%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM472+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 11:47:59 EDT 2023 % Result : Theorem 9.43s 2.06s % Output : Proof 12.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM472+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n009.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 15:35:21 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.03/1.13 Prover 4: Preprocessing ... % 3.03/1.13 Prover 1: Preprocessing ... % 3.03/1.17 Prover 5: Preprocessing ... % 3.03/1.17 Prover 0: Preprocessing ... % 3.03/1.17 Prover 3: Preprocessing ... % 3.03/1.17 Prover 6: Preprocessing ... % 3.03/1.17 Prover 2: Preprocessing ... % 7.64/1.74 Prover 1: Constructing countermodel ... % 8.38/1.84 Prover 3: Constructing countermodel ... % 8.38/1.89 Prover 6: Proving ... % 8.87/1.95 Prover 5: Constructing countermodel ... % 9.43/2.06 Prover 3: proved (1428ms) % 9.43/2.06 % 9.43/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.43/2.06 % 9.43/2.06 Prover 6: stopped % 9.43/2.06 Prover 5: stopped % 10.21/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.21/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.21/2.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.21/2.07 Prover 2: Proving ... % 10.40/2.10 Prover 2: stopped % 10.40/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.61/2.15 Prover 10: Preprocessing ... % 10.61/2.16 Prover 7: Preprocessing ... % 10.61/2.17 Prover 4: Constructing countermodel ... % 10.61/2.17 Prover 8: Preprocessing ... % 10.61/2.17 Prover 0: Proving ... % 10.61/2.19 Prover 11: Preprocessing ... % 10.61/2.19 Prover 0: stopped % 10.61/2.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.61/2.27 Prover 13: Preprocessing ... % 11.70/2.34 Prover 1: Found proof (size 84) % 11.70/2.34 Prover 1: proved (1710ms) % 11.70/2.34 Prover 4: stopped % 11.70/2.36 Prover 10: Constructing countermodel ... % 11.70/2.36 Prover 8: Warning: ignoring some quantifiers % 11.70/2.36 Prover 13: stopped % 11.70/2.37 Prover 11: stopped % 11.70/2.37 Prover 10: stopped % 11.70/2.37 Prover 8: Constructing countermodel ... % 12.39/2.38 Prover 8: stopped % 12.39/2.38 Prover 7: Constructing countermodel ... % 12.39/2.40 Prover 7: stopped % 12.39/2.40 % 12.39/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.39/2.40 % 12.39/2.41 % SZS output start Proof for theBenchmark % 12.39/2.41 Assumptions after simplification: % 12.39/2.41 --------------------------------- % 12.39/2.41 % 12.39/2.41 (mAddComm) % 12.39/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 12.39/2.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 12.39/2.44 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 12.39/2.44 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 12.39/2.44 % 12.39/2.44 (mDefLE) % 12.39/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (sdtlseqdt0(v0, v1) = v2) | ~ % 12.39/2.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 12.39/2.44 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 12.39/2.44 | ? [v3: $i] : (sdtpldt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 12.39/2.44 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtpldt0(v0, v3) = v1) | ~ % 12.39/2.44 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 12.39/2.44 % 12.39/2.44 (mDefQuot) % 12.39/2.45 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 12.39/2.45 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 12.39/2.45 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 12.39/2.45 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 12.39/2.45 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 12.39/2.45 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 12.39/2.45 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 12.39/2.45 0)))) % 12.39/2.45 % 12.39/2.45 (mLETotal) % 12.39/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = % 12.39/2.45 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 12.39/2.45 (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 12.39/2.45 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) % 12.39/2.45 % 12.39/2.45 (mSortsB) % 12.76/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 12.76/2.