%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM477+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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:48:02 EDT 2023 % Result : Theorem 9.73s 2.22s % Output : Proof 14.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM477+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n020.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 09:29:00 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.66 ________ _____ % 0.20/0.66 ___ __ \_________(_)________________________________ % 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.66 % 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.66 (2023-06-19) % 0.20/0.66 % 0.20/0.66 (c) Philipp Rümmer, 2009-2023 % 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.66 Amanda Stjerna. % 0.20/0.66 Free software under BSD-3-Clause. % 0.20/0.66 % 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.66 % 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.45/1.24 Prover 4: Preprocessing ... % 3.45/1.25 Prover 1: Preprocessing ... % 3.45/1.28 Prover 2: Preprocessing ... % 3.45/1.28 Prover 3: Preprocessing ... % 3.45/1.28 Prover 0: Preprocessing ... % 3.45/1.28 Prover 5: Preprocessing ... % 3.45/1.28 Prover 6: Preprocessing ... % 7.61/1.89 Prover 1: Constructing countermodel ... % 8.34/1.93 Prover 3: Constructing countermodel ... % 8.34/1.95 Prover 6: Proving ... % 8.99/2.00 Prover 5: Constructing countermodel ... % 9.73/2.13 Prover 2: Proving ... % 9.73/2.22 Prover 3: proved (1529ms) % 9.73/2.22 % 9.73/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.73/2.22 % 10.47/2.23 Prover 5: stopped % 10.64/2.24 Prover 6: stopped % 10.64/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.64/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.64/2.26 Prover 2: stopped % 10.64/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.64/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.64/2.28 Prover 4: Constructing countermodel ... % 11.41/2.36 Prover 7: Preprocessing ... % 11.41/2.36 Prover 8: Preprocessing ... % 11.41/2.37 Prover 10: Preprocessing ... % 11.41/2.38 Prover 11: Preprocessing ... % 11.41/2.38 Prover 0: Proving ... % 11.41/2.38 Prover 0: stopped % 11.41/2.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.95/2.45 Prover 13: Preprocessing ... % 12.49/2.47 Prover 1: Found proof (size 113) % 12.49/2.47 Prover 1: proved (1787ms) % 12.49/2.48 Prover 4: stopped % 12.49/2.53 Prover 13: stopped % 12.49/2.53 Prover 11: stopped % 12.49/2.55 Prover 10: Constructing countermodel ... % 12.49/2.56 Prover 10: stopped % 12.49/2.56 Prover 8: Warning: ignoring some quantifiers % 13.23/2.58 Prover 8: Constructing countermodel ... % 13.23/2.58 Prover 8: stopped % 13.40/2.60 Prover 7: Constructing countermodel ... % 13.40/2.61 Prover 7: stopped % 13.40/2.61 % 13.40/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.40/2.61 % 13.40/2.62 % SZS output start Proof for theBenchmark % 13.55/2.63 Assumptions after simplification: % 13.55/2.63 --------------------------------- % 13.55/2.63 % 13.55/2.63 (mDefDiv) % 13.55/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 13.55/2.65 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 13.55/2.65 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 13.55/2.65 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 13.55/2.65 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 13.55/2.65 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 13.55/2.65 % 13.55/2.65 (mLETotal) % 13.55/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = % 13.55/2.