%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM523+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 : n007.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 11:48:22 EDT 2023 % Result : Theorem 74.19s 10.49s % Output : Proof 79.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM523+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n007.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 07:28:40 EDT 2023 % 0.13/0.35 % 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 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 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 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 % 3.31/1.20 Prover 1: Preprocessing ... % 3.31/1.20 Prover 4: Preprocessing ... % 3.93/1.24 Prover 3: Preprocessing ... % 3.93/1.24 Prover 5: Preprocessing ... % 3.93/1.24 Prover 2: Preprocessing ... % 3.93/1.24 Prover 6: Preprocessing ... % 3.93/1.24 Prover 0: Preprocessing ... % 8.62/2.01 Prover 1: Constructing countermodel ... % 8.62/2.03 Prover 3: Constructing countermodel ... % 10.42/2.12 Prover 6: Proving ... % 10.47/2.16 Prover 5: Constructing countermodel ... % 11.59/2.35 Prover 2: Proving ... % 12.78/2.45 Prover 4: Constructing countermodel ... % 13.37/2.61 Prover 0: Proving ... % 72.54/10.30 Prover 2: stopped % 72.54/10.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.48/10.40 Prover 7: Preprocessing ... % 74.19/10.49 Prover 3: proved (9853ms) % 74.19/10.49 % 74.19/10.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 74.19/10.49 % 74.19/10.49 Prover 6: stopped % 74.19/10.49 Prover 5: stopped % 74.19/10.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 74.19/10.49 Prover 0: stopped % 74.19/10.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 74.19/10.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 74.19/10.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 74.95/10.55 Prover 7: Constructing countermodel ... % 75.37/10.61 Prover 11: Preprocessing ... % 75.37/10.61 Prover 8: Preprocessing ... % 75.80/10.66 Prover 13: Preprocessing ... % 75.80/10.67 Prover 10: Preprocessing ... % 76.17/10.73 Prover 8: Warning: ignoring some quantifiers % 76.17/10.74 Prover 8: Constructing countermodel ... % 76.51/10.78 Prover 10: Constructing countermodel ... % 76.51/10.83 Prover 13: Constructing countermodel ... % 78.54/11.02 Prover 11: Constructing countermodel ... % 78.78/11.07 Prover 10: Found proof (size 32) % 78.78/11.07 Prover 10: proved (561ms) % 78.78/11.07 Prover 7: stopped % 78.78/11.07 Prover 13: stopped % 78.78/11.07 Prover 11: stopped % 78.78/11.07 Prover 8: stopped % 78.78/11.07 Prover 1: stopped % 78.78/11.07 Prover 4: stopped % 78.78/11.07 % 78.78/11.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 78.78/11.07 % 78.78/11.07 % SZS output start Proof for theBenchmark % 78.78/11.08 Assumptions after simplification: % 78.78/11.08 --------------------------------- % 78.78/11.08 % 78.78/11.08 (mDefDiv) % 78.78/11.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 78.78/11.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 78.78/11.10 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 78.78/11.10 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 78.78/11.10 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 78.78/11.10 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 78.78/11.11 % 78.78/11.11 (mDefPrime) % 78.78/11.11 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 78.78/11.11 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 78.78/11.11 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 78.78/11.11 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 78.78/11.11 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 78.78/11.11 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 78.78/11.11 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 78.78/11.11 % 78.78/11.11 (mMulComm) % 78.78/11.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 78.78/11.11 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 78.78/11.11 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 78.78/11.11 % 78.78/11.11 (mPDP) % 78.78/11.