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 12.76/2.45 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 12.76/2.45 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 12.76/2.45 % 12.76/2.45 (m__) % 12.76/2.45 $i(xn) & $i(xm) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & sdtlseqdt0(xm, % 12.76/2.45 v0) = v1 & sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.45 % 12.76/2.45 (m__1324) % 12.76/2.45 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & % 12.76/2.45 $i(xn) & $i(xm) & $i(xl) % 12.76/2.45 % 12.76/2.45 (m__1324_04) % 12.76/2.45 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (doDivides0(xl, v0) = 0 & % 12.76/2.45 doDivides0(xl, xm) = 0 & sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.45 % 12.76/2.45 (m__1347) % 12.76/2.45 ~ (xl = sz00) & $i(xl) & $i(sz00) % 12.76/2.45 % 12.76/2.45 (m__1379) % 12.76/2.45 $i(xq) & $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (sdtsldt0(v0, xl) = xq & % 12.76/2.45 sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.45 % 12.76/2.45 (function-axioms) % 12.76/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.76/2.46 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 12.76/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.76/2.46 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 12.76/2.46 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.76/2.46 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 12.76/2.46 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.76/2.46 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 12.76/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.76/2.46 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 12.76/2.46 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.76/2.46 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 12.76/2.46 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 12.76/2.46 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.76/2.46 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 12.76/2.46 | ~ (aNaturalNumber0(v2) = v0)) % 12.76/2.46 % 12.76/2.46 Further assumptions not needed in the proof: % 12.76/2.46 -------------------------------------------- % 12.76/2.46 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDivSum, mDivTrans, mIH, % 12.76/2.46 mIH_03, mLEAsym, mLENTr, mLERefl, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, % 12.76/2.46 mMulCanc, mMulComm, mNatSort, mSortsB_02, mSortsC, mSortsC_01, mZeroAdd, % 12.76/2.46 mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1360 % 12.76/2.46 % 12.76/2.46 Those formulas are unsatisfiable: % 12.76/2.46 --------------------------------- % 12.76/2.46 % 12.76/2.46 Begin of proof % 12.76/2.46 | % 12.76/2.46 | ALPHA: (mDefQuot) implies: % 12.76/2.46 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 12.76/2.46 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 12.76/2.46 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 12.76/2.46 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 12.76/2.46 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 12.76/2.46 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 12.76/2.46 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 12.76/2.46 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 12.76/2.46 | % 12.76/2.46 | ALPHA: (m__1324) implies: % 12.76/2.46 | (2) aNaturalNumber0(xm) = 0 % 12.76/2.46 | (3) aNaturalNumber0(xn) = 0 % 12.76/2.46 | % 12.76/2.46 | ALPHA: (m__1324_04) implies: % 12.76/2.46 | (4) ? [v0: $i] : (doDivides0(xl, v0) = 0 & doDivides0(xl, xm) = 0 & % 12.76/2.46 | sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.46 | % 12.76/2.46 | ALPHA: (m__1347) implies: % 12.76/2.46 | (5) ~ (xl = sz00) % 12.76/2.46 | % 12.76/2.46 | ALPHA: (m__1379) implies: % 12.76/2.46 | (6) $i(xl) % 12.76/2.46 | (7) ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.46 | % 12.76/2.46 | ALPHA: (m__) implies: % 12.76/2.46 | (8) $i(xm) % 12.76/2.46 | (9) $i(xn) % 12.76/2.46 | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & sdtlseqdt0(xm, v0) = v1 & % 12.76/2.46 | sdtpldt0(xm, xn) = v0 & $i(v0)) % 12.76/2.46 | % 12.76/2.46 | ALPHA: (function-axioms) implies: % 12.76/2.47 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 12.76/2.47 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 12.76/2.47 | v0)) % 12.76/2.47 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.76/2.47 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 12.76/2.47 | % 12.76/2.47 | DELTA: instantiating (7) with fresh symbol all_33_0 gives: % 12.76/2.47 | (13) sdtsldt0(all_33_0, xl) = xq & sdtpldt0(xm, xn) = all_33_0 & % 12.76/2.47 | $i(all_33_0) % 12.76/2.47 | % 12.76/2.47 | ALPHA: (13) implies: % 12.76/2.47 | (14) sdtpldt0(xm, xn) = all_33_0 % 12.76/2.47 | (15) sdtsldt0(all_33_0, xl) = xq % 12.76/2.47 | % 12.76/2.47 | DELTA: instantiating (10) with fresh symbols all_35_0, all_35_1 gives: % 12.76/2.47 | (16) ~ (all_35_0 = 0) & sdtlseqdt0(xm, all_35_1) = all_35_0 & sdtpldt0(xm, % 12.76/2.47 | xn) = all_35_1 & $i(all_35_1) % 12.76/2.47 | % 12.76/2.47 | ALPHA: (16) implies: % 12.76/2.47 | (17) ~ (all_35_0 = 0) % 12.76/2.47 | (18) $i(all_35_1) % 12.76/2.47 | (19) sdtpldt0(xm, xn) = all_35_1 % 12.76/2.47 | (20) sdtlseqdt0(xm, all_35_1) = all_35_0 % 12.76/2.47 | % 12.76/2.47 | DELTA: instantiating (4) with fresh symbol all_37_0 gives: % 12.76/2.47 | (21) doDivides0(xl, all_37_0) = 0 & doDivides0(xl, xm) = 0 & sdtpldt0(xm, % 12.76/2.47 | xn) = all_37_0 & $i(all_37_0) % 12.76/2.47 | % 12.76/2.47 | ALPHA: (21) implies: % 12.76/2.47 | (22) sdtpldt0(xm, xn) = all_37_0 % 12.76/2.47 | % 12.76/2.47 | GROUND_INST: instantiating (12) with all_35_1, all_37_0, xn, xm, simplifying % 12.76/2.47 | with (19), (22) gives: % 12.76/2.47 | (23) all_37_0 = all_35_1 % 12.76/2.47 | % 12.76/2.47 | GROUND_INST: instantiating (12) with all_33_0, all_37_0, xn, xm, simplifying % 12.76/2.47 | with (14), (22) gives: % 12.76/2.47 | (24) all_37_0 = all_33_0 % 12.76/2.47 | % 12.76/2.47 | COMBINE_EQS: (23), (24) imply: % 12.76/2.47 | (25) all_35_1 = all_33_0 % 12.76/2.47 | % 12.87/2.47 | SIMP: (25) implies: % 12.87/2.47 | (26) all_35_1 = all_33_0 % 12.87/2.47 | % 12.87/2.47 | REDUCE: (20), (26) imply: % 12.87/2.47 | (27) sdtlseqdt0(xm, all_33_0) = all_35_0 % 12.87/2.47 | % 12.87/2.47 | REDUCE: (18), (26) imply: % 12.87/2.47 | (28) $i(all_33_0) % 12.87/2.47 | % 12.87/2.47 | GROUND_INST: instantiating (mAddComm) with xm, xn, all_33_0, simplifying with % 12.87/2.47 | (8), (9), (14) gives: % 12.87/2.47 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xn, xm) = v2 & % 12.87/2.47 | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ % 12.87/2.47 | (v1 = 0) | ~ (v0 = 0) | v2 = all_33_0)) % 12.87/2.47 | % 12.87/2.47 | GROUND_INST: instantiating (mSortsB) with xm, xn, all_33_0, simplifying with % 12.87/2.47 | (8), (9), (14) gives: % 12.87/2.47 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 12.87/2.47 | (aNaturalNumber0(all_33_0) = v2 & aNaturalNumber0(xn) = v1 & % 12.87/2.47 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 12.87/2.47 | % 12.87/2.47 | GROUND_INST: instantiating (mLETotal) with xm, all_33_0, all_35_0, simplifying % 12.87/2.47 | with (8), (27), (28) gives: % 12.87/2.47 | (31) all_35_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 12.87/2.48 | (sdtlseqdt0(all_33_0, xm) = v2 & aNaturalNumber0(all_33_0) = v1 & % 12.87/2.48 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ % 12.87/2.48 | (all_33_0 = xm)))) % 12.87/2.48 | % 12.87/2.48 | GROUND_INST: instantiating (mDefLE) with xm, all_33_0, all_35_0, simplifying % 12.87/2.48 | with (8), (27), (28) gives: % 12.87/2.48 | (32) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_0) = v1 & % 12.87/2.48 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~ % 12.87/2.48 | (all_35_0 = 0) | ? [v0: $i] : (sdtpldt0(xm, v0) = all_33_0 & % 12.87/2.48 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_35_0 = 0 | ! [v0: $i] % 12.87/2.48 | : ( ~ (sdtpldt0(xm, v0) = all_33_0) | ~ $i(v0) | ? [v1: int] : ( % 12.87/2.48 | ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))) % 12.87/2.48 | % 12.87/2.48 | GROUND_INST: instantiating (1) with xl, all_33_0, xq, simplifying with (6), % 12.87/2.48 | (15), (28) gives: % 12.87/2.48 | (33) xl = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 12.87/2.48 | (doDivides0(xl, all_33_0) = v2 & aNaturalNumber0(all_33_0) = v1 & % 12.87/2.48 | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 12.87/2.48 | 0))) | ( ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xl, v0) = % 12.87/2.48 | all_33_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 12.87/2.48 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xl, xq) % 12.87/2.48 | = v0) | ~ $i(xq) | (v0 = all_33_0 & aNaturalNumber0(xq) = 0))) % 12.87/2.48 | % 12.87/2.48 | DELTA: instantiating (30) with fresh symbols all_48_0, all_48_1, all_48_2 % 12.87/2.48 | gives: % 12.87/2.48 | (34) aNaturalNumber0(all_33_0) = all_48_0 & aNaturalNumber0(xn) = all_48_1 % 12.87/2.48 | & aNaturalNumber0(xm) = all_48_2 & ( ~ (all_48_1 = 0) | ~ (all_48_2 = % 12.87/2.48 | 0) | all_48_0 = 0) % 12.87/2.48 | % 12.87/2.48 | ALPHA: (34) implies: % 12.87/2.48 | (35) aNaturalNumber0(xm) = all_48_2 % 12.87/2.48 | (36) aNaturalNumber0(xn) = all_48_1 % 12.87/2.48 | (37) aNaturalNumber0(all_33_0) = all_48_0 % 12.87/2.48 | (38) ~ (all_48_1 = 0) | ~ (all_48_2 = 0) | all_48_0 = 0 % 12.87/2.48 | % 12.87/2.48 | DELTA: instantiating (29) with fresh symbols all_50_0, all_50_1, all_50_2 % 12.87/2.48 | gives: % 12.87/2.48 | (39) sdtpldt0(xn, xm) = all_50_0 & aNaturalNumber0(xn) = all_50_1 & % 12.87/2.48 | aNaturalNumber0(xm) = all_50_2 & $i(all_50_0) & ( ~ (all_50_1 = 0) | % 12.87/2.48 | ~ (all_50_2 = 0) | all_50_0 = all_33_0) % 12.87/2.48 | % 12.87/2.48 | ALPHA: (39) implies: % 12.87/2.48 | (40) aNaturalNumber0(xm) = all_50_2 % 12.87/2.48 | (41) aNaturalNumber0(xn) = all_50_1 % 12.87/2.48 | % 12.87/2.48 | BETA: splitting (31) gives: % 12.87/2.48 | % 12.87/2.48 | Case 1: % 12.87/2.48 | | % 12.87/2.48 | | (42) all_35_0 = 0 % 12.87/2.48 | | % 12.87/2.48 | | REDUCE: (17), (42) imply: % 12.87/2.48 | | (43) $false % 12.87/2.48 | | % 12.87/2.48 | | CLOSE: (43) is inconsistent. % 12.87/2.48 | | % 12.87/2.48 | Case 2: % 12.87/2.48 | | % 12.87/2.48 | | (44) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(all_33_0, % 12.87/2.48 | | xm) = v2 & aNaturalNumber0(all_33_0) = v1 & aNaturalNumber0(xm) % 12.87/2.48 | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (all_33_0 = % 12.87/2.48 | | xm)))) % 12.87/2.48 | | % 12.87/2.48 | | DELTA: instantiating (44) with fresh symbols all_64_0, all_64_1, all_64_2 % 12.87/2.48 | | gives: % 12.87/2.49 | | (45) sdtlseqdt0(all_33_0, xm) = all_64_0 & aNaturalNumber0(all_33_0) = % 12.87/2.49 | | all_64_1 & aNaturalNumber0(xm) = all_64_2 & ( ~ (all_64_1 = 0) | ~ % 12.87/2.49 | | (all_64_2 = 0) | (all_64_0 = 0 & ~ (all_33_0 = xm))) % 12.87/2.49 | | % 12.87/2.49 | | ALPHA: (45) implies: % 12.87/2.49 | | (46) aNaturalNumber0(xm) = all_64_2 % 12.87/2.49 | | (47) aNaturalNumber0(all_33_0) = all_64_1 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with 0, all_64_2, xm, simplifying with (2), % 12.87/2.49 | | (46) gives: % 12.87/2.49 | | (48) all_64_2 = 0 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with all_50_2, all_64_2, xm, simplifying % 12.87/2.49 | | with (40), (46) gives: % 12.87/2.49 | | (49) all_64_2 = all_50_2 