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 13.55/2.66 (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 13.55/2.66 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0))))) % 13.55/2.66 % 13.55/2.66 (mMonAdd) % 13.55/2.66 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) % 13.55/2.66 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 13.55/2.66 aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ! [v2: $i] : ! % 13.55/2.66 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (sdtlseqdt0(v3, v4) = v5) | ~ % 13.55/2.66 (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ? [v6: % 13.55/2.66 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : (sdtlseqdt0(v7, v8) = % 13.55/2.66 v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) % 13.55/2.66 = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) % 13.55/2.66 & ~ (v4 = v3)))))) % 13.55/2.66 % 13.55/2.66 (mMonMul2) % 13.55/2.66 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 13.55/2.66 v0 = sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 13.55/2.66 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (aNaturalNumber0(v1) = v5 % 13.55/2.66 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 13.55/2.66 % 13.55/2.66 (mMulComm) % 13.55/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 13.55/2.67 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 13.55/2.67 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 13.55/2.67 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 13.55/2.67 % 13.55/2.67 (m_MulZero) % 13.55/2.67 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ % 13.55/2.67 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & % 13.55/2.67 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = % 13.55/2.67 sz00)))) % 13.55/2.67 % 13.55/2.67 (m__) % 13.55/2.67 $i(xn) & $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xn) = v0) % 13.55/2.67 % 13.55/2.67 (m__1494) % 13.55/2.67 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & $i(xn) & $i(xm) % 13.55/2.67 % 13.55/2.67 (m__1494_04) % 13.55/2.67 ~ (xn = sz00) & doDivides0(xm, xn) = 0 & $i(xn) & $i(xm) & $i(sz00) % 13.55/2.67 % 13.55/2.67 (function-axioms) % 13.55/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.55/2.67 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 13.55/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.55/2.67 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 13.55/2.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.55/2.67 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 13.55/2.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.55/2.67 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 13.55/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.55/2.67 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 13.55/2.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.55/2.67 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 13.55/2.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 13.55/2.67 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.55/2.67 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 13.55/2.67 | ~ (aNaturalNumber0(v2) = v0)) % 13.55/2.67 % 13.55/2.67 Further assumptions not needed in the proof: % 13.55/2.67 -------------------------------------------- % 13.55/2.67 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefQuot, mDivMin, % 13.55/2.67 mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETran, mMonMul, % 13.55/2.67 mMulAsso, mMulCanc, mNatSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, % 13.55/2.67 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit % 13.55/2.67 % 13.55/2.67 Those formulas are unsatisfiable: % 13.55/2.67 --------------------------------- % 13.55/2.67 % 13.55/2.67 Begin of proof % 13.55/2.67 | % 13.55/2.67 | ALPHA: (m_MulZero) implies: % 13.55/2.68 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | % 13.55/2.68 | ? [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & % 13.55/2.68 | aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 % 13.55/2.68 | = sz00)))) % 13.55/2.68 | % 13.55/2.68 | ALPHA: (mMonMul2) implies: % 13.55/2.