%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM480+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 : n027.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 10.56s 2.20s % Output : Proof 15.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM480+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n027.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Fri Aug 25 17:46:18 EDT 2023 % 0.16/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.84/1.20 Prover 4: Preprocessing ... % 2.84/1.20 Prover 1: Preprocessing ... % 3.48/1.24 Prover 0: Preprocessing ... % 3.48/1.24 Prover 6: Preprocessing ... % 3.48/1.24 Prover 5: Preprocessing ... % 3.48/1.24 Prover 3: Preprocessing ... % 3.48/1.25 Prover 2: Preprocessing ... % 8.77/1.95 Prover 1: Constructing countermodel ... % 8.77/2.00 Prover 3: Constructing countermodel ... % 9.24/2.04 Prover 6: Proving ... % 9.60/2.14 Prover 5: Constructing countermodel ... % 10.56/2.20 Prover 3: proved (1544ms) % 10.56/2.20 % 10.56/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.56/2.20 % 10.56/2.20 Prover 5: stopped % 10.56/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.56/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.56/2.21 Prover 6: stopped % 10.56/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.96/2.25 Prover 2: Proving ... % 10.96/2.25 Prover 2: stopped % 10.96/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.96/2.27 Prover 7: Preprocessing ... % 10.96/2.29 Prover 4: Constructing countermodel ... % 10.96/2.31 Prover 8: Preprocessing ... % 10.96/2.31 Prover 10: Preprocessing ... % 10.96/2.36 Prover 11: Preprocessing ... % 11.70/2.43 Prover 0: Proving ... % 11.70/2.44 Prover 0: stopped % 11.70/2.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.58/2.49 Prover 10: Constructing countermodel ... % 12.58/2.49 Prover 8: Warning: ignoring some quantifiers % 12.95/2.51 Prover 8: Constructing countermodel ... % 12.95/2.54 Prover 13: Preprocessing ... % 13.18/2.56 Prover 7: Constructing countermodel ... % 14.14/2.69 Prover 13: Constructing countermodel ... % 15.10/2.85 Prover 10: Found proof (size 37) % 15.10/2.85 Prover 10: proved (632ms) % 15.10/2.85 Prover 13: stopped % 15.10/2.85 Prover 8: stopped % 15.10/2.85 Prover 7: stopped % 15.10/2.85 Prover 4: stopped % 15.40/2.85 Prover 1: stopped % 15.40/2.88 Prover 11: Constructing countermodel ... % 15.40/2.90 Prover 11: stopped % 15.40/2.90 % 15.40/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.40/2.90 % 15.40/2.91 % SZS output start Proof for theBenchmark % 15.40/2.91 Assumptions after simplification: % 15.40/2.91 --------------------------------- % 15.40/2.91 % 15.40/2.91 (mDefQuot) % 15.79/2.94 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 15.79/2.94 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 15.79/2.94 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.79/2.94 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 15.79/2.94 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 15.79/2.94 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 15.79/2.94 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 15.79/2.94 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 15.79/2.94 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 15.79/2.