%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM478+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 : n032.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 11:48:02 EDT 2023 % Result : Theorem 10.21s 2.17s % Output : Proof 16.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM478+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.30 % Computer : n032.cluster.edu % 0.12/0.30 % Model : x86_64 x86_64 % 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.30 % Memory : 8042.1875MB % 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.30 % CPULimit : 300 % 0.12/0.30 % WCLimit : 300 % 0.12/0.30 % DateTime : Fri Aug 25 08:55:12 EDT 2023 % 0.12/0.30 % CPUTime : % 0.14/0.53 ________ _____ % 0.14/0.53 ___ __ \_________(_)________________________________ % 0.14/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.14/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.14/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.14/0.53 % 0.14/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.14/0.53 (2023-06-19) % 0.14/0.53 % 0.14/0.53 (c) Philipp Rümmer, 2009-2023 % 0.14/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.14/0.53 Amanda Stjerna. % 0.14/0.53 Free software under BSD-3-Clause. % 0.14/0.53 % 0.14/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.14/0.53 % 0.14/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.14/0.54 Running up to 7 provers in parallel. % 0.14/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.14/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.14/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.14/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.14/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.14/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.14/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.80/1.07 Prover 1: Preprocessing ... % 2.80/1.07 Prover 4: Preprocessing ... % 3.24/1.11 Prover 0: Preprocessing ... % 3.24/1.11 Prover 6: Preprocessing ... % 3.24/1.11 Prover 3: Preprocessing ... % 3.24/1.11 Prover 5: Preprocessing ... % 3.24/1.11 Prover 2: Preprocessing ... % 7.60/1.76 Prover 1: Constructing countermodel ... % 7.99/1.83 Prover 3: Constructing countermodel ... % 8.48/1.85 Prover 6: Proving ... % 8.61/1.86 Prover 5: Constructing countermodel ... % 9.20/2.02 Prover 2: Proving ... % 10.21/2.15 Prover 4: Constructing countermodel ... % 10.21/2.17 Prover 3: proved (1612ms) % 10.21/2.17 % 10.21/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.21/2.17 % 10.21/2.19 Prover 5: stopped % 10.21/2.20 Prover 6: stopped % 10.21/2.22 Prover 2: stopped % 10.21/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.21/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.21/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.21/2.22 Prover 0: Proving ... % 10.21/2.22 Prover 0: stopped % 10.21/2.24 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.21/2.