%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM475+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 : 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 11:48:01 EDT 2023 % Result : Theorem 11.58s 2.31s % Output : Proof 19.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM475+2 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.13 % 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 % 0.19/0.34 % CPULimit : 300 % 0.19/0.34 % WCLimit : 300 % 0.19/0.34 % DateTime : Fri Aug 25 15:04:26 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.59/1.17 Prover 4: Preprocessing ... % 3.59/1.18 Prover 1: Preprocessing ... % 3.59/1.21 Prover 6: Preprocessing ... % 3.59/1.21 Prover 3: Preprocessing ... % 3.59/1.21 Prover 5: Preprocessing ... % 3.59/1.21 Prover 0: Preprocessing ... % 3.59/1.22 Prover 2: Preprocessing ... % 8.70/1.96 Prover 3: Constructing countermodel ... % 8.70/1.96 Prover 1: Constructing countermodel ... % 8.70/1.96 Prover 6: Proving ... % 9.99/2.09 Prover 5: Constructing countermodel ... % 10.50/2.19 Prover 2: Proving ... % 11.58/2.31 Prover 3: proved (1673ms) % 11.58/2.31 % 11.58/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.58/2.31 % 11.58/2.32 Prover 5: stopped % 11.58/2.32 Prover 6: stopped % 11.58/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.58/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.58/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.58/2.32 Prover 4: Constructing countermodel ... % 11.58/2.35 Prover 0: Proving ... % 12.16/2.36 Prover 0: stopped % 12.16/2.36 Prover 2: stopped % 12.16/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.16/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.26/2.40 Prover 8: Preprocessing ... % 12.57/2.43 Prover 7: Preprocessing ... % 12.77/2.44 Prover 10: Preprocessing ... % 12.77/2.45 Prover 13: Preprocessing ... % 12.77/2.46 Prover 11: Preprocessing ... % 13.58/2.65 Prover 10: Constructing countermodel ... % 13.58/2.66 Prover 8: Warning: ignoring some quantifiers % 13.58/2.66 Prover 8: Constructing countermodel ... % 14.54/2.70 Prover 13: Constructing countermodel ... % 14.54/2.73 Prover 7: Constructing countermodel ... % 16.42/2.97 Prover 11: Constructing countermodel ... % 19.30/3.32 Prover 10: Found proof (size 83) % 19.30/3.32 Prover 10: proved (1001ms) % 19.30/3.32 Prover 13: stopped % 19.30/3.32 Prover 7: stopped % 19.30/3.33 Prover 11: stopped % 19.30/3.33 Prover 4: stopped % 19.30/3.33 Prover 1: stopped % 19.30/3.33 Prover 8: stopped % 19.30/3.33 % 19.30/3.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.30/3.33 % 19.30/3.34 % SZS output start Proof for theBenchmark % 19.30/3.34 Assumptions after simplification: % 19.30/3.34 --------------------------------- % 19.30/3.34 % 19.30/3.34 (mAMDistr) % 19.60/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.60/3.37 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 19.60/3.37 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.60/3.37 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 19.60/3.37 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 % 19.60/3.37 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & % 19.60/3.37 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & % 19.60/3.37 $i(v6) & $i(v5))) % 19.60/3.37 % 19.60/3.37 (mAddCanc) % 19.60/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 % 19.60/3.37 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 19.60/3.37 