % 28.12/4.68 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.12/4.68 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 28.12/4.68 | % 28.12/4.68 | DELTA: instantiating (13) with fresh symbol all_42_0 gives: % 28.12/4.68 | (15) sdtasdt0(xr, xm) = all_42_0 & $i(all_42_0) & ~ doDivides0(xp, % 28.12/4.68 | all_42_0) & ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_42_0) | ~ % 28.12/4.68 | $i(v0) | ~ aNaturalNumber0(v0)) % 28.12/4.68 | % 28.12/4.68 | ALPHA: (15) implies: % 28.12/4.68 | (16) ~ doDivides0(xp, all_42_0) % 28.12/4.68 | (17) sdtasdt0(xr, xm) = all_42_0 % 28.12/4.68 | % 28.12/4.68 | DELTA: instantiating (7) with fresh symbols all_45_0, all_45_1, all_45_2 % 28.12/4.68 | gives: % 28.12/4.68 | (18) sdtasdt0(xr, xm) = all_45_0 & sdtasdt0(xp, xm) = all_45_1 & % 28.12/4.68 | sdtasdt0(xn, xm) = all_45_2 & sdtpldt0(all_45_1, all_45_0) = all_45_2 % 28.12/4.68 | & $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 28.12/4.68 | % 28.12/4.68 | ALPHA: (18) implies: % 28.12/4.68 | (19) sdtpldt0(all_45_1, all_45_0) = all_45_2 % 28.12/4.68 | (20) sdtasdt0(xn, xm) = all_45_2 % 28.12/4.68 | (21) sdtasdt0(xp, xm) = all_45_1 % 28.12/4.68 | (22) sdtasdt0(xr, xm) = all_45_0 % 28.12/4.68 | % 28.12/4.68 | DELTA: instantiating (8) with fresh symbols all_47_0, all_47_1, all_47_2 % 28.12/4.68 | gives: % 28.12/4.69 | (23) sdtmndt0(all_47_0, all_47_2) = all_47_1 & sdtasdt0(xr, xm) = all_47_1 % 28.12/4.69 | & sdtasdt0(xp, xm) = all_47_2 & sdtasdt0(xn, xm) = all_47_0 & % 28.12/4.69 | sdtpldt0(all_47_2, all_47_1) = all_47_0 & $i(all_47_0) & $i(all_47_1) % 28.12/4.69 | & $i(all_47_2) % 28.12/4.69 | % 28.12/4.69 | ALPHA: (23) implies: % 28.12/4.69 | (24) sdtasdt0(xn, xm) = all_47_0 % 28.12/4.69 | (25) sdtasdt0(xp, xm) = all_47_2 % 28.12/4.69 | (26) sdtasdt0(xr, xm) = all_47_1 % 28.12/4.69 | % 28.12/4.69 | DELTA: instantiating (9) with fresh symbols all_49_0, all_49_1, all_49_2, % 28.12/4.69 | all_49_3 gives: % 28.12/4.69 | (27) sdtasdt0(xp, all_49_0) = all_49_3 & sdtasdt0(xp, all_49_1) = all_49_2 % 28.12/4.69 | & sdtasdt0(xp, xm) = all_49_2 & sdtasdt0(xn, xm) = all_49_3 & % 28.12/4.69 | $i(all_49_0) & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & % 28.12/4.69 | doDivides0(xp, all_49_2) & aNaturalNumber0(all_49_0) & % 28.12/4.69 | aNaturalNumber0(all_49_1) % 28.12/4.69 | % 28.12/4.69 | ALPHA: (27) implies: % 28.12/4.69 | (28) aNaturalNumber0(all_49_1) % 28.12/4.69 | (29) doDivides0(xp, all_49_2) % 28.12/4.69 | (30) $i(all_49_1) % 28.12/4.69 | (31) sdtasdt0(xn, xm) = all_49_3 % 28.12/4.69 | (32) sdtasdt0(xp, xm) = all_49_2 % 28.12/4.69 | (33) sdtasdt0(xp, all_49_1) = all_49_2 % 28.12/4.69 | % 28.12/4.69 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives: % 28.12/4.69 | (34) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_51_0) = all_51_1 & % 28.12/4.69 | sdtasdt0(xn, xm) = all_51_1 & $i(all_51_0) & $i(all_51_1) & % 28.12/4.69 | isPrime0(xp) & doDivides0(xp, all_51_1) & aNaturalNumber0(all_51_0) & % 28.12/4.69 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) % 28.12/4.69 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 28.12/4.69 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 28.12/4.69 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 28.12/4.69 | % 28.12/4.69 | ALPHA: (34) implies: % 28.12/4.69 | (35) doDivides0(xp, all_51_1) % 28.12/4.70 | (36) sdtasdt0(xn, xm) = all_51_1 % 28.12/4.70 | % 28.12/4.70 | BETA: splitting (2) gives: % 28.12/4.70 | % 28.12/4.70 | Case 1: % 28.12/4.70 | | % 28.12/4.70 | | (37) ~ aNaturalNumber0(sz10) % 28.12/4.70 | | % 28.12/4.70 | | PRED_UNIFY: (1), (37) imply: % 28.12/4.70 | | (38) $false % 28.12/4.70 | | % 28.12/4.70 | | CLOSE: (38) is inconsistent. % 28.12/4.70 | | % 28.12/4.70 | Case 2: % 28.12/4.70 | | % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_45_2, all_49_3, xm, xn, simplifying % 28.12/4.70 | | with (20), (31) gives: % 28.12/4.70 | | (39) all_49_3 = all_45_2 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_49_3, all_51_1, xm, xn, simplifying % 28.12/4.70 | | with (31), (36) gives: % 28.12/4.70 | | (40) all_51_1 = all_49_3 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_47_0, all_51_1, xm, xn, simplifying % 28.12/4.70 | | with (24), (36) gives: % 28.12/4.70 | | (41) all_51_1 = all_47_0 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_47_2, all_49_2, xm, xp, simplifying % 28.12/4.70 | | with (25), (32) gives: % 28.12/4.70 | | (42) all_49_2 = all_47_2 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_45_1, all_49_2, xm, xp, simplifying % 28.12/4.70 | | with (21), (32) gives: % 28.12/4.70 | | (43) all_49_2 = all_45_1 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_45_0, all_47_1, xm, xr, simplifying % 28.12/4.70 | | with (22), (26) gives: % 28.12/4.70 | | (44) all_47_1 = all_45_0 % 28.12/4.70 | | % 28.12/4.70 | | GROUND_INST: instantiating (14) with all_42_0, all_47_1, xm, xr, simplifying % 28.12/4.70 | | with (17), (26) gives: % 28.12/4.70 | | (45) all_47_1 = all_42_0 % 28.12/4.70 | | % 28.12/4.70 | | COMBINE_EQS: (40), (41) imply: % 28.12/4.70 | | (46) all_49_3 = all_47_0 % 28.12/4.70 | | % 28.12/4.70 | | SIMP: (46) implies: % 28.12/4.70 | | (47) all_49_3 = all_47_0 % 28.12/4.70 | | % 28.12/4.70 | | COMBINE_EQS: (42), (43) imply: % 28.12/4.71 | | (48) all_47_2 = all_45_1 % 28.12/4.71 | | % 28.12/4.71 | | COMBINE_EQS: (39), (47) imply: % 28.12/4.71 | | (49) all_47_0 = all_45_2 % 28.12/4.71 | | % 28.12/4.71 | | SIMP: (49) implies: % 28.12/4.71 | | (50) all_47_0 = all_45_2 % 28.12/4.71 | | % 28.12/4.71 | | COMBINE_EQS: (44), (45) imply: % 28.12/4.71 | | (51) all_45_0 = all_42_0 % 28.12/4.71 | | % 28.12/4.71 | | COMBINE_EQS: (41), (50) imply: % 28.12/4.71 | | (52) all_51_1 = all_45_2 % 28.12/4.71 | | % 28.12/4.71 | | REDUCE: (33), (43) imply: % 28.12/4.71 | | (53) sdtasdt0(xp, all_49_1) = all_45_1 % 28.12/4.71 | | % 28.12/4.71 | | REDUCE: (19), (51) imply: % 28.12/4.71 | | (54) sdtpldt0(all_45_1, all_42_0) = all_45_2 % 28.12/4.71 | | % 28.12/4.71 | | REDUCE: (35), (52) imply: % 28.12/4.71 | | (55) doDivides0(xp, all_45_2) % 28.12/4.71 | | % 28.12/4.71 | | REDUCE: (29), (43) imply: % 28.12/4.71 | | (56) doDivides0(xp, all_45_1) % 28.12/4.71 | | % 28.12/4.71 | | GROUND_INST: instantiating (mSortsB_02) with xp, all_49_1, all_45_1, % 28.12/4.71 | | simplifying with (4), (11), (28), (30), (53) gives: % 28.12/4.71 | | (57) aNaturalNumber0(all_45_1) % 28.12/4.71 | | % 28.12/4.71 | | GROUND_INST: instantiating (mMulComm) with xp, all_49_1, all_45_1, % 28.12/4.71 | | simplifying with (4), (11), (28), (30), (53) gives: % 28.12/4.71 | | (58) sdtasdt0(all_49_1, xp) = all_45_1 & $i(all_45_1) % 28.12/4.71 | | % 28.12/4.71 | | ALPHA: (58) implies: % 28.12/4.71 | | (59) $i(all_45_1) % 28.12/4.71 | | % 28.12/4.71 | | GROUND_INST: instantiating (mSortsB_02) with xr, xm, all_42_0, simplifying % 28.12/4.71 | | with (3), (6), (10), (12), (17) gives: % 28.12/4.71 | | (60) aNaturalNumber0(all_42_0) % 28.12/4.71 | | % 28.12/4.71 | | GROUND_INST: instantiating (mMulComm) with xr, xm, all_42_0, simplifying % 28.12/4.71 | | with (3), (6), (10), (12), (17) gives: % 28.12/4.71 | | (61) sdtasdt0(xm, xr) = all_42_0 & $i(all_42_0) % 28.12/4.71 | | % 28.12/4.71 | | ALPHA: (61) implies: % 28.12/4.71 | | (62) $i(all_42_0) % 28.12/4.71 | | % 28.12/4.71 | | GROUND_INST: instantiating (mDivMin) with xp, all_45_1, all_42_0, all_45_2, % 28.12/4.71 | | simplifying with (4), (11), (16), (54), (55), (56), (57), (59), % 28.12/4.71 | | (60), (62) gives: % 28.12/4.71 | | (63) $false % 28.12/4.71 | | % 28.12/4.71 | | CLOSE: (63) is inconsistent. % 28.12/4.71 | | % 28.12/4.71 | End of split % 28.12/4.71 | % 28.12/4.71 End of proof % 28.12/4.72 % SZS output end Proof for theBenchmark % 28.12/4.72 % 28.12/4.72 4092ms %------------------------------------------------------------------------------