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v0 = % 13.55/2.68 | sz00 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtasdt0(v1, v0) = v2) | ~ % 13.55/2.68 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 13.55/2.68 | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | % 13.55/2.68 | ~ (v4 = 0)))) % 13.55/2.68 | % 13.55/2.68 | ALPHA: (m__1494) implies: % 13.55/2.68 | (3) aNaturalNumber0(xm) = 0 % 13.55/2.68 | (4) aNaturalNumber0(xn) = 0 % 13.55/2.68 | % 13.55/2.68 | ALPHA: (m__1494_04) implies: % 13.55/2.68 | (5) ~ (xn = sz00) % 13.55/2.68 | (6) doDivides0(xm, xn) = 0 % 13.55/2.68 | % 13.55/2.68 | ALPHA: (m__) implies: % 13.55/2.68 | (7) $i(xm) % 13.55/2.68 | (8) $i(xn) % 13.55/2.68 | (9) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xn) = v0) % 13.55/2.68 | % 13.55/2.68 | ALPHA: (function-axioms) implies: % 13.55/2.68 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.55/2.68 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 13.55/2.68 | v0)) % 13.55/2.68 | % 13.55/2.68 | DELTA: instantiating (9) with fresh symbol all_34_0 gives: % 13.55/2.68 | (11) ~ (all_34_0 = 0) & sdtlseqdt0(xm, xn) = all_34_0 % 13.55/2.68 | % 13.55/2.68 | ALPHA: (11) implies: % 13.55/2.68 | (12) ~ (all_34_0 = 0) % 13.55/2.68 | (13) sdtlseqdt0(xm, xn) = all_34_0 % 13.55/2.68 | % 13.55/2.68 | GROUND_INST: instantiating (mLETotal) with xm, xn, all_34_0, simplifying with % 13.55/2.68 | (7), (8), (13) gives: % 13.55/2.68 | (14) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 13.55/2.68 | (sdtlseqdt0(xn, xm) = v2 & aNaturalNumber0(xn) = v1 & % 13.55/2.68 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ % 13.55/2.68 | (xn = xm)))) % 13.55/2.68 | % 13.55/2.68 | GROUND_INST: instantiating (mDefDiv) with xm, xn, 0, simplifying with (6), % 13.55/2.68 | (7), (8) gives: % 13.55/2.69 | (15) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 13.55/2.69 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 13.55/2.69 | $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 13.55/2.69 | % 13.55/2.69 | BETA: splitting (15) gives: % 13.55/2.69 | % 13.55/2.69 | Case 1: % 13.55/2.69 | | % 13.55/2.69 | | (16) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 13.55/2.69 | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.55/2.69 | | % 13.55/2.69 | | DELTA: instantiating (16) with fresh symbols all_42_0, all_42_1 gives: % 13.55/2.69 | | (17) aNaturalNumber0(xn) = all_42_0 & aNaturalNumber0(xm) = all_42_1 & ( % 13.55/2.69 | | ~ (all_42_0 = 0) | ~ (all_42_1 = 0)) % 13.55/2.69 | | % 13.55/2.69 | | ALPHA: (17) implies: % 13.55/2.69 | | (18) aNaturalNumber0(xm) = all_42_1 % 13.55/2.69 | | (19) aNaturalNumber0(xn) = all_42_0 % 13.55/2.69 | | (20) ~ (all_42_0 = 0) | ~ (all_42_1 = 0) % 13.55/2.69 | | % 13.55/2.69 | | BETA: splitting (14) gives: % 13.55/2.69 | | % 13.55/2.69 | | Case 1: % 13.55/2.69 | | | % 13.55/2.69 | | | (21) all_34_0 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | REDUCE: (12), (21) imply: % 13.55/2.69 | | | (22) $false % 13.55/2.69 | | | % 13.55/2.69 | | | CLOSE: (22) is inconsistent. % 13.55/2.69 | | | % 13.55/2.69 | | Case 2: % 13.55/2.69 | | | % 13.55/2.69 | | | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, xm) = % 13.55/2.69 | | | v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ % 13.55/2.69 | | | (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xn = xm)))) % 13.55/2.69 | | | % 13.55/2.69 | | | DELTA: instantiating (23) with fresh symbols all_56_0, all_56_1, all_56_2 % 13.55/2.69 | | | gives: % 13.55/2.69 | | | (24) sdtlseqdt0(xn, xm) = all_56_0 & aNaturalNumber0(xn) = all_56_1 & % 13.55/2.69 | | | aNaturalNumber0(xm) = all_56_2 & ( ~ (all_56_1 = 0) | ~ (all_56_2 % 13.55/2.69 | | | = 0) | (all_56_0 = 0 & ~ (xn = xm))) % 13.55/2.69 | | | % 13.55/2.69 | | | ALPHA: (24) implies: % 13.55/2.69 | | | (25) aNaturalNumber0(xm) = all_56_2 % 13.55/2.69 | | | (26) aNaturalNumber0(xn) = all_56_1 % 13.55/2.69 | | | % 13.55/2.69 | | | GROUND_INST: instantiating (10) with 0, all_56_2, xm, simplifying with % 13.55/2.69 | | | (3), (25) gives: % 13.55/2.69 | | | (27) all_56_2 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | GROUND_INST: instantiating (10) with all_42_1, all_56_2, xm, simplifying % 13.55/2.69 | | | with (18), (25) gives: % 13.55/2.69 | | | (28) all_56_2 = all_42_1 % 13.55/2.69 | | | % 13.55/2.69 | | | GROUND_INST: instantiating (10) with 0, all_56_1, xn, simplifying with % 