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 19.60/3.37 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 19.60/3.37 sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & $i(v6) & $i(v5))) & ! % 19.60/3.37 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 19.60/3.37 (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 19.60/3.37 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 19.60/3.37 aNaturalNumber0(v0)) % 19.60/3.37 % 19.60/3.37 (mAddComm) % 19.60/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 19.60/3.38 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 19.60/3.38 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 19.60/3.38 % 19.60/3.38 (mDefDiff) % 19.60/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 19.60/3.38 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1) % 19.60/3.38 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ % 19.60/3.38 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 19.60/3.38 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ % 19.60/3.38 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.60/3.38 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 19.60/3.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) = % 19.60/3.38 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 19.60/3.38 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 19.60/3.38 aNaturalNumber0(v2)) % 19.60/3.38 % 19.60/3.38 (mDefQuot) % 19.60/3.38 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 19.60/3.38 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 19.60/3.38 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 19.60/3.38 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 19.60/3.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 19.60/3.38 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 19.60/3.38 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 19.60/3.38 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.60/3.38 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 19.60/3.38 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 19.60/3.38 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 19.60/3.38 % 19.60/3.38 (mMulComm) % 19.60/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 19.60/3.39 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 19.60/3.39 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 19.60/3.39 % 19.60/3.39 (mSortsB_02) % 19.60/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 19.60/3.39 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 19.60/3.39 aNaturalNumber0(v2)) % 19.60/3.39 % 19.60/3.39 (m__) % 19.60/3.39 $i(xr) & $i(xn) & $i(xl) & ? [v0: $i] : ( ~ (v0 = xn) & sdtasdt0(xl, xr) = v0 % 19.60/3.39 & $i(v0)) % 19.60/3.39 % 19.60/3.39 (m__1324) % 19.60/3.39 $i(xn) & $i(xm) & $i(xl) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & % 19.60/3.39 aNaturalNumber0(xl) % 19.60/3.39 % 19.60/3.39 (m__1324_04) % 19.60/3.39 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 19.60/3.39 (sdtasdt0(xl, v2) = xm & sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & % 19.60/3.39 $i(v2) & $i(v1) & $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 19.60/3.39 aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 19.60/3.39 % 19.60/3.39 (m__1347) % 19.60/3.39 ~ (xl = sz00) & $i(xl) & $i(sz00) % 19.60/3.39 % 19.60/3.39 (m__1360) % 19.60/3.39 sdtsldt0(xm, xl) = xp & sdtasdt0(xl, xp) = xm & $i(xp) & $i(xm) & $i(xl) & % 19.60/3.39 aNaturalNumber0(xp) % 19.60/3.39 % 