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v0, v1) % 78.78/11.11 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ isPrime0(v2) | ~ % 78.78/11.11 doDivides0(v2, v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 78.78/11.11 aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0)) % 78.78/11.11 % 78.78/11.11 (mSortsB_02) % 78.78/11.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 78.78/11.11 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 78.78/11.11 aNaturalNumber0(v2)) % 78.78/11.11 % 78.78/11.11 (mSortsC_01) % 78.78/11.11 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 78.78/11.11 % 78.78/11.11 (m__) % 78.78/11.12 $i(xp) & $i(xn) & ? [v0: $i] : ((sdtasdt0(xn, xn) = v0 & $i(v0) & ~ % 78.78/11.12 doDivides0(xp, v0) & ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) % 78.78/11.12 | ~ aNaturalNumber0(v1))) | ( ~ doDivides0(xp, xn) & ! [v1: $i] : ( ~ % 78.78/11.12 (sdtasdt0(xp, v1) = xn) | ~ $i(v1) | ~ aNaturalNumber0(v1)))) % 78.78/11.12 % 78.78/11.12 (m__2987) % 78.78/11.12 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) & % 78.78/11.12 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) % 78.78/11.12 % 78.78/11.12 (m__3014) % 78.78/11.12 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 % 78.78/11.12 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 78.78/11.12 % 78.78/11.12 (m__3025) % 78.78/11.12 ~ (xp = sz10) & $i(xp) & $i(sz10) & isPrime0(xp) & ! [v0: $i] : ! [v1: $i] % 78.78/11.12 : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ $i(v1) | ~ $i(v0) | % 78.78/11.12 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | % 78.78/11.12 v0 = sz10 | ~ $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 78.78/11.12 % 78.78/11.12 (function-axioms) % 78.78/11.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.78/11.12 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 78.78/11.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 78.78/11.12 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.78/11.12 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 78.78/11.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.78/11.12 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 78.78/11.12 % 78.78/11.12 Further assumptions not needed in the proof: % 78.78/11.12 -------------------------------------------- % 78.78/11.12 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefQuot, mDivAsso, % 78.78/11.12 mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, % 78.78/11.12 mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, % 78.78/11.12 mPrimDiv, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, % 78.78/11.12 m__2963 % 78.78/11.12 % 78.78/11.12 Those formulas are unsatisfiable: % 78.78/11.12 --------------------------------- % 78.78/11.12 % 78.78/11.12 Begin of proof % 78.78/11.12 | % 78.78/11.12 | ALPHA: (mSortsC_01) implies: % 78.78/11.12 | (1) aNaturalNumber0(sz10) % 78.78/11.12 | % 78.78/11.12 | ALPHA: (mDefDiv) implies: % 78.78/11.12 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | % 78.78/11.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 78.78/11.12 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) % 78.78/11.12 | % 78.78/11.12 | ALPHA: (mDefPrime) implies: % 78.78/11.12 | (3) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 78.78/11.12 | % 78.78/11.12 | ALPHA: (m__2987) implies: % 78.78/11.13 | (4) aNaturalNumber0(xn) % 78.78/11.13 | (5) aNaturalNumber0(xm) % 78.78/11.13 | (6) aNaturalNumber0(xp) % 78.78/11.13 | % 78.78/11.13 | ALPHA: (m__3014) implies: % 78.78/11.13 | (7) $i(xm) % 78.78/11.13 | (8) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = % 78.78/11.13 | v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 78.78/11.13 | % 78.78/11.13 | ALPHA: (m__3025) implies: % 78.78/11.13 | (9) isPrime0(xp) % 78.78/11.13 | % 78.78/11.13 | ALPHA: (m__) implies: % 78.78/11.13 | (10) $i(xn) % 78.78/11.13 | (11) $i(xp) % 79.18/11.13 | (12) ? [v0: $i] : ((sdtasdt0(xn, xn) = v0 & $i(v0) & ~ doDivides0(xp, v0) % 79.18/11.13 | & ! [v1: $i] : ( ~ (sdtasdt0(xp, v1) = v0) | ~ $i(v1) | ~ % 79.18/11.13 | aNaturalNumber0(v1))) | ( ~ doDivides0(xp, xn) & ! [v1: $i] : ( % 79.18/11.13 | ~ (sdtasdt0(xp, v1) = xn) | ~ $i(v1) | ~ % 79.18/11.13 | aNaturalNumber0(v1)))) % 79.18/11.13 | % 79.18/11.13 | ALPHA: (function-axioms) implies: % 79.18/11.13 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.18/11.13 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 79.18/11.13 | % 79.18/11.13 | DELTA: instantiating (8) with fresh symbols all_41_0, all_41_1 gives: % 79.18/11.13 | (14) sdtasdt0(xp, all_41_1) = all_41_0 & sdtasdt0(xm, xm) = all_41_1 & % 79.18/11.13 | sdtasdt0(xn, xn) = all_41_0 & $i(all_41_0) & $i(all_41_1) % 79.18/11.13 | % 79.18/11.13 | ALPHA: (14) implies: % 79.18/11.13 | (15) $i(all_41_1) % 79.18/11.13 | (16) sdtasdt0(xn, xn) = all_41_0 % 79.18/11.13 | (17) sdtasdt0(xm, xm) = all_41_1 % 79.18/11.13 | (18) sdtasdt0(xp, all_41_1) = all_41_0 % 79.18/11.13 | % 79.18/11.13 | DELTA: instantiating (12) with fresh symbol all_43_0 gives: % 79.18/11.13 | (19) (sdtasdt0(xn, xn) = all_43_0 & $i(all_43_0) & ~ doDivides0(xp, % 79.18/11.13 | all_43_0) & ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_43_0) | ~ % 79.18/11.13 | $i(v0) | ~ aNaturalNumber0(v0))) | ( ~ doDivides0(xp, xn) & ! % 79.18/11.13 | [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ~ % 79.18/11.13 | aNaturalNumber0(v0))) % 79.18/11.13 | % 79.18/11.13 | BETA: splitting (3) gives: % 79.18/11.13 | % 79.18/11.13 | Case 1: % 79.18/11.13 | | % 79.18/11.13 | | (20) ~ aNaturalNumber0(sz10) % 79.18/11.13 | | % 79.18/11.13 | | PRED_UNIFY: (1), (20) imply: % 79.18/11.13 | | (21) $false % 79.18/11.13 | | % 79.18/11.13 | | CLOSE: (21) is inconsistent. % 79.18/11.13 | | % 79.18/11.13 | Case 2: % 79.18/11.13 | | % 79.18/11.13 | | % 79.18/11.13 | | GROUND_INST: instantiating (mSortsB_02) with xn, xn, all_41_0, simplifying % 79.18/11.13 | | with (4), (10), (16) gives: % 79.18/11.13 | | (22) aNaturalNumber0(all_41_0) % 79.18/11.13 | | % 79.18/11.14 | | GROUND_INST: instantiating (mSortsB_02) with xm, xm, all_41_1, simplifying % 79.18/11.14 | | with (5), (7), (17) gives: % 79.18/11.14 | | (23) aNaturalNumber0(all_41_1) % 79.18/11.14 | | % 79.18/11.14 | | GROUND_INST: instantiating (mMulComm) with xp, all_41_1, all_41_0, % 79.18/11.14 | | simplifying with (6), (11), (15), (18), (23) gives: % 79.18/11.14 | | (24) sdtasdt0(all_41_1, xp) = all_41_0 & $i(all_41_0) % 79.18/11.14 | | % 79.18/11.14 | | ALPHA: (24) implies: % 79.18/11.14 | | (25) $i(all_41_0) % 79.18/11.14 | | % 79.18/11.14 | | GROUND_INST: instantiating (2) with xp, all_41_0, all_41_1, simplifying with % 79.18/11.14 | | (6), (11), (15), (18), (22), (23), (25) gives: % 79.18/11.14 | | (26) doDivides0(xp, all_41_0) % 79.18/11.14 | | % 79.18/11.14 | | BETA: splitting (19) gives: % 79.18/11.14 | | % 79.18/11.14 | | Case 1: % 79.18/11.14 | | | % 79.18/11.14 | | | (27) sdtasdt0(xn, xn) = all_43_0 & $i(all_43_0) & ~ doDivides0(xp, % 79.18/11.14 | | | all_43_0) & ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_43_0) | ~ % 79.18/11.14 | | | $i(v0) | ~ aNaturalNumber0(v0)) % 79.18/11.14 | | | % 79.18/11.14 | | | ALPHA: (27) implies: % 79.18/11.14 | | | (28) ~ doDivides0(xp, all_43_0) % 79.18/11.14 | | | (29) sdtasdt0(xn, xn) = all_43_0 % 79.18/11.14 | | | % 79.18/11.14 | | | GROUND_INST: instantiating (13) with all_41_0, all_43_0, xn, xn, % 79.18/11.14 | | | simplifying with (16), (29) gives: % 79.18/11.14 | | | (30) all_43_0 = all_41_0 % 79.18/11.14 | | | % 79.18/11.14 | | | REDUCE: (28), (30) imply: % 79.18/11.14 | | | (31) ~ doDivides0(xp, all_41_0) % 79.18/11.14 | | | % 79.18/11.14 | | | PRED_UNIFY: (26), (31) imply: % 79.18/11.14 | | | (32) $false % 79.18/11.14 | | | % 79.18/11.14 | | | CLOSE: (32) is inconsistent. % 79.18/11.14 | | | % 79.18/11.14 | | Case 2: % 79.18/11.14 | | | % 79.18/11.14 | | | (33) ~ doDivides0(xp, xn) & ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) % 79.18/11.14 | | | | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 79.18/11.14 | | | % 79.18/11.14 | | | ALPHA: (33) implies: % 79.18/11.14 | | | (34) ~ doDivides0(xp, xn) % 79.18/11.14 | | | % 79.18/11.14 | | | GROUND_INST: instantiating (mPDP) with xn, xn, xp, all_41_0, simplifying % 79.18/11.14 | | | with (4), (6), (9), (10), (11), (16), (26), (34) gives: % 79.18/11.14 | | | (35) $false % 79.18/11.14 | | | % 79.18/11.14 | | | CLOSE: (35) is inconsistent. % 79.18/11.14 | | | % 79.18/11.14 | | End of split % 79.18/11.14 | | % 79.18/11.14 | End of split % 79.18/11.14 | % 79.18/11.14 End of proof % 79.18/11.14 % SZS output end Proof for theBenchmark % 79.18/11.14 % 79.18/11.14 10529ms %------------------------------------------------------------------------------