%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 11:48:07 EDT 2023 % Result : Theorem 137.74s 19.08s % Output : Proof 138.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM490+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 08:52:50 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.67/1.24 Prover 1: Preprocessing ... % 3.67/1.24 Prover 4: Preprocessing ... % 3.94/1.28 Prover 5: Preprocessing ... % 3.94/1.28 Prover 3: Preprocessing ... % 3.94/1.28 Prover 0: Preprocessing ... % 3.94/1.28 Prover 6: Preprocessing ... % 3.94/1.30 Prover 2: Preprocessing ... % 9.17/2.07 Prover 1: Constructing countermodel ... % 9.17/2.09 Prover 3: Constructing countermodel ... % 9.17/2.15 Prover 6: Proving ... % 10.46/2.23 Prover 5: Constructing countermodel ... % 11.80/2.37 Prover 2: Proving ... % 11.80/2.41 Prover 4: Constructing countermodel ... % 12.82/2.50 Prover 0: Proving ... % 72.23/10.28 Prover 2: stopped % 72.23/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.23/10.37 Prover 7: Preprocessing ... % 73.16/10.50 Prover 7: Constructing countermodel ... % 100.10/13.97 Prover 5: stopped % 100.10/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.69/14.07 Prover 8: Preprocessing ... % 101.81/14.24 Prover 8: Warning: ignoring some quantifiers % 101.81/14.24 Prover 8: Constructing countermodel ... % 115.15/15.97 Prover 1: stopped % 115.15/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.15/16.04 Prover 9: Preprocessing ... % 118.36/16.41 Prover 9: Constructing countermodel ... % 128.77/17.89 Prover 6: stopped % 128.77/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 129.66/17.97 Prover 10: Preprocessing ... % 129.66/18.07 Prover 10: Constructing countermodel ... % 137.74/19.07 Prover 10: Found proof (size 56) % 137.74/19.07 Prover 10: proved (1182ms) % 137.74/19.08 Prover 0: stopped % 137.74/19.08 Prover 3: stopped % 137.74/19.08 Prover 7: stopped % 137.74/19.08 Prover 8: stopped % 137.74/19.08 Prover 4: stopped % 137.74/19.08 Prover 9: stopped % 137.74/19.08 % 137.74/19.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 137.74/19.08 % 137.74/19.09 % SZS output start Proof for theBenchmark % 137.74/19.09 Assumptions after simplification: % 137.74/19.09 --------------------------------- % 137.74/19.09 % 137.74/19.09 (mAddComm) % 138.16/19.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 138.16/19.12 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 138.16/19.12 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 138.16/19.12 % 138.16/19.12 (mDefDiff) % 138.16/19.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 138.16/19.12 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1) % 138.16/19.12 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ % 138.16/19.12 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 138.16/19.12 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ % 138.16/19.12 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 138.16/19.12 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 138.16/19.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) = % 138.16/19.12 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 138.16/19.12 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 138.16/19.12 aNaturalNumber0(v2)) % 138.16/19.12 % 138.16/19.12 (mDefDiv) % 138.16/19.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 138.16/19.12 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 138.16/19.12 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 138.16/19.12 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 138.16/19.12 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 138.16/19.12 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 138.16/19.12 % 138.16/19.12 (mDefLE) % 138.16/19.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 138.16/19.13 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 138.16/19.13 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 138.16/19.13 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 138.16/19.13 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 138.16/19.13 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 138.16/19.13 % 138.16/19.13 (mDefPrime) % 138.16/19.13 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 138.16/19.13 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 138.16/19.13 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 138.16/19.13 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 138.16/19.13 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 138.16/19.13 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 138.16/19.13 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 138.16/19.13 % 138.16/19.13 (mMulComm) % 138.16/19.