19.60/3.39 (m__1379) % 19.60/3.39 $i(xq) & $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (sdtsldt0(v0, xl) = xq & % 19.60/3.39 sdtasdt0(xl, xq) = v0 & sdtpldt0(xm, xn) = v0 & $i(v0) & % 19.60/3.39 aNaturalNumber0(xq)) % 19.60/3.39 % 19.60/3.39 (m__1395) % 19.60/3.39 $i(xq) & $i(xp) & ? [v0: $i] : (sdtpldt0(xp, v0) = xq & $i(v0) & % 19.60/3.39 sdtlseqdt0(xp, xq) & aNaturalNumber0(v0)) % 19.60/3.39 % 19.60/3.39 (m__1422) % 19.60/3.39 sdtmndt0(xq, xp) = xr & sdtpldt0(xp, xr) = xq & $i(xr) & $i(xq) & $i(xp) & % 19.60/3.39 aNaturalNumber0(xr) % 19.60/3.39 % 19.60/3.39 (m__1459) % 19.60/3.39 $i(xr) & $i(xp) & $i(xn) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 19.60/3.39 (sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = v2 & % 19.60/3.39 sdtpldt0(v0, xn) = v2 & $i(v2) & $i(v1) & $i(v0)) % 19.60/3.39 % 19.60/3.39 (function-axioms) % 19.60/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.60/3.39 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 19.60/3.39 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 19.60/3.39 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.60/3.39 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 19.60/3.39 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.60/3.39 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 19.60/3.39 % 19.60/3.39 Further assumptions not needed in the proof: % 19.60/3.39 -------------------------------------------- % 19.60/3.39 mAddAsso, mDefDiv, mDefLE, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, % 19.60/3.39 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, % 19.60/3.39 mNatSort, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, % 19.60/3.39 m_MulUnit, m_MulZero % 19.60/3.39 % 19.60/3.39 Those formulas are unsatisfiable: % 19.60/3.39 --------------------------------- % 19.60/3.39 % 19.60/3.39 Begin of proof % 19.60/3.40 | % 19.60/3.40 | ALPHA: (mAddCanc) implies: % 19.60/3.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 19.60/3.40 | (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 19.60/3.40 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 19.60/3.40 | | ~ aNaturalNumber0(v0)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (mDefDiff) implies: % 19.60/3.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 19.60/3.40 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ % 19.60/3.40 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | % 19.60/3.40 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (mDefQuot) implies: % 19.60/3.40 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 19.60/3.40 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 19.60/3.40 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 19.60/3.40 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 19.60/3.40 | aNaturalNumber0(v0)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1324) implies: % 19.60/3.40 | (4) aNaturalNumber0(xl) % 19.60/3.40 | (5) aNaturalNumber0(xm) % 19.60/3.40 | (6) aNaturalNumber0(xn) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1324_04) implies: % 19.60/3.40 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xl, v2) = xm & % 19.60/3.40 | sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & $i(v2) & $i(v1) & % 19.60/3.40 | $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 19.60/3.40 | aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1347) implies: % 19.60/3.40 | (8) ~ (xl = sz00) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1360) implies: % 19.60/3.40 | (9) aNaturalNumber0(xp) % 19.60/3.40 | (10) sdtasdt0(xl, xp) = xm % 19.60/3.40 | (11) sdtsldt0(xm, xl) = xp % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1379) implies: % 19.60/3.40 | (12) ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtasdt0(xl, xq) = v0 & % 19.60/3.40 | sdtpldt0(xm, xn) = v0 & $i(v0) & aNaturalNumber0(xq)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1395) implies: % 19.60/3.40 | (13) ? [v0: $i] : (sdtpldt0(xp, v0) = xq & $i(v0) & sdtlseqdt0(xp, xq) & % 19.60/3.40 | aNaturalNumber0(v0)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1422) implies: % 19.60/3.40 | (14) aNaturalNumber0(xr) % 19.60/3.40 | (15) sdtmndt0(xq, xp) = xr % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__1459) implies: % 19.60/3.40 | (16) $i(xp) % 19.60/3.40 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xl, xr) = v1 & % 19.60/3.40 | sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = v2 & sdtpldt0(v0, xn) = % 19.60/3.40 | v2 & $i(v2) & $i(v1) & $i(v0)) % 19.60/3.40 | % 19.60/3.40 | ALPHA: (m__) implies: % 19.60/3.41 | (18) $i(xl) % 19.60/3.41 | (19) $i(xn) % 19.60/3.41 | (20) $i(xr) % 19.60/3.41 | (21) ? [v0: $i] : ( ~ (v0 = xn) & sdtasdt0(xl, xr) = v0 & $i(v0)) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (function-axioms) implies: % 19.60/3.41 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.60/3.41 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 19.60/3.41 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.60/3.41 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 19.60/3.41 | % 19.60/3.41 | DELTA: instantiating (21) with fresh symbol all_33_0 gives: % 19.60/3.41 | (24) ~ (all_33_0 = xn) & sdtasdt0(xl, xr) = all_33_0 & $i(all_33_0) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (24) implies: % 19.60/3.41 | (25) ~ (all_33_0 = xn) % 19.60/3.41 | (26) sdtasdt0(xl, xr) = all_33_0 % 19.60/3.41 | % 19.60/3.41 | DELTA: instantiating (13) with fresh symbol all_35_0 gives: % 19.60/3.41 | (27) sdtpldt0(xp, all_35_0) = xq & $i(all_35_0) & sdtlseqdt0(xp, xq) & % 19.60/3.41 | aNaturalNumber0(all_35_0) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (27) implies: % 19.60/3.41 | (28) aNaturalNumber0(all_35_0) % 19.60/3.41 | (29) sdtlseqdt0(xp, xq) % 19.60/3.41 | (30) $i(all_35_0) % 19.60/3.41 | (31) sdtpldt0(xp, all_35_0) = xq % 19.60/3.41 | % 19.60/3.41 | DELTA: instantiating (12) with fresh symbol all_37_0 gives: % 19.60/3.41 | (32) sdtsldt0(all_37_0, xl) = xq & sdtasdt0(xl, xq) = all_37_0 & % 19.60/3.41 | sdtpldt0(xm, xn) = all_37_0 & $i(all_37_0) & aNaturalNumber0(xq) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (32) implies: % 19.60/3.41 | (33) aNaturalNumber0(xq) % 19.60/3.41 | (34) sdtpldt0(xm, xn) = all_37_0 % 19.60/3.41 | (35) sdtasdt0(xl, xq) = all_37_0 % 19.60/3.41 | % 19.60/3.41 | DELTA: instantiating (17) with fresh symbols all_39_0, all_39_1, all_39_2 % 19.60/3.41 | gives: % 19.60/3.41 | (36) sdtasdt0(xl, xr) = all_39_1 & sdtasdt0(xl, xp) = all_39_2 & % 19.60/3.41 | sdtpldt0(all_39_2, all_39_1) = all_39_0 & sdtpldt0(all_39_2, xn) = % 19.60/3.41 | all_39_0 & $i(all_39_0) & $i(all_39_1) & $i(all_39_2) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (36) implies: % 19.60/3.41 | (37) sdtpldt0(all_39_2, xn) = all_39_0 % 19.60/3.41 | (38) sdtpldt0(all_39_2, all_39_1) = all_39_0 % 19.60/3.41 | (39) sdtasdt0(xl, xp) = all_39_2 % 19.60/3.41 | (40) sdtasdt0(xl, xr) = all_39_1 % 19.60/3.41 | % 