%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM479+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 : n019.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 11:48:03 EDT 2023 % Result : Theorem 14.05s 2.67s % Output : Proof 22.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM479+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n019.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 12:25:28 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.33/1.15 Prover 4: Preprocessing ... % 3.33/1.15 Prover 1: Preprocessing ... % 3.33/1.19 Prover 0: Preprocessing ... % 3.33/1.19 Prover 6: Preprocessing ... % 3.33/1.19 Prover 5: Preprocessing ... % 3.33/1.19 Prover 3: Preprocessing ... % 3.33/1.19 Prover 2: Preprocessing ... % 8.71/1.97 Prover 1: Constructing countermodel ... % 8.71/1.97 Prover 6: Proving ... % 8.71/1.98 Prover 3: Constructing countermodel ... % 8.71/2.00 Prover 5: Constructing countermodel ... % 10.12/2.21 Prover 2: Proving ... % 10.93/2.29 Prover 4: Constructing countermodel ... % 12.46/2.48 Prover 0: Proving ... % 13.74/2.66 Prover 3: proved (2020ms) % 14.05/2.67 % 14.05/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.05/2.67 % 14.05/2.67 Prover 5: stopped % 14.05/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.05/2.68 Prover 2: stopped % 14.05/2.68 Prover 6: stopped % 14.05/2.68 Prover 0: stopped % 14.05/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.05/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.05/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.05/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.57/2.85 Prover 7: Preprocessing ... % 14.57/2.85 Prover 10: Preprocessing ... % 14.57/2.86 Prover 8: Preprocessing ... % 14.57/2.88 Prover 11: Preprocessing ... % 14.57/2.89 Prover 13: Preprocessing ... % 17.36/3.15 Prover 10: Constructing countermodel ... % 17.36/3.18 Prover 8: Warning: ignoring some quantifiers % 17.89/3.20 Prover 13: Constructing countermodel ... % 17.89/3.21 Prover 8: Constructing countermodel ... % 17.89/3.23 Prover 7: Constructing countermodel ... % 20.13/3.64 Prover 11: Constructing countermodel ... % 21.67/3.73 Prover 1: Found proof (size 349) % 21.67/3.73 Prover 1: proved (3105ms) % 21.67/3.74 Prover 4: stopped % 21.67/3.74 Prover 13: stopped % 21.67/3.74 Prover 11: stopped % 21.67/3.74 Prover 10: stopped % 21.67/3.74 Prover 7: stopped % 21.67/3.74 Prover 8: stopped % 21.67/3.74 % 21.67/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.67/3.74 % 21.93/3.78 % SZS output start Proof for theBenchmark % 21.93/3.79 Assumptions after simplification: % 21.93/3.79 --------------------------------- % 21.93/3.79 % 21.93/3.79 (mDefDiv) % 21.93/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 21.93/3.81 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 21.93/3.81 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 21.93/3.81 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 21.93/3.81 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 21.93/3.81 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 21.93/3.81 % 21.93/3.81 (mDefQuot) % 21.93/3.81 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 21.93/3.81 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 21.93/3.81 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 21.93/3.81 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 21.93/3.81 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 21.93/3.81 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 21.93/3.81 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 21.93/3.81 0)))) % 21.93/3.81 % 21.93/3.81 (mMulAsso) % 21.93/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 21.93/3.82 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 21.93/3.82 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 21.93/3.82 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 21.93/3.82 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 21.93/3.82 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 21.93/3.82 v4))) % 21.93/3.82 % 21.93/3.82 (mMulComm) % 21.93/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.93/3.82 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 21.93/3.82 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 21.93/3.82 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 21.93/3.82 % 21.93/3.82 (mSortsB_02) % 21.93/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.93/3.82 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 21.93/3.82 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 21.93/3.82 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 21.93/3.82 % 21.93/3.82 (m__) % 21.93/3.82 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 21.93/3.82 $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v2) & sdtsldt0(v3, xl) = v4 & % 21.93/3.82 sdtsldt0(xm, xl) = v1 & sdtasdt0(v0, v1) = v2 & sdtasdt0(xn, xm) = v3 & % 21.93/3.82 sdtasdt0(xl, v4) = v5 & sdtasdt0(xl, xn) = v0 & $i(v5) & $i(v4) & $i(v3) & % 21.93/3.82 $i(v2) & $i(v1) & $i(v0)) % 21.93/3.82 % 21.93/3.82 (m__1524) % 21.93/3.82 aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & $i(xm) & $i(xl) % 21.93/3.82 % 21.93/3.82 (m__1524_04) % 21.93/3.82 ~ (xl = sz00) & doDivides0(xl, xm) = 0 & $i(xm) & $i(xl) & $i(sz00) % 21.93/3.82 % 21.93/3.82 (m__1553) % 21.93/3.82 aNaturalNumber0(xn) = 0 & $i(xn) % 21.93/3.82 % 21.93/3.82 (function-axioms) % 21.93/3.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.93/3.83 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 21.93/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.93/3.83 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 21.93/3.83 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.93/3.83 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 21.93/3.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.93/3.83 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 21.93/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.93/3.83 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 21.93/3.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.93/3.83 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 21.93/3.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 21.93/3.83 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.93/3.83 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 21.93/3.83 | ~ (aNaturalNumber0(v2) = v0)) % 21.93/3.83 % 21.93/3.83 Further assumptions not needed in the proof: % 21.93/3.83 -------------------------------------------- % 21.93/3.83 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDivLE, mDivMin, % 21.93/3.83 mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, % 21.93/3.83 mMonAdd, mMonMul, mMonMul2, mMulCanc, mNatSort, mSortsB, mSortsC, mSortsC_01, % 21.93/3.83 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero % 21.93/3.83 % 21.93/3.83 Those formulas are unsatisfiable: % 21.93/3.83 --------------------------------- % 21.93/3.83 % 21.93/3.83 Begin of proof % 21.93/3.83 | % 21.93/3.83 | ALPHA: (mDefQuot) implies: % 21.93/3.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 21.93/3.83 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.93/3.83 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 21.93/3.83 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 21.93/3.83 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 21.93/3.83 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 21.93/3.83 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 21.93/3.83 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 21.93/3.83 | % 21.93/3.83 | ALPHA: (m__1524) implies: % 21.93/3.83 | (2) aNaturalNumber0(xl) = 0 % 21.93/3.83 | (3) aNaturalNumber0(xm) = 0 % 21.93/3.83 | % 21.93/3.83 | ALPHA: (m__1524_04) implies: % 21.93/3.83 | (4) ~ (xl = sz00) % 21.93/3.83 | (5) doDivides0(xl, xm) = 0 % 21.93/3.83 | % 21.93/3.83 | ALPHA: (m__1553) implies: % 21.93/3.83 | (6) aNaturalNumber0(xn) = 0 % 21.93/3.83 | % 21.93/3.83 | ALPHA: (m__) implies: % 21.93/3.83 | (7) $i(xl) % 21.93/3.83 | (8) $i(xm) % 21.93/3.83 | (9) $i(xn) % 21.93/3.83 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.93/3.83 | ? [v5: $i] : ( ~ (v5 = v2) & sdtsldt0(v3, xl) = v4 & sdtsldt0(xm, xl) % 21.93/3.83 | = v1 & sdtasdt0(v0, v1) = v2 & sdtasdt0(xn, xm) = v3 & sdtasdt0(xl, % 21.93/3.83 | v4) = v5 & sdtasdt0(xl, xn) = v0 & $i(v5) & $i(v4) & $i(v3) & % 21.93/3.83 | $i(v2) & $i(v1) & $i(v0)) % 21.93/3.83 | % 21.93/3.83 | ALPHA: (function-axioms) implies: % 21.93/3.83 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.93/3.83 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 21.93/3.83 | v0)) % 21.93/3.83 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.93/3.83 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 21.93/3.83 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.93/3.83 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 21.93/3.83 | (doDivides0(v3, v2) = v0)) % 21.93/3.84 | % 21.93/3.84 | DELTA: instantiating (10) with fresh symbols all_35_0, all_35_1, all_35_2, % 21.93/3.84 | all_35_3, all_35_4, all_35_5 gives: % 21.93/3.84 | (14) ~ (all_35_0 = all_35_3) & sdtsldt0(all_35_2, xl) = all_35_1 & % 21.93/3.84 | sdtsldt0(xm, xl) = all_35_4 & sdtasdt0(all_35_5, all_35_4) = all_35_3 % 21.93/3.84 | & sdtasdt0(xn, xm) = all_35_2 & sdtasdt0(xl, all_35_1) = all_35_0 & % 21.93/3.84 | sdtasdt0(xl, xn) = all_35_5 & $i(all_35_0) & $i(all_35_1) & % 21.93/3.84 | $i(all_35_2) & $i(all_35_3) & $i(all_35_4) & $i(all_35_5) % 21.93/3.84 | % 21.93/3.84 | ALPHA: (14) implies: % 21.93/3.84 | (15) ~ (all_35_0 = all_35_3) % 21.93/3.84 | (16) $i(all_35_5) % 21.93/3.84 | (17) $i(all_35_4) % 21.93/3.84 | (18) $i(all_35_2) % 21.93/3.84 | (19) $i(all_35_1) % 21.93/3.84 | (20) sdtasdt0(xl, xn) = all_35_5 % 21.93/3.84 | (21) sdtasdt0(xl, all_35_1) = all_35_0 % 21.93/3.84 | (22) sdtasdt0(xn, xm) = all_35_2 % 21.93/3.84 | (23) sdtasdt0(all_35_5, all_35_4) = all_35_3 % 21.93/3.84 | (24) sdtsldt0(xm, xl) = all_35_4 % 21.93/3.84 | (25) sdtsldt0(all_35_2, xl) = all_35_1 % 21.93/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mMulComm) with xl, xn, all_35_5, simplifying with % 22.33/3.84 | (7), (9), (20) gives: % 22.33/3.84 | (26) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xn, xl) = v2 & % 22.33/3.84 | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ % 22.33/3.84 | (v1 = 0) | ~ (v0 = 0) | v2 = all_35_5)) % 22.33/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mSortsB_02) with xl, xn, all_35_5, simplifying % 22.33/3.84 | with (7), (9), (20) gives: % 22.33/3.84 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.84 | (aNaturalNumber0(all_35_5) = v2 & aNaturalNumber0(xn) = v1 & % 22.33/3.84 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.33/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mMulComm) with xl, all_35_1, all_35_0, simplifying % 22.33/3.84 | with (7), (19), (21) gives: % 22.33/3.84 | (28) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_35_1, xl) = % 22.33/3.84 | v2 & aNaturalNumber0(all_35_1) = v1 & aNaturalNumber0(xl) = v0 & % 22.33/3.84 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_35_0)) % 22.33/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mSortsB_02) with xl, all_35_1, all_35_0, % 22.33/3.84 | simplifying with (7), (19), (21) gives: % 22.33/3.84 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.84 | (aNaturalNumber0(all_35_0) = v2 & aNaturalNumber0(all_35_1) = v1 & % 22.33/3.84 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.33/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_35_2, simplifying with % 22.33/3.84 | (8), (9), (22) gives: % 22.33/3.84 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 & % 22.33/3.84 | aNaturalNumber0(xn) = v0 & aNaturalNumber0(xm) = v1 & $i(v2) & ( ~ % 22.33/3.84 | (v1 = 0) | ~ (v0 = 0) | v2 = all_35_2)) % 22.33/3.84 | % 22.33/3.84 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_35_2, simplifying % 22.33/3.84 | with (8), (9), (22) gives: % 22.33/3.84 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.85 | (aNaturalNumber0(all_35_2) = v2 & aNaturalNumber0(xn) = v0 & % 22.33/3.85 | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (mMulAsso) with xl, xn, all_35_4, all_35_5, % 22.33/3.85 | all_35_3, simplifying with (7), (9), (17), (20), (23) gives: % 22.33/3.85 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 22.33/3.85 | : (sdtasdt0(xn, all_35_4) = v3 & sdtasdt0(xl, v3) = v4 & % 22.33/3.85 | aNaturalNumber0(all_35_4) = v2 & aNaturalNumber0(xn) = v1 & % 22.33/3.85 | aNaturalNumber0(xl) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 22.33/3.85 | 0) | ~ (v0 = 0) | v4 = all_35_3)) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (mMulComm) with all_35_5, all_35_4, all_35_3, % 22.33/3.85 | simplifying with (16), (17), (23) gives: % 22.33/3.85 | (33) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_35_4, % 22.33/3.85 | all_35_5) = v2 & aNaturalNumber0(all_35_4) = v1 & % 22.33/3.85 | aNaturalNumber0(all_35_5) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) % 22.33/3.85 | | v2 = all_35_3)) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (mSortsB_02) with all_35_5, all_35_4, all_35_3, % 22.33/3.85 | simplifying with (16), (17), (23) gives: % 22.33/3.85 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.85 | (aNaturalNumber0(all_35_3) = v2 & aNaturalNumber0(all_35_4) = v1 & % 22.33/3.85 | aNaturalNumber0(all_35_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 22.33/3.85 | 0)) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (5), % 22.33/3.85 | (7), (8) gives: % 22.33/3.85 | (35) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 22.33/3.85 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 22.33/3.85 | $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0)) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (1) with xl, xm, all_35_4, simplifying with (7), % 22.33/3.85 | (8), (24) gives: % 22.33/3.85 | (36) xl = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.85 | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & % 22.33/3.85 | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.33/3.85 | 0))) | ( ! [v0: any] : (v0 = all_35_4 | ~ (sdtasdt0(xl, v0) = % 22.33/3.85 | xm) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.33/3.85 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xl, % 22.33/3.85 | all_35_4) = v0) | ~ $i(all_35_4) | (v0 = xm & % 22.33/3.85 | aNaturalNumber0(all_35_4) = 0))) % 22.33/3.85 | % 22.33/3.85 | GROUND_INST: instantiating (1) with xl, all_35_2, all_35_1, simplifying with % 22.33/3.85 | (7), (18), (25) gives: % 22.33/3.85 | (37) xl = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.33/3.85 | (doDivides0(xl, all_35_2) = v2 & aNaturalNumber0(all_35_2) = v1 & % 22.33/3.85 | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.33/3.85 | 0))) | ( ! [v0: any] : (v0 = all_35_1 | ~ (sdtasdt0(xl, v0) = % 22.33/3.85 | all_35_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.33/3.85 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xl, % 22.33/3.85 | all_35_1) = v0) | ~ $i(all_35_1) | (v0 = all_35_2 & % 22.33/3.85 | aNaturalNumber0(all_35_1) = 0))) % 22.33/3.85 | % 22.33/3.85 | DELTA: instantiating (34) with fresh symbols all_42_0, all_42_1, all_42_2 % 22.33/3.85 | gives: % 22.33/3.85 | (38) aNaturalNumber0(all_35_3) = all_42_0 & aNaturalNumber0(all_35_4) = % 22.33/3.85 | all_42_1 & aNaturalNumber0(all_35_5) = all_42_2 & ( ~ (all_42_1 = 0) | % 22.33/3.85 | ~ (all_42_2 = 0) | all_42_0 = 0) % 22.33/3.85 | % 22.33/3.85 | ALPHA: (38) implies: % 22.33/3.85 | (39) aNaturalNumber0(all_35_4) = all_42_1 % 22.33/3.85 | % 22.33/3.85 | DELTA: instantiating (31) with fresh symbols all_44_0, all_44_1, all_44_2 % 22.33/3.85 | gives: % 22.33/3.85 | (40) aNaturalNumber0(all_35_2) = all_44_0 & aNaturalNumber0(xn) = all_44_2 % 22.33/3.85 | & aNaturalNumber0(xm) = all_44_1 & ( ~ (all_44_1 = 0) | ~ (all_44_2 = % 22.33/3.85 | 0) | all_44_0 = 0) % 22.33/3.85 | % 22.33/3.85 | ALPHA: (40) implies: % 22.33/3.85 | (41) aNaturalNumber0(xm) = all_44_1 % 22.33/3.85 | (42) aNaturalNumber0(xn) = all_44_2 % 22.33/3.86 | (43) aNaturalNumber0(all_35_2) = all_44_0 % 22.33/3.86 | (44) ~ (all_44_1 = 0) | ~ (all_44_2 = 0) | all_44_0 = 0 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (29) with fresh symbols all_46_0, all_46_1, all_46_2 % 22.33/3.86 | gives: % 22.33/3.86 | (45) aNaturalNumber0(all_35_0) = all_46_0 & aNaturalNumber0(all_35_1) = % 22.33/3.86 | all_46_1 & aNaturalNumber0(xl) = all_46_2 & ( ~ (all_46_1 = 0) | ~ % 22.33/3.86 | (all_46_2 = 0) | all_46_0 = 0) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (45) implies: % 22.33/3.86 | (46) aNaturalNumber0(xl) = all_46_2 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (27) with fresh symbols all_48_0, all_48_1, all_48_2 % 22.33/3.86 | gives: % 22.33/3.86 | (47) aNaturalNumber0(all_35_5) = all_48_0 & aNaturalNumber0(xn) = all_48_1 % 22.33/3.86 | & aNaturalNumber0(xl) = all_48_2 & ( ~ (all_48_1 = 0) | ~ (all_48_2 = % 22.33/3.86 | 0) | all_48_0 = 0) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (47) implies: % 22.33/3.86 | (48) aNaturalNumber0(xl) = all_48_2 % 22.33/3.86 | (49) aNaturalNumber0(xn) = all_48_1 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (26) with fresh symbols all_50_0, all_50_1, all_50_2 % 22.33/3.86 | gives: % 22.33/3.86 | (50) sdtasdt0(xn, xl) = all_50_0 & aNaturalNumber0(xn) = all_50_1 & % 22.33/3.86 | aNaturalNumber0(xl) = all_50_2 & $i(all_50_0) & ( ~ (all_50_1 = 0) | % 22.33/3.86 | ~ (all_50_2 = 0) | all_50_0 = all_35_5) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (50) implies: % 22.33/3.86 | (51) $i(all_50_0) % 22.33/3.86 | (52) aNaturalNumber0(xl) = all_50_2 % 22.33/3.86 | (53) aNaturalNumber0(xn) = all_50_1 % 22.33/3.86 | (54) sdtasdt0(xn, xl) = all_50_0 % 22.33/3.86 | (55) ~ (all_50_1 = 0) | ~ (all_50_2 = 0) | all_50_0 = all_35_5 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (30) with fresh symbols all_52_0, all_52_1, all_52_2 % 22.33/3.86 | gives: % 22.33/3.86 | (56) sdtasdt0(xm, xn) = all_52_0 & aNaturalNumber0(xn) = all_52_2 & % 22.33/3.86 | aNaturalNumber0(xm) = all_52_1 & $i(all_52_0) & ( ~ (all_52_1 = 0) | % 22.33/3.86 | ~ (all_52_2 = 0) | all_52_0 = all_35_2) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (56) implies: % 22.33/3.86 | (57) aNaturalNumber0(xm) = all_52_1 % 22.33/3.86 | (58) aNaturalNumber0(xn) = all_52_2 % 22.33/3.86 | (59) sdtasdt0(xm, xn) = all_52_0 % 22.33/3.86 | (60) ~ (all_52_1 = 0) | ~ (all_52_2 = 0) | all_52_0 = all_35_2 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (28) with fresh symbols all_54_0, all_54_1, all_54_2 % 22.33/3.86 | gives: % 22.33/3.86 | (61) sdtasdt0(all_35_1, xl) = all_54_0 & aNaturalNumber0(all_35_1) = % 22.33/3.86 | all_54_1 & aNaturalNumber0(xl) = all_54_2 & $i(all_54_0) & ( ~ % 22.33/3.86 | (all_54_1 = 0) | ~ (all_54_2 = 0) | all_54_0 = all_35_0) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (61) implies: % 22.33/3.86 | (62) aNaturalNumber0(xl) = all_54_2 % 22.33/3.86 | (63) sdtasdt0(all_35_1, xl) = all_54_0 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (33) with fresh symbols all_56_0, all_56_1, all_56_2 % 22.33/3.86 | gives: % 22.33/3.86 | (64) sdtasdt0(all_35_4, all_35_5) = all_56_0 & aNaturalNumber0(all_35_4) = % 22.33/3.86 | all_56_1 & aNaturalNumber0(all_35_5) = all_56_2 & $i(all_56_0) & ( ~ % 22.33/3.86 | (all_56_1 = 0) | ~ (all_56_2 = 0) | all_56_0 = all_35_3) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (64) implies: % 22.33/3.86 | (65) aNaturalNumber0(all_35_4) = all_56_1 % 22.33/3.86 | (66) sdtasdt0(all_35_4, all_35_5) = all_56_0 % 22.33/3.86 | % 22.33/3.86 | DELTA: instantiating (32) with fresh symbols all_58_0, all_58_1, all_58_2, % 22.33/3.86 | all_58_3, all_58_4 gives: % 22.33/3.86 | (67) sdtasdt0(xn, all_35_4) = all_58_1 & sdtasdt0(xl, all_58_1) = all_58_0 % 22.33/3.86 | & aNaturalNumber0(all_35_4) = all_58_2 & aNaturalNumber0(xn) = % 22.33/3.86 | all_58_3 & aNaturalNumber0(xl) = all_58_4 & $i(all_58_0) & % 22.33/3.86 | $i(all_58_1) & ( ~ (all_58_2 = 0) | ~ (all_58_3 = 0) | ~ (all_58_4 = % 22.33/3.86 | 0) | all_58_0 = all_35_3) % 22.33/3.86 | % 22.33/3.86 | ALPHA: (67) implies: % 22.33/3.86 | (68) $i(all_58_1) % 22.33/3.86 | (69) aNaturalNumber0(xl) = all_58_4 % 22.33/3.86 | (70) aNaturalNumber0(xn) = all_58_3 % 22.33/3.86 | (71) aNaturalNumber0(all_35_4) = all_58_2 % 22.33/3.86 | (72) sdtasdt0(xl, all_58_1) = all_58_0 % 22.33/3.86 | (73) sdtasdt0(xn, all_35_4) = all_58_1 % 22.33/3.86 | % 22.33/3.86 | GROUND_INST: instantiating (11) with all_48_2, all_54_2, xl, simplifying with % 22.33/3.86 | (48), (62) gives: % 22.33/3.86 | (74) all_54_2 = all_48_2 % 22.33/3.86 | % 22.33/3.86 | GROUND_INST: instantiating (11) with 0, all_58_4, xl, simplifying with (2), % 22.33/3.86 | (69) gives: % 22.33/3.86 | (75) all_58_4 = 0 % 22.33/3.86 | % 22.33/3.86 | GROUND_INST: instantiating (11) with all_54_2, all_58_4, xl, simplifying with % 22.33/3.86 | (62), (69) gives: % 22.33/3.87 | (76) all_58_4 = all_54_2 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_50_2, all_58_4, xl, simplifying with % 22.33/3.87 | (52), (69) gives: % 22.33/3.87 | (77) all_58_4 = all_50_2 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_46_2, all_58_4, xl, simplifying with % 22.33/3.87 | (46), (69) gives: % 22.33/3.87 | (78) all_58_4 = all_46_2 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with 0, all_52_1, xm, simplifying with (3), % 22.33/3.87 | (57) gives: % 22.33/3.87 | (79) all_52_1 = 0 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_44_1, all_52_1, xm, simplifying with % 22.33/3.87 | (41), (57) gives: % 22.33/3.87 | (80) all_52_1 = all_44_1 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with 0, all_50_1, xn, simplifying with (6), % 22.33/3.87 | (53) gives: % 22.33/3.87 | (81) all_50_1 = 0 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_52_2, all_58_3, xn, simplifying with % 22.33/3.87 | (58), (70) gives: % 22.33/3.87 | (82) all_58_3 = all_52_2 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_50_1, all_58_3, xn, simplifying with % 22.33/3.87 | (53), (70) gives: % 22.33/3.87 | (83) all_58_3 = all_50_1 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_48_1, all_58_3, xn, simplifying with % 22.33/3.87 | (49), (70) gives: % 22.33/3.87 | (84) all_58_3 = all_48_1 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_44_2, all_58_3, xn, simplifying with % 22.33/3.87 | (42), (70) gives: % 22.33/3.87 | (85) all_58_3 = all_44_2 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_56_1, all_58_2, all_35_4, simplifying % 22.33/3.87 | with (65), (71) gives: % 22.33/3.87 | (86) all_58_2 = all_56_1 % 22.33/3.87 | % 22.33/3.87 | GROUND_INST: instantiating (11) with all_42_1, all_58_2, all_35_4, simplifying % 22.33/3.87 | with (39), (71) gives: % 22.33/3.87 | (87) all_58_2 = all_42_1 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (86), (87) imply: % 22.33/3.87 | (88) all_56_1 = all_42_1 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (82), (83) imply: % 22.33/3.87 | (89) all_52_2 = all_50_1 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (82), (84) imply: % 22.33/3.87 | (90) all_52_2 = all_48_1 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (82), (85) imply: % 22.33/3.87 | (91) all_52_2 = all_44_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (77), (78) imply: % 22.33/3.87 | (92) all_50_2 = all_46_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (75), (77) imply: % 22.33/3.87 | (93) all_50_2 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (76), (77) imply: % 22.33/3.87 | (94) all_54_2 = all_50_2 % 22.33/3.87 | % 22.33/3.87 | SIMP: (94) implies: % 22.33/3.87 | (95) all_54_2 = all_50_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (74), (95) imply: % 22.33/3.87 | (96) all_50_2 = all_48_2 % 22.33/3.87 | % 22.33/3.87 | SIMP: (96) implies: % 22.33/3.87 | (97) all_50_2 = all_48_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (79), (80) imply: % 22.33/3.87 | (98) all_44_1 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (90), (91) imply: % 22.33/3.87 | (99) all_48_1 = all_44_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (89), (90) imply: % 22.33/3.87 | (100) all_50_1 = all_48_1 % 22.33/3.87 | % 22.33/3.87 | SIMP: (100) implies: % 22.33/3.87 | (101) all_50_1 = all_48_1 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (81), (101) imply: % 22.33/3.87 | (102) all_48_1 = 0 % 22.33/3.87 | % 22.33/3.87 | SIMP: (102) implies: % 22.33/3.87 | (103) all_48_1 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (92), (97) imply: % 22.33/3.87 | (104) all_48_2 = all_46_2 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (93), (97) imply: % 22.33/3.87 | (105) all_48_2 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (99), (103) imply: % 22.33/3.87 | (106) all_44_2 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (104), (105) imply: % 22.33/3.87 | (107) all_46_2 = 0 % 22.33/3.87 | % 22.33/3.87 | SIMP: (107) implies: % 22.33/3.87 | (108) all_46_2 = 0 % 22.33/3.87 | % 22.33/3.87 | COMBINE_EQS: (90), (103) imply: % 22.33/3.87 | (109) all_52_2 = 0 % 22.33/3.87 | % 22.33/3.87 | BETA: splitting (44) gives: % 22.33/3.87 | % 22.33/3.87 | Case 1: % 22.33/3.87 | | % 22.33/3.87 | | (110) ~ (all_44_1 = 0) % 22.33/3.87 | | % 22.33/3.87 | | REDUCE: (98), (110) imply: % 22.33/3.87 | | (111) $false % 22.33/3.87 | | % 22.33/3.87 | | CLOSE: (111) is inconsistent. % 22.33/3.87 | | % 22.33/3.87 | Case 2: % 22.33/3.87 | | % 22.33/3.87 | | (112) ~ (all_44_2 = 0) | all_44_0 = 0 % 22.33/3.88 | | % 22.33/3.88 | | BETA: splitting (60) gives: % 22.33/3.88 | | % 22.33/3.88 | | Case 1: % 22.33/3.88 | | | % 22.33/3.88 | | | (113) ~ (all_52_1 = 0) % 22.33/3.88 | | | % 22.33/3.88 | | | REDUCE: (79), (113) imply: % 22.33/3.88 | | | (114) $false % 22.33/3.88 | | | % 22.33/3.88 | | | CLOSE: (114) is inconsistent. % 22.33/3.88 | | | % 22.33/3.88 | | Case 2: % 22.33/3.88 | | | % 22.33/3.88 | | | (115) ~ (all_52_2 = 0) | all_52_0 = all_35_2 % 22.33/3.88 | | | % 22.33/3.88 | | | BETA: splitting (36) gives: % 22.33/3.88 | | | % 22.33/3.88 | | | Case 1: % 22.33/3.88 | | | | % 22.33/3.88 | | | | (116) xl = sz00 % 22.33/3.88 | | | | % 22.33/3.88 | | | | REDUCE: (4), (116) imply: % 22.33/3.88 | | | | (117) $false % 22.33/3.88 | | | | % 22.33/3.88 | | | | CLOSE: (117) is inconsistent. % 22.33/3.88 | | | | % 22.33/3.88 | | | Case 2: % 22.33/3.88 | | | | % 22.33/3.88 | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xl, % 22.33/3.88 | | | | xm) = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = % 22.33/3.88 | | | | v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: % 22.33/3.88 | | | | any] : (v0 = all_35_4 | ~ (sdtasdt0(xl, v0) = xm) | ~ % 22.33/3.88 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) % 22.33/3.88 | | | | = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xl, all_35_4) = v0) % 22.33/3.88 | | | | | ~ $i(all_35_4) | (v0 = xm & aNaturalNumber0(all_35_4) = % 22.33/3.88 | | | | 0))) % 22.33/3.88 | | | | % 22.33/3.88 | | | | BETA: splitting (35) gives: % 22.33/3.88 | | | | % 22.33/3.88 | | | | Case 1: % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | (119) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 22.33/3.88 | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | DELTA: instantiating (119) with fresh symbols all_86_0, all_86_1 % 22.33/3.88 | | | | | gives: % 22.33/3.88 | | | | | (120) aNaturalNumber0(xm) = all_86_0 & aNaturalNumber0(xl) = % 22.33/3.88 | | | | | all_86_1 & ( ~ (all_86_0 = 0) | ~ (all_86_1 = 0)) % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | ALPHA: (120) implies: % 22.33/3.88 | | | | | (121) aNaturalNumber0(xl) = all_86_1 % 22.33/3.88 | | | | | (122) aNaturalNumber0(xm) = all_86_0 % 22.33/3.88 | | | | | (123) ~ (all_86_0 = 0) | ~ (all_86_1 = 0) % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | GROUND_INST: instantiating (11) with 0, all_86_1, xl, simplifying with % 22.33/3.88 | | | | | (2), (121) gives: % 22.33/3.88 | | | | | (124) all_86_1 = 0 % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | GROUND_INST: instantiating (11) with 0, all_86_0, xm, simplifying with % 22.33/3.88 | | | | | (3), (122) gives: % 22.33/3.88 | | | | | (125) all_86_0 = 0 % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | BETA: splitting (123) gives: % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | Case 1: % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | (126) ~ (all_86_0 = 0) % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | REDUCE: (125), (126) imply: % 22.33/3.88 | | | | | | (127) $false % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | CLOSE: (127) is inconsistent. % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | Case 2: % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | (128) ~ (all_86_1 = 0) % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | REDUCE: (124), (128) imply: % 22.33/3.88 | | | | | | (129) $false % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | CLOSE: (129) is inconsistent. % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | End of split % 22.33/3.88 | | | | | % 22.33/3.88 | | | | Case 2: % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | (130) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = % 22.33/3.88 | | | | | 0 & $i(v0)) % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | DELTA: instantiating (130) with fresh symbol all_86_0 gives: % 22.33/3.88 | | | | | (131) sdtasdt0(xl, all_86_0) = xm & aNaturalNumber0(all_86_0) = 0 & % 22.33/3.88 | | | | | $i(all_86_0) % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | ALPHA: (131) implies: % 22.33/3.88 | | | | | (132) $i(all_86_0) % 22.33/3.88 | | | | | (133) aNaturalNumber0(all_86_0) = 0 % 22.33/3.88 | | | | | (134) sdtasdt0(xl, all_86_0) = xm % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | BETA: splitting (112) gives: % 22.33/3.88 | | | | | % 22.33/3.88 | | | | | Case 1: % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | (135) ~ (all_44_2 = 0) % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | REDUCE: (106), (135) imply: % 22.33/3.88 | | | | | | (136) $false % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | CLOSE: (136) is inconsistent. % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | Case 2: % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | (137) all_44_0 = 0 % 22.33/3.88 | | | | | | % 22.33/3.88 | | | | | | REDUCE: (43), (137) imply: % 22.33/3.88 | | | | | | (138) aNaturalNumber0(all_35_2) = 0 % 22.33/3.88 | | | | | | % 22.54/3.88 | | | | | | BETA: splitting (118) gives: % 22.54/3.88 | | | | | | % 22.54/3.88 | | | | | | Case 1: % 22.54/3.88 | | | | | | | % 22.54/3.88 | | | | | | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.88 | | | | | | | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & % 22.54/3.88 | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 22.54/3.88 | | | | | | | ~ (v0 = 0))) % 22.54/3.88 | | | | | | | % 22.54/3.88 | | | | | | | DELTA: instantiating (139) with fresh symbols all_94_0, all_94_1, % 22.54/3.88 | | | | | | | all_94_2 gives: % 22.54/3.88 | | | | | | | (140) doDivides0(xl, xm) = all_94_0 & aNaturalNumber0(xm) = % 22.54/3.88 | | | | | | | all_94_1 & aNaturalNumber0(xl) = all_94_2 & ( ~ (all_94_0 % 22.54/3.88 | | | | | | | = 0) | ~ (all_94_1 = 0) | ~ (all_94_2 = 0)) % 22.54/3.88 | | | | | | | % 22.54/3.88 | | | | | | | ALPHA: (140) implies: % 22.54/3.88 | | | | | | | (141) aNaturalNumber0(xl) = all_94_2 % 22.54/3.88 | | | | | | | (142) aNaturalNumber0(xm) = all_94_1 % 22.54/3.88 | | | | | | | (143) doDivides0(xl, xm) = all_94_0 % 22.54/3.88 | | | | | | | (144) ~ (all_94_0 = 0) | ~ (all_94_1 = 0) | ~ (all_94_2 = 0) % 22.54/3.88 | | | | | | | % 22.54/3.88 | | | | | | | GROUND_INST: instantiating (11) with 0, all_94_2, xl, simplifying % 22.54/3.88 | | | | | | | with (2), (141) gives: % 22.54/3.88 | | | | | | | (145) all_94_2 = 0 % 22.54/3.88 | | | | | | | % 22.54/3.88 | | | | | | | GROUND_INST: instantiating (11) with 0, all_94_1, xm, simplifying % 22.54/3.88 | | | | | | | with (3), (142) gives: % 22.54/3.89 | | | | | | | (146) all_94_1 = 0 % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | GROUND_INST: instantiating (13) with 0, all_94_0, xm, xl, % 22.54/3.89 | | | | | | | simplifying with (5), (143) gives: % 22.54/3.89 | | | | | | | (147) all_94_0 = 0 % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | BETA: splitting (144) gives: % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | Case 1: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | (148) ~ (all_94_0 = 0) % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | REDUCE: (147), (148) imply: % 22.54/3.89 | | | | | | | | (149) $false % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | CLOSE: (149) is inconsistent. % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | Case 2: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | (150) ~ (all_94_1 = 0) | ~ (all_94_2 = 0) % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | BETA: splitting (150) gives: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | Case 1: % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | (151) ~ (all_94_1 = 0) % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | REDUCE: (146), (151) imply: % 22.54/3.89 | | | | | | | | | (152) $false % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | CLOSE: (152) is inconsistent. % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | Case 2: % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | (153) ~ (all_94_2 = 0) % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | REDUCE: (145), (153) imply: % 22.54/3.89 | | | | | | | | | (154) $false % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | CLOSE: (154) is inconsistent. % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | End of split % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | End of split % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | Case 2: % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | (155) ! [v0: any] : (v0 = all_35_4 | ~ (sdtasdt0(xl, v0) = % 22.54/3.89 | | | | | | | xm) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.54/3.89 | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 22.54/3.89 | | | | | | | (sdtasdt0(xl, all_35_4) = v0) | ~ $i(all_35_4) | (v0 = % 22.54/3.89 | | | | | | | xm & aNaturalNumber0(all_35_4) = 0)) % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | ALPHA: (155) implies: % 22.54/3.89 | | | | | | | (156) ! [v0: any] : (v0 = all_35_4 | ~ (sdtasdt0(xl, v0) = % 22.54/3.89 | | | | | | | xm) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.54/3.89 | | | | | | | aNaturalNumber0(v0) = v1)) % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | BETA: splitting (115) gives: % 22.54/3.89 | | | | | | | % 22.54/3.89 | | | | | | | Case 1: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | (157) ~ (all_52_2 = 0) % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | REDUCE: (109), (157) imply: % 22.54/3.89 | | | | | | | | (158) $false % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | CLOSE: (158) is inconsistent. % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | Case 2: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | (159) all_52_0 = all_35_2 % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | REDUCE: (59), (159) imply: % 22.54/3.89 | | | | | | | | (160) sdtasdt0(xm, xn) = all_35_2 % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | BETA: splitting (55) gives: % 22.54/3.89 | | | | | | | | % 22.54/3.89 | | | | | | | | Case 1: % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | (161) ~ (all_50_1 = 0) % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | REDUCE: (81), (161) imply: % 22.54/3.89 | | | | | | | | | (162) $false % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | CLOSE: (162) is inconsistent. % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | Case 2: % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | (163) ~ (all_50_2 = 0) | all_50_0 = all_35_5 % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | BETA: splitting (163) gives: % 22.54/3.89 | | | | | | | | | % 22.54/3.89 | | | | | | | | | Case 1: % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | (164) ~ (all_50_2 = 0) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | REDUCE: (93), (164) imply: % 22.54/3.89 | | | | | | | | | | (165) $false % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | CLOSE: (165) is inconsistent. % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | Case 2: % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | (166) all_50_0 = all_35_5 % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | REDUCE: (54), (166) imply: % 22.54/3.89 | | | | | | | | | | (167) sdtasdt0(xn, xl) = all_35_5 % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_58_1, % 22.54/3.89 | | | | | | | | | | all_58_0, simplifying with (7), (68), (72) gives: % 22.54/3.89 | | | | | | | | | | (168) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.54/3.89 | | | | | | | | | | (sdtasdt0(all_58_1, xl) = v2 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_58_1) = v1 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.54/3.89 | | | | | | | | | | | ~ (v0 = 0) | v2 = all_58_0)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xl, all_58_1, % 22.54/3.89 | | | | | | | | | | all_58_0, simplifying with (7), (68), (72) gives: % 22.54/3.89 | | | | | | | | | | (169) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.89 | | | | | | | | | | (aNaturalNumber0(all_58_0) = v2 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_58_1) = v1 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 % 22.54/3.89 | | | | | | | | | | = 0) | v2 = 0)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (156) with all_86_0, simplifying % 22.54/3.89 | | | | | | | | | | with (132), (134) gives: % 22.54/3.89 | | | | | | | | | | (170) all_86_0 = all_35_4 | ? [v0: int] : ( ~ (v0 = 0) & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_86_0) = v0) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_86_0, xm, % 22.54/3.89 | | | | | | | | | | simplifying with (7), (132), (134) gives: % 22.54/3.89 | | | | | | | | | | (171) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.54/3.89 | | | | | | | | | | (sdtasdt0(all_86_0, xl) = v2 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_86_0) = v1 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.54/3.89 | | | | | | | | | | | ~ (v0 = 0) | v2 = xm)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xl, all_86_0, xn, % 22.54/3.89 | | | | | | | | | | xm, all_35_2, simplifying with (7), (9), (132), % 22.54/3.89 | | | | | | | | | | (134), (160) gives: % 22.54/3.89 | | | | | | | | | | (172) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.54/3.89 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_86_0, xn) = % 22.54/3.89 | | | | | | | | | | v3 & sdtasdt0(xl, v3) = v4 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_86_0) = v1 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xn) = v2 & aNaturalNumber0(xl) = % 22.54/3.89 | | | | | | | | | | v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) % 22.54/3.89 | | | | | | | | | | | ~ (v0 = 0) | v4 = all_35_2)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xn, xl, all_35_4, % 22.54/3.89 | | | | | | | | | | all_35_5, all_35_3, simplifying with (7), (9), % 22.54/3.89 | | | | | | | | | | (17), (23), (167) gives: % 22.54/3.89 | | | | | | | | | | (173) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.54/3.89 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(xn, v3) = v4 & % 22.54/3.89 | | | | | | | | | | sdtasdt0(xl, all_35_4) = v3 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_35_4) = v2 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xn) = v0 & aNaturalNumber0(xl) = % 22.54/3.89 | | | | | | | | | | v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) % 22.54/3.89 | | | | | | | | | | | ~ (v0 = 0) | v4 = all_35_3)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xn, all_35_4, % 22.54/3.89 | | | | | | | | | | all_58_1, simplifying with (9), (17), (73) gives: % 22.54/3.89 | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.54/3.89 | | | | | | | | | | (sdtasdt0(all_35_4, xn) = v2 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(all_35_4) = v1 & % 22.54/3.89 | | | | | | | | | | aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.54/3.89 | | | | | | | | | | | ~ (v0 = 0) | v2 = all_58_1)) % 22.54/3.89 | | | | | | | | | | % 22.54/3.89 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xn, all_35_4, % 22.54/3.89 | | | | | | | | | | all_58_1, simplifying with (9), (17), (73) gives: % 22.54/3.90 | | | | | | | | | | (175) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.90 | | | | | | | | | | (aNaturalNumber0(all_58_1) = v2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = v1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 % 22.54/3.90 | | | | | | | | | | = 0) | v2 = 0)) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_35_4, all_35_5, % 22.54/3.90 | | | | | | | | | | all_56_0, simplifying with (16), (17), (66) gives: % 22.54/3.90 | | | | | | | | | | (176) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.54/3.90 | | | | | | | | | | (sdtasdt0(all_35_5, all_35_4) = v2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = v0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_5) = v1 & $i(v2) & ( ~ (v1 % 22.54/3.90 | | | | | | | | | | = 0) | ~ (v0 = 0) | v2 = all_56_0)) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_35_4, % 22.54/3.90 | | | | | | | | | | all_35_5, all_56_0, simplifying with (16), (17), % 22.54/3.90 | | | | | | | | | | (66) gives: % 22.54/3.90 | | | | | | | | | | (177) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.90 | | | | | | | | | | (aNaturalNumber0(all_56_0) = v2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = v0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_5) = v1 & ( ~ (v1 = 0) | % 22.54/3.90 | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_35_1, xl, % 22.54/3.90 | | | | | | | | | | all_54_0, simplifying with (7), (19), (63) gives: % 22.54/3.90 | | | | | | | | | | (178) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.54/3.90 | | | | | | | | | | (sdtasdt0(xl, all_35_1) = v2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_1) = v0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = 0) % 22.54/3.90 | | | | | | | | | | | ~ (v0 = 0) | v2 = all_54_0)) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_35_1, xl, % 22.54/3.90 | | | | | | | | | | all_54_0, simplifying with (7), (19), (63) gives: % 22.54/3.90 | | | | | | | | | | (179) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.90 | | | | | | | | | | (aNaturalNumber0(all_54_0) = v2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_1) = v0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = v1 & ( ~ (v1 = 0) | ~ (v0 % 22.54/3.90 | | | | | | | | | | = 0) | v2 = 0)) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (179) with fresh symbols all_119_0, % 22.54/3.90 | | | | | | | | | | all_119_1, all_119_2 gives: % 22.54/3.90 | | | | | | | | | | (180) aNaturalNumber0(all_54_0) = all_119_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_1) = all_119_2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_119_1 & ( ~ (all_119_1 = % 22.54/3.90 | | | | | | | | | | 0) | ~ (all_119_2 = 0) | all_119_0 = 0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (180) implies: % 22.54/3.90 | | | | | | | | | | (181) aNaturalNumber0(xl) = all_119_1 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (169) with fresh symbols all_121_0, % 22.54/3.90 | | | | | | | | | | all_121_1, all_121_2 gives: % 22.54/3.90 | | | | | | | | | | (182) aNaturalNumber0(all_58_0) = all_121_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_58_1) = all_121_1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_121_2 & ( ~ (all_121_1 = % 22.54/3.90 | | | | | | | | | | 0) | ~ (all_121_2 = 0) | all_121_0 = 0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (182) implies: % 22.54/3.90 | | | | | | | | | | (183) aNaturalNumber0(xl) = all_121_2 % 22.54/3.90 | | | | | | | | | | (184) aNaturalNumber0(all_58_1) = all_121_1 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (177) with fresh symbols all_123_0, % 22.54/3.90 | | | | | | | | | | all_123_1, all_123_2 gives: % 22.54/3.90 | | | | | | | | | | (185) aNaturalNumber0(all_56_0) = all_123_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = all_123_2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_5) = all_123_1 & ( ~ % 22.54/3.90 | | | | | | | | | | (all_123_1 = 0) | ~ (all_123_2 = 0) | all_123_0 % 22.54/3.90 | | | | | | | | | | = 0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (185) implies: % 22.54/3.90 | | | | | | | | | | (186) aNaturalNumber0(all_35_4) = all_123_2 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (175) with fresh symbols all_125_0, % 22.54/3.90 | | | | | | | | | | all_125_1, all_125_2 gives: % 22.54/3.90 | | | | | | | | | | (187) aNaturalNumber0(all_58_1) = all_125_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = all_125_1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xn) = all_125_2 & ( ~ (all_125_1 = % 22.54/3.90 | | | | | | | | | | 0) | ~ (all_125_2 = 0) | all_125_0 = 0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (187) implies: % 22.54/3.90 | | | | | | | | | | (188) aNaturalNumber0(xn) = all_125_2 % 22.54/3.90 | | | | | | | | | | (189) aNaturalNumber0(all_35_4) = all_125_1 % 22.54/3.90 | | | | | | | | | | (190) aNaturalNumber0(all_58_1) = all_125_0 % 22.54/3.90 | | | | | | | | | | (191) ~ (all_125_1 = 0) | ~ (all_125_2 = 0) | all_125_0 % 22.54/3.90 | | | | | | | | | | = 0 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (168) with fresh symbols all_127_0, % 22.54/3.90 | | | | | | | | | | all_127_1, all_127_2 gives: % 22.54/3.90 | | | | | | | | | | (192) sdtasdt0(all_58_1, xl) = all_127_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_58_1) = all_127_1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_127_2 & $i(all_127_0) & ( % 22.54/3.90 | | | | | | | | | | ~ (all_127_1 = 0) | ~ (all_127_2 = 0) | % 22.54/3.90 | | | | | | | | | | all_127_0 = all_58_0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (192) implies: % 22.54/3.90 | | | | | | | | | | (193) aNaturalNumber0(xl) = all_127_2 % 22.54/3.90 | | | | | | | | | | (194) aNaturalNumber0(all_58_1) = all_127_1 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (178) with fresh symbols all_129_0, % 22.54/3.90 | | | | | | | | | | all_129_1, all_129_2 gives: % 22.54/3.90 | | | | | | | | | | (195) sdtasdt0(xl, all_35_1) = all_129_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_1) = all_129_2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_129_1 & $i(all_129_0) & ( % 22.54/3.90 | | | | | | | | | | ~ (all_129_1 = 0) | ~ (all_129_2 = 0) | % 22.54/3.90 | | | | | | | | | | all_129_0 = all_54_0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (195) implies: % 22.54/3.90 | | | | | | | | | | (196) aNaturalNumber0(xl) = all_129_1 % 22.54/3.90 | | | | | | | | | | (197) sdtasdt0(xl, all_35_1) = all_129_0 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (176) with fresh symbols all_131_0, % 22.54/3.90 | | | | | | | | | | all_131_1, all_131_2 gives: % 22.54/3.90 | | | | | | | | | | (198) sdtasdt0(all_35_5, all_35_4) = all_131_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = all_131_2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_5) = all_131_1 & % 22.54/3.90 | | | | | | | | | | $i(all_131_0) & ( ~ (all_131_1 = 0) | ~ (all_131_2 % 22.54/3.90 | | | | | | | | | | = 0) | all_131_0 = all_56_0) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (198) implies: % 22.54/3.90 | | | | | | | | | | (199) aNaturalNumber0(all_35_4) = all_131_2 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_133_0, % 22.54/3.90 | | | | | | | | | | all_133_1, all_133_2 gives: % 22.54/3.90 | | | | | | | | | | (200) sdtasdt0(all_35_4, xn) = all_133_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_35_4) = all_133_1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xn) = all_133_2 & $i(all_133_0) & ( % 22.54/3.90 | | | | | | | | | | ~ (all_133_1 = 0) | ~ (all_133_2 = 0) | % 22.54/3.90 | | | | | | | | | | all_133_0 = all_58_1) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (200) implies: % 22.54/3.90 | | | | | | | | | | (201) aNaturalNumber0(xn) = all_133_2 % 22.54/3.90 | | | | | | | | | | (202) aNaturalNumber0(all_35_4) = all_133_1 % 22.54/3.90 | | | | | | | | | | (203) sdtasdt0(all_35_4, xn) = all_133_0 % 22.54/3.90 | | | | | | | | | | (204) ~ (all_133_1 = 0) | ~ (all_133_2 = 0) | all_133_0 % 22.54/3.90 | | | | | | | | | | = all_58_1 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (171) with fresh symbols all_135_0, % 22.54/3.90 | | | | | | | | | | all_135_1, all_135_2 gives: % 22.54/3.90 | | | | | | | | | | (205) sdtasdt0(all_86_0, xl) = all_135_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_86_0) = all_135_1 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_135_2 & $i(all_135_0) & ( % 22.54/3.90 | | | | | | | | | | ~ (all_135_1 = 0) | ~ (all_135_2 = 0) | % 22.54/3.90 | | | | | | | | | | all_135_0 = xm) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (205) implies: % 22.54/3.90 | | | | | | | | | | (206) aNaturalNumber0(xl) = all_135_2 % 22.54/3.90 | | | | | | | | | | (207) aNaturalNumber0(all_86_0) = all_135_1 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (173) with fresh symbols all_137_0, % 22.54/3.90 | | | | | | | | | | all_137_1, all_137_2, all_137_3, all_137_4 gives: % 22.54/3.90 | | | | | | | | | | (208) sdtasdt0(xn, all_137_1) = all_137_0 & sdtasdt0(xl, % 22.54/3.90 | | | | | | | | | | all_35_4) = all_137_1 & aNaturalNumber0(all_35_4) % 22.54/3.90 | | | | | | | | | | = all_137_2 & aNaturalNumber0(xn) = all_137_4 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_137_3 & $i(all_137_0) & % 22.54/3.90 | | | | | | | | | | $i(all_137_1) & ( ~ (all_137_2 = 0) | ~ (all_137_3 % 22.54/3.90 | | | | | | | | | | = 0) | ~ (all_137_4 = 0) | all_137_0 = % 22.54/3.90 | | | | | | | | | | all_35_3) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (208) implies: % 22.54/3.90 | | | | | | | | | | (209) aNaturalNumber0(xl) = all_137_3 % 22.54/3.90 | | | | | | | | | | (210) aNaturalNumber0(xn) = all_137_4 % 22.54/3.90 | | | | | | | | | | (211) aNaturalNumber0(all_35_4) = all_137_2 % 22.54/3.90 | | | | | | | | | | (212) sdtasdt0(xl, all_35_4) = all_137_1 % 22.54/3.90 | | | | | | | | | | (213) sdtasdt0(xn, all_137_1) = all_137_0 % 22.54/3.90 | | | | | | | | | | (214) ~ (all_137_2 = 0) | ~ (all_137_3 = 0) | ~ % 22.54/3.90 | | | | | | | | | | (all_137_4 = 0) | all_137_0 = all_35_3 % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | DELTA: instantiating (172) with fresh symbols all_139_0, % 22.54/3.90 | | | | | | | | | | all_139_1, all_139_2, all_139_3, all_139_4 gives: % 22.54/3.90 | | | | | | | | | | (215) sdtasdt0(all_86_0, xn) = all_139_1 & sdtasdt0(xl, % 22.54/3.90 | | | | | | | | | | all_139_1) = all_139_0 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(all_86_0) = all_139_3 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xn) = all_139_2 & % 22.54/3.90 | | | | | | | | | | aNaturalNumber0(xl) = all_139_4 & $i(all_139_0) & % 22.54/3.90 | | | | | | | | | | $i(all_139_1) & ( ~ (all_139_2 = 0) | ~ (all_139_3 % 22.54/3.90 | | | | | | | | | | = 0) | ~ (all_139_4 = 0) | all_139_0 = % 22.54/3.90 | | | | | | | | | | all_35_2) % 22.54/3.90 | | | | | | | | | | % 22.54/3.90 | | | | | | | | | | ALPHA: (215) implies: % 22.54/3.91 | | | | | | | | | | (216) $i(all_139_1) % 22.54/3.91 | | | | | | | | | | (217) $i(all_139_0) % 22.54/3.91 | | | | | | | | | | (218) aNaturalNumber0(xl) = all_139_4 % 22.54/3.91 | | | | | | | | | | (219) aNaturalNumber0(xn) = all_139_2 % 22.54/3.91 | | | | | | | | | | (220) aNaturalNumber0(all_86_0) = all_139_3 % 22.54/3.91 | | | | | | | | | | (221) sdtasdt0(xl, all_139_1) = all_139_0 % 22.54/3.91 | | | | | | | | | | (222) sdtasdt0(all_86_0, xn) = all_139_1 % 22.54/3.91 | | | | | | | | | | (223) ~ (all_139_2 = 0) | ~ (all_139_3 = 0) | ~ % 22.54/3.91 | | | | | | | | | | (all_139_4 = 0) | all_139_0 = all_35_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_135_2, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (2), (206) gives: % 22.54/3.91 | | | | | | | | | | (224) all_135_2 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_129_1, all_135_2, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (196), (206) gives: % 22.54/3.91 | | | | | | | | | | (225) all_135_2 = all_129_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_127_2, all_135_2, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (193), (206) gives: % 22.54/3.91 | | | | | | | | | | (226) all_135_2 = all_127_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_121_2, all_135_2, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (183), (206) gives: % 22.54/3.91 | | | | | | | | | | (227) all_135_2 = all_121_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_127_2, all_137_3, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (193), (209) gives: % 22.54/3.91 | | | | | | | | | | (228) all_137_3 = all_127_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_137_3, all_139_4, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (209), (218) gives: % 22.54/3.91 | | | | | | | | | | (229) all_139_4 = all_137_3 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_119_1, all_139_4, xl, % 22.54/3.91 | | | | | | | | | | simplifying with (181), (218) gives: % 22.54/3.91 | | | | | | | | | | (230) all_139_4 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_133_2, xn, % 22.54/3.91 | | | | | | | | | | simplifying with (6), (201) gives: % 22.54/3.91 | | | | | | | | | | (231) all_133_2 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_133_2, all_137_4, xn, % 22.54/3.91 | | | | | | | | | | simplifying with (201), (210) gives: % 22.54/3.91 | | | | | | | | | | (232) all_137_4 = all_133_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_137_4, all_139_2, xn, % 22.54/3.91 | | | | | | | | | | simplifying with (210), (219) gives: % 22.54/3.91 | | | | | | | | | | (233) all_139_2 = all_137_4 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_125_2, all_139_2, xn, % 22.54/3.91 | | | | | | | | | | simplifying with (188), (219) gives: % 22.54/3.91 | | | | | | | | | | (234) all_139_2 = all_125_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_131_2, all_133_1, % 22.54/3.91 | | | | | | | | | | all_35_4, simplifying with (199), (202) gives: % 22.54/3.91 | | | | | | | | | | (235) all_133_1 = all_131_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_123_2, all_133_1, % 22.54/3.91 | | | | | | | | | | all_35_4, simplifying with (186), (202) gives: % 22.54/3.91 | | | | | | | | | | (236) all_133_1 = all_123_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_42_1, all_137_2, % 22.54/3.91 | | | | | | | | | | all_35_4, simplifying with (39), (211) gives: % 22.54/3.91 | | | | | | | | | | (237) all_137_2 = all_42_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_131_2, all_137_2, % 22.54/3.91 | | | | | | | | | | all_35_4, simplifying with (199), (211) gives: % 22.54/3.91 | | | | | | | | | | (238) all_137_2 = all_131_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_125_1, all_137_2, % 22.54/3.91 | | | | | | | | | | all_35_4, simplifying with (189), (211) gives: % 22.54/3.91 | | | | | | | | | | (239) all_137_2 = all_125_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_125_0, all_127_1, % 22.54/3.91 | | | | | | | | | | all_58_1, simplifying with (190), (194) gives: % 22.54/3.91 | | | | | | | | | | (240) all_127_1 = all_125_0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_121_1, all_127_1, % 22.54/3.91 | | | | | | | | | | all_58_1, simplifying with (184), (194) gives: % 22.54/3.91 | | | | | | | | | | (241) all_127_1 = all_121_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_139_3, all_86_0, % 22.54/3.91 | | | | | | | | | | simplifying with (133), (220) gives: % 22.54/3.91 | | | | | | | | | | (242) all_139_3 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (11) with all_135_1, all_139_3, % 22.54/3.91 | | | | | | | | | | all_86_0, simplifying with (207), (220) gives: % 22.54/3.91 | | | | | | | | | | (243) all_139_3 = all_135_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | GROUND_INST: instantiating (12) with all_35_0, all_129_0, % 22.54/3.91 | | | | | | | | | | all_35_1, xl, simplifying with (21), (197) gives: % 22.54/3.91 | | | | | | | | | | (244) all_129_0 = all_35_0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (233), (234) imply: % 22.54/3.91 | | | | | | | | | | (245) all_137_4 = all_125_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (245) implies: % 22.54/3.91 | | | | | | | | | | (246) all_137_4 = all_125_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (242), (243) imply: % 22.54/3.91 | | | | | | | | | | (247) all_135_1 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (247) implies: % 22.54/3.91 | | | | | | | | | | (248) all_135_1 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (229), (230) imply: % 22.54/3.91 | | | | | | | | | | (249) all_137_3 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (249) implies: % 22.54/3.91 | | | | | | | | | | (250) all_137_3 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (238), (239) imply: % 22.54/3.91 | | | | | | | | | | (251) all_131_2 = all_125_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (251) implies: % 22.54/3.91 | | | | | | | | | | (252) all_131_2 = all_125_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (237), (239) imply: % 22.54/3.91 | | | | | | | | | | (253) all_125_1 = all_42_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (228), (250) imply: % 22.54/3.91 | | | | | | | | | | (254) all_127_2 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (254) implies: % 22.54/3.91 | | | | | | | | | | (255) all_127_2 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (232), (246) imply: % 22.54/3.91 | | | | | | | | | | (256) all_133_2 = all_125_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (256) implies: % 22.54/3.91 | | | | | | | | | | (257) all_133_2 = all_125_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (225), (226) imply: % 22.54/3.91 | | | | | | | | | | (258) all_129_1 = all_127_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (225), (227) imply: % 22.54/3.91 | | | | | | | | | | (259) all_129_1 = all_121_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (224), (225) imply: % 22.54/3.91 | | | | | | | | | | (260) all_129_1 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (235), (236) imply: % 22.54/3.91 | | | | | | | | | | (261) all_131_2 = all_123_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (261) implies: % 22.54/3.91 | | | | | | | | | | (262) all_131_2 = all_123_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (231), (257) imply: % 22.54/3.91 | | | | | | | | | | (263) all_125_2 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (252), (262) imply: % 22.54/3.91 | | | | | | | | | | (264) all_125_1 = all_123_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (264) implies: % 22.54/3.91 | | | | | | | | | | (265) all_125_1 = all_123_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (258), (259) imply: % 22.54/3.91 | | | | | | | | | | (266) all_127_2 = all_121_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (266) implies: % 22.54/3.91 | | | | | | | | | | (267) all_127_2 = all_121_2 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (259), (260) imply: % 22.54/3.91 | | | | | | | | | | (268) all_121_2 