%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM479+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 11:48:03 EDT 2023 % Result : Theorem 11.99s 2.35s % Output : Proof 18.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM479+2 : 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 : n018.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 17:42:29 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.15/1.17 Prover 4: Preprocessing ... % 3.15/1.17 Prover 1: Preprocessing ... % 3.72/1.21 Prover 3: Preprocessing ... % 3.72/1.21 Prover 0: Preprocessing ... % 3.72/1.21 Prover 5: Preprocessing ... % 3.72/1.21 Prover 2: Preprocessing ... % 3.72/1.21 Prover 6: Preprocessing ... % 8.31/1.87 Prover 1: Constructing countermodel ... % 8.31/1.88 Prover 3: Constructing countermodel ... % 8.31/1.89 Prover 6: Proving ... % 8.77/1.90 Prover 5: Constructing countermodel ... % 9.21/1.99 Prover 2: Proving ... % 9.21/2.15 Prover 4: Constructing countermodel ... % 10.54/2.22 Prover 0: Proving ... % 11.99/2.34 Prover 3: proved (1706ms) % 11.99/2.34 % 11.99/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.99/2.35 % 11.99/2.35 Prover 5: stopped % 11.99/2.35 Prover 0: stopped % 11.99/2.35 Prover 6: stopped % 11.99/2.35 Prover 2: stopped % 12.23/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.23/2.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.23/2.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.23/2.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.23/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.91/2.48 Prover 8: Preprocessing ... % 12.91/2.49 Prover 10: Preprocessing ... % 12.91/2.49 Prover 7: Preprocessing ... % 12.91/2.49 Prover 11: Preprocessing ... % 12.91/2.49 Prover 13: Preprocessing ... % 14.41/2.68 Prover 8: Warning: ignoring some quantifiers % 14.41/2.70 Prover 8: Constructing countermodel ... % 14.41/2.71 Prover 10: Constructing countermodel ... % 14.41/2.75 Prover 13: Constructing countermodel ... % 14.41/2.77 Prover 7: Constructing countermodel ... % 16.66/3.00 Prover 11: Constructing countermodel ... % 17.85/3.16 Prover 10: Found proof (size 36) % 17.85/3.16 Prover 10: proved (807ms) % 17.85/3.16 Prover 4: stopped % 17.85/3.16 Prover 7: stopped % 17.85/3.16 Prover 1: stopped % 17.85/3.16 Prover 13: stopped % 17.85/3.16 Prover 8: stopped % 17.85/3.16 Prover 11: stopped % 17.85/3.16 % 17.85/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.85/3.16 % 17.85/3.17 % SZS output start Proof for theBenchmark % 17.85/3.17 Assumptions after simplification: % 17.85/3.17 --------------------------------- % 17.85/3.17 % 17.85/3.17 (mDefQuot) % 17.85/3.20 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 17.85/3.20 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 17.85/3.20 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 17.85/3.20 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 17.85/3.