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with all_48_2, all_64_2, xm, simplifying % 12.87/2.49 | | with (35), (46) gives: % 12.87/2.49 | | (50) all_64_2 = all_48_2 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with 0, all_50_1, xn, simplifying with (3), % 12.87/2.49 | | (41) gives: % 12.87/2.49 | | (51) all_50_1 = 0 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with all_48_1, all_50_1, xn, simplifying % 12.87/2.49 | | with (36), (41) gives: % 12.87/2.49 | | (52) all_50_1 = all_48_1 % 12.87/2.49 | | % 12.87/2.49 | | GROUND_INST: instantiating (11) with all_48_0, all_64_1, all_33_0, % 12.87/2.49 | | simplifying with (37), (47) gives: % 12.87/2.49 | | (53) all_64_1 = all_48_0 % 12.87/2.49 | | % 12.87/2.49 | | COMBINE_EQS: (49), (50) imply: % 12.87/2.49 | | (54) all_50_2 = all_48_2 % 12.87/2.49 | | % 12.87/2.49 | | COMBINE_EQS: (48), (49) imply: % 12.87/2.49 | | (55) all_50_2 = 0 % 12.87/2.49 | | % 12.87/2.49 | | COMBINE_EQS: (51), (52) imply: % 12.87/2.49 | | (56) all_48_1 = 0 % 12.87/2.49 | | % 12.87/2.49 | | SIMP: (56) implies: % 12.87/2.49 | | (57) all_48_1 = 0 % 12.87/2.49 | | % 12.87/2.49 | | COMBINE_EQS: (54), (55) imply: % 12.87/2.49 | | (58) all_48_2 = 0 % 12.87/2.49 | | % 12.87/2.49 | | BETA: splitting (38) gives: % 12.87/2.49 | | % 12.87/2.49 | | Case 1: % 12.87/2.49 | | | % 12.87/2.49 | | | (59) ~ (all_48_1 = 0) % 12.87/2.49 | | | % 12.87/2.49 | | | REDUCE: (57), (59) imply: % 12.87/2.49 | | | (60) $false % 12.87/2.49 | | | % 12.87/2.49 | | | CLOSE: (60) is inconsistent. % 12.87/2.49 | | | % 12.87/2.49 | | Case 2: % 12.87/2.49 | | | % 12.87/2.49 | | | (61) ~ (all_48_2 = 0) | all_48_0 = 0 % 12.87/2.49 | | | % 12.87/2.49 | | | BETA: splitting (61) gives: % 12.87/2.49 | | | % 12.87/2.49 | | | Case 1: % 12.87/2.49 | | | | % 12.87/2.49 | | | | (62) ~ (all_48_2 = 0) % 12.87/2.49 | | | | % 12.87/2.49 | | | | REDUCE: (58), (62) imply: % 12.87/2.49 | | | | (63) $false % 12.87/2.49 | | | | % 12.87/2.49 | | | | CLOSE: (63) is inconsistent. % 12.87/2.49 | | | | % 12.87/2.49 | | | Case 2: % 12.87/2.49 | | | | % 12.87/2.49 | | | | (64) all_48_0 = 0 % 12.87/2.49 | | | | % 12.87/2.49 | | | | REDUCE: (37), (64) imply: % 12.87/2.49 | | | | (65) aNaturalNumber0(all_33_0) = 0 % 12.87/2.49 | | | | % 12.87/2.49 | | | | BETA: splitting (32) gives: % 12.87/2.49 | | | | % 12.87/2.49 | | | | Case 1: % 12.87/2.49 | | | | | % 12.87/2.49 | | | | | (66) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_0) = v1 % 12.87/2.49 | | | | | & aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.87/2.49 | | | | | % 12.87/2.49 | | | | | BETA: splitting (33) gives: % 12.87/2.49 | | | | | % 12.87/2.49 | | | | | Case 1: % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | (67) xl = sz00 % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | REDUCE: (5), (67) imply: % 12.87/2.49 | | | | | | (68) $false % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | CLOSE: (68) is inconsistent. % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | Case 2: % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | DELTA: instantiating (66) with fresh symbols all_97_0, all_97_1 % 12.87/2.49 | | | | | | gives: % 12.87/2.49 | | | | | | (69) aNaturalNumber0(all_33_0) = all_97_0 & aNaturalNumber0(xm) = % 12.87/2.49 | | | | | | all_97_1 & ( ~ (all_97_0 = 0) | ~ (all_97_1 = 0)) % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | ALPHA: (69) implies: % 12.87/2.49 | | | | | | (70) aNaturalNumber0(xm) = all_97_1 % 12.87/2.49 | | | | | | (71) aNaturalNumber0(all_33_0) = all_97_0 % 12.87/2.49 | | | | | | (72) ~ (all_97_0 = 0) | ~ (all_97_1 = 0) % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | GROUND_INST: instantiating (11) with 0, all_97_1, xm, simplifying % 12.87/2.49 | | | | | | with (2), (70) gives: % 12.87/2.49 | | | | | | (73) all_97_1 = 0 % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | GROUND_INST: instantiating (11) with 