13.55/2.69 | | | (4), (26) gives: % 13.55/2.69 | | | (29) all_56_1 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | GROUND_INST: instantiating (10) with all_42_0, all_56_1, xn, simplifying % 13.55/2.69 | | | with (19), (26) gives: % 13.55/2.69 | | | (30) all_56_1 = all_42_0 % 13.55/2.69 | | | % 13.55/2.69 | | | COMBINE_EQS: (29), (30) imply: % 13.55/2.69 | | | (31) all_42_0 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | COMBINE_EQS: (27), (28) imply: % 13.55/2.69 | | | (32) all_42_1 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | SIMP: (32) implies: % 13.55/2.69 | | | (33) all_42_1 = 0 % 13.55/2.69 | | | % 13.55/2.69 | | | BETA: splitting (20) gives: % 13.55/2.69 | | | % 13.55/2.69 | | | Case 1: % 13.55/2.69 | | | | % 13.55/2.69 | | | | (34) ~ (all_42_0 = 0) % 13.55/2.69 | | | | % 13.55/2.69 | | | | REDUCE: (31), (34) imply: % 13.55/2.69 | | | | (35) $false % 13.55/2.69 | | | | % 13.55/2.69 | | | | CLOSE: (35) is inconsistent. % 13.55/2.69 | | | | % 13.55/2.69 | | | Case 2: % 13.55/2.69 | | | | % 13.55/2.69 | | | | (36) ~ (all_42_1 = 0) % 13.55/2.69 | | | | % 13.55/2.69 | | | | REDUCE: (33), (36) imply: % 13.55/2.69 | | | | (37) $false % 13.55/2.69 | | | | % 13.55/2.69 | | | | CLOSE: (37) is inconsistent. % 13.55/2.69 | | | | % 13.55/2.69 | | | End of split % 13.55/2.69 | | | % 13.55/2.69 | | End of split % 13.55/2.69 | | % 13.55/2.69 | Case 2: % 13.55/2.69 | | % 13.55/2.70 | | (38) ? [v0: $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & % 13.55/2.70 | | $i(v0)) % 13.55/2.70 | | % 13.55/2.70 | | DELTA: instantiating (38) with fresh symbol all_42_0 gives: % 13.55/2.70 | | (39) sdtasdt0(xm, all_42_0) = xn & aNaturalNumber0(all_42_0) = 0 & % 13.55/2.70 | | $i(all_42_0) % 13.55/2.70 | | % 13.55/2.70 | | ALPHA: (39) implies: % 13.55/2.70 | | (40) $i(all_42_0) % 13.55/2.70 | | (41) aNaturalNumber0(all_42_0) = 0 % 13.55/2.70 | | (42) sdtasdt0(xm, all_42_0) = xn % 13.55/2.70 | | % 13.55/2.70 | | BETA: splitting (14) gives: % 13.55/2.70 | | % 13.55/2.70 | | Case 1: % 13.55/2.70 | | | % 13.55/2.70 | | | (43) all_34_0 = 0 % 13.55/2.70 | | | % 13.55/2.70 | | | REDUCE: (12), (43) imply: % 13.55/2.70 | | | (44) $false % 13.55/2.70 | | | % 13.55/2.70 | | | CLOSE: (44) is inconsistent. % 13.55/2.70 | | | % 13.55/2.70 | | Case 2: % 13.55/2.70 | | | % 13.55/2.70 | | | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, xm) = % 13.55/2.70 | | | v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & ( ~ % 13.55/2.70 | | | (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xn = xm)))) % 13.55/2.70 | | | % 13.55/2.70 | | | DELTA: instantiating (45) with fresh symbols all_54_0, all_54_1, all_54_2 % 13.55/2.70 | | | gives: % 13.55/2.70 | | | (46) sdtlseqdt0(xn, xm) = all_54_0 & aNaturalNumber0(xn) = all_54_1 & % 13.55/2.70 | | | aNaturalNumber0(xm) = all_54_2 & ( ~ (all_54_1 = 0) | ~ (all_54_2 % 13.55/2.70 | | | = 0) | (all_54_0 = 0 & ~ (xn = xm))) % 13.55/2.70 | | | % 13.55/2.70 | | | ALPHA: (46) implies: % 13.55/2.70 | | | (47) aNaturalNumber0(xm) = all_54_2 % 13.55/2.70 | | | (48) aNaturalNumber0(xn) = all_54_1 % 13.55/2.70 | | | (49) sdtlseqdt0(xn, xm) = all_54_0 % 13.55/2.70 | | | (50) ~ (all_54_1 = 0) | ~ (all_54_2 = 0) | (all_54_0 = 0 & ~ (xn = % 13.55/2.70 | | | xm)) % 13.55/2.70 | | | % 13.55/2.70 | | | GROUND_INST: instantiating (10) with 0, all_54_2, xm, simplifying with % 13.55/2.70 | | | (3), (47) gives: % 13.55/2.70 | | | (51) all_54_2 = 0 % 13.55/2.70 | | | % 13.55/2.70 | | | GROUND_INST: instantiating (10) with 0, all_54_1, xn, simplifying with % 13.55/2.70 | | | (4), (48) gives: % 13.55/2.70 | | | (52) all_54_1 = 0 % 13.55/2.70 | | | % 13.55/2.70 | | | BETA: splitting (50) gives: % 13.55/2.70 | | | % 13.55/2.70 | | | Case 1: % 13.55/2.70 | | | | % 13.55/2.70 | | | | (53) ~ (all_54_1 = 0) % 13.55/2.70 | | | | % 13.55/2.70 | | | | REDUCE: (52), (53) imply: % 13.55/2.70 | | | | (54) $false % 13.55/2.70 | | | | % 13.55/2.70 | | | | CLOSE: (54) is inconsistent. % 13.55/2.70 | | | | % 13.55/2.70 | | | Case 2: % 13.55/2.70 | | | | % 13.55/2.70 | | | | (55) ~ (all_54_2 = 0) | (all_54_0 = 0 & ~ (xn = xm)) % 13.55/2.70 | | | | % 13.55/2.70 | | | | BETA: splitting (55) gives: % 13.55/2.70 | | | | % 13.55/2.70 | | | | Case 1: % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | (56) ~ (all_54_2 = 0) % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | REDUCE: (51), (56) imply: % 13.55/2.70 | | | | | (57) $false % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | CLOSE: (57) is inconsistent. % 13.55/2.70 | | | | | % 13.55/2.70 | | | | Case 2: % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | (58) all_54_0 = 0 & ~ (xn = xm) % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | ALPHA: (58) implies: % 13.55/2.70 | | | | | (59) all_54_0 = 0 % 13.55/2.70 | | | | | (60) ~ (xn = xm) % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | REDUCE: (49), (59) imply: % 13.55/2.70 | | | | | (61) sdtlseqdt0(xn, xm) = 0 % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | GROUND_INST: instantiating (2) with all_42_0, xm, xn, all_34_0, % 13.55/2.70 | | | | | simplifying with (7), (13), (40), (42) gives: % 13.55/2.70 | | | | | (62) all_42_0 = sz00 | all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 13.55/2.70 | | | | | (aNaturalNumber0(all_42_0) = v0 & aNaturalNumber0(xm) = v1 & ( % 13.55/2.70 | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 13.55/2.70 | | | | | % 13.55/2.70 | | | | | GROUND_INST: instantiating (mMulComm) with xm, all_42_0, xn, % 13.55/2.70 | | | | | simplifying with (7), (40), (42) gives: % 13.55/2.71 | | | | | (63) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 13.55/2.71 | | | | | (sdtasdt0(all_42_0, xm) = v2 & aNaturalNumber0(all_42_0) = v1 % 13.55/2.71 | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 % 13.55/2.71 | | | | | = 0) | v2 = xn)) % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | GROUND_INST: instantiating (mMonAdd) with xn, xm, simplifying with % 13.55/2.71 | | | | | (7), (8), (61) gives: % 13.55/2.71 | | | | | (64) xn = xm | ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = % 13.55/2.71 | | | | | v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.55/2.71 | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 13.55/2.71 | | | | | (sdtlseqdt0(v1, v2) = v3) | ~ (sdtpldt0(xn, v0) = v1) | ~ % 13.55/2.71 | | | | | (sdtpldt0(xm, v0) = v2) | ~ $i(v0) | ? [v4: any] : ? [v5: % 13.55/2.71 | | | | | $i] : ? [v6: $i] : ? [v7: any] : (sdtlseqdt0(v5, v6) = % 13.55/2.71 | | | | | v7 & sdtpldt0(v0, xn) = v5 & sdtpldt0(v0, xm) = v6 & % 13.55/2.71 | | | | | aNaturalNumber0(v0) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) % 13.55/2.71 | | | | | | (v7 = 0 & v3 = 0 & ~ (v6 = v5) & ~ (v2 = v1))))) % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | DELTA: instantiating (63) with fresh symbols all_82_0, all_82_1, % 13.55/2.71 | | | | | all_82_2 gives: % 13.55/2.71 | | | | | (65) sdtasdt0(all_42_0, xm) = all_82_0 & aNaturalNumber0(all_42_0) % 13.55/2.71 | | | | | = all_82_1 & aNaturalNumber0(xm) = all_82_2 & $i(all_82_0) & ( % 13.55/2.71 | | | | | ~ (all_82_1 = 0) | ~ (all_82_2 = 0) | all_82_0 = xn) % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | ALPHA: (65) implies: % 13.55/2.71 | | | | | (66) aNaturalNumber0(xm) = all_82_2 % 13.55/2.71 | | | | | (67) aNaturalNumber0(all_42_0) = all_82_1 % 13.55/2.71 | | | | | (68) sdtasdt0(all_42_0, xm) = all_82_0 % 13.55/2.71 | | | | | (69) ~ (all_82_1 = 0) | ~ (all_82_2 = 0) | all_82_0 = xn % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | GROUND_INST: instantiating (10) with 0, all_82_2, xm, simplifying with % 13.55/2.71 | | | | | (3), (66) gives: % 13.55/2.71 | | | | | (70) all_82_2 = 0 % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | GROUND_INST: instantiating (10) with 0, all_82_1, all_42_0, % 13.55/2.71 | | | | | simplifying with (41), (67) gives: % 13.55/2.71 | | | | | (71) all_82_1 = 0 % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | BETA: splitting (69) gives: % 13.55/2.71 | | | | | % 13.55/2.71 | | | | | Case 1: % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | (72) ~ (all_82_1 = 0) % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | REDUCE: (71), (72) imply: % 13.55/2.71 | | | | | | (73) $false % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | CLOSE: (73) is inconsistent. % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | Case 2: % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | (74) ~ (all_82_2 = 0) | all_82_0 = xn % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | BETA: splitting (62) gives: % 13.55/2.71 | | | | | | % 13.55/2.71 | | | | | | Case 1: % 13.55/2.71 | | | | | | | % 13.55/2.71 | | | | | | | (75) all_42_0 = sz00 % 13.55/2.71 | | | | | | | % 13.55/2.71 | | | | | | | REDUCE: (68), (75) imply: % 13.55/2.71 | | | | | | | (76) sdtasdt0(sz00, xm) = all_82_0 % 13.55/2.71 | | | | | | | % 13.55/2.71 | | | | | | | BETA: splitting (74) gives: % 13.55/2.71 | | | | | | | % 13.55/2.71 | | | | | | | Case 1: % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | (77) ~ (all_82_2 = 0) % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | REDUCE: (70), (77) imply: % 13.55/2.71 | | | | | | | | (78) $false % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | CLOSE: (78) is inconsistent. % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | Case 2: % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | (79) all_82_0 = xn % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | REDUCE: (76), (79) imply: % 13.55/2.71 | | | | | | | | (80) sdtasdt0(sz00, xm) = xn % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | GROUND_INST: instantiating (1) with xm, xn, simplifying with % 13.55/2.71 | | | | | | | | (7), (80) gives: % 13.55/2.71 | | | | | | | | (81) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xm, sz00) = v1 & % 13.55/2.71 | | | | | | | | aNaturalNumber0(xm) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 % 13.55/2.71 | | | | | | | | = sz00 & xn = sz00))) % 13.55/2.71 | | | | | | | | % 13.55/2.71 | | | | | | | | DELTA: instantiating (81) with fresh symbols all_114_0, % 13.55/2.71 | | | | | | | | all_114_1 gives: % 13.55/2.72 | | | | | | | | (82) sdtasdt0(xm, sz00) = all_114_0 & aNaturalNumber0(xm) = % 13.55/2.72 | | | | | | | | all_114_1 & $i(all_114_0) & ( ~ (all_114_1 = 0) | % 13.55/2.72 | | | | | | | | (all_114_0 = sz00 & xn = sz00)) % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | ALPHA: (82) implies: % 13.55/2.72 | | | | | | | | (83) aNaturalNumber0(xm) = all_114_1 % 13.55/2.72 | | | | | | | | (84) ~ (all_114_1 = 0) | (all_114_0 = sz00 & xn = sz00) % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | BETA: splitting (84) gives: % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | Case 1: % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | (85) ~ (all_114_1 = 0) % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_114_1, xm, % 13.55/2.72 | | | | | | | | | simplifying with (3), (83) gives: % 13.55/2.72 | | | | | | | | | (86) all_114_1 = 0 % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | REDUCE: (85), (86) imply: % 13.55/2.72 | | | | | | | | | (87) $false % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | CLOSE: (87) is inconsistent. % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | Case 2: % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | (88) all_114_0 = sz00 & xn = sz00 % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | ALPHA: (88) implies: % 13.55/2.72 | | | | | | | | | (89) xn = sz00 % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | REDUCE: (5), (89) imply: % 13.55/2.72 | | | | | | | | | (90) $false % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | CLOSE: (90) is inconsistent. % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | End of split % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | End of split % 13.55/2.72 | | | | | | | % 13.55/2.72 | | | | | | Case 2: % 13.55/2.72 | | | | | | | % 13.55/2.72 | | | | | | | (91) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : % 13.55/2.72 | | | | | | | (aNaturalNumber0(all_42_0) = v0 & aNaturalNumber0(xm) = v1 % 13.55/2.72 | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.55/2.72 | | | | | | | % 13.55/2.72 | | | | | | | BETA: splitting (64) gives: % 13.55/2.72 | | | | | | | % 13.55/2.72 | | | | | | | Case 1: % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | (92) xn = xm % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | REDUCE: (60), (92) imply: % 13.55/2.72 | | | | | | | | (93) $false % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | CLOSE: (93) is inconsistent. % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | Case 2: % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | (94) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v0 % 13.55/2.72 | | | | | | | | & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 13.55/2.72 | | | | | | | | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.55/2.72 | | | | | | | | ! [v3: any] : ( ~ (sdtlseqdt0(v1, v2) = v3) | ~ % 13.55/2.72 | | | | | | | | (sdtpldt0(xn, v0) = v1) | ~ (sdtpldt0(xm, v0) = v2) | % 13.55/2.72 | | | | | | | | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 13.55/2.72 | | | | | | | | ? [v7: any] : (sdtlseqdt0(v5, v6) = v7 & sdtpldt0(v0, % 13.55/2.72 | | | | | | | | xn) = v5 & sdtpldt0(v0, xm) = v6 & % 13.55/2.72 | | | | | | | | aNaturalNumber0(v0) = v4 & $i(v6) & $i(v5) & ( ~ (v4 % 13.55/2.72 | | | | | | | | = 0) | (v7 = 0 & v3 = 0 & ~ (v6 = v5) & ~ (v2 % 13.55/2.72 | | | | | | | | = v1))))) % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | BETA: splitting (91) gives: % 13.55/2.72 | | | | | | | | % 13.55/2.72 | | | | | | | | Case 1: % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | (95) all_34_0 = 0 % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | REDUCE: (12), (95) imply: % 13.55/2.72 | | | | | | | | | (96) $false % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | CLOSE: (96) is inconsistent. % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | Case 2: % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | (97) ? [v0: any] : ? [v1: any] : % 13.55/2.72 | | | | | | | | | (aNaturalNumber0(all_42_0) = v0 & aNaturalNumber0(xm) % 13.55/2.72 | | | | | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | BETA: splitting (94) gives: % 13.55/2.72 | | | | | | | | | % 13.55/2.72 | | | | | | | | | Case 1: % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = % 13.55/2.72 | | | | | | | | | | v0 & aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ % 13.55/2.72 | | | | | | | | | | (v0 = 0))) % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_109_0, % 13.55/2.72 | | | | | | | | | | all_109_1 gives: % 13.55/2.72 | | | | | | | | | | (99) aNaturalNumber0(all_42_0) = all_109_1 & % 13.55/2.72 | | | | | | | | | | aNaturalNumber0(xm) = all_109_0 & ( ~ (all_109_0 = % 13.55/2.72 | | | | | | | | | | 0) | ~ (all_109_1 = 0)) % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | ALPHA: (99) implies: % 13.55/2.72 | | | | | | | | | | (100) aNaturalNumber0(xm) = all_109_0 % 13.55/2.72 | | | | | | | | | | (101) aNaturalNumber0(all_42_0) = all_109_1 % 13.55/2.72 | | | | | | | | | | (102) ~ (all_109_0 = 0) | ~ (all_109_1 = 0) % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_111_0, % 13.55/2.72 | | | | | | | | | | all_111_1 gives: % 13.55/2.72 | | | | | | | | | | (103) aNaturalNumber0(xn) = all_111_1 & % 13.55/2.72 | | | | | | | | | | aNaturalNumber0(xm) = all_111_0 & ( ~ (all_111_0 = % 13.55/2.72 | | | | | | | | | | 0) | ~ (all_111_1 = 0)) % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | ALPHA: (103) implies: % 13.55/2.72 | | | | | | | | | | (104) aNaturalNumber0(xm) = all_111_0 % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_111_0, xm, % 13.55/2.72 | | | | | | | | | | simplifying with (3), (104) gives: % 13.55/2.72 | | | | | | | | | | (105) all_111_0 = 0 % 13.55/2.72 | | | | | | | | | | % 13.55/2.72 | | | | | | | | | | GROUND_INST: instantiating (10) with all_109_0, all_111_0, xm, % 13.55/2.72 | | | | | | | | | | simplifying with (100), (104) gives: % 13.55/2.72 | | | | | | | | | | (106) all_111_0 = all_109_0 % 13.55/2.72 