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 17.85/3.20 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 17.85/3.20 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 17.85/3.20 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.85/3.20 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 17.85/3.20 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 17.85/3.20 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 17.85/3.20 % 17.85/3.20 (mMulAsso) % 17.85/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 17.85/3.20 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 17.85/3.20 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 17.85/3.20 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 17.85/3.20 v5) = v4 & $i(v5) & $i(v4))) % 17.85/3.20 % 17.85/3.20 (mMulComm) % 17.85/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 17.85/3.20 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 17.85/3.20 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 17.85/3.20 % 17.85/3.20 (mSortsB_02) % 17.85/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 17.85/3.20 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 17.85/3.20 aNaturalNumber0(v2)) % 17.85/3.20 % 17.85/3.20 (m__) % 17.85/3.20 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 17.85/3.20 $i] : ? [v4: $i] : ( ~ (v4 = v1) & sdtsldt0(v1, xl) = v2 & sdtsldt0(xm, xl) % 17.85/3.20 = v0 & sdtasdt0(v3, v0) = v4 & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, v2) = v1 % 17.85/3.20 & sdtasdt0(xl, v0) = xm & sdtasdt0(xl, xn) = v3 & $i(v4) & $i(v3) & $i(v2) & % 17.85/3.20 $i(v1) & $i(v0) & aNaturalNumber0(v2) & aNaturalNumber0(v0)) % 17.85/3.20 % 17.85/3.20 (m__1524) % 17.85/3.20 $i(xm) & $i(xl) & aNaturalNumber0(xm) & aNaturalNumber0(xl) % 17.85/3.20 % 17.85/3.20 (m__1524_04) % 17.85/3.20 $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) % 17.85/3.20 = xm & $i(v0) & doDivides0(xl, xm) & aNaturalNumber0(v0)) % 17.85/3.21 % 17.85/3.21 (m__1553) % 17.85/3.21 $i(xn) & aNaturalNumber0(xn) % 17.85/3.21 % 17.85/3.21 (function-axioms) % 17.85/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.85/3.21 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 17.85/3.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 17.85/3.21 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.85/3.21 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 17.85/3.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.85/3.21 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 17.85/3.21 % 17.85/3.21 Further assumptions not needed in the proof: % 17.85/3.21 -------------------------------------------- % 17.85/3.21 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDivLE, % 17.85/3.21 mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, % 17.85/3.21 mLETran, mMonAdd, mMonMul, mMonMul2, mMulCanc, mNatSort, mSortsB, mSortsC, % 17.85/3.21 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 17.85/3.21 % 17.85/3.21 Those formulas are unsatisfiable: % 17.85/3.21 --------------------------------- % 17.85/3.21 % 17.85/3.21 Begin of proof % 17.85/3.21 | % 17.85/3.21 | ALPHA: (mDefQuot) implies: % 18.33/3.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 18.33/3.21 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 18.33/3.21 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 18.33/3.21 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 18.33/3.21 | aNaturalNumber0(v0)) % 18.33/3.21 | % 18.33/3.21 | ALPHA: (m__1524) implies: % 18.33/3.21 | (2) aNaturalNumber0(xl) % 18.33/3.21 | (3) aNaturalNumber0(xm) % 18.33/3.21 | % 18.33/3.21 | ALPHA: (m__1524_04) implies: % 18.33/3.21 | (4) ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) = xm & $i(v0) & % 18.33/3.21 | doDivides0(xl, xm) & aNaturalNumber0(v0)) % 18.33/3.21 | % 18.33/3.21 | ALPHA: (m__1553) implies: % 18.33/3.21 | (5) aNaturalNumber0(xn) % 18.33/3.21 | % 18.33/3.21 | ALPHA: (m__) implies: % 18.33/3.21 | (6) $i(xl) % 18.33/3.21 | (7) $i(xn) % 18.33/3.21 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( % 18.33/3.21 | ~ (v4 = v1) & sdtsldt0(v1, xl) = v2 & sdtsldt0(xm, xl) = v0 & % 18.33/3.21 | sdtasdt0(v3, v0) = v4 & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, v2) = v1 % 18.33/3.21 | & sdtasdt0(xl, v0) = xm & sdtasdt0(xl, xn) = v3 & $i(v4) & $i(v3) & % 18.33/3.21 | $i(v2) & $i(v1) & $i(v0) & aNaturalNumber0(v2) & aNaturalNumber0(v0)) % 18.33/3.21 | % 18.33/3.21 | ALPHA: (function-axioms) implies: % 18.33/3.21 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.33/3.21 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 18.33/3.21 | % 18.33/3.22 | DELTA: instantiating (4) with fresh symbol all_35_0 gives: % 18.33/3.22 | (10) ~ (xl = sz00) & sdtasdt0(xl, all_35_0) = xm & $i(all_35_0) & % 18.33/3.22 | doDivides0(xl, xm) & aNaturalNumber0(all_35_0) % 18.33/3.22 | % 18.33/3.22 | ALPHA: (10) implies: % 18.33/3.22 | (11) ~ (xl = sz00) % 18.33/3.22 | (12) aNaturalNumber0(all_35_0) % 18.33/3.22 | (13) doDivides0(xl, xm) % 18.33/3.22 | (14) $i(all_35_0) % 18.33/3.22 | (15) sdtasdt0(xl, all_35_0) = xm % 18.33/3.22 | % 18.33/3.22 | DELTA: instantiating (8) with fresh symbols all_37_0, all_37_1, all_37_2, % 18.33/3.22 | all_37_3, all_37_4 gives: % 18.33/3.22 | (16) ~ (all_37_0 = all_37_3) & sdtsldt0(all_37_3, xl) = all_37_2 & % 18.33/3.22 | sdtsldt0(xm, xl) = all_37_4 & sdtasdt0(all_37_1, all_37_4) = all_37_0 % 18.33/3.22 | & sdtasdt0(xn, xm) = all_37_3 & sdtasdt0(xl, all_37_2) = all_37_3 & % 18.33/3.22 | sdtasdt0(xl, all_37_4) = xm & sdtasdt0(xl, xn) = all_37_1 & % 18.33/3.22 | $i(all_37_0) & $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & % 18.33/3.22 | $i(all_37_4) & aNaturalNumber0(all_37_2) & aNaturalNumber0(all_37_4) % 18.33/3.22 | % 18.33/3.22 | ALPHA: (16) implies: % 18.33/3.22 | (17) ~ (all_37_0 = all_37_3) % 18.33/3.22 | (18) aNaturalNumber0(all_37_4) % 18.33/3.22 | (19) $i(all_37_4) % 18.33/3.22 | (20) sdtasdt0(xl, xn) = all_37_1 % 18.33/3.22 | (21) sdtasdt0(xl, all_37_4) = xm % 18.33/3.22 | (22) sdtasdt0(xn, xm) = all_37_3 % 18.33/3.22 | (23) sdtasdt0(all_37_1, all_37_4) = all_37_0 % 18.33/3.22 | (24) sdtsldt0(xm, xl) = all_37_4 % 18.33/3.22 | % 18.33/3.22 | GROUND_INST: instantiating (mSortsB_02) with xl, xn, all_37_1, simplifying % 18.33/3.22 | with (2), (5), (6), (7), (20) gives: % 18.33/3.22 | (25) aNaturalNumber0(all_37_1) % 18.33/3.22 | % 18.33/3.22 | GROUND_INST: instantiating (mMulComm) with xl, xn, all_37_1, simplifying with % 18.33/3.22 | (2), (5), (6), (7), (20) gives: % 18.33/3.22 | (26) sdtasdt0(xn, xl) = all_37_1 & $i(all_37_1) % 18.33/3.22 | % 18.33/3.22 | ALPHA: (26) implies: % 18.33/3.22 | (27) $i(all_37_1) % 18.33/3.22 | % 18.33/3.22 | GROUND_INST: instantiating (mMulComm) with xl, all_37_4, xm, simplifying with % 18.33/3.22 | (2), (6), (18), (19), (21) gives: % 18.33/3.22 | (28) sdtasdt0(all_37_4, xl) = xm & $i(xm) % 18.33/3.22 | % 18.33/3.22 | ALPHA: (28) implies: % 18.33/3.22 | (29) $i(xm) % 