19.60/3.41 | DELTA: instantiating (7) with fresh symbols all_41_0, all_41_1, all_41_2 % 19.60/3.41 | gives: % 19.60/3.41 | (41) sdtasdt0(xl, all_41_0) = xm & sdtasdt0(xl, all_41_1) = all_41_2 & % 19.60/3.41 | sdtpldt0(xm, xn) = all_41_2 & $i(all_41_0) & $i(all_41_1) & % 19.60/3.41 | $i(all_41_2) & doDivides0(xl, all_41_2) & doDivides0(xl, xm) & % 19.60/3.41 | aNaturalNumber0(all_41_0) & aNaturalNumber0(all_41_1) % 19.60/3.41 | % 19.60/3.41 | ALPHA: (41) implies: % 19.60/3.41 | (42) aNaturalNumber0(all_41_0) % 19.60/3.41 | (43) doDivides0(xl, xm) % 19.60/3.41 | (44) $i(all_41_0) % 19.60/3.41 | (45) sdtpldt0(xm, xn) = all_41_2 % 19.60/3.41 | (46) sdtasdt0(xl, all_41_0) = xm % 19.60/3.41 | % 19.60/3.41 | GROUND_INST: instantiating (22) with all_37_0, all_41_2, xn, xm, simplifying % 19.60/3.41 | with (34), (45) gives: % 19.60/3.41 | (47) all_41_2 = all_37_0 % 19.60/3.41 | % 19.60/3.42 | GROUND_INST: instantiating (23) with xm, all_39_2, xp, xl, simplifying with % 19.60/3.42 | (10), (39) gives: % 19.60/3.42 | (48) all_39_2 = xm % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (23) with all_33_0, all_39_1, xr, xl, simplifying % 19.60/3.42 | with (26), (40) gives: % 19.60/3.42 | (49) all_39_1 = all_33_0 % 19.60/3.42 | % 19.60/3.42 | REDUCE: (38), (48), (49) imply: % 19.60/3.42 | (50) sdtpldt0(xm, all_33_0) = all_39_0 % 19.60/3.42 | % 19.60/3.42 | REDUCE: (37), (48) imply: % 19.60/3.42 | (51) sdtpldt0(xm, xn) = all_39_0 % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (22) with all_37_0, all_39_0, xn, xm, simplifying % 19.60/3.42 | with (34), (51) gives: % 19.60/3.42 | (52) all_39_0 = all_37_0 % 19.60/3.42 | % 19.60/3.42 | REDUCE: (50), (52) imply: % 19.60/3.42 | (53) sdtpldt0(xm, all_33_0) = all_37_0 % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mAddComm) with xp, all_35_0, xq, simplifying with % 19.60/3.42 | (9), (16), (28), (30), (31) gives: % 19.60/3.42 | (54) sdtpldt0(all_35_0, xp) = xq & $i(xq) % 19.60/3.42 | % 19.60/3.42 | ALPHA: (54) implies: % 19.60/3.42 | (55) $i(xq) % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mMulComm) with xl, xq, all_37_0, simplifying with % 19.60/3.42 | (4), (18), (33), (35), (55) gives: % 19.60/3.42 | (56) sdtasdt0(xq, xl) = all_37_0 & $i(all_37_0) % 19.60/3.42 | % 19.60/3.42 | ALPHA: (56) implies: % 19.60/3.42 | (57) sdtasdt0(xq, xl) = all_37_0 % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mAMDistr) with xl, xp, xr, xm, all_33_0, all_37_0, % 19.60/3.42 | simplifying with (4), (9), (10), (14), (16), (18), (20), (26), % 19.60/3.42 | (53) gives: % 19.60/3.42 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 19.60/3.42 | xl) = v1 & sdtasdt0(xr, xl) = v3 & sdtasdt0(xp, xl) = v2 & % 19.60/3.42 | sdtasdt0(xl, v0) = all_37_0 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xp, % 19.60/3.42 | xr) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_37_0)) % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mSortsB_02) with xl, xr, all_33_0, simplifying % 19.60/3.42 | with (4), (14), (18), (20), (26) gives: % 19.60/3.42 | (59) aNaturalNumber0(all_33_0) % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mMulComm) with xl, xr, all_33_0, simplifying with % 19.60/3.42 | (4), (14), (18), (20), (26) gives: % 19.60/3.42 | (60) sdtasdt0(xr, xl) = all_33_0 & $i(all_33_0) % 19.60/3.42 | % 19.60/3.42 | ALPHA: (60) implies: % 19.60/3.42 | (61) sdtasdt0(xr, xl) = all_33_0 % 19.60/3.42 | % 19.60/3.42 | GROUND_INST: instantiating (mAMDistr) with