%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM469+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 : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:47:57 EDT 2023 % Result : Theorem 11.02s 2.20s % Output : Proof 18.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM469+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 08:31:32 EDT 2023 % 0.20/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.03/1.12 Prover 4: Preprocessing ... % 3.03/1.12 Prover 1: Preprocessing ... % 3.03/1.16 Prover 3: Preprocessing ... % 3.03/1.16 Prover 5: Preprocessing ... % 3.03/1.16 Prover 0: Preprocessing ... % 3.03/1.16 Prover 6: Preprocessing ... % 3.03/1.17 Prover 2: Preprocessing ... % 7.48/1.76 Prover 3: Constructing countermodel ... % 7.48/1.77 Prover 1: Constructing countermodel ... % 8.11/1.87 Prover 6: Proving ... % 8.80/1.89 Prover 5: Constructing countermodel ... % 9.39/2.02 Prover 2: Proving ... % 10.39/2.15 Prover 4: Constructing countermodel ... % 11.02/2.20 Prover 3: proved (1552ms) % 11.02/2.20 % 11.02/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.02/2.20 % 11.02/2.20 Prover 5: stopped % 11.02/2.21 Prover 2: stopped % 11.02/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.02/2.21 Prover 6: stopped % 11.02/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.02/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.02/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.02/2.24 Prover 0: Proving ... % 11.02/2.26 Prover 0: stopped % 11.02/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.89/2.31 Prover 8: Preprocessing ... % 11.95/2.32 Prover 7: Preprocessing ... % 11.95/2.32 Prover 10: Preprocessing ... % 11.95/2.33 Prover 11: Preprocessing ... % 11.95/2.36 Prover 13: Preprocessing ... % 12.66/2.48 Prover 10: Constructing countermodel ... % 13.31/2.53 Prover 8: Warning: ignoring some quantifiers % 13.31/2.55 Prover 8: Constructing countermodel ... % 14.03/2.59 Prover 7: Constructing countermodel ... % 14.03/2.60 Prover 13: Constructing countermodel ... % 14.95/2.81 Prover 11: Constructing countermodel ... % 17.30/3.03 Prover 1: Found proof (size 276) % 17.30/3.03 Prover 1: proved (2391ms) % 17.30/3.03 Prover 10: stopped % 17.30/3.03 Prover 13: stopped % 17.30/3.03 Prover 11: stopped % 17.30/3.03 Prover 4: stopped % 17.30/3.03 Prover 7: stopped % 17.30/3.03 Prover 8: stopped % 17.30/3.03 % 17.30/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.30/3.03 % 17.30/3.06 % SZS output start Proof for theBenchmark % 17.30/3.07 Assumptions after simplification: % 17.30/3.07 --------------------------------- % 17.30/3.07 % 17.30/3.07 (mAMDistr) % 17.30/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.30/3.09 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 17.30/3.09 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 17.30/3.09 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 17.30/3.09 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v9, v0) = v11 & % 17.30/3.09 sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & % 17.30/3.09 sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = % 17.30/3.09 v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & $i(v14) & % 17.30/3.09 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = % 17.30/3.09 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) % 17.30/3.09 % 17.30/3.09 (mAddComm) % 17.30/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 17.30/3.10 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 17.30/3.10 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 17.30/3.10 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 17.30/3.10 % 17.30/3.10 (mDefDiv) % 17.30/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 17.30/3.10 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 17.30/3.10 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 17.30/3.10 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 17.30/3.10 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 17.30/3.10 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 17.30/3.10 % 17.30/3.10 (mDivTrans) % 17.30/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.30/3.10 (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ~ $i(v2) | ~ % 17.30/3.10 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 17.30/3.10 any] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & % 17.30/3.10 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ % 17.30/3.10 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 17.30/3.10 % 17.30/3.10 (mMulComm) % 17.30/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 17.30/3.10 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 17.30/3.10 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 17.30/3.10 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 17.30/3.10 % 17.30/3.10 (mSortsB) % 17.30/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 17.30/3.10 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 17.30/3.10 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 17.30/3.11 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 17.30/3.11 % 17.30/3.11 (mSortsB_02) % 17.30/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 17.30/3.11 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 17.30/3.11 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 17.30/3.11 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 17.30/3.11 % 17.30/3.11 (m__) % 17.79/3.11 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 17.79/3.11 doDivides0(xl, v0) = v1 & sdtpldt0(xm, xn) = v0 & $i(v0)) % 17.79/3.11 % 17.79/3.11 (m__1240) % 17.79/3.11 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & % 17.79/3.11 $i(xn) & $i(xm) & $i(xl) % 17.79/3.11 % 17.79/3.11 (m__1240_04) % 17.79/3.11 doDivides0(xl, xn) = 0 & doDivides0(xl, xm) = 0 & $i(xn) & $i(xm) & $i(xl) % 17.79/3.11 % 17.79/3.11 (m__1298) % 17.79/3.11 $i(xn) & $i(xm) & $i(xl) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 17.79/3.11 : ? [v3: $i] : ? [v4: $i] : (sdtsldt0(xn, xl) = v2 & sdtsldt0(xm, xl) = v1 & % 17.79/3.11 sdtasdt0(xl, v3) = v4 & sdtpldt0(v1, v2) = v3 & sdtpldt0(xm, xn) = v0 & % 17.79/3.11 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = v0 | xl = sz00)) % 17.79/3.11 % 17.79/3.11 (function-axioms) % 17.79/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.79/3.11 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 17.79/3.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.79/3.11 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 17.79/3.11 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.79/3.11 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 17.79/3.11 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.79/3.11 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 17.79/3.