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.21/2.29 Prover 7: Preprocessing ... % 11.97/2.33 Prover 10: Preprocessing ... % 11.97/2.34 Prover 8: Preprocessing ... % 11.97/2.36 Prover 11: Preprocessing ... % 11.97/2.37 Prover 13: Preprocessing ... % 12.39/2.45 Prover 10: Constructing countermodel ... % 13.35/2.54 Prover 7: Constructing countermodel ... % 13.59/2.56 Prover 8: Warning: ignoring some quantifiers % 13.59/2.58 Prover 8: Constructing countermodel ... % 14.23/2.64 Prover 13: Constructing countermodel ... % 15.34/2.81 Prover 10: Found proof (size 51) % 15.34/2.81 Prover 10: proved (592ms) % 15.34/2.81 Prover 7: stopped % 15.34/2.81 Prover 13: stopped % 15.34/2.81 Prover 4: stopped % 15.34/2.81 Prover 8: stopped % 15.34/2.81 Prover 1: stopped % 15.34/2.85 Prover 11: Constructing countermodel ... % 15.34/2.87 Prover 11: stopped % 15.34/2.87 % 15.34/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.34/2.87 % 15.34/2.88 % SZS output start Proof for theBenchmark % 15.34/2.89 Assumptions after simplification: % 15.34/2.89 --------------------------------- % 15.34/2.89 % 15.34/2.89 (mDefDiv) % 15.34/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 16.15/2.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 16.15/2.93 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 16.15/2.93 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.15/2.93 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 16.15/2.93 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 16.15/2.93 % 16.15/2.93 (mDefQuot) % 16.15/2.93 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 16.15/2.93 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 16.15/2.93 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.15/2.93 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 16.15/2.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 16.15/2.93 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 16.15/2.93 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 16.15/2.93 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 16.15/2.93 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 16.15/2.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.15/2.93 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 16.15/2.93 % 16.15/2.93 (mMulAsso) % 16.15/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.15/2.94 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 16.15/2.94 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 16.15/2.94 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 16.15/2.94 v5) = v4 & $i(v5) & $i(v4))) % 16.15/2.94 % 16.15/2.94 (mMulComm) % 16.15/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 16.15/2.94 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.15/2.94 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 16.15/2.94 % 16.15/2.94 (m__) % 16.15/2.94 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 16.15/2.94 $i] : ? [v4: $i] : ( ~ (v4 = v2) & ~ (v3 = v1) & sdtsldt0(v1, xl) = v4 & % 16.15/2.94 sdtsldt0(xm, xl) = v0 & sdtasdt0(xn, v0) = v2 & sdtasdt0(xn, xm) = v1 & % 16.15/2.94 sdtasdt0(xl, v2) = v3 & sdtasdt0(xl, v0) = xm & $i(v4) & $i(v3) & $i(v2) & % 16.15/2.94 $i(v1) & $i(v0) & aNaturalNumber0(v0)) % 16.15/2.94 % 16.15/2.94 (m__1524) % 16.15/2.94 $i(xm) & $i(xl) & aNaturalNumber0(xm) & aNaturalNumber0(xl) % 16.15/2.94 % 16.15/2.94 (m__1524_04) % 16.15/2.94 $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) % 16.15/2.94 = xm & $i(v0) & doDivides0(xl, xm) & aNaturalNumber0(v0)) % 16.15/2.94 % 16.15/2.94 (m__1553) % 16.15/2.95 $i(xn) & aNaturalNumber0(xn) % 16.15/2.95 % 16.15/2.95 (function-axioms) % 16.15/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.15/2.95 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.15/2.95 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 16.15/2.95 