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (240), (241) imply: % 22.54/3.91 | | | | | | | | | | (269) all_125_0 = all_121_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (255), (267) imply: % 22.54/3.91 | | | | | | | | | | (270) all_121_2 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (270) implies: % 22.54/3.91 | | | | | | | | | | (271) all_121_2 = all_119_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (253), (265) imply: % 22.54/3.91 | | | | | | | | | | (272) all_123_2 = all_42_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (268), (271) imply: % 22.54/3.91 | | | | | | | | | | (273) all_119_1 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | SIMP: (273) implies: % 22.54/3.91 | | | | | | | | | | (274) all_119_1 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (236), (272) imply: % 22.54/3.91 | | | | | | | | | | (275) all_133_1 = all_42_1 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (246), (263) imply: % 22.54/3.91 | | | | | | | | | | (276) all_137_4 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (250), (274) imply: % 22.54/3.91 | | | | | | | | | | (277) all_137_3 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (230), (274) imply: % 22.54/3.91 | | | | | | | | | | (278) all_139_4 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | COMBINE_EQS: (234), (263) imply: % 22.54/3.91 | | | | | | | | | | (279) all_139_2 = 0 % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | BETA: splitting (170) gives: % 22.54/3.91 | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | Case 1: % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | (280) all_86_0 = all_35_4 % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | REDUCE: (222), (280) imply: % 22.54/3.91 | | | | | | | | | | | (281) sdtasdt0(all_35_4, xn) = all_139_1 % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | REDUCE: (134), (280) imply: % 22.54/3.91 | | | | | | | | | | | (282) sdtasdt0(xl, all_35_4) = xm % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | REDUCE: (133), (280) imply: % 22.54/3.91 | | | | | | | | | | | (283) aNaturalNumber0(all_35_4) = 0 % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | BETA: splitting (223) gives: % 22.54/3.91 | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | Case 1: % 22.54/3.91 | | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | | (284) ~ (all_139_2 = 0) % 22.54/3.91 | | | | | | | | | | | | % 22.54/3.91 | | | | | | | | | | | | REDUCE: (279), (284) imply: % 22.54/3.92 | | | | | | | | | | | | (285) $false % 22.54/3.92 | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | (286) ~ (all_139_3 = 0) | ~ (all_139_4 = 0) | % 22.54/3.92 | | | | | | | | | | | | all_139_0 = all_35_2 % 22.54/3.92 | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | BETA: splitting (286) gives: % 22.54/3.92 | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | (287) ~ (all_139_3 = 0) % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | REDUCE: (242), (287) imply: % 22.54/3.92 | | | | | | | | | | | | | (288) $false % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | (289) ~ (all_139_4 = 0) | all_139_0 = all_35_2 % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | BETA: splitting (289) gives: % 22.54/3.92 | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | (290) ~ (all_139_4 = 0) % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | REDUCE: (278), (290) imply: % 22.54/3.92 | | | | | | | | | | | | | | (291) $false % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | (292) all_139_0 = all_35_2 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | REDUCE: (221), (292) imply: % 22.54/3.92 | | | | | | | | | | | | | | (293) sdtasdt0(xl, all_139_1) = all_35_2 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_42_1, 0, all_35_4, % 22.54/3.92 | | | | | | | | | | | | | | simplifying with (39), (283) gives: % 22.54/3.92 | | | | | | | | | | | | | | (294) all_42_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_137_1, xm, all_35_4, % 22.54/3.92 | | | | | | | | | | | | | | xl, simplifying with (212), (282) gives: % 22.54/3.92 | | | | | | | | | | | | | | (295) all_137_1 = xm % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_133_0, all_139_1, xn, % 22.54/3.92 | | | | | | | | | | | | | | all_35_4, simplifying with (203), (281) gives: % 22.54/3.92 | | | | | | | | | | | | | | (296) all_139_1 = all_133_0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | COMBINE_EQS: (253), (294) imply: % 22.54/3.92 | | | | | | | | | | | | | | (297) all_125_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | COMBINE_EQS: (275), (294) imply: % 22.54/3.92 | | | | | | | | | | | | | | (298) all_133_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | COMBINE_EQS: (237), (294) imply: % 22.54/3.92 | | | | | | | | | | | | | | (299) all_137_2 = 0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | REDUCE: (213), (295) imply: % 22.54/3.92 | | | | | | | | | | | | | | (300) sdtasdt0(xn, xm) = all_137_0 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | REDUCE: (293), (296) imply: % 22.54/3.92 | | | | | | | | | | | | | | (301) sdtasdt0(xl, all_133_0) = all_35_2 % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | REDUCE: (216), (296) imply: % 22.54/3.92 | | | | | | | | | | | | | | (302) $i(all_133_0) % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | BETA: splitting (214) gives: % 22.54/3.92 | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | (303) ~ (all_137_2 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | REDUCE: (299), (303) imply: % 22.54/3.92 | | | | | | | | | | | | | | | (304) $false % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | (305) ~ (all_137_3 = 0) | ~ (all_137_4 = 0) | % 22.54/3.92 | | | | | | | | | | | | | | | all_137_0 = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 22.54/3.92 | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | (306) ~ (all_137_3 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | REDUCE: (277), (306) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | (307) $false % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | (308) ~ (all_137_4 = 0) | all_137_0 = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | (309) ~ (all_133_1 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | REDUCE: (298), (309) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | (310) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | (311) ~ (all_133_2 = 0) | all_133_0 = all_58_1 % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | (312) ~ (all_133_2 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | REDUCE: (231), (312) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | (313) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | (314) all_133_0 = all_58_1 % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | REDUCE: (301), (314) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | (315) sdtasdt0(xl, all_58_1) = all_35_2 % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | (316) ~ (all_125_1 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | REDUCE: (297), (316) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | (317) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | (318) ~ (all_125_2 = 0) | all_125_0 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (319) ~ (all_125_2 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (319) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (320) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | CLOSE: (320) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (321) all_125_0 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (321) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (322) all_121_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (323) all_121_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (323) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | (324) aNaturalNumber0(all_58_1) = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (325) ~ (all_137_4 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (276), (325) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (326) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | CLOSE: (326) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (327) all_137_0 = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (300), (327) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (328) sdtasdt0(xn, xm) = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_35_2, all_35_3, xm, % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | xn, simplifying with (22), (328) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (329) all_35_2 = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (315), (329) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (330) sdtasdt0(xl, all_58_1) = all_35_3 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (329) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (331) aNaturalNumber0(all_35_3) = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (329) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | (332) $i(all_35_3) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | (333) xl = sz00 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (333) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | (334) $false % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent. % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | (335) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xl, all_35_2) = v2 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_2) = v1 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: any] : (v0 = % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | all_35_1 | ~ (sdtasdt0(xl, v0) = all_35_2) | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(xl, all_35_1) = v0) | ~ % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | $i(all_35_1) | (v0 = all_35_2 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_1) = 