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.79/2.94 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 15.79/2.94 % 15.79/2.94 (mMulAsso) % 15.79/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.79/2.94 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 15.79/2.94 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 15.79/2.94 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 15.79/2.94 v5) = v4 & $i(v5) & $i(v4))) % 15.79/2.94 % 15.79/2.94 (mMulComm) % 15.79/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 15.79/2.94 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 15.79/2.94 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 15.79/2.94 % 15.79/2.94 (m__) % 15.79/2.94 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 15.79/2.94 $i] : ? [v4: $i] : ( ~ (v4 = v2) & ~ (v3 = v1) & sdtsldt0(v1, xl) = v4 & % 15.79/2.94 sdtsldt0(xm, xl) = v0 & sdtasdt0(xn, v0) = v2 & sdtasdt0(xn, xm) = v1 & % 15.79/2.94 sdtasdt0(xl, v2) = v3 & sdtasdt0(xl, v0) = xm & $i(v4) & $i(v3) & $i(v2) & % 15.79/2.94 $i(v1) & $i(v0) & aNaturalNumber0(v0)) % 15.79/2.94 % 15.79/2.94 (m__1524) % 15.79/2.94 $i(xm) & $i(xl) & aNaturalNumber0(xm) & aNaturalNumber0(xl) % 15.79/2.94 % 15.79/2.94 (m__1524_04) % 15.79/2.94 $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) % 15.79/2.94 = xm & $i(v0) & doDivides0(xl, xm) & aNaturalNumber0(v0)) % 15.79/2.94 % 15.79/2.94 (m__1553) % 15.79/2.94 $i(xn) & aNaturalNumber0(xn) % 15.79/2.94 % 15.79/2.94 (m__1594) % 15.79/2.95 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 15.79/2.95 $i] : (sdtsldt0(v1, xl) = v2 & sdtsldt0(xm, xl) = v0 & sdtasdt0(v3, v0) = v1 % 15.79/2.95 & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, v2) = v1 & sdtasdt0(xl, v0) = xm & % 15.79/2.95 sdtasdt0(xl, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 15.79/2.95 aNaturalNumber0(v2) & aNaturalNumber0(v0)) % 15.79/2.95 % 15.79/2.95 (function-axioms) % 15.79/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.79/2.95 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 15.79/2.95 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 15.79/2.95 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.79/2.95 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 15.79/2.95 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.79/2.95 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.79/2.95 % 15.79/2.95 Further assumptions not needed in the proof: % 15.79/2.95 -------------------------------------------- % 15.79/2.95 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDivLE, % 15.79/2.95 mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, % 15.79/2.95 mLETran, mMonAdd, mMonMul, mMonMul2, mMulCanc, mNatSort, mSortsB, mSortsB_02, % 15.79/2.95 mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 15.79/2.95 % 15.79/2.95 Those formulas are unsatisfiable: % 15.79/2.95 --------------------------------- % 15.79/2.95 % 15.79/2.95 Begin of proof % 15.79/2.95 | % 15.79/2.95 | ALPHA: (mDefQuot) implies: % 15.79/2.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 15.79/2.95 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 15.79/2.95 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.79/2.95 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 15.79/2.95 | aNaturalNumber0(v0)) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (m__1524) implies: % 15.79/2.95 | (2) aNaturalNumber0(xl) % 15.79/2.95 | (3) aNaturalNumber0(xm) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (m__1524_04) implies: % 15.79/2.95 | (4) ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) = xm & $i(v0) & % 15.79/2.95 | doDivides0(xl, xm) & aNaturalNumber0(v0)) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (m__1553) implies: % 15.79/2.95 | (5) aNaturalNumber0(xn) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (m__1594) implies: % 15.79/2.95 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtsldt0(v1, % 