%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM468+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 : n023.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 11:47:57 EDT 2023 % Result : Theorem 9.82s 2.07s % Output : Proof 15.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : NUM468+2 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 12:12:42 EDT 2023 % 0.12/0.33 % CPUTime : % 0.20/0.58 ________ _____ % 0.20/0.58 ___ __ \_________(_)________________________________ % 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.58 % 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.58 (2023-06-19) % 0.20/0.58 % 0.20/0.58 (c) Philipp Rümmer, 2009-2023 % 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.58 Amanda Stjerna. % 0.20/0.58 Free software under BSD-3-Clause. % 0.20/0.58 % 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.58 % 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.60 Running up to 7 provers in parallel. % 0.67/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.67/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.17/1.11 Prover 1: Preprocessing ... % 3.17/1.11 Prover 4: Preprocessing ... % 3.17/1.14 Prover 3: Preprocessing ... % 3.17/1.14 Prover 2: Preprocessing ... % 3.17/1.14 Prover 0: Preprocessing ... % 3.17/1.14 Prover 6: Preprocessing ... % 3.17/1.14 Prover 5: Preprocessing ... % 7.54/1.77 Prover 1: Constructing countermodel ... % 7.54/1.77 Prover 3: Constructing countermodel ... % 8.24/1.78 Prover 6: Proving ... % 8.51/1.83 Prover 5: Constructing countermodel ... % 9.82/2.02 Prover 2: Proving ... % 9.82/2.07 Prover 3: proved (1455ms) % 9.82/2.07 % 9.82/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.82/2.07 % 9.82/2.07 Prover 6: stopped % 9.82/2.07 Prover 5: stopped % 10.45/2.08 Prover 2: stopped % 10.45/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.45/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.45/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.49/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.49/2.10 Prover 4: Constructing countermodel ... % 10.76/2.16 Prover 10: Preprocessing ... % 10.76/2.17 Prover 7: Preprocessing ... % 10.76/2.20 Prover 8: Preprocessing ... % 10.76/2.21 Prover 0: Proving ... % 11.50/2.21 Prover 0: stopped % 11.50/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.50/2.23 Prover 11: Preprocessing ... % 11.50/2.28 Prover 13: Preprocessing ... % 12.16/2.32 Prover 10: Constructing countermodel ... % 12.88/2.40 Prover 7: Constructing countermodel ... % 12.98/2.44 Prover 8: Warning: ignoring some quantifiers % 12.98/2.44 Prover 8: Constructing countermodel ... % 13.69/2.53 Prover 13: Constructing countermodel ... % 14.35/2.65 Prover 11: Constructing countermodel ... % 15.25/2.77 Prover 10: Found proof (size 53) % 15.25/2.77 Prover 10: proved (689ms) % 15.25/2.77 Prover 11: stopped % 15.25/2.77 Prover 13: stopped % 15.25/2.77 Prover 4: stopped % 15.25/2.77 Prover 8: stopped % 15.25/2.77 Prover 7: stopped % 15.25/2.79 Prover 1: Found proof (size 243) % 15.25/2.79 Prover 1: proved (2181ms) % 15.25/2.79 % 15.25/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.25/2.79 % 15.25/2.80 % SZS output start Proof for theBenchmark % 15.25/2.80 Assumptions after simplification: % 15.25/2.80 --------------------------------- % 15.25/2.80 % 15.25/2.80 (mAMDistr) % 