0))) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (336) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xl, all_35_2) = v2 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_2) = v1 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (336) with fresh symbols all_264_0, % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | all_264_1, all_264_2 gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (337) doDivides0(xl, all_35_2) = all_264_0 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_2) = all_264_1 & % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_264_2 & ( ~ (all_264_0 = % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_264_1 = 0) | ~ (all_264_2 = 0)) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (338) aNaturalNumber0(xl) = all_264_2 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (339) aNaturalNumber0(all_35_2) = all_264_1 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (340) doDivides0(xl, all_35_2) = all_264_0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (341) ~ (all_264_0 = 0) | ~ (all_264_1 = 0) | ~ % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (all_264_2 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (340) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (342) doDivides0(xl, all_35_3) = all_264_0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (339) imply: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (343) aNaturalNumber0(all_35_3) = all_264_1 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_264_2, xl, % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (338) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (344) all_264_2 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_264_1, all_35_3, % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (331), (343) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | (345) all_264_1 = 0 % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_264_0 = 0) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mDefDiv) with xl, all_35_3, % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | all_264_0, simplifying with (7), (332), (342) % 22.54/3.92 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | (347) ? [v0: any] : ? [v1: any] : % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_35_3) = v1 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | = 0))) | (( ~ (all_264_0 = 0) | ? [v0: $i] % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | : (sdtasdt0(xl, v0) = all_35_3 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))) & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | (all_264_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | v0) = all_35_3) | ~ $i(v0) | ? [v1: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | = v1)))) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (348) ? [v0: any] : ? [v1: any] : % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_35_3) = v1 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | = 0))) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (348) with fresh symbols all_307_0, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | all_307_1 gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (349) aNaturalNumber0(all_35_3) = all_307_0 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_307_1 & ( ~ (all_307_0 = % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_307_1 = 0)) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (350) aNaturalNumber0(xl) = all_307_1 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (351) aNaturalNumber0(all_35_3) = all_307_0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_307_0 = 0) | ~ (all_307_1 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_307_1, xl, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (350) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_307_1 = 0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_307_0, all_35_3, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (331), (351) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_307_0 = 0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (355) ~ (all_307_0 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (355) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (356) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) ~ (all_307_1 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (353), (357) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (359) ( ~ (all_264_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | v0) = all_35_3 & aNaturalNumber0(v0) = 0 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0))) & (all_264_0 = 0 | ! [v0: $i] : ( ~ % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(xl, v0) = all_35_3) | ~ $i(v0) | ? % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | = v1))) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_264_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | v0) = all_35_3) | ~ $i(v0) | ? [v1: int] : % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_264_0 = 0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (361) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = all_35_3) | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (363) with all_58_1, simplifying % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | with (68), (330) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ? [v0: int] : ( ~ (v0 = 0) & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_58_1) = v0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (364) with fresh symbol all_314_0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_314_0 = 0) & aNaturalNumber0(all_58_1) = % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | all_314_0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) ~ (all_314_0 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) aNaturalNumber0(all_58_1) = all_314_0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_314_0, all_58_1, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (324), (367) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_314_0 = 0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (368) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | (370) ~ (all_264_1 = 0) | ~ (all_264_2 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_264_1 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (371) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (372) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_264_2 = 0) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (373) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | (374) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (375) ! [v0: any] : (v0 = all_35_1 | ~ (sdtasdt0(xl, % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | v0) = all_35_2) | ~ $i(v0) | ? [v1: int] : % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xl, all_35_1) = v0) | ~ % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | $i(all_35_1) | (v0 = all_35_2 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_1) = 0)) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (376) ! [v0: $i] : ( ~ (sdtasdt0(xl, all_35_1) = v0) | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | ~ $i(all_35_1) | (v0 = all_35_2 & % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_35_1) = 0)) % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (376) with all_35_0, simplifying % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | with (19), (21) gives: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (377) all_35_0 = all_35_2 & aNaturalNumber0(all_35_1) = % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | 0 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (378) all_35_0 = all_35_2 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (378) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (379) all_35_0 = all_35_3 % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (379) imply: % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | (380) $false % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (380) is inconsistent. % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | Case 2: % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | (381) ? [v0: int] : ( ~ (v0 = 0) & % 22.54/3.93 | | | | | | | | | | | aNaturalNumber0(all_86_0) = v0) % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | DELTA: instantiating (381) with fresh symbol all_149_0 % 22.54/3.93 | | | | | | | | | | | gives: % 22.54/3.93 | | | | | | | | | | | (382) ~ (all_149_0 = 0) & aNaturalNumber0(all_86_0) = % 22.54/3.93 | | | | | | | | | | | all_149_0 % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | ALPHA: (382) implies: % 22.54/3.93 | | | | | | | | | | | (383) ~ (all_149_0 = 0) % 22.54/3.93 | | | | | | | | | | | (384) aNaturalNumber0(all_86_0) = all_149_0 % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_149_0, all_86_0, % 22.54/3.93 | | | | | | | | | | | simplifying with (133), (384) gives: % 22.54/3.93 | | | | | | | | | | | (385) all_149_0 = 0 % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | REDUCE: (383), (385) imply: % 22.54/3.93 | | | | | | | | | | | (386) $false % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | | CLOSE: (386) is inconsistent. % 22.54/3.93 | | | | | | | | | | | % 22.54/3.93 | | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | | % 22.54/3.93 | | | | | | | | | End of split % 22.54/3.93 | | | | | | | | | % 22.54/3.93 | | | | | | | | End of split % 22.54/3.93 | | | | | | | | % 22.54/3.93 | | | | | | | End of split % 22.54/3.93 | | | | | | | % 22.54/3.93 | | | | | | End of split % 22.54/3.93 | | | | | | % 22.54/3.93 | | | | | End of split % 22.54/3.93 | | | | | % 22.54/3.93 | | | | End of split % 22.54/3.93 | | | | % 22.54/3.93 | | | End of split % 22.54/3.93 | | | % 22.54/3.93 | | End of split % 22.54/3.93 | | % 22.54/3.93 | End of split % 22.54/3.93 | % 22.54/3.93 End of proof % 22.54/3.93 % SZS output end Proof for theBenchmark % 22.54/3.94 % 22.54/3.94 3329ms %------------------------------------------------------------------------------