xl, all_41_0, xr, xm, all_33_0, % 19.60/3.42 | all_37_0, simplifying with (4), (14), (18), (20), (26), (42), % 19.60/3.42 | (44), (46), (53) gives: % 19.60/3.42 | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 19.60/3.42 | xl) = v1 & sdtasdt0(all_41_0, xl) = v2 & sdtasdt0(xr, xl) = v3 & % 19.60/3.42 | sdtasdt0(xl, v0) = all_37_0 & sdtpldt0(v2, v3) = v1 & % 19.60/3.42 | sdtpldt0(all_41_0, xr) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 19.60/3.42 | $i(all_37_0)) % 19.60/3.42 | % 19.60/3.43 | GROUND_INST: instantiating (mMulComm) with xl, all_41_0, xm, simplifying with % 19.60/3.43 | (4), (18), (42), (44), (46) gives: % 19.60/3.43 | (63) sdtasdt0(all_41_0, xl) = xm & $i(xm) % 19.60/3.43 | % 19.60/3.43 | ALPHA: (63) implies: % 19.60/3.43 | (64) $i(xm) % 19.60/3.43 | (65) sdtasdt0(all_41_0, xl) = xm % 19.60/3.43 | % 19.60/3.43 | GROUND_INST: instantiating (2) with xp, xq, xr, all_35_0, simplifying with % 19.60/3.43 | (9), (15), (16), (28), (29), (30), (31), (33), (55) gives: % 19.60/3.43 | (66) all_35_0 = xr % 19.60/3.43 | % 19.60/3.43 | GROUND_INST: instantiating (3) with xl, xm, xp, all_41_0, simplifying with % 19.60/3.43 | (4), (5), (11), (18), (42), (43), (44), (46), (64) gives: % 19.60/3.43 | (67) all_41_0 = xp | xl = sz00 % 19.60/3.43 | % 19.60/3.43 | DELTA: instantiating (58) with fresh symbols all_61_0, all_61_1, all_61_2, % 19.60/3.43 | all_61_3 gives: % 19.60/3.43 | (68) sdtasdt0(all_61_3, xl) = all_61_2 & sdtasdt0(xr, xl) = all_61_0 & % 19.60/3.43 | sdtasdt0(xp, xl) = all_61_1 & sdtasdt0(xl, all_61_3) = all_37_0 & % 19.60/3.43 | sdtpldt0(all_61_1, all_61_0) = all_61_2 & sdtpldt0(xp, xr) = all_61_3 % 19.60/3.43 | & $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3) & % 19.60/3.43 | $i(all_37_0) % 19.60/3.43 | % 19.60/3.43 | ALPHA: (68) implies: % 19.60/3.43 | (69) $i(all_61_1) % 19.60/3.43 | (70) $i(all_61_0) % 19.60/3.43 | (71) sdtpldt0(xp, xr) = all_61_3 % 19.60/3.43 | (72) sdtpldt0(all_61_1, all_61_0) = all_61_2 % 19.60/3.43 | (73) sdtasdt0(xp, xl) = all_61_1 % 19.60/3.43 | (74) sdtasdt0(xr, xl) = all_61_0 % 19.60/3.43 | (75) sdtasdt0(all_61_3, xl) = all_61_2 % 19.60/3.43 | % 19.60/3.43 | DELTA: instantiating (62) with fresh symbols all_63_0, all_63_1, all_63_2, % 19.60/3.43 | all_63_3 gives: % 19.60/3.43 | (76) sdtasdt0(all_63_3, xl) = all_63_2 & sdtasdt0(all_41_0, xl) = all_63_1 % 19.60/3.43 | & sdtasdt0(xr, xl) = all_63_0 & sdtasdt0(xl, all_63_3) = all_37_0 & % 19.60/3.43 | sdtpldt0(all_63_1, all_63_0) = all_63_2 & sdtpldt0(all_41_0, xr) = % 19.60/3.43 | all_63_3 & $i(all_63_0) & $i(all_63_1) & $i(all_63_2) & $i(all_63_3) & % 19.60/3.43 | $i(all_37_0) % 19.60/3.43 | % 19.60/3.43 | ALPHA: (76) implies: % 19.60/3.43 | (77) sdtpldt0(all_41_0, xr) = all_63_3 % 19.60/3.43 | (78) sdtasdt0(xr, xl) = all_63_0 % 19.60/3.43 | (79) sdtasdt0(all_41_0, xl) = all_63_1 % 19.60/3.43 | (80) sdtasdt0(all_63_3, xl) = all_63_2 % 19.60/3.43 | % 19.60/3.43 | REDUCE: (31), (66) imply: % 19.60/3.43 | (81) sdtpldt0(xp, xr) = xq % 19.60/3.43 | % 19.60/3.43 | BETA: splitting (67) gives: % 19.60/3.43 | % 19.60/3.43 | Case 1: % 19.60/3.43 | | % 19.60/3.43 | | (82) xl = sz00 % 19.60/3.43 | | % 19.60/3.43 | | REDUCE: (8), (82) imply: % 19.60/3.43 | | (83) $false % 19.60/3.43 | | % 19.60/3.43 | | CLOSE: (83) is inconsistent. % 19.60/3.43 | | % 19.60/3.43 | Case 2: % 19.60/3.43 | | % 19.60/3.43 | | (84) all_41_0 = xp % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (79), (84) imply: % 19.60/3.44 | | (85) sdtasdt0(xp, xl) = all_63_1 % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (65), (84) imply: % 19.60/3.44 | | (86) sdtasdt0(xp, xl) = xm % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (77), (84) imply: % 19.60/3.44 | | (87) sdtpldt0(xp, xr) = all_63_3 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (22) with xq, all_63_3, xr, xp, simplifying with % 19.60/3.44 | | (81), (87) gives: % 19.60/3.44 | | (88) all_63_3 = xq % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (22) with all_61_3, all_63_3, xr, xp, simplifying % 19.60/3.44 | | with (71), (87) gives: % 19.60/3.44 | | (89) all_63_3 = all_61_3 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with all_61_1, all_63_1, xl, xp, simplifying % 19.60/3.44 | | with (73), (85) gives: % 19.60/3.44 | | (90) all_63_1 = all_61_1 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with xm, all_63_1, xl, xp, simplifying with % 19.60/3.44 | | (85), (86) gives: % 19.60/3.44 | | (91) all_63_1 = xm % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with all_61_0, all_63_0, xl, xr, simplifying % 19.60/3.44 | | with (74), (78) gives: % 19.60/3.44 | | (92) all_63_0 = all_61_0 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with all_33_0, all_63_0, xl, xr, simplifying % 19.60/3.44 | | with (61), (78) gives: % 19.60/3.44 | | (93) all_63_0 = all_33_0 % 19.60/3.44 | | % 19.60/3.44 | | COMBINE_EQS: (92), (93) imply: % 19.60/3.44 | | (94) all_61_0 = all_33_0 % 19.60/3.44 | | % 19.60/3.44 | | SIMP: (94) implies: % 19.60/3.44 | | (95) all_61_0 = all_33_0 % 19.60/3.44 | | % 19.60/3.44 | | COMBINE_EQS: (90), (91) imply: % 19.60/3.44 | | (96) all_61_1 = xm % 19.60/3.44 | | % 19.60/3.44 | | SIMP: (96) implies: % 19.60/3.44 | | (97) all_61_1 = xm % 19.60/3.44 | | % 19.60/3.44 | | COMBINE_EQS: (88), (89) imply: % 19.60/3.44 | | (98) all_61_3 = xq % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (80), (88) imply: % 19.60/3.44 | | (99) sdtasdt0(xq, xl) = all_63_2 % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (75), (98) imply: % 19.60/3.44 | | (100) sdtasdt0(xq, xl) = all_61_2 % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (72), (95), (97) imply: % 19.60/3.44 | | (101) sdtpldt0(xm, all_33_0) = all_61_2 % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (70), (95) imply: % 19.60/3.44 | | (102) $i(all_33_0) % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with all_37_0, all_63_2, xl, xq, simplifying % 19.60/3.44 | | with (57), (99) gives: % 19.60/3.44 | | (103) all_63_2 = all_37_0 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (23) with all_61_2, all_63_2, xl, xq, simplifying % 19.60/3.44 | | with (99), (100) gives: % 19.60/3.44 | | (104) all_63_2 = all_61_2 % 19.60/3.44 | | % 19.60/3.44 | | COMBINE_EQS: (103), (104) imply: % 19.60/3.44 | | (105) all_61_2 = all_37_0 % 19.60/3.44 | | % 19.60/3.44 | | GROUND_INST: instantiating (1) with xm, xn, all_33_0, all_37_0, simplifying % 19.60/3.44 | | with (5), (6), (19), (34), (53), (59), (64), (102) gives: % 19.60/3.44 | | (106) all_33_0 = xn % 19.60/3.44 | | % 19.60/3.44 | | REDUCE: (25), (106) imply: % 19.60/3.44 | | (107) $false % 19.60/3.44 | | % 19.60/3.44 | | CLOSE: (107) is inconsistent. % 19.60/3.44 | | % 19.60/3.44 | End of split % 19.60/3.44 | % 19.60/3.44 End of proof % 19.60/3.44 % SZS output end Proof for theBenchmark % 19.60/3.44 % 19.60/3.44 2830ms %------------------------------------------------------------------------------