15.90/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.90/2.83 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 15.90/2.83 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.90/2.83 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 15.90/2.83 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 % 15.90/2.83 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & % 15.90/2.83 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & % 15.90/2.83 $i(v6) & $i(v5))) % 15.90/2.83 % 15.90/2.83 (mDefQuot) % 15.90/2.84 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 15.90/2.84 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 15.90/2.84 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.90/2.84 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 15.90/2.84 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 15.90/2.84 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 15.90/2.84 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 15.90/2.84 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 15.90/2.84 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 15.90/2.84 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.90/2.84 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 15.90/2.84 % 15.90/2.84 (mMulComm) % 15.90/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 15.90/2.84 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 15.90/2.84 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 15.90/2.84 % 15.90/2.84 (m__) % 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 15.90/2.84 : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v2) & ~ (xl = sz00) & sdtsldt0(xn, % 15.90/2.84 xl) = v1 & sdtsldt0(xm, xl) = v0 & sdtasdt0(xl, v3) = v4 & sdtasdt0(xl, % 15.90/2.84 v1) = xn & sdtasdt0(xl, v0) = xm & sdtpldt0(v0, v1) = v3 & sdtpldt0(xm, % 15.90/2.84 xn) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 15.90/2.84 aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 15.90/2.84 % 15.90/2.84 (m__1240) % 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & % 15.90/2.84 aNaturalNumber0(xl) % 15.90/2.84 % 15.90/2.84 (m__1240_04) % 15.90/2.84 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xl, v1) = xm % 15.90/2.84 & sdtasdt0(xl, v0) = xn & $i(v1) & $i(v0) & doDivides0(xl, xn) & % 15.90/2.84 doDivides0(xl, xm) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 15.90/2.84 % 15.90/2.84 (function-axioms) % 15.90/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.90/2.84 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 15.90/2.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 15.90/2.84 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.90/2.84 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 15.90/2.84 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.90/2.84 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.90/2.84 % 15.90/2.84 Further assumptions not needed in the proof: % 15.90/2.84 -------------------------------------------- % 15.90/2.84 mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDivTrans, mIH, mIH_03, % 15.90/2.84 mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, % 15.90/2.84 mMulAsso, mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, % 15.90/2.84 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 15.90/2.84 % 15.90/2.84 Those formulas are unsatisfiable: % 15.90/2.84 --------------------------------- % 15.90/2.84 % 15.90/2.84 Begin of proof % 15.90/2.84 | % 15.90/2.84 | ALPHA: (mDefQuot) implies: % 15.90/2.