15.79/2.95 | xl) = v2 & sdtsldt0(xm, xl) = v0 & sdtasdt0(v3, v0) = v1 & % 15.79/2.95 | sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, v2) = v1 & sdtasdt0(xl, v0) = xm % 15.79/2.95 | & sdtasdt0(xl, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 15.79/2.95 | aNaturalNumber0(v2) & aNaturalNumber0(v0)) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (m__) implies: % 15.79/2.95 | (7) $i(xl) % 15.79/2.95 | (8) $i(xn) % 15.79/2.95 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( % 15.79/2.95 | ~ (v4 = v2) & ~ (v3 = v1) & sdtsldt0(v1, xl) = v4 & sdtsldt0(xm, xl) % 15.79/2.95 | = v0 & sdtasdt0(xn, v0) = v2 & sdtasdt0(xn, xm) = v1 & sdtasdt0(xl, % 15.79/2.95 | v2) = v3 & sdtasdt0(xl, v0) = xm & $i(v4) & $i(v3) & $i(v2) & % 15.79/2.95 | $i(v1) & $i(v0) & aNaturalNumber0(v0)) % 15.79/2.95 | % 15.79/2.95 | ALPHA: (function-axioms) implies: % 15.79/2.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.79/2.96 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 15.79/2.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.79/2.96 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 15.79/2.96 | % 15.79/2.96 | DELTA: instantiating (4) with fresh symbol all_35_0 gives: % 15.79/2.96 | (12) ~ (xl = sz00) & sdtasdt0(xl, all_35_0) = xm & $i(all_35_0) & % 15.79/2.96 | doDivides0(xl, xm) & aNaturalNumber0(all_35_0) % 15.79/2.96 | % 15.79/2.96 | ALPHA: (12) implies: % 15.79/2.96 | (13) ~ (xl = sz00) % 15.79/2.96 | (14) aNaturalNumber0(all_35_0) % 15.79/2.96 | (15) doDivides0(xl, xm) % 15.79/2.96 | (16) $i(all_35_0) % 15.79/2.96 | (17) sdtasdt0(xl, all_35_0) = xm % 15.79/2.96 | % 15.79/2.96 | DELTA: instantiating (6) with fresh symbols all_37_0, all_37_1, all_37_2, % 15.79/2.96 | all_37_3 gives: % 15.79/2.96 | (18) sdtsldt0(all_37_2, xl) = all_37_1 & sdtsldt0(xm, xl) = all_37_3 & % 15.79/2.96 | sdtasdt0(all_37_0, all_37_3) = all_37_2 & sdtasdt0(xn, xm) = all_37_2 % 15.79/2.96 | & sdtasdt0(xl, all_37_1) = all_37_2 & sdtasdt0(xl, all_37_3) = xm & % 15.79/2.96 | sdtasdt0(xl, xn) = all_37_0 & $i(all_37_0) & $i(all_37_1) & % 15.79/2.96 | $i(all_37_2) & $i(all_37_3) & aNaturalNumber0(all_37_1) & % 15.79/2.96 | aNaturalNumber0(all_37_3) % 15.79/2.96 | % 15.79/2.96 | ALPHA: (18) implies: % 15.79/2.96 | (19) sdtasdt0(xl, xn) = all_37_0 % 15.79/2.96 | (20) sdtasdt0(xn, xm) = all_37_2 % 15.79/2.96 | (21) sdtasdt0(all_37_0, all_37_3) = all_37_2 % 15.79/2.96 | (22) sdtsldt0(xm, xl) = all_37_3 % 15.79/2.96 | % 15.79/2.96 | DELTA: instantiating (9) with fresh symbols all_39_0, all_39_1, all_39_2, % 15.79/2.96 | all_39_3, all_39_4 gives: % 15.79/2.96 | (23) ~ (all_39_0 = all_39_2) & ~ (all_39_1 = all_39_3) & % 15.79/2.96 | sdtsldt0(all_39_3, xl) = all_39_0 & sdtsldt0(xm, xl) = all_39_4 & % 15.79/2.96 | sdtasdt0(xn, all_39_4) = all_39_2 & sdtasdt0(xn, xm) = all_39_3 & % 15.79/2.96 | sdtasdt0(xl, all_39_2) = all_39_1 & sdtasdt0(xl, all_39_4) = xm & % 15.79/2.96 | $i(all_39_0) & $i(all_39_1) & $i(all_39_2) & $i(all_39_3) & % 15.79/2.96 | $i(all_39_4) & aNaturalNumber0(all_39_4) % 15.79/2.96 | % 15.79/2.96 | ALPHA: (23) implies: % 15.79/2.96 | (24) ~ (all_39_1 = all_39_3) % 15.79/2.96 | (25) aNaturalNumber0(all_39_4) % 15.79/2.96 | (26) $i(all_39_4) % 15.79/2.96 | (27) sdtasdt0(xl, all_39_4) = xm % 15.79/2.96 | (28) sdtasdt0(xl, all_39_2) = all_39_1 % 15.79/2.96 | (29) sdtasdt0(xn, xm) = all_39_3 % 15.79/2.96 | (30) sdtasdt0(xn, all_39_4) = all_39_2 % 15.79/2.96 | (31) sdtsldt0(xm, xl) = all_39_4 % 15.79/2.96 | % 15.79/2.96 | GROUND_INST: instantiating (10) with all_37_2, all_39_3, xm, xn, simplifying % 15.79/2.96 | with (20), (29) gives: % 15.79/2.96 | (32) all_39_3 = all_37_2 % 15.79/2.96 | % 15.79/2.96 | GROUND_INST: instantiating (11) with all_37_3, all_39_4, xl, xm, simplifying % 15.79/2.96 | with (22), (31) gives: % 15.79/2.96 | (33) all_39_4 = all_37_3 % 15.79/2.96 | % 15.79/2.96 | REDUCE: (24), (32) imply: % 15.79/2.96 | (34) ~ (all_39_1 = all_37_2) % 15.79/2.96 | % 15.79/2.96 | REDUCE: (30), (33) imply: % 15.79/2.96 | (35) sdtasdt0(xn, all_37_3) = all_39_2 % 15.79/2.96 | % 15.79/2.96 | REDUCE: (27), (33) imply: % 15.79/2.96 | (36) sdtasdt0(xl, all_37_3) = xm % 15.79/2.96 | % 15.79/2.96 | REDUCE: (26), (33) imply: % 15.79/2.96 | (37) $i(all_37_3) % 15.79/2.96 | % 15.79/2.96 | REDUCE: (25), (33) imply: % 15.79/2.96 | (38) aNaturalNumber0(all_37_3) % 15.79/2.96 | % 15.79/2.96 | GROUND_INST: instantiating (mMulComm) with xl, all_37_3, xm, simplifying with % 15.79/2.96 | (2), (7), (36), (37), (38) gives: % 15.79/2.97 | (39) sdtasdt0(all_37_3, xl) = xm & $i(xm) % 15.79/2.97 | % 15.79/2.97 | ALPHA: (39) implies: % 15.79/2.97 | (40) $i(xm) % 15.79/2.97 | % 15.79/2.97 | GROUND_INST: instantiating (mMulAsso) with xl, xn, all_37_3, all_37_0, % 15.79/2.97 | all_37_2, simplifying with (2), (5), (7), (8), (19), (21), (37), % 15.79/2.97 | (38) gives: % 15.79/2.97 | (41) ? [v0: $i] : (sdtasdt0(xn, all_37_3) = v0 & sdtasdt0(xl, v0) = % 15.79/2.97 | all_37_2 & $i(v0) & $i(all_37_2)) % 15.79/2.97 | % 15.79/2.97 | GROUND_INST: instantiating (1) with xl, xm, all_37_3, all_35_0, simplifying % 15.79/2.97 | with (2), (3), (7), (14), (15), (16), (17), (22), (40) gives: % 15.79/2.97 | (42) all_37_3 = all_35_0 | xl = sz00 % 15.79/2.97 | % 15.79/2.97 | DELTA: instantiating (41) with fresh symbol all_57_0 gives: % 15.79/2.97 | (43) sdtasdt0(xn, all_37_3) = all_57_0 & sdtasdt0(xl, all_57_0) = all_37_2 % 15.79/2.97 | & $i(all_57_0) & $i(all_37_2) % 15.79/2.97 | % 15.79/2.97 | ALPHA: (43) implies: % 15.79/2.97 | (44) sdtasdt0(xl, all_57_0) = all_37_2 % 15.79/2.97 | (45) sdtasdt0(xn, all_37_3) = all_57_0 % 15.79/2.97 | % 15.79/2.97 | BETA: splitting (42) gives: % 15.79/2.97 | % 15.79/2.97 | Case 1: % 15.79/2.97 | | % 15.79/2.97 | | (46) xl = sz00 % 15.79/2.97 | | % 15.79/2.97 | | REDUCE: (13), (46) imply: % 15.79/2.97 | | (47) $false % 15.79/2.97 | | % 15.79/2.97 | | CLOSE: (47) is inconsistent. % 15.79/2.97 | | % 15.79/2.97 | Case 2: % 15.79/2.97 | | % 15.79/2.97 | | (48) all_37_3 = all_35_0 % 15.79/2.97 | | % 15.79/2.97 | | REDUCE: (45), (48) imply: % 15.79/2.97 | | (49) sdtasdt0(xn, all_35_0) = all_57_0 % 15.79/2.97 | | % 15.79/2.97 | | REDUCE: (35), (48) imply: % 15.79/2.97 | | (50) sdtasdt0(xn, all_35_0) = all_39_2 % 15.79/2.97 | | % 15.79/2.97 | | GROUND_INST: instantiating (10) with all_39_2, all_57_0, all_35_0, xn, % 15.79/2.97 | | simplifying with (49), (50) gives: % 15.79/2.97 | | (51) all_57_0 = all_39_2 % 15.79/2.97 | | % 15.79/2.97 | | REDUCE: (44), (51) imply: % 15.79/2.97 | | (52) sdtasdt0(xl, all_39_2) = all_37_2 % 15.79/2.97 | | % 15.79/2.97 | | GROUND_INST: instantiating (10) with all_39_1, all_37_2, all_39_2, xl, % 15.79/2.97 | | simplifying with (28), (52) gives: % 15.79/2.97 | | (53) all_39_1 = all_37_2 % 15.79/2.97 | | % 15.79/2.97 | | REDUCE: (34), (53) imply: % 15.79/2.97 | | (54) $false % 15.79/2.97 | | % 15.79/2.97 | | CLOSE: (54) is inconsistent. % 15.79/2.97 | | % 15.79/2.97 | End of split % 15.79/2.97 | % 15.79/2.97 End of proof % 15.79/2.97 % SZS output end Proof for theBenchmark % 15.79/2.97 % 15.79/2.97 2339ms %------------------------------------------------------------------------------