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.15/2.95 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.15/2.95 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.15/2.95 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.15/2.95 % 16.15/2.95 Further assumptions not needed in the proof: % 16.15/2.95 -------------------------------------------- % 16.15/2.95 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDivLE, mDivMin, % 16.15/2.95 mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, % 16.15/2.95 mMonAdd, mMonMul, mMonMul2, mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, % 16.15/2.95 mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 16.15/2.95 % 16.15/2.95 Those formulas are unsatisfiable: % 16.15/2.95 --------------------------------- % 16.15/2.95 % 16.15/2.95 Begin of proof % 16.15/2.95 | % 16.15/2.95 | ALPHA: (mDefDiv) implies: % 16.33/2.96 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 16.33/2.96 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 16.33/2.96 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 16.33/2.96 | % 16.33/2.96 | ALPHA: (mDefQuot) implies: % 16.33/2.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 16.33/2.96 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 16.33/2.96 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 16.33/2.96 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 16.33/2.96 | aNaturalNumber0(v0)) % 16.33/2.96 | % 16.33/2.96 | ALPHA: (m__1524) implies: % 16.33/2.96 | (3) aNaturalNumber0(xl) % 16.33/2.96 | (4) aNaturalNumber0(xm) % 16.33/2.96 | % 16.33/2.96 | ALPHA: (m__1524_04) implies: % 16.33/2.96 | (5) ? [v0: $i] : ( ~ (xl = sz00) & sdtasdt0(xl, v0) = xm & $i(v0) & % 16.33/2.96 | doDivides0(xl, xm) & aNaturalNumber0(v0)) % 16.33/2.96 | % 16.33/2.96 | ALPHA: (m__1553) implies: % 16.33/2.96 | (6) aNaturalNumber0(xn) % 16.33/2.96 | % 16.33/2.96 | ALPHA: (m__) implies: % 16.33/2.96 | (7) $i(xl) % 16.33/2.96 | (8) $i(xm) % 16.33/2.96 | (9) $i(xn) % 16.33/2.97 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.33/2.97 | ( ~ (v4 = v2) & ~ (v3 = v1) & sdtsldt0(v1, xl) = v4 & sdtsldt0(xm, % 16.33/2.97 | xl) = v0 & sdtasdt0(xn, v0) = v2 & sdtasdt0(xn, xm) = v1 & % 16.33/2.97 | sdtasdt0(xl, v2) = v3 & sdtasdt0(xl, v0) = xm & $i(v4) & $i(v3) & % 16.33/2.97 | $i(v2) & $i(v1) & $i(v0) & aNaturalNumber0(v0)) % 16.33/2.97 | % 16.33/2.97 | ALPHA: (function-axioms) implies: % 16.33/2.97 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.33/2.97 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.33/2.97 | % 16.33/2.97 | DELTA: instantiating (5) with fresh symbol all_35_0 gives: % 16.33/2.97 | (12) ~ (xl = sz00) & sdtasdt0(xl, all_35_0) = xm & $i(all_35_0) & % 16.33/2.97 | doDivides0(xl, xm) & aNaturalNumber0(all_35_0) % 16.33/2.97 | % 16.33/2.97 | ALPHA: (12) implies: % 16.33/2.97 | (13) ~ (xl = sz00) % 16.33/2.97 | (14) aNaturalNumber0(all_35_0) % 16.33/2.97 | (15) doDivides0(xl, xm) % 16.33/2.97 | (16) $i(all_35_0) % 16.33/2.97 | (17) sdtasdt0(xl, all_35_0) = xm % 16.33/2.97 | % 16.33/2.97 | DELTA: instantiating (10) with fresh symbols all_37_0, all_37_1, all_37_2, % 16.33/2.97 | all_37_3, all_37_4 gives: % 16.33/2.97 | (18) ~ (all_37_0 = all_37_2) & ~ (all_37_1 = all_37_3) & % 16.33/2.97 | sdtsldt0(all_37_3, xl) = all_37_0 & sdtsldt0(xm, xl) = all_37_4 & % 16.33/2.97 | sdtasdt0(xn, all_37_4) = all_37_2 & sdtasdt0(xn, xm) = all_37_3 & % 16.33/2.97 | sdtasdt0(xl, all_37_2) = all_37_1 & sdtasdt0(xl, all_37_4) = xm & % 16.33/2.97 | $i(all_37_0) & $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & % 16.33/2.97 | $i(all_37_4) & aNaturalNumber0(all_37_4) % 16.33/2.97 | % 16.33/2.97 | ALPHA: (18) implies: % 16.33/2.97 | (19) ~ (all_37_1 = all_37_3) % 16.33/2.97 | (20) aNaturalNumber0(all_37_4) % 16.33/2.97 | (21) $i(all_37_4) % 16.33/2.97 | (22) sdtasdt0(xl, all_37_4) = xm % 16.33/2.97 | (23) sdtasdt0(xl, all_37_2) = all_37_1 % 16.33/2.97 | (24) sdtasdt0(xn, xm) = all_37_3 % 16.33/2.97 | (25) sdtasdt0(xn, all_37_4) = all_37_2 % 16.33/2.97 | (26) sdtsldt0(xm, xl) = all_37_4 % 16.33/2.97 | % 16.33/2.97 | GROUND_INST: instantiating (1) with xl, xm, simplifying with (3), (4), (7), % 16.33/2.97 | (8), (15) gives: % 16.33/2.97 | (27) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & $i(v0) & aNaturalNumber0(v0)) % 16.33/2.97 | % 16.33/2.97 | GROUND_INST: instantiating (mMulComm) with xl, all_37_4, xm, simplifying with % 16.33/2.98 | (3), (7), (20), (21), (22) gives: % 16.33/2.98 | (28) sdtasdt0(all_37_4, xl) = xm & $i(xm) % 16.33/2.98 | % 16.33/2.98 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_37_3, simplifying with % 16.33/2.98 | (4), (6), (8), (9), (24) gives: % 16.33/2.98 | (29) sdtasdt0(xm, xn) = all_37_3 & $i(all_37_3) % 16.33/2.98 | % 16.33/2.98 | ALPHA: (29) implies: % 16.33/2.98 | (30) sdtasdt0(xm, xn) = all_37_3 % 16.33/2.98 | % 16.33/2.98 | GROUND_INST: instantiating (mMulComm) with xn, all_37_4, all_37_2, simplifying % 16.33/2.98 | with (6), (9), (20), (21), (25) gives: % 16.33/2.98 | (31) sdtasdt0(all_37_4, xn) = all_37_2 & $i(all_37_2) % 16.33/2.98 | % 16.33/2.98 | ALPHA: (31) implies: % 16.33/2.98 | (32) sdtasdt0(all_37_4, xn) = all_37_2 % 16.33/2.98 | % 16.33/2.98 | GROUND_INST: instantiating (2) with xl, xm, all_37_4, all_35_0, simplifying % 16.33/2.98 | with (3), (4), (7), (8), (14), (15), (16), (17), (26) gives: % 16.33/2.98 | (33) all_37_4 = all_35_0 | xl = sz00 % 16.33/2.98 | % 16.33/2.98 | DELTA: instantiating (27) with fresh symbol all_45_0 gives: % 16.33/2.98 | (34) sdtasdt0(xl, all_45_0) = xm & $i(all_45_0) & aNaturalNumber0(all_45_0) % 16.33/2.98 | % 16.33/2.98 | ALPHA: (34) implies: % 16.33/2.98 | (35) aNaturalNumber0(all_45_0) % 16.33/2.98 | (36) $i(all_45_0) % 16.33/2.98 | (37) sdtasdt0(xl, all_45_0) = xm % 16.33/2.98 | % 16.33/2.98 | BETA: splitting (33) gives: % 16.33/2.98 | % 16.33/2.98 | Case 1: % 16.33/2.98 | | % 16.33/2.98 | | (38) xl = sz00 % 16.33/2.98 | | % 16.33/2.98 | | REDUCE: (13), (38) imply: % 16.33/2.98 | | (39) $false % 16.33/2.98 | | % 16.33/2.98 | | CLOSE: (39) is inconsistent. % 16.33/2.98 | | % 16.33/2.98 | Case 2: % 16.33/2.98 | | % 16.33/2.98 | | (40) all_37_4 = all_35_0 % 16.33/2.98 | | % 16.33/2.98 | | REDUCE: (26), (40) imply: % 16.33/2.98 | | (41) sdtsldt0(xm, xl) = all_35_0 % 16.33/2.98 | | % 16.33/2.98 | | REDUCE: (32), (40) imply: % 16.33/2.98 | | (42) sdtasdt0(all_35_0, xn) = all_37_2 % 16.33/2.98 | | % 16.33/2.98 | | GROUND_INST: instantiating (mMulComm) with xl, all_45_0, xm, simplifying % 16.33/2.98 | | with (3), (7), (35), (36), (37) gives: % 16.33/2.98 | | (43) sdtasdt0(all_45_0, xl) = xm & $i(xm) % 16.33/2.98 | | % 16.33/2.98 | | GROUND_INST: instantiating (mMulAsso) with xl, all_35_0, xn, xm, all_37_3, % 16.33/2.98 | | simplifying with (3), (6), (7), (9), (14), (16), (17), (30) % 