%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM529+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 : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:48:24 EDT 2023 % Result : Theorem 59.12s 8.64s % Output : Proof 68.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM529+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n014.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 12:42:48 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.75/1.24 Prover 1: Preprocessing ... % 3.75/1.24 Prover 4: Preprocessing ... % 3.75/1.27 Prover 3: Preprocessing ... % 3.75/1.27 Prover 2: Preprocessing ... % 3.75/1.27 Prover 6: Preprocessing ... % 3.75/1.27 Prover 5: Preprocessing ... % 3.75/1.27 Prover 0: Preprocessing ... % 9.19/2.02 Prover 1: Constructing countermodel ... % 9.19/2.02 Prover 3: Constructing countermodel ... % 9.19/2.13 Prover 6: Proving ... % 9.19/2.17 Prover 5: Constructing countermodel ... % 11.23/2.29 Prover 2: Proving ... % 12.19/2.45 Prover 4: Constructing countermodel ... % 12.63/2.51 Prover 0: Proving ... % 59.12/8.64 Prover 0: proved (7978ms) % 59.12/8.64 % 59.12/8.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 59.12/8.64 % 59.12/8.64 Prover 3: stopped % 59.12/8.65 Prover 5: stopped % 59.12/8.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 59.12/8.67 Prover 6: stopped % 59.12/8.68 Prover 2: stopped % 59.12/8.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 59.12/8.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 59.12/8.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 59.12/8.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 59.12/8.73 Prover 7: Preprocessing ... % 59.12/8.75 Prover 10: Preprocessing ... % 59.12/8.76 Prover 8: Preprocessing ... % 60.08/8.82 Prover 10: Constructing countermodel ... % 60.08/8.84 Prover 11: Preprocessing ... % 60.08/8.84 Prover 8: Warning: ignoring some quantifiers % 60.08/8.85 Prover 8: Constructing countermodel ... % 61.04/8.87 Prover 13: Preprocessing ... % 61.04/8.90 Prover 7: Constructing countermodel ... % 62.37/9.06 Prover 13: Constructing countermodel ... % 62.90/9.13 Prover 11: Constructing countermodel ... % 67.11/9.74 Prover 10: Found proof (size 69) % 67.11/9.74 Prover 10: proved (1070ms) % 67.11/9.74 Prover 7: stopped % 67.11/9.74 Prover 11: stopped % 67.11/9.74 Prover 8: stopped % 67.11/9.74 Prover 13: stopped % 67.11/9.75 Prover 4: stopped % 67.11/9.75 Prover 1: stopped % 67.11/9.75 % 67.11/9.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 67.11/9.75 % 67.82/9.75 % SZS output start Proof for theBenchmark % 67.82/9.76 Assumptions after simplification: % 67.82/9.76 --------------------------------- % 67.82/9.76 % 67.82/9.76 (mAddComm) % 67.82/9.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 67.82/9.78 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 67.82/9.78 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 67.82/9.78 % 67.82/9.78 (mDefLE) % 67.82/9.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 67.82/9.78 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 67.82/9.78 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 67.82/9.78 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 67.82/9.78 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 67.82/9.78 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 67.82/9.78 % 67.82/9.78 (mDefPrime) % 67.82/9.79 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 67.82/9.79 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 67.82/9.79 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 67.82/9.79 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 67.82/9.79 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 67.82/9.79 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 67.82/9.79 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 67.82/9.79 % 67.82/9.79 (mIH_03) % 67.82/9.79 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 67.82/9.79 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 67.82/9.79 iLess0(v0, v1)) % 67.82/9.79 % 67.82/9.79 (mLENTr) % 68.01/9.79 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 68.01/9.79 aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 68.01/9.79 % 68.01/9.79 (mMulComm) % 68.01/9.