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 138.16/19.13 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 138.16/19.13 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 138.16/19.13 % 138.16/19.13 (mSortsB_02) % 138.16/19.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 138.16/19.13 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 138.16/19.13 aNaturalNumber0(v2)) % 138.16/19.13 % 138.16/19.13 (mSortsC_01) % 138.16/19.13 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 138.16/19.13 % 138.16/19.13 (m__) % 138.16/19.14 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 138.16/19.14 ? [v3: $i] : ( ~ (v3 = v0) & sdtmndt0(v1, v2) = v3 & sdtasdt0(xr, xm) = v0 & % 138.16/19.14 sdtasdt0(xp, xm) = v2 & sdtasdt0(xn, xm) = v1 & $i(v3) & $i(v2) & $i(v1) & % 138.16/19.14 $i(v0)) % 138.16/19.14 % 138.16/19.14 (m__1837) % 138.16/19.14 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 138.16/19.14 aNaturalNumber0(xn) % 138.16/19.14 % 138.16/19.14 (m__1860) % 138.16/19.14 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtasdt0(xn, xm) = v0 & $i(v0) & % 138.16/19.14 isPrime0(xp) & doDivides0(xp, v0)) % 138.16/19.14 % 138.16/19.14 (m__1870) % 138.16/19.14 $i(xp) & $i(xn) & sdtlseqdt0(xp, xn) % 138.16/19.14 % 138.16/19.14 (m__1883) % 138.16/19.14 sdtmndt0(xn, xp) = xr & $i(xr) & $i(xp) & $i(xn) % 138.16/19.14 % 138.16/19.14 (m__1924) % 138.16/19.14 sdtpldt0(xp, xr) = xn & $i(xr) & $i(xp) & $i(xn) % 138.16/19.14 % 138.16/19.14 (m__1951) % 138.16/19.14 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 138.16/19.14 (sdtasdt0(xr, xm) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & % 138.16/19.14 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 138.16/19.14 % 138.16/19.14 (function-axioms) % 138.16/19.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 138.16/19.14 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 138.16/19.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 138.16/19.14 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 138.16/19.14 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 138.16/19.14 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 138.16/19.14 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 138.16/19.14 % 138.16/19.14 Further assumptions not needed in the proof: % 138.16/19.14 -------------------------------------------- % 138.16/19.14 mAMDistr, mAddAsso, mAddCanc, mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, % 138.16/19.14 mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, % 138.16/19.14 mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, mPrimDiv, mSortsB, mSortsC, % 138.16/19.14 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, m__1894 % 138.16/19.14 % 138.16/19.14 Those formulas are unsatisfiable: % 138.16/19.14 --------------------------------- % 138.16/19.14 % 138.16/19.14 Begin of proof % 138.16/19.14 | % 138.16/19.14 | ALPHA: (mSortsC_01) implies: % 138.16/19.14 | (1) aNaturalNumber0(sz10) % 138.16/19.14 | % 138.16/19.14 | ALPHA: (mDefLE) implies: % 138.16/19.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | % 138.16/19.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 138.16/19.15 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (mDefDiff) implies: % 138.16/19.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 138.16/19.15 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ % 138.16/19.15 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | % 138.16/19.15 | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 138.16/19.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 138.16/19.15 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ % 138.16/19.15 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | % 138.16/19.15 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (mDefDiv) implies: % 138.16/19.15 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 138.16/19.15 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 138.16/19.15 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (mDefPrime) implies: % 138.16/19.15 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1837) implies: % 138.16/19.15 | (7) aNaturalNumber0(xn) % 138.16/19.15 | (8) aNaturalNumber0(xm) % 138.16/19.15 | (9) aNaturalNumber0(xp) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1860) implies: % 138.16/19.15 | (10) ? [v0: $i] : (sdtasdt0(xn, xm) = v0 & $i(v0) & isPrime0(xp) & % 138.16/19.15 | doDivides0(xp, v0)) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1870) implies: % 138.16/19.15 | (11) sdtlseqdt0(xp, xn) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1883) implies: % 138.16/19.15 | (12) sdtmndt0(xn, xp) = xr % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1924) implies: % 138.16/19.15 | (13) sdtpldt0(xp, xr) = xn % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__1951) implies: % 138.16/19.15 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, xm) = v2 & % 138.16/19.15 | sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v2) = % 138.16/19.15 | v0 & $i(v2) & $i(v1) & $i(v0)) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (m__) implies: % 138.16/19.15 | (15) $i(xn) % 138.16/19.15 | (16) $i(xm) % 138.16/19.15 | (17) $i(xp) % 138.16/19.15 | (18) $i(xr) % 138.16/19.15 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v0) % 138.16/19.15 | & sdtmndt0(v1, v2) = v3 & sdtasdt0(xr, xm) = v0 & sdtasdt0(xp, xm) = % 138.16/19.15 | v2 & sdtasdt0(xn, xm) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 138.16/19.15 | % 138.16/19.15 | ALPHA: (function-axioms) implies: % 138.16/19.15 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 138.16/19.15 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 138.16/19.15 | % 138.16/19.16 | DELTA: instantiating (10) with fresh symbol all_38_0 gives: % 138.16/19.16 | (21) sdtasdt0(xn, xm) = all_38_0 & $i(all_38_0) & isPrime0(xp) & % 138.16/19.16 | doDivides0(xp, all_38_0) % 138.16/19.16 | % 138.16/19.16 | ALPHA: (21) implies: % 138.16/19.16 | (22) doDivides0(xp, all_38_0) % 138.16/19.16 | (23) sdtasdt0(xn, xm) = all_38_0 % 138.16/19.16 | % 138.16/19.16 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2 % 138.16/19.16 | gives: % 138.16/19.16 | (24) sdtasdt0(xr, xm) = all_40_0 & sdtasdt0(xp, xm) = all_40_1 & % 138.16/19.16 | sdtasdt0(xn, xm) = all_40_2 & sdtpldt0(all_40_1, all_40_0) = all_40_2 % 138.16/19.16 | & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) % 138.16/19.16 | % 138.16/19.16 | ALPHA: (24) implies: % 138.16/19.16 | (25) sdtpldt0(all_40_1, all_40_0) = all_40_2 % 138.16/19.16 | (26) sdtasdt0(xn, xm) = all_40_2 % 138.16/19.16 | (27) sdtasdt0(xp, xm) = all_40_1 % 138.16/19.16 | (28) sdtasdt0(xr, xm) = all_40_0 % 138.16/19.16 | % 138.16/19.16 | DELTA: instantiating (19) with fresh symbols all_42_0, all_42_1, all_42_2, % 138.16/19.16 | all_42_3 gives: % 138.16/19.16 | (29) ~ (all_42_0 = all_42_3) & sdtmndt0(all_42_2, all_42_1) = all_42_0 & % 138.16/19.16 | sdtasdt0(xr, xm) = all_42_3 & sdtasdt0(xp, xm) = all_42_1 & % 138.16/19.16 | sdtasdt0(xn, xm) = all_42_2 & $i(all_42_0) & $i(all_42_1) & % 138.16/19.16 | $i(all_42_2) & $i(all_42_3) % 138.16/19.16 | % 138.16/19.16 | ALPHA: (29) implies: % 138.16/19.16 | (30) ~ (all_42_0 = all_42_3) % 138.16/19.16 | (31) sdtasdt0(xn, xm) = all_42_2 % 138.16/19.16 | (32) sdtasdt0(xp, xm) = all_42_1 % 138.16/19.16 | (33) sdtasdt0(xr, xm) = all_42_3 % 138.16/19.16 | (34) sdtmndt0(all_42_2, all_42_1) = all_42_0 % 138.16/19.16 | % 138.16/19.16 | BETA: splitting (6) gives: % 138.16/19.16 | % 138.16/19.16 | Case 1: % 138.16/19.16 | | % 138.16/19.16 | | (35) ~ aNaturalNumber0(sz10) % 138.16/19.16 | | % 138.16/19.16 | | PRED_UNIFY: (1), (35) imply: % 138.16/19.16 | | (36) $false % 138.46/19.16 | | % 138.46/19.16 | | CLOSE: (36) is inconsistent. % 138.46/19.16 | | % 138.46/19.16 | Case 2: % 138.46/19.16 | | % 138.46/19.16 | | % 138.46/19.16 | | GROUND_INST: instantiating (20) with all_40_2, all_42_2, xm, xn, simplifying % 138.46/19.16 | | with (26), (31) gives: % 138.46/19.16 | | (37) all_42_2 = all_40_2 % 138.46/19.16 | | % 138.46/19.16 | | GROUND_INST: instantiating (20) with all_38_0, all_42_2, xm, xn, simplifying % 138.46/19.16 | | with (23), (31) gives: % 138.46/19.16 | | (38) all_42_2 = all_38_0 % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (20) with all_40_1, all_42_1, xm, xp, simplifying % 138.46/19.17 | | with (27), (32) gives: % 138.46/19.17 | | (39) all_42_1 = all_40_1 % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (20) with all_40_0, all_42_3, xm, xr, simplifying % 138.46/19.17 | | with (28), (33) gives: % 138.46/19.17 | | (40) all_42_3 = all_40_0 % 138.46/19.17 | | % 138.46/19.17 | | COMBINE_EQS: (37), (38) imply: % 138.46/19.17 | | (41) all_40_2 = all_38_0 % 138.46/19.17 | | % 138.46/19.17 | | SIMP: (41) implies: % 138.46/19.17 | | (42) all_40_2 = all_38_0 % 138.46/19.17 | | % 138.46/19.17 | | REDUCE: (30), (40) imply: % 138.46/19.17 | | (43) ~ (all_42_0 = all_40_0) % 138.46/19.17 | | % 138.46/19.17 | | REDUCE: (34), (38), (39) imply: % 138.46/19.17 | | (44) sdtmndt0(all_38_0, all_40_1) = all_42_0 % 138.46/19.17 | | % 138.46/19.17 | | REDUCE: (25), (42) imply: % 138.46/19.17 | | (45) sdtpldt0(all_40_1, all_40_0) = all_38_0 % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_38_0, simplifying % 138.46/19.17 | | with (7), (8), (15), (16), (23) gives: % 138.46/19.17 | | (46) aNaturalNumber0(all_38_0) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mMulComm) with xn, xm, all_38_0, simplifying % 138.46/19.17 | | with (7), (8), (15), (16), (23) gives: % 138.46/19.17 | | (47) sdtasdt0(xm, xn) = all_38_0 & $i(all_38_0) % 138.46/19.17 | | % 138.46/19.17 | | ALPHA: (47) implies: % 138.46/19.17 | | (48) $i(all_38_0) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mSortsB_02) with xp, xm, all_40_1, simplifying % 138.46/19.17 | | with (8), (9), (16), (17), (27) gives: % 138.46/19.17 | | (49) aNaturalNumber0(all_40_1) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mMulComm) with xp, xm, all_40_1, simplifying % 138.46/19.17 | | with (8), (9), (16), (17), (27) gives: % 138.46/19.17 | | (50) sdtasdt0(xm, xp) = all_40_1 & $i(all_40_1) % 138.46/19.17 | | % 138.46/19.17 | | ALPHA: (50) implies: % 138.46/19.17 | | (51) $i(all_40_1) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (3) with xp, xn, xr, xn, simplifying with (7), % 138.46/19.17 | | (9), (11), (12), (13), (15), (17), (18) gives: % 138.46/19.17 | | (52) aNaturalNumber0(xr) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mSortsB_02) with xr, xm, all_40_0, simplifying % 138.46/19.17 | | with (8), (16), (18), (28), (52) gives: % 138.46/19.17 | | (53) aNaturalNumber0(all_40_0) % 138.46/19.17 | | % 138.46/19.17 | | GROUND_INST: instantiating (mMulComm) with xr, xm, all_40_0, simplifying % 138.46/19.17 | | with (8), (16), (18), (28), (52) gives: % 138.46/19.17 | | (54) sdtasdt0(xm, xr) = all_40_0 & $i(all_40_0) % 138.46/19.17 | | % 138.46/19.17 | | ALPHA: (54) implies: % 138.46/19.17 | | (55) $i(all_40_0) % 138.46/19.17 | | % 138.46/19.18 | | GROUND_INST: instantiating (5) with xp, all_38_0, simplifying with (9), % 138.46/19.18 | | (17), (22), (46), (48) gives: % 138.46/19.18 | | (56) ? [v0: $i] : (sdtasdt0(xp, v0) = all_38_0 & $i(v0) & % 138.46/19.18 | | aNaturalNumber0(v0)) % 138.46/19.18 | | % 138.46/19.18 | | DELTA: instantiating (56) with fresh symbol all_77_0 gives: % 138.46/19.18 | | (57) sdtasdt0(xp, all_77_0) = all_38_0 & $i(all_77_0) & % 138.46/19.18 | | aNaturalNumber0(all_77_0) % 138.46/19.18 | | % 138.46/19.18 | | ALPHA: (57) implies: % 138.46/19.18 | | (58) aNaturalNumber0(all_77_0) % 138.46/19.18 | | (59) $i(all_77_0) % 138.46/19.18 | | (60) sdtasdt0(xp, all_77_0) = all_38_0 % 138.46/19.18 | | % 138.46/19.18 | | GROUND_INST: instantiating (mAddComm) with all_40_1, all_40_0, all_38_0, % 138.46/19.18 | | simplifying with (45), (49), (51), (53), (55) gives: % 138.46/19.18 | | (61) sdtpldt0(all_40_0, all_40_1) = all_38_0 & $i(all_38_0) % 138.46/19.18 | | % 138.46/19.18 | | GROUND_INST: instantiating (2) with all_40_1, all_38_0, all_40_0, % 138.46/19.18 | | simplifying with (45), (46), (48), (49), (51), (53), (55) % 138.46/19.18 | | gives: % 138.46/19.18 | | (62) sdtlseqdt0(all_40_1, all_38_0) % 138.46/19.18 | | % 138.46/19.18 | | GROUND_INST: instantiating (mMulComm) with xp, all_77_0, all_38_0, % 138.46/19.18 | | simplifying with (9), (17), (58), (59), (60) gives: % 138.46/19.18 | | (63) sdtasdt0(all_77_0, xp) = all_38_0 & $i(all_38_0) % 138.46/19.18 | | % 138.46/19.18 | | GROUND_INST: instantiating (4) with all_40_1, all_38_0, all_42_0, all_40_0, % 138.46/19.18 | | simplifying with (44), (45), (46), (48), (49), (51), (53), % 138.46/19.18 | | (55), (62) gives: % 138.46/19.18 | | (64) all_42_0 = all_40_0 % 138.46/19.18 | | % 138.46/19.18 | | REDUCE: (43), (64) imply: % 138.46/19.18 | | (65) $false % 138.46/19.18 | | % 138.46/19.18 | | CLOSE: (65) is inconsistent. % 138.46/19.18 | | % 138.46/19.18 | End of split % 138.46/19.18 | % 138.46/19.18 End of proof % 138.46/19.18 % SZS output end Proof for theBenchmark % 138.46/19.18 % 138.46/19.18 18583ms %------------------------------------------------------------------------------