16.33/2.98 | | gives: % 16.33/2.99 | | (44) ? [v0: $i] : (sdtasdt0(all_35_0, xn) = v0 & sdtasdt0(xl, v0) = % 16.33/2.99 | | all_37_3 & $i(v0) & $i(all_37_3)) % 16.33/2.99 | | % 16.33/2.99 | | GROUND_INST: instantiating (mMulAsso) with xl, all_45_0, xn, xm, all_37_3, % 16.33/2.99 | | simplifying with (3), (6), (7), (9), (30), (35), (36), (37) % 16.33/2.99 | | gives: % 16.33/2.99 | | (45) ? [v0: $i] : (sdtasdt0(all_45_0, xn) = v0 & sdtasdt0(xl, v0) = % 16.33/2.99 | | all_37_3 & $i(v0) & $i(all_37_3)) % 16.33/2.99 | | % 16.33/2.99 | | GROUND_INST: instantiating (2) with xl, xm, all_35_0, all_45_0, simplifying % 16.33/2.99 | | with (3), (4), (7), (8), (15), (35), (36), (37), (41) gives: % 16.33/2.99 | | (46) all_45_0 = all_35_0 | xl = sz00 % 16.33/2.99 | | % 16.33/2.99 | | DELTA: instantiating (45) with fresh symbol all_75_0 gives: % 16.33/2.99 | | (47) sdtasdt0(all_45_0, xn) = all_75_0 & sdtasdt0(xl, all_75_0) = % 16.33/2.99 | | all_37_3 & $i(all_75_0) & $i(all_37_3) % 16.33/2.99 | | % 16.33/2.99 | | ALPHA: (47) implies: % 16.33/2.99 | | (48) sdtasdt0(xl, all_75_0) = all_37_3 % 16.33/2.99 | | (49) sdtasdt0(all_45_0, xn) = all_75_0 % 16.33/2.99 | | % 16.33/2.99 | | DELTA: instantiating (44) with fresh symbol all_77_0 gives: % 16.33/2.99 | | (50) sdtasdt0(all_35_0, xn) = all_77_0 & sdtasdt0(xl, all_77_0) = % 16.33/2.99 | | all_37_3 & $i(all_77_0) & $i(all_37_3) % 16.33/2.99 | | % 16.33/2.99 | | ALPHA: (50) implies: % 16.33/2.99 | | (51) sdtasdt0(all_35_0, xn) = all_77_0 % 16.33/2.99 | | % 16.33/2.99 | | BETA: splitting (46) gives: % 16.33/2.99 | | % 16.33/2.99 | | Case 1: % 16.33/2.99 | | | % 16.33/2.99 | | | (52) xl = sz00 % 16.33/2.99 | | | % 16.33/2.99 | | | REDUCE: (13), (52) imply: % 16.33/2.99 | | | (53) $false % 16.33/2.99 | | | % 16.33/2.99 | | | CLOSE: (53) is inconsistent. % 16.33/2.99 | | | % 16.33/2.99 | | Case 2: % 16.33/2.99 | | | % 16.33/2.99 | | | (54) all_45_0 = all_35_0 % 16.33/2.99 | | | % 16.33/2.99 | | | REDUCE: (49), (54) imply: % 16.33/2.99 | | | (55) sdtasdt0(all_35_0, xn) = all_75_0 % 16.33/2.99 | | | % 16.33/2.99 | | | GROUND_INST: instantiating (11) with all_37_2, all_77_0, xn, all_35_0, % 16.33/2.99 | | | simplifying with (42), (51) gives: % 16.33/2.99 | | | (56) all_77_0 = all_37_2 % 16.33/2.99 | | | % 16.33/2.99 | | | GROUND_INST: instantiating (11) with all_75_0, all_77_0, xn, all_35_0, % 16.33/2.99 | | | simplifying with (51), (55) gives: % 16.33/2.99 | | | (57) all_77_0 = all_75_0 % 16.33/2.99 | | | % 16.33/2.99 | | | COMBINE_EQS: (56), (57) imply: % 16.33/2.99 | | | (58) all_75_0 = all_37_2 % 16.33/2.99 | | | % 16.33/2.99 | | | REDUCE: (48), (58) imply: % 16.33/2.99 | | | (59) sdtasdt0(xl, all_37_2) = all_37_3 % 16.33/2.99 | | | % 16.33/2.99 | | | GROUND_INST: instantiating (11) with all_37_1, all_37_3, all_37_2, xl, % 16.33/2.99 | | | simplifying with (23), (59) gives: % 16.33/2.99 | | | (60) all_37_1 = all_37_3 % 16.33/2.99 | | | % 16.33/2.99 | | | REDUCE: (19), (60) imply: % 16.33/2.99 | | | (61) $false % 16.33/2.99 | | | % 16.33/2.99 | | | CLOSE: (61) is inconsistent. % 16.33/2.99 | | | % 16.33/2.99 | | End of split % 16.33/2.99 | | % 16.33/2.99 | End of split % 16.33/2.99 | % 16.33/2.99 End of proof % 16.33/2.99 % SZS output end Proof for theBenchmark % 16.33/2.99 % 16.33/2.99 2463ms %------------------------------------------------------------------------------