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 68.01/9.79 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 68.01/9.79 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 68.01/9.79 % 68.01/9.79 (mPrimDiv) % 68.01/9.79 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 68.01/9.79 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1, % 68.01/9.79 v0) & aNaturalNumber0(v1))) % 68.01/9.79 % 68.01/9.79 (mSortsC_01) % 68.01/9.79 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 68.01/9.79 % 68.01/9.79 (m_MulZero) % 68.01/9.79 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = % 68.01/9.79 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ( % 68.01/9.79 ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 68.01/9.79 sdtasdt0(v0, sz00) = sz00) % 68.01/9.79 % 68.01/9.79 (m__2963) % 68.01/9.80 $i(xn) & $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 68.01/9.80 [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ % 68.01/9.80 (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) % 68.01/9.80 = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v0, xn) | ~ % 68.01/9.80 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 68.01/9.80 [v5: $i] : ? [v6: $i] : ( ~ (v5 = v2) & ~ (v5 = sz10) & sdtasdt0(v5, v6) = % 68.01/9.80 v2 & $i(v6) & $i(v5) & doDivides0(v5, v2) & aNaturalNumber0(v6) & % 68.01/9.80 aNaturalNumber0(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 68.01/9.80 $i] : ! [v4: $i] : (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, % 68.01/9.80 v3) = v4) | ~ (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ % 68.01/9.80 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~ % 68.01/9.80 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 68.01/9.80 % 68.01/9.80 (m__2987) % 68.01/9.80 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) & % 68.01/9.80 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) % 68.01/9.80 % 68.01/9.80 (m__3014) % 68.01/9.80 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 % 68.01/9.80 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 68.01/9.80 % 68.01/9.80 (m__3025) % 68.01/9.80 ~ (xp = sz10) & $i(xp) & $i(sz10) & isPrime0(xp) & ! [v0: $i] : ! [v1: $i] % 68.01/9.80 : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ $i(v1) | ~ $i(v0) | % 68.01/9.80 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | % 68.01/9.80 v0 = sz10 | ~ $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 68.01/9.80 % 68.01/9.80 (m__3059) % 68.01/9.80 sdtsldt0(xn, xp) = xq & sdtasdt0(xp, xq) = xn & $i(xq) & $i(xp) & $i(xn) & % 68.01/9.80 aNaturalNumber0(xq) % 68.01/9.80 % 68.01/9.80 (m__3082) % 68.01/9.80 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xq) = v1 % 68.01/9.80 & sdtasdt0(xp, v1) = v0 & sdtasdt0(xm, xm) = v0 & $i(v1) & $i(v0)) % 68.01/9.80 % 68.01/9.80 (m__3124) % 68.01/9.80 $i(xm) & $i(xn) & ? [v0: $i] : ( ~ (xm = xn) & sdtpldt0(xm, v0) = xn & $i(v0) % 68.01/9.80 & sdtlseqdt0(xm, xn) & aNaturalNumber0(v0)) % 68.01/9.80 % 68.01/9.80 (function-axioms) % 68.01/9.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.01/9.80 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 68.01/9.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 68.01/9.80 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 68.01/9.80 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 68.01/9.80 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.01/9.80 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 68.01/9.80 % 68.01/9.80 Further assumptions not needed in the proof: % 68.01/9.80 -------------------------------------------- % 68.01/9.81 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDefQuot, mDivAsso, mDivLE, % 68.01/9.81 mDivMin, mDivSum, mDivTrans, mIH, mLEAsym, mLERefl, mLETotal, mLETran, mMonAdd, % 68.01/9.81 mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, mPDP, mSortsB, mSortsB_02, % 68.01/9.81 mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m__, m__3046 % 68.01/9.81 % 68.01/9.81 Those formulas are unsatisfiable: % 68.01/9.81 --------------------------------- % 68.01/9.81 % 68.01/9.81 Begin of proof % 68.01/9.81 | % 68.01/9.81 | ALPHA: (mSortsC_01) implies: % 68.01/9.81 | (1) aNaturalNumber0(sz10) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m_MulZero) implies: % 68.01/9.81 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | % 68.01/9.81 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (mDefLE) implies: % 68.01/9.81 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 68.01/9.81 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 68.01/9.81 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (mLENTr) implies: % 68.01/9.81 | (4) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 68.01/9.81 | aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (mDefPrime) implies: % 68.01/9.81 | (5) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (mPrimDiv) implies: % 68.01/9.81 | (6) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 68.01/9.81 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & % 68.01/9.81 | doDivides0(v1, v0) & aNaturalNumber0(v1))) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__2987) implies: % 68.01/9.81 | (7) ~ (xn = sz00) % 68.01/9.81 | (8) ~ (xm = sz00) % 68.01/9.81 | (9) ~ (xp = sz00) % 68.01/9.81 | (10) aNaturalNumber0(xn) % 68.01/9.81 | (11) aNaturalNumber0(xm) % 68.01/9.81 | (12) aNaturalNumber0(xp) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__2963) implies: % 68.01/9.81 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 68.01/9.81 | (v2 = sz00 | v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v2, v3) = v4) | ~ % 68.01/9.81 | (sdtasdt0(v1, v1) = v3) | ~ (sdtasdt0(v0, v0) = v4) | ~ $i(v2) | % 68.01/9.81 | ~ $i(v1) | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v0, xn) | ~ % 68.01/9.81 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 68.01/9.81 | aNaturalNumber0(v0)) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__3014) implies: % 68.01/9.81 | (14) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) % 68.01/9.81 | = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__3025) implies: % 68.01/9.81 | (15) ~ (xp = sz10) % 68.01/9.81 | (16) isPrime0(xp) % 68.01/9.81 | (17) $i(sz10) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__3059) implies: % 68.01/9.81 | (18) aNaturalNumber0(xq) % 68.01/9.81 | (19) sdtasdt0(xp, xq) = xn % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__3082) implies: % 68.01/9.81 | (20) $i(xp) % 68.01/9.81 | (21) $i(xq) % 68.01/9.81 | (22) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xq) = v1 & sdtasdt0(xp, v1) % 68.01/9.81 | = v0 & sdtasdt0(xm, xm) = v0 & $i(v1) & $i(v0)) % 68.01/9.81 | % 68.01/9.81 | ALPHA: (m__3124) implies: % 68.01/9.82 | (23) $i(xn) % 68.01/9.82 | (24) $i(xm) % 68.01/9.82 | (25) ? [v0: $i] : ( ~ (xm = xn) & sdtpldt0(xm, v0) = xn & $i(v0) & % 68.01/9.82 | sdtlseqdt0(xm, xn) & aNaturalNumber0(v0)) % 68.01/9.82 | % 68.01/9.82 | ALPHA: (function-axioms) implies: % 68.01/9.82 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.01/9.82 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 68.01/9.82 | % 68.01/9.82 | DELTA: instantiating (14) with fresh symbols all_41_0, all_41_1 gives: % 68.01/9.82 | (27) sdtasdt0(xp, all_41_1) = all_41_0 & sdtasdt0(xm, xm) = all_41_1 & % 68.01/9.82 | sdtasdt0(xn, xn) = all_41_0 & $i(all_41_0) & $i(all_41_1) % 68.01/9.82 | % 68.01/9.82 | ALPHA: (27) implies: % 68.01/9.82 | (28) sdtasdt0(xm, xm) = all_41_1 % 68.01/9.82 | % 68.01/9.82 | DELTA: instantiating (22) with fresh symbols all_43_0, all_43_1 gives: % 68.01/9.82 | (29) sdtasdt0(xq, xq) = all_43_0 & sdtasdt0(xp, all_43_0) = all_43_1 & % 68.01/9.82 | sdtasdt0(xm, xm) = all_43_1 & $i(all_43_0) & $i(all_43_1) % 68.01/9.82 | % 68.01/9.82 | ALPHA: (29) implies: % 68.01/9.82 | (30) sdtasdt0(xm, xm) = all_43_1 % 68.01/9.82 | (31) sdtasdt0(xp, all_43_0) = all_43_1 % 68.01/9.82 | (32) sdtasdt0(xq, xq) = all_43_0 % 68.01/9.82 | % 68.01/9.82 | DELTA: instantiating (25) with fresh symbol all_45_0 gives: % 