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_109_1, all_42_0, % 13.55/2.73 | | | | | | | | | | simplifying with (41), (101) gives: % 13.55/2.73 | | | | | | | | | | (107) all_109_1 = 0 % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | COMBINE_EQS: (105), (106) imply: % 13.55/2.73 | | | | | | | | | | (108) all_109_0 = 0 % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | BETA: splitting (102) gives: % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | Case 1: % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | (109) ~ (all_109_0 = 0) % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | REDUCE: (108), (109) imply: % 13.55/2.73 | | | | | | | | | | | (110) $false % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | CLOSE: (110) is inconsistent. % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | Case 2: % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | (111) ~ (all_109_1 = 0) % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | REDUCE: (107), (111) imply: % 13.55/2.73 | | | | | | | | | | | (112) $false % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | | CLOSE: (112) is inconsistent. % 13.55/2.73 | | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | End of split % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | Case 2: % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | % 13.55/2.73 | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_110_0, % 13.55/2.73 | | | | | | | | | | all_110_1 gives: % 14.03/2.73 | | | | | | | | | | (113) aNaturalNumber0(all_42_0) = all_110_1 & % 14.03/2.73 | | | | | | | | | | aNaturalNumber0(xm) = all_110_0 & ( ~ (all_110_0 = % 14.03/2.73 | | | | | | | | | | 0) | ~ (all_110_1 = 0)) % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | ALPHA: (113) implies: % 14.03/2.73 | | | | | | | | | | (114) aNaturalNumber0(xm) = all_110_0 % 14.03/2.73 | | | | | | | | | | (115) aNaturalNumber0(all_42_0) = all_110_1 % 14.03/2.73 | | | | | | | | | | (116) ~ (all_110_0 = 0) | ~ (all_110_1 = 0) % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_110_0, xm, % 14.03/2.73 | | | | | | | | | | simplifying with (3), (114) gives: % 14.03/2.73 | | | | | | | | | | (117) all_110_0 = 0 % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_110_1, all_42_0, % 14.03/2.73 | | | | | | | | | | simplifying with (41), (115) gives: % 14.03/2.73 | | | | | | | | | | (118) all_110_1 = 0 % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | BETA: splitting (116) gives: % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | Case 1: % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | (119) ~ (all_110_0 = 0) % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | REDUCE: (117), (119) imply: % 14.03/2.73 | | | | | | | | | | | (120) $false % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | CLOSE: (120) is inconsistent. % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | Case 2: % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | (121) ~ (all_110_1 = 0) % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | REDUCE: (118), (121) imply: % 14.03/2.73 | | | | | | | | | | | (122) $false % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | | CLOSE: (122) is inconsistent. % 14.03/2.73 | | | | | | | | | | | % 14.03/2.73 | | | | | | | | | | End of split % 14.03/2.73 | | | | | | | | | | % 14.03/2.73 | | | | | | | | | End of split % 14.03/2.73 | | | | | | | | | % 14.03/2.73 | | | | | | | | End of split % 14.03/2.73 | | | | | | | | % 14.03/2.73 | | | | | | | End of split % 14.03/2.73 | | | | | | | % 14.03/2.73 | | | | | | End of split % 14.03/2.73 | | | | | | % 14.03/2.73 | | | | | End of split % 14.03/2.73 | | | | | % 14.03/2.73 | | | | End of split % 14.03/2.73 | | | | % 14.03/2.73 | | | End of split % 14.03/2.73 | | | % 14.03/2.73 | | End of split % 14.03/2.73 | | % 14.03/2.73 | End of split % 14.03/2.73 | % 14.03/2.73 End of proof % 14.03/2.73 % SZS output end Proof for theBenchmark % 14.03/2.73 % 14.03/2.73 2065ms %------------------------------------------------------------------------------