18.33/3.22 | (30) sdtasdt0(all_37_4, xl) = xm % 18.33/3.22 | % 18.33/3.22 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_37_3, simplifying with % 18.33/3.22 | (3), (5), (7), (22), (29) gives: % 18.33/3.22 | (31) sdtasdt0(xm, xn) = all_37_3 & $i(all_37_3) % 18.33/3.22 | % 18.33/3.22 | ALPHA: (31) implies: % 18.33/3.22 | (32) sdtasdt0(xm, xn) = all_37_3 % 18.33/3.22 | % 18.33/3.22 | GROUND_INST: instantiating (1) with xl, xm, all_37_4, all_35_0, simplifying % 18.33/3.22 | with (2), (3), (6), (12), (13), (14), (15), (24), (29) gives: % 18.33/3.22 | (33) all_37_4 = all_35_0 | xl = sz00 % 18.33/3.22 | % 18.33/3.22 | BETA: splitting (33) gives: % 18.33/3.22 | % 18.33/3.22 | Case 1: % 18.33/3.22 | | % 18.33/3.22 | | (34) xl = sz00 % 18.33/3.22 | | % 18.33/3.22 | | REDUCE: (11), (34) imply: % 18.33/3.22 | | (35) $false % 18.33/3.23 | | % 18.33/3.23 | | CLOSE: (35) is inconsistent. % 18.33/3.23 | | % 18.33/3.23 | Case 2: % 18.33/3.23 | | % 18.33/3.23 | | (36) all_37_4 = all_35_0 % 18.33/3.23 | | % 18.33/3.23 | | REDUCE: (23), (36) imply: % 18.33/3.23 | | (37) sdtasdt0(all_37_1, all_35_0) = all_37_0 % 18.33/3.23 | | % 18.33/3.23 | | REDUCE: (30), (36) imply: % 18.33/3.23 | | (38) sdtasdt0(all_35_0, xl) = xm % 18.33/3.23 | | % 18.33/3.23 | | GROUND_INST: instantiating (mMulAsso) with all_35_0, xl, xn, xm, all_37_3, % 18.33/3.23 | | simplifying with (2), (5), (6), (7), (12), (14), (32), (38) % 18.33/3.23 | | gives: % 18.33/3.23 | | (39) ? [v0: $i] : (sdtasdt0(all_35_0, v0) = all_37_3 & sdtasdt0(xl, xn) % 18.33/3.23 | | = v0 & $i(v0) & $i(all_37_3)) % 18.33/3.23 | | % 18.33/3.23 | | GROUND_INST: instantiating (mMulComm) with all_37_1, all_35_0, all_37_0, % 18.33/3.23 | | simplifying with (12), (14), (25), (27), (37) gives: % 18.33/3.23 | | (40) sdtasdt0(all_35_0, all_37_1) = all_37_0 & $i(all_37_0) % 18.33/3.23 | | % 18.33/3.23 | | ALPHA: (40) implies: % 18.33/3.23 | | (41) sdtasdt0(all_35_0, all_37_1) = all_37_0 % 18.33/3.23 | | % 18.33/3.23 | | DELTA: instantiating (39) with fresh symbol all_77_0 gives: % 18.33/3.23 | | (42) sdtasdt0(all_35_0, all_77_0) = all_37_3 & sdtasdt0(xl, xn) = % 18.33/3.23 | | all_77_0 & $i(all_77_0) & $i(all_37_3) % 18.33/3.23 | | % 18.33/3.23 | | ALPHA: (42) implies: % 18.33/3.23 | | (43) sdtasdt0(xl, xn) = all_77_0 % 18.33/3.23 | | (44) sdtasdt0(all_35_0, all_77_0) = all_37_3 % 18.33/3.23 | | % 18.33/3.23 | | GROUND_INST: instantiating (9) with all_37_1, all_77_0, xn, xl, simplifying % 18.33/3.23 | | with (20), (43) gives: % 18.33/3.23 | | (45) all_77_0 = all_37_1 % 18.33/3.23 | | % 18.33/3.23 | | REDUCE: (44), (45) imply: % 18.33/3.23 | | (46) sdtasdt0(all_35_0, all_37_1) = all_37_3 % 18.33/3.23 | | % 18.33/3.23 | | GROUND_INST: instantiating (9) with all_37_0, all_37_3, all_37_1, all_35_0, % 18.33/3.23 | | simplifying with (41), (46) gives: % 18.33/3.23 | | (47) all_37_0 = all_37_3 % 18.33/3.23 | | % 18.33/3.23 | | REDUCE: (17), (47) imply: % 18.33/3.23 | | (48) $false % 18.33/3.23 | | % 18.33/3.23 | | CLOSE: (48) is inconsistent. % 18.33/3.23 | | % 18.33/3.23 | End of split % 18.33/3.23 | % 18.33/3.23 End of proof % 18.33/3.23 % SZS output end Proof for theBenchmark % 18.33/3.23 % 18.33/3.23 2618ms %------------------------------------------------------------------------------