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 15.90/2.85 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 15.90/2.85 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 15.90/2.85 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 15.90/2.85 | aNaturalNumber0(v0)) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (m__1240) implies: % 15.90/2.85 | (2) aNaturalNumber0(xl) % 15.90/2.85 | (3) aNaturalNumber0(xm) % 15.90/2.85 | (4) aNaturalNumber0(xn) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (m__1240_04) implies: % 15.90/2.85 | (5) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xl, v1) = xm & sdtasdt0(xl, v0) = % 15.90/2.85 | xn & $i(v1) & $i(v0) & doDivides0(xl, xn) & doDivides0(xl, xm) & % 15.90/2.85 | aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (m__) implies: % 15.90/2.85 | (6) $i(xl) % 15.90/2.85 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( % 15.90/2.85 | ~ (v4 = v2) & ~ (xl = sz00) & sdtsldt0(xn, xl) = v1 & sdtsldt0(xm, % 15.90/2.85 | xl) = v0 & sdtasdt0(xl, v3) = v4 & sdtasdt0(xl, v1) = xn & % 15.90/2.85 | sdtasdt0(xl, v0) = xm & sdtpldt0(v0, v1) = v3 & sdtpldt0(xm, xn) = v2 % 15.90/2.85 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aNaturalNumber0(v1) & % 15.90/2.85 | aNaturalNumber0(v0)) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (function-axioms) implies: % 15.90/2.85 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.90/2.85 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.90/2.85 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.90/2.85 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 15.90/2.85 | % 15.90/2.85 | DELTA: instantiating (5) with fresh symbols all_32_0, all_32_1 gives: % 15.90/2.85 | (10) sdtasdt0(xl, all_32_0) = xm & sdtasdt0(xl, all_32_1) = xn & % 15.90/2.85 | $i(all_32_0) & $i(all_32_1) & doDivides0(xl, xn) & doDivides0(xl, xm) % 15.90/2.85 | & aNaturalNumber0(all_32_0) & aNaturalNumber0(all_32_1) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (10) implies: % 15.90/2.85 | (11) aNaturalNumber0(all_32_1) % 15.90/2.85 | (12) aNaturalNumber0(all_32_0) % 15.90/2.85 | (13) doDivides0(xl, xm) % 15.90/2.85 | (14) doDivides0(xl, xn) % 15.90/2.85 | (15) $i(all_32_1) % 15.90/2.85 | (16) $i(all_32_0) % 15.90/2.85 | (17) sdtasdt0(xl, all_32_1) = xn % 15.90/2.85 | (18) sdtasdt0(xl, all_32_0) = xm % 15.90/2.85 | % 15.90/2.85 | DELTA: instantiating (7) with fresh symbols all_34_0, all_34_1, all_34_2, % 15.90/2.85 | all_34_3, all_34_4 gives: % 15.90/2.85 | (19) ~ (all_34_0 = all_34_2) & ~ (xl = sz00) & sdtsldt0(xn, xl) = % 15.90/2.85 | all_34_3 & sdtsldt0(xm, xl) = all_34_4 & sdtasdt0(xl, all_34_1) = % 15.90/2.85 | all_34_0 & sdtasdt0(xl, all_34_3) = xn & sdtasdt0(xl, all_34_4) = xm & % 15.90/2.85 | sdtpldt0(all_34_4, all_34_3) = all_34_1 & sdtpldt0(xm, xn) = all_34_2 % 15.90/2.85 | & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) & % 15.90/2.85 | $i(all_34_4) & aNaturalNumber0(all_34_3) & aNaturalNumber0(all_34_4) % 15.90/2.85 | % 15.90/2.85 | ALPHA: (19) implies: % 15.90/2.86 | (20) ~ (xl = sz00) % 15.90/2.86 | (21) ~ (all_34_0 = all_34_2) % 15.90/2.86 | (22) aNaturalNumber0(all_34_4) % 15.90/2.86 | (23) aNaturalNumber0(all_34_3) % 15.90/2.86 | (24) $i(all_34_4) % 15.90/2.86 | (25) $i(all_34_3) % 15.90/2.86 | (26) sdtpldt0(xm, xn) = all_34_2 % 15.90/2.86 | (27) sdtpldt0(all_34_4, all_34_3) = all_34_1 % 15.90/2.86 | (28) sdtasdt0(xl, all_34_4) = xm % 15.90/2.86 | (29) sdtasdt0(xl, all_34_3) = xn % 15.90/2.86 | (30) sdtasdt0(xl, all_34_1) = all_34_0 % 15.90/2.86 | (31) sdtsldt0(xm, xl) = all_34_4 % 15.90/2.86 | (32) sdtsldt0(xn, xl) = all_34_3 % 15.90/2.86 | % 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0, all_32_1, xm, xn, % 15.90/2.86 | all_34_2, simplifying with (2), (6), (11), (12), (15), (16), % 15.90/2.86 | (17), (18), (26) gives: % 15.90/2.86 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 15.90/2.86 | xl) = v1 & sdtasdt0(all_32_0, xl) = v2 & sdtasdt0(all_32_1, xl) = % 15.90/2.86 | v3 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 & % 15.90/2.86 | sdtpldt0(all_32_0, all_32_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 15.90/2.86 | $i(v0) & $i(all_34_2)) % 15.90/2.86 | % 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_34_4, all_32_1, xm, xn, % 15.90/2.86 | all_34_2, simplifying with (2), (6), (11), (15), (17), (22), % 15.90/2.86 | (24), (26), (28) gives: % 15.90/2.86 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 15.90/2.86 | xl) = v1 & sdtasdt0(all_34_4, xl) = v2 & sdtasdt0(all_32_1, xl) = % 15.90/2.86 | v3 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 & % 15.90/2.86 | sdtpldt0(all_34_4, all_32_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 15.90/2.86 | $i(v0) & $i(all_34_2)) % 15.90/2.86 | % 15.90/2.86 | GROUND_INST: instantiating (mMulComm) with xl, all_34_4, xm, simplifying with % 15.90/2.86 | (2), (6), (22), (24), (28) gives: % 15.90/2.86 | (35) sdtasdt0(all_34_4, xl) = xm & $i(xm) % 15.90/2.86 | % 15.90/2.86 | ALPHA: (35) implies: % 15.90/2.86 | (36) $i(xm) % 15.90/2.86 | % 15.90/2.86 | GROUND_INST: instantiating (mAMDistr) with xl, all_34_4, all_34_3, xm, xn, % 15.90/2.86 | all_34_2, simplifying with (2), (6), (22), (23), (24), (25), % 15.90/2.86 | (26), (28), (29) gives: % 15.90/2.86 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 15.90/2.86 | xl) = v1 & sdtasdt0(all_34_3, xl) = v3 & sdtasdt0(all_34_4, xl) = % 15.90/2.86 | v2 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 & % 15.90/2.86 | sdtpldt0(all_34_4, all_34_3) = v0 & $i(v3) & $i(v2) & $i(v1) & % 15.90/2.86 | $i(v0) & $i(all_34_2)) % 15.90/2.86 | % 15.90/2.87 | GROUND_INST: instantiating (mAMDistr) with xl, all_32_0, all_34_3, xm, xn, % 15.90/2.87 | all_34_2, simplifying with (2), (6), (12), (16), (18), (23), % 15.90/2.87 | (25), (26), (29) gives: % 15.90/2.87 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 15.90/2.87 | xl) = v1 & sdtasdt0(all_34_3, xl) = v3 & sdtasdt0(all_32_0, xl) = % 15.90/2.87 | v2 & sdtasdt0(xl, v0) = all_34_2 & sdtpldt0(v2, v3) = v1 & % 15.90/2.87 | sdtpldt0(all_32_0, all_34_3) = v0 & $i(v3) & $i(v2) & $i(v1) & % 15.90/2.87 | $i(v0) & $i(all_34_2)) % 15.90/2.87 | % 15.90/2.87 | GROUND_INST: instantiating (mMulComm) with xl, all_34_3, xn, simplifying with % 15.90/2.87 | (2), (6), (23), (25), (29) gives: % 15.90/2.87 | (39) sdtasdt0(all_34_3, xl) = xn & $i(xn) % 15.90/2.87 | % 15.90/2.87 | ALPHA: (39) implies: % 15.90/2.87 | (40) $i(xn) % 15.90/2.87 | % 15.90/2.87 | GROUND_INST: instantiating (1) with xl, xm, all_34_4, all_32_0, simplifying % 15.90/2.87 | with (2), (3), (6), (12), (13), (16), (18), (31), (36) gives: % 15.90/2.87 | (41) all_34_4 = all_32_0 | xl = sz00 % 15.90/2.87 | % 15.90/2.87 | GROUND_INST: instantiating (1) with xl, xn, all_34_3, all_32_1, simplifying % 15.90/2.87 | with (2), (4), (6), (11), (14), (15), (17), (32), (40) gives: % 15.90/2.87 | (42) all_34_3 = all_32_1 | xl = sz00 % 15.90/2.87 | % 15.90/2.87 | DELTA: instantiating (33) with fresh symbols all_46_0, all_46_1, all_46_2, % 15.90/2.87 | all_46_3 gives: % 15.90/2.87 | (43) sdtasdt0(all_46_3, xl) = all_46_2 & sdtasdt0(all_32_0, xl) = all_46_1 % 15.90/2.87 | & sdtasdt0(all_32_1, xl) = all_46_0 & sdtasdt0(xl, all_46_3) = % 15.90/2.87 | all_34_2 & sdtpldt0(all_46_1, all_46_0) = all_46_2 & % 15.90/2.87 | sdtpldt0(all_32_0, all_32_1) = all_46_3 & $i(all_46_0) & $i(all_46_1) % 15.90/2.87 | & $i(all_46_2) & $i(all_46_3) & $i(all_34_2) % 15.90/2.87 | % 15.90/2.87 | ALPHA: (43) implies: % 15.90/2.87 | (44) sdtpldt0(all_32_0, all_32_1) = all_46_3 % 15.90/2.87 | (45) sdtasdt0(xl, all_46_3) = all_34_2 % 15.90/2.87 | % 15.90/2.87 | DELTA: instantiating (38) with fresh symbols all_48_0, all_48_1, all_48_2, % 15.90/2.87 | all_48_3 gives: % 15.90/2.87 | (46) sdtasdt0(all_48_3, xl) = all_48_2 & sdtasdt0(all_34_3, xl) = all_48_0 % 15.90/2.87 | & sdtasdt0(all_32_0, xl) = all_48_1 & sdtasdt0(xl, all_48_3) = % 15.90/2.87 | all_34_2 & sdtpldt0(all_48_1, all_48_0) = all_48_2 & % 15.90/2.87 | sdtpldt0(all_32_0, all_34_3) = all_48_3 & $i(all_48_0) & $i(all_48_1) % 15.90/2.87 | & $i(all_48_2) & $i(all_48_3) & $i(all_34_2) % 15.90/2.87 | % 15.90/2.87 | ALPHA: (46) implies: % 15.90/2.87 | (47) sdtpldt0(all_32_0, all_34_3) = all_48_3 % 15.90/2.87 | % 15.90/2.87 | DELTA: instantiating (37) with fresh symbols all_50_0, all_50_1, all_50_2, % 15.90/2.87 | all_50_3 gives: % 15.90/2.87 | (48) sdtasdt0(all_50_3, xl) = all_50_2 & sdtasdt0(all_34_3, xl) = all_50_0 % 15.90/2.87 | & sdtasdt0(all_34_4, xl) = all_50_1 & sdtasdt0(xl, all_50_3) = % 15.90/2.87 | all_34_2 & sdtpldt0(all_50_1, all_50_0) = all_50_2 & % 15.90/2.87 | sdtpldt0(all_34_4, all_34_3) = all_50_3 & $i(all_50_0) & $i(all_50_1) % 15.90/2.87 | & $i(all_50_2) & $i(all_50_3) & $i(all_34_2) % 15.90/2.87 | % 15.90/2.87 | ALPHA: (48) implies: % 15.90/2.87 | (49) sdtpldt0(all_34_4, all_34_3) = all_50_3 % 15.90/2.87 | % 15.90/2.87 | DELTA: instantiating (34) with fresh symbols all_52_0, all_52_1, all_52_2, % 15.90/2.87 | all_52_3 gives: % 15.90/2.87 | (50) sdtasdt0(all_52_3, xl) = all_52_2 & sdtasdt0(all_34_4, xl) = all_52_1 % 15.90/2.87 | & sdtasdt0(all_32_1, xl) = all_52_0 & sdtasdt0(xl, all_52_3) = % 15.90/2.87 | all_34_2 & sdtpldt0(all_52_1, all_52_0) = all_52_2 & % 15.90/2.87 | sdtpldt0(all_34_4, all_32_1) = all_52_3 & $i(all_52_0) & $i(all_52_1) % 15.90/2.87 | & $i(all_52_2) & $i(all_52_3) & $i(all_34_2) % 15.90/2.87 | % 15.90/2.87 | ALPHA: (50) implies: % 15.90/2.87 | (51) sdtpldt0(all_34_4, all_32_1) = all_52_3 % 15.90/2.87 | % 15.90/2.87 | BETA: splitting (42) gives: % 15.90/2.87 | % 15.90/2.87 | Case 1: % 15.90/2.87 | | % 15.90/2.87 | | (52) xl = sz00 % 15.90/2.87 | | % 15.90/2.88 | | REDUCE: (20), (52) imply: % 15.90/2.88 | | (53) $false % 15.90/2.88 | | % 15.90/2.88 | | CLOSE: (53) is inconsistent. % 15.90/2.88 | | % 15.90/2.88 | Case 2: % 15.90/2.88 | | % 15.90/2.88 | | (54) all_34_3 = all_32_1 % 15.90/2.88 | | % 15.90/2.88 | | REDUCE: (49), (54) imply: % 15.90/2.88 | | (55) sdtpldt0(all_34_4, all_32_1) = all_50_3 % 15.90/2.88 | | % 15.90/2.88 | | REDUCE: (27), (54) imply: % 15.90/2.88 | | (56) sdtpldt0(all_34_4, all_32_1) = all_34_1 % 15.90/2.88 | | % 15.90/2.88 | | REDUCE: (47), (54) imply: % 15.90/2.88 | | (57) sdtpldt0(all_32_0, all_32_1) = all_48_3 % 15.90/2.88 | | % 15.90/2.88 | | BETA: splitting (41) gives: % 15.90/2.88 | | % 15.90/2.88 | | Case 1: % 15.90/2.88 | | | % 15.90/2.88 | | | (58) xl = sz00 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (20), (58) imply: % 15.90/2.88 | | | (59) $false % 15.90/2.88 | | | % 15.90/2.88 | | | CLOSE: (59) is inconsistent. % 15.90/2.88 | | | % 15.90/2.88 | | Case 2: % 15.90/2.88 | | | % 15.90/2.88 | | | (60) all_34_4 = all_32_0 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (51), (60) imply: % 15.90/2.88 | | | (61) sdtpldt0(all_32_0, all_32_1) = all_52_3 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (55), (60) imply: % 15.90/2.88 | | | (62) sdtpldt0(all_32_0, all_32_1) = all_50_3 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (56), (60) imply: % 15.90/2.88 | | | (63) sdtpldt0(all_32_0, all_32_1) = all_34_1 % 15.90/2.88 | | | % 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_46_3, all_50_3, all_32_1, % 15.90/2.88 | | | all_32_0, simplifying with (44), (62) gives: % 15.90/2.88 | | | (64) all_50_3 = all_46_3 % 15.90/2.88 | | | % 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_50_3, all_52_3, all_32_1, % 15.90/2.88 | | | all_32_0, simplifying with (61), (62) gives: % 15.90/2.88 | | | (65) all_52_3 = all_50_3 % 15.90/2.88 | | | % 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_48_3, all_52_3, all_32_1, % 15.90/2.88 | | | all_32_0, simplifying with (57), (61) gives: % 15.90/2.88 | | | (66) all_52_3 = all_48_3 % 15.90/2.88 | | | % 15.90/2.88 | | | GROUND_INST: instantiating (8) with all_34_1, all_52_3, all_32_1, % 15.90/2.88 | | | all_32_0, simplifying with (61), (63) gives: % 15.90/2.88 | | | (67) all_52_3 = all_34_1 % 15.90/2.88 | | | % 15.90/2.88 | | | COMBINE_EQS: (65), (66) imply: % 15.90/2.88 | | | (68) all_50_3 = all_48_3 % 15.90/2.88 | | | % 15.90/2.88 | | | SIMP: (68) implies: % 15.90/2.88 | | | (69) all_50_3 = all_48_3 % 15.90/2.88 | | | % 15.90/2.88 | | | COMBINE_EQS: (66), (67) imply: % 15.90/2.88 | | | (70) all_48_3 = all_34_1 % 15.90/2.88 | | | % 15.90/2.88 | | | COMBINE_EQS: (64), (69) imply: % 15.90/2.88 | | | (71) all_48_3 = all_46_3 % 15.90/2.88 | | | % 15.90/2.88 | | | SIMP: (71) implies: % 15.90/2.88 | | | (72) all_48_3 = all_46_3 % 15.90/2.88 | | | % 15.90/2.88 | | | COMBINE_EQS: (70), (72) imply: % 15.90/2.88 | | | (73) all_46_3 = all_34_1 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (45), (73) imply: % 15.90/2.88 | | | (74) sdtasdt0(xl, all_34_1) = all_34_2 % 15.90/2.88 | | | % 15.90/2.88 | | | GROUND_INST: instantiating (9) with all_34_0, all_34_2, all_34_1, xl, % 15.90/2.88 | | | simplifying with (30), (74) gives: % 15.90/2.88 | | | (75) all_34_0 = all_34_2 % 15.90/2.88 | | | % 15.90/2.88 | | | REDUCE: (21), (75) imply: % 15.90/2.88 | | | (76) $false % 15.90/2.88 | | | % 15.90/2.88 | | | CLOSE: (76) is inconsistent. % 15.90/2.88 | | | % 15.90/2.88 | | End of split % 15.90/2.88 | | % 15.90/2.88 | End of split % 15.90/2.88 | % 15.90/2.88 End of proof % 15.90/2.88 % SZS output end Proof for theBenchmark % 15.90/2.88 % 15.90/2.88 2301ms %------------------------------------------------------------------------------