0, all_97_0, all_33_0, % 12.87/2.49 | | | | | | simplifying with (65), (71) gives: % 12.87/2.49 | | | | | | (74) all_97_0 = 0 % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | BETA: splitting (72) gives: % 12.87/2.49 | | | | | | % 12.87/2.49 | | | | | | Case 1: % 12.87/2.49 | | | | | | | % 12.87/2.49 | | | | | | | (75) ~ (all_97_0 = 0) % 12.87/2.49 | | | | | | | % 12.87/2.49 | | | | | | | REDUCE: (74), (75) imply: % 12.87/2.49 | | | | | | | (76) $false % 12.87/2.49 | | | | | | | % 12.87/2.49 | | | | | | | CLOSE: (76) is inconsistent. % 12.87/2.49 | | | | | | | % 12.87/2.49 | | | | | | Case 2: % 12.87/2.49 | | | | | | | % 12.87/2.49 | | | | | | | (77) ~ (all_97_1 = 0) % 12.87/2.50 | | | | | | | % 12.87/2.50 | | | | | | | REDUCE: (73), (77) imply: % 12.87/2.50 | | | | | | | (78) $false % 12.87/2.50 | | | | | | | % 12.87/2.50 | | | | | | | CLOSE: (78) is inconsistent. % 12.87/2.50 | | | | | | | % 12.87/2.50 | | | | | | End of split % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | End of split % 12.87/2.50 | | | | | % 12.87/2.50 | | | | Case 2: % 12.87/2.50 | | | | | % 12.87/2.50 | | | | | (79) ( ~ (all_35_0 = 0) | ? [v0: $i] : (sdtpldt0(xm, v0) = % 12.87/2.50 | | | | | all_33_0 & aNaturalNumber0(v0) = 0 & $i(v0))) & (all_35_0 % 12.87/2.50 | | | | | = 0 | ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = all_33_0) | ~ % 12.87/2.50 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) % 12.87/2.50 | | | | | = v1))) % 12.87/2.50 | | | | | % 12.87/2.50 | | | | | ALPHA: (79) implies: % 12.87/2.50 | | | | | (80) all_35_0 = 0 | ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = all_33_0) % 12.87/2.50 | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 12.87/2.50 | | | | | aNaturalNumber0(v0) = v1)) % 12.87/2.50 | | | | | % 12.87/2.50 | | | | | BETA: splitting (80) gives: % 12.87/2.50 | | | | | % 12.87/2.50 | | | | | Case 1: % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | (81) all_35_0 = 0 % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | REDUCE: (17), (81) imply: % 12.87/2.50 | | | | | | (82) $false % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | CLOSE: (82) is inconsistent. % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | Case 2: % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | (83) ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = all_33_0) | ~ $i(v0) % 12.87/2.50 | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | GROUND_INST: instantiating (83) with xn, simplifying with (9), (14) % 12.87/2.50 | | | | | | gives: % 12.87/2.50 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xn) = v0) % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | DELTA: instantiating (84) with fresh symbol all_109_0 gives: % 12.87/2.50 | | | | | | (85) ~ (all_109_0 = 0) & aNaturalNumber0(xn) = all_109_0 % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | ALPHA: (85) implies: % 12.87/2.50 | | | | | | (86) ~ (all_109_0 = 0) % 12.87/2.50 | | | | | | (87) aNaturalNumber0(xn) = all_109_0 % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | GROUND_INST: instantiating (11) with 0, all_109_0, xn, simplifying % 12.87/2.50 | | | | | | with (3), (87) gives: % 12.87/2.50 | | | | | | (88) all_109_0 = 0 % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | REDUCE: (86), (88) imply: % 12.87/2.50 | | | | | | (89) $false % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | | CLOSE: (89) is inconsistent. % 12.87/2.50 | | | | | | % 12.87/2.50 | | | | | End of split % 12.87/2.50 | | | | | % 12.87/2.50 | | | | End of split % 12.87/2.50 | | | | % 12.87/2.50 | | | End of split % 12.87/2.50 | | | % 12.87/2.50 | | End of split % 12.87/2.50 | | % 12.87/2.50 | End of split % 12.87/2.50 | % 12.87/2.50 End of proof % 12.87/2.50 % SZS output end Proof for theBenchmark % 12.87/2.50 % 12.87/2.50 1895ms %------------------------------------------------------------------------------