68.01/9.82 | (33) ~ (xm = xn) & sdtpldt0(xm, all_45_0) = xn & $i(all_45_0) & % 68.01/9.82 | sdtlseqdt0(xm, xn) & aNaturalNumber0(all_45_0) % 68.01/9.82 | % 68.01/9.82 | ALPHA: (33) implies: % 68.01/9.82 | (34) ~ (xm = xn) % 68.01/9.82 | (35) sdtlseqdt0(xm, xn) % 68.01/9.82 | % 68.01/9.82 | BETA: splitting (5) gives: % 68.01/9.82 | % 68.01/9.82 | Case 1: % 68.01/9.82 | | % 68.01/9.82 | | (36) ~ aNaturalNumber0(sz10) % 68.01/9.82 | | % 68.01/9.82 | | PRED_UNIFY: (1), (36) imply: % 68.01/9.82 | | (37) $false % 68.01/9.82 | | % 68.01/9.82 | | CLOSE: (37) is inconsistent. % 68.01/9.82 | | % 68.01/9.82 | Case 2: % 68.01/9.82 | | % 68.01/9.82 | | % 68.01/9.82 | | GROUND_INST: instantiating (26) with all_41_1, all_43_1, xm, xm, simplifying % 68.01/9.82 | | with (28), (30) gives: % 68.01/9.82 | | (38) all_43_1 = all_41_1 % 68.01/9.82 | | % 68.01/9.82 | | REDUCE: (31), (38) imply: % 68.01/9.82 | | (39) sdtasdt0(xp, all_43_0) = all_41_1 % 68.01/9.82 | | % 68.01/9.82 | | GROUND_INST: instantiating (4) with xp, simplifying with (12), (20) gives: % 68.01/9.82 | | (40) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp) % 68.01/9.82 | | % 68.01/9.82 | | GROUND_INST: instantiating (6) with xp, simplifying with (12), (20) gives: % 68.01/9.82 | | (41) xp = sz10 | xp = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) & % 68.01/9.82 | | doDivides0(v0, xp) & aNaturalNumber0(v0)) % 68.01/9.82 | | % 68.01/9.82 | | GROUND_INST: instantiating (mIH_03) with xm, xn, simplifying with (10), % 68.01/9.82 | | (11), (23), (24), (35) gives: % 68.01/9.82 | | (42) xm = xn | iLess0(xm, xn) % 68.01/9.82 | | % 68.01/9.82 | | GROUND_INST: instantiating (mMulComm) with xp, xq, xn, simplifying with % 68.01/9.82 | | (12), (18), (19), (20), (21) gives: % 68.01/9.82 | | (43) sdtasdt0(xq, xp) = xn & $i(xn) % 68.01/9.82 | | % 68.01/9.82 | | ALPHA: (43) implies: % 68.01/9.83 | | (44) sdtasdt0(xq, xp) = xn % 68.01/9.83 | | % 68.01/9.83 | | BETA: splitting (42) gives: % 68.01/9.83 | | % 68.01/9.83 | | Case 1: % 68.01/9.83 | | | % 68.01/9.83 | | | (45) iLess0(xm, xn) % 68.01/9.83 | | | % 68.01/9.83 | | | BETA: splitting (40) gives: % 68.01/9.83 | | | % 68.01/9.83 | | | Case 1: % 68.01/9.83 | | | | % 68.01/9.83 | | | | (46) sdtlseqdt0(sz10, xp) % 68.01/9.83 | | | | % 68.01/9.83 | | | | BETA: splitting (41) gives: % 68.01/9.83 | | | | % 68.01/9.83 | | | | Case 1: % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | (47) xp = sz00 % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | REDUCE: (9), (47) imply: % 68.01/9.83 | | | | | (48) $false % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | CLOSE: (48) is inconsistent. % 68.01/9.83 | | | | | % 68.01/9.83 | | | | Case 2: % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | (49) xp = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) & % 68.01/9.83 | | | | | doDivides0(v0, xp) & aNaturalNumber0(v0)) % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | BETA: splitting (49) gives: % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | Case 1: % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | (50) xp = sz10 % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | REDUCE: (15), (50) imply: % 68.01/9.83 | | | | | | (51) $false % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | CLOSE: (51) is inconsistent. % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | Case 2: % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | GROUND_INST: instantiating (3) with sz10, xp, simplifying with (1), % 68.01/9.83 | | | | | | (12), (17), (20), (46) gives: % 68.01/9.83 | | | | | | (52) ? [v0: $i] : (sdtpldt0(sz10, v0) = xp & $i(v0) & % 68.01/9.83 | | | | | | aNaturalNumber0(v0)) % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | GROUND_INST: instantiating (13) with xm, xq, xp, all_43_0, all_41_1, % 68.01/9.83 | | | | | | simplifying with (11), (12), (16), (18), (20), (21), % 68.01/9.83 | | | | | | (24), (28), (32), (39), (45) gives: % 68.01/9.83 | | | | | | (53) xq = sz00 | xp = sz00 | xm = sz00 % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | DELTA: instantiating (52) with fresh symbol all_128_0 gives: % 68.01/9.83 | | | | | | (54) sdtpldt0(sz10, all_128_0) = xp & $i(all_128_0) & % 68.01/9.83 | | | | | | aNaturalNumber0(all_128_0) % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | ALPHA: (54) implies: % 68.01/9.83 | | | | | | (55) aNaturalNumber0(all_128_0) % 68.01/9.83 | | | | | | (56) $i(all_128_0) % 68.01/9.83 | | | | | | (57) sdtpldt0(sz10, all_128_0) = xp % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | BETA: splitting (53) gives: % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | | Case 1: % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | (58) xq = sz00 % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | REDUCE: (44), (58) imply: % 68.01/9.83 | | | | | | | (59) sdtasdt0(sz00, xp) = xn % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_128_0, xp, % 68.01/9.83 | | | | | | | simplifying with (1), (17), (55), (56), (57) gives: % 68.01/9.83 | | | | | | | (60) sdtpldt0(all_128_0, sz10) = xp & $i(xp) % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | GROUND_INST: instantiating (2) with xp, xn, simplifying with (12), % 68.01/9.83 | | | | | | | (20), (59) gives: % 68.01/9.83 | | | | | | | (61) xn = sz00 % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | REDUCE: (7), (61) imply: % 68.01/9.83 | | | | | | | (62) $false % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | CLOSE: (62) is inconsistent. % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | Case 2: % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | (63) xp = sz00 | xm = sz00 % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | BETA: splitting (63) gives: % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | | Case 1: % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | (64) xp = sz00 % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | REDUCE: (9), (64) imply: % 68.01/9.83 | | | | | | | | (65) $false % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | CLOSE: (65) is inconsistent. % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | Case 2: % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | (66) xm = sz00 % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | REDUCE: (8), (66) imply: % 68.01/9.83 | | | | | | | | (67) $false % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | | CLOSE: (67) is inconsistent. % 68.01/9.83 | | | | | | | | % 68.01/9.83 | | | | | | | End of split % 68.01/9.83 | | | | | | | % 68.01/9.83 | | | | | | End of split % 68.01/9.83 | | | | | | % 68.01/9.83 | | | | | End of split % 68.01/9.83 | | | | | % 68.01/9.83 | | | | End of split % 68.01/9.83 | | | | % 68.01/9.83 | | | Case 2: % 68.01/9.83 | | | | % 68.01/9.83 | | | | (68) xp = sz10 | xp = sz00 % 68.01/9.83 | | | | % 68.01/9.83 | | | | BETA: splitting (68) gives: % 68.01/9.83 | | | | % 68.01/9.83 | | | | Case 1: % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | (69) xp = sz00 % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | REDUCE: (9), (69) imply: % 68.01/9.83 | | | | | (70) $false % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | CLOSE: (70) is inconsistent. % 68.01/9.83 | | | | | % 68.01/9.83 | | | | Case 2: % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | (71) xp = sz10 % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | REDUCE: (15), (71) imply: % 68.01/9.83 | | | | | (72) $false % 68.01/9.83 | | | | | % 68.01/9.83 | | | | | CLOSE: (72) is inconsistent. % 68.01/9.83 | | | | | % 68.01/9.83 | | | | End of split % 68.01/9.83 | | | | % 68.01/9.83 | | | End of split % 68.01/9.83 | | | % 68.01/9.83 | | Case 2: % 68.01/9.83 | | | % 68.01/9.83 | | | (73) xm = xn % 68.01/9.83 | | | % 68.01/9.83 | | | REDUCE: (34), (73) imply: % 68.01/9.83 | | | (74) $false % 68.01/9.83 | | | % 68.01/9.83 | | | CLOSE: (74) is inconsistent. % 68.01/9.83 | | | % 68.01/9.83 | | End of split % 68.01/9.83 | | % 68.01/9.83 | End of split % 68.01/9.83 | % 68.01/9.83 End of proof % 68.01/9.83 % SZS output end Proof for theBenchmark % 68.01/9.84 % 68.01/9.84 9230ms %------------------------------------------------------------------------------