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.79/3.11 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 17.79/3.11 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.79/3.11 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 17.79/3.11 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 17.79/3.11 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.79/3.11 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 17.79/3.11 | ~ (aNaturalNumber0(v2) = v0)) % 17.79/3.11 % 17.79/3.11 Further assumptions not needed in the proof: % 17.79/3.11 -------------------------------------------- % 17.79/3.12 mAddAsso, mAddCanc, mDefDiff, mDefLE, mDefQuot, mIH, mIH_03, mLEAsym, mLENTr, % 17.79/3.12 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, % 17.79/3.12 mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, % 17.79/3.12 m_MulZero % 17.79/3.12 % 17.79/3.12 Those formulas are unsatisfiable: % 17.79/3.12 --------------------------------- % 17.79/3.12 % 17.79/3.12 Begin of proof % 17.79/3.12 | % 17.79/3.12 | ALPHA: (m__1240) implies: % 17.79/3.12 | (1) aNaturalNumber0(xl) = 0 % 17.79/3.12 | (2) aNaturalNumber0(xm) = 0 % 17.79/3.12 | (3) aNaturalNumber0(xn) = 0 % 17.79/3.12 | % 17.79/3.12 | ALPHA: (m__1240_04) implies: % 17.79/3.12 | (4) doDivides0(xl, xm) = 0 % 17.79/3.12 | (5) doDivides0(xl, xn) = 0 % 17.79/3.12 | % 17.79/3.12 | ALPHA: (m__1298) implies: % 17.79/3.12 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.79/3.12 | (sdtsldt0(xn, xl) = v2 & sdtsldt0(xm, xl) = v1 & sdtasdt0(xl, v3) = v4 % 17.79/3.12 | & sdtpldt0(v1, v2) = v3 & sdtpldt0(xm, xn) = v0 & $i(v4) & $i(v3) & % 17.79/3.12 | $i(v2) & $i(v1) & $i(v0) & (v4 = v0 | xl = sz00)) % 17.79/3.12 | % 17.79/3.12 | ALPHA: (m__) implies: % 17.79/3.12 | (7) $i(xl) % 17.79/3.12 | (8) $i(xm) % 17.79/3.12 | (9) $i(xn) % 17.79/3.12 | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & doDivides0(xl, v0) = v1 & % 17.79/3.12 | sdtpldt0(xm, xn) = v0 & $i(v0)) % 17.79/3.12 | % 17.79/3.12 | ALPHA: (function-axioms) implies: % 17.79/3.12 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.79/3.12 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 17.79/3.12 | v0)) % 17.79/3.12 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.79/3.12 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 17.79/3.12 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.79/3.12 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 17.79/3.12 | % 17.79/3.12 | DELTA: instantiating (10) with fresh symbols all_32_0, all_32_1 gives: % 17.79/3.12 | (14) ~ (all_32_0 = 0) & doDivides0(xl, all_32_1) = all_32_0 & sdtpldt0(xm, % 17.79/3.12 | xn) = all_32_1 & $i(all_32_1) % 17.79/3.12 | % 17.79/3.12 | ALPHA: (14) implies: % 17.79/3.12 | (15) ~ (all_32_0 = 0) % 17.79/3.12 | (16) sdtpldt0(xm, xn) = all_32_1 % 17.79/3.12 | (17) doDivides0(xl, all_32_1) = all_32_0 % 17.79/3.12 | % 17.79/3.12 | DELTA: instantiating (6) with fresh symbols all_34_0, all_34_1, all_34_2, % 17.79/3.12 | all_34_3, all_34_4 gives: % 17.79/3.13 | (18) sdtsldt0(xn, xl) = all_34_2 & sdtsldt0(xm, xl) = all_34_3 & % 17.79/3.13 | sdtasdt0(xl, all_34_1) = all_34_0 & sdtpldt0(all_34_3, all_34_2) = % 17.79/3.13 | all_34_1 & sdtpldt0(xm, xn) = all_34_4 & $i(all_34_0) & $i(all_34_1) & % 17.79/3.13 | $i(all_34_2) & $i(all_34_3) & $i(all_34_4) & (all_34_0 = all_34_4 | xl % 17.79/3.13 | = sz00) % 17.79/3.13 | % 17.79/3.13 | ALPHA: (18) implies: % 17.79/3.13 | (19) $i(all_34_4) % 17.79/3.13 | (20) $i(all_34_1) % 17.79/3.13 | (21) sdtpldt0(xm, xn) = all_34_4 % 17.79/3.13 | (22) sdtasdt0(xl, all_34_1) = all_34_0 % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (12) with all_32_1, all_34_4, xn, xm, simplifying % 17.79/3.13 | with (16), (21) gives: % 17.79/3.13 | (23) all_34_4 = all_32_1 % 17.79/3.13 | % 17.79/3.13 | REDUCE: (19), (23) imply: % 17.79/3.13 | (24) $i(all_32_1) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mAddComm) with xm, xn, all_32_1, simplifying with % 17.79/3.13 | (8), (9), (16) gives: % 17.79/3.13 | (25) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xn, xm) = v2 & % 17.79/3.13 | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ % 17.79/3.13 | (v1 = 0) | ~ (v0 = 0) | v2 = all_32_1)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mSortsB) with xm, xn, all_32_1, simplifying with % 17.79/3.13 | (8), (9), (16) gives: % 17.79/3.13 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 17.79/3.13 | (aNaturalNumber0(all_32_1) = v2 & aNaturalNumber0(xn) = v1 & % 17.79/3.13 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mMulComm) with xl, all_34_1, all_34_0, simplifying % 17.79/3.13 | with (7), (20), (22) gives: % 17.79/3.13 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_34_1, xl) = % 17.79/3.13 | v2 & aNaturalNumber0(all_34_1) = v1 & aNaturalNumber0(xl) = v0 & % 17.79/3.13 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_34_0)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mSortsB_02) with xl, all_34_1, all_34_0, % 17.79/3.13 | simplifying with (7), (20), (22) gives: % 17.79/3.13 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 17.79/3.13 | (aNaturalNumber0(all_34_0) = v2 & aNaturalNumber0(all_34_1) = v1 & % 17.79/3.13 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (4), % 17.79/3.13 | (7), (8) gives: % 17.79/3.13 | (29) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 17.79/3.13 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 17.79/3.13 | $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mDefDiv) with xl, xn, 0, simplifying with (5), % 17.79/3.13 | (7), (9) gives: % 17.79/3.13 | (30) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 17.79/3.13 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 17.79/3.13 | $i] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 17.79/3.13 | % 17.79/3.13 | GROUND_INST: instantiating (mDivTrans) with xl, xn, all_32_1, all_32_0, % 17.79/3.13 | simplifying with (5), (7), (9), (17), (24) gives: % 17.79/3.14 | (31) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 17.79/3.14 | any] : (doDivides0(xn, all_32_1) = v3 & aNaturalNumber0(all_32_1) = % 17.79/3.14 | v2 & aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = % 17.79/3.14 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.14 | % 17.79/3.14 | GROUND_INST: instantiating (mDivTrans) with xl, xm, all_32_1, all_32_0, % 17.79/3.14 | simplifying with (4), (7), (8), (17), (24) gives: % 17.79/3.14 | (32) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 17.79/3.14 | any] : (doDivides0(xm, all_32_1) = v3 & aNaturalNumber0(all_32_1) = % 17.79/3.14 | v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = % 17.79/3.14 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.14 | % 17.79/3.14 | GROUND_INST: instantiating (mDefDiv) with xl, all_32_1, all_32_0, simplifying % 17.79/3.14 | with (7), (17), (24) gives: % 17.79/3.14 | (33) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_32_1) = v1 & % 17.79/3.14 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~ % 17.79/3.14 | (all_32_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) = all_32_1 & % 17.79/3.14 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_32_0 = 0 | ! [v0: $i] % 17.79/3.14 | : ( ~ (sdtasdt0(xl, v0) = all_32_1) | ~ $i(v0) | ? [v1: int] : ( % 17.79/3.14 | ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))) % 17.79/3.14 | % 17.79/3.14 | DELTA: instantiating (28) with fresh symbols all_45_0, all_45_1, all_45_2 % 17.79/3.14 | gives: % 17.79/3.14 | (34) aNaturalNumber0(all_34_0) = all_45_0 & aNaturalNumber0(all_34_1) = % 17.79/3.14 | all_45_1 & aNaturalNumber0(xl) = all_45_2 & ( ~ (all_45_1 = 0) | ~ % 17.79/3.14 | (all_45_2 = 0) | all_45_0 = 0) % 17.79/3.14 | % 17.79/3.14 | ALPHA: (34) implies: % 17.79/3.14 | (35) aNaturalNumber0(xl) = all_45_2 % 17.79/3.14 | % 17.79/3.14 | DELTA: instantiating (26) with fresh symbols all_49_0, all_49_1, all_49_2 % 17.79/3.14 | gives: % 17.79/3.14 | (36) aNaturalNumber0(all_32_1) = all_49_0 & aNaturalNumber0(xn) = all_49_1 % 17.79/3.14 | & aNaturalNumber0(xm) = all_49_2 & ( ~ (all_49_1 = 0) | ~ (all_49_2 = % 17.79/3.14 | 0) | all_49_0 = 0) % 17.79/3.14 | % 17.79/3.14 | ALPHA: (36) implies: % 17.79/3.14 | (37) aNaturalNumber0(xm) = all_49_2 % 17.79/3.14 | (38) aNaturalNumber0(xn) = all_49_1 % 17.79/3.14 | (39) aNaturalNumber0(all_32_1) = all_49_0 % 17.79/3.14 | (40) ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | all_49_0 = 0 % 17.79/3.14 | % 17.79/3.14 | DELTA: instantiating (27) with fresh symbols all_53_0, all_53_1, all_53_2 % 17.79/3.14 | gives: % 17.79/3.14 | (41) sdtasdt0(all_34_1, xl) = all_53_0 & aNaturalNumber0(all_34_1) = % 17.79/3.14 | all_53_1 & aNaturalNumber0(xl) = all_53_2 & $i(all_53_0) & ( ~ % 17.79/3.14 | (all_53_1 = 0) | ~ (all_53_2 = 0) | all_53_0 = all_34_0) % 17.79/3.14 | % 17.79/3.14 | ALPHA: (41) implies: % 17.79/3.14 | (42) aNaturalNumber0(xl) = all_53_2 % 17.79/3.14 | (43) sdtasdt0(all_34_1, xl) = all_53_0 % 17.79/3.14 | % 17.79/3.14 | DELTA: instantiating (25) with fresh symbols all_55_0, all_55_1, all_55_2 % 17.79/3.14 | gives: % 17.79/3.14 | (44) sdtpldt0(xn, xm) = all_55_0 & aNaturalNumber0(xn) = all_55_1 & % 17.79/3.14 | aNaturalNumber0(xm) = all_55_2 & $i(all_55_0) & ( ~ (all_55_1 = 0) | % 17.79/3.14 | ~ (all_55_2 = 0) | all_55_0 = all_32_1) % 17.79/3.14 | % 17.79/3.14 | ALPHA: (44) implies: % 17.79/3.14 | (45) aNaturalNumber0(xm) = all_55_2 % 17.79/3.14 | (46) aNaturalNumber0(xn) = all_55_1 % 17.79/3.14 | (47) sdtpldt0(xn, xm) = all_55_0 % 17.79/3.14 | (48) ~ (all_55_1 = 0) | ~ (all_55_2 = 0) | all_55_0 = all_32_1 % 17.79/3.14 | % 17.79/3.14 | BETA: splitting (32) gives: % 17.79/3.14 | % 17.79/3.14 | Case 1: % 17.79/3.14 | | % 17.79/3.14 | | (49) all_32_0 = 0 % 17.79/3.14 | | % 17.79/3.14 | | REDUCE: (15), (49) imply: % 17.79/3.14 | | (50) $false % 17.79/3.15 | | % 17.79/3.15 | | CLOSE: (50) is inconsistent. % 17.79/3.15 | | % 17.79/3.15 | Case 2: % 17.79/3.15 | | % 17.79/3.15 | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 17.79/3.15 | | (doDivides0(xm, all_32_1) = v3 & aNaturalNumber0(all_32_1) = v2 & % 17.79/3.15 | | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = 0) % 17.79/3.15 | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.15 | | % 17.79/3.15 | | DELTA: instantiating (51) with fresh symbols all_65_0, all_65_1, all_65_2, % 17.79/3.15 | | all_65_3 gives: % 17.79/3.15 | | (52) doDivides0(xm, all_32_1) = all_65_0 & aNaturalNumber0(all_32_1) = % 17.79/3.15 | | all_65_1 & aNaturalNumber0(xm) = all_65_2 & aNaturalNumber0(xl) = % 17.79/3.15 | | all_65_3 & ( ~ (all_65_0 = 0) | ~ (all_65_1 = 0) | ~ (all_65_2 = % 17.79/3.15 | | 0) | ~ (all_65_3 = 0)) % 17.79/3.15 | | % 17.79/3.15 | | ALPHA: (52) implies: % 17.79/3.15 | | (53) aNaturalNumber0(xl) = all_65_3 % 17.79/3.15 | | (54) aNaturalNumber0(xm) = all_65_2 % 17.79/3.15 | | (55) aNaturalNumber0(all_32_1) = all_65_1 % 17.79/3.15 | | % 17.79/3.15 | | BETA: splitting (31) gives: % 17.79/3.15 | | % 17.79/3.15 | | Case 1: % 17.79/3.15 | | | % 17.79/3.15 | | | (56) all_32_0 = 0 % 17.79/3.15 | | | % 17.79/3.15 | | | REDUCE: (15), (56) imply: % 17.79/3.15 | | | (57) $false % 17.79/3.15 | | | % 17.79/3.15 | | | CLOSE: (57) is inconsistent. % 17.79/3.15 | | | % 17.79/3.15 | | Case 2: % 17.79/3.15 | | | % 17.79/3.15 | | | (58) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 17.79/3.15 | | | (doDivides0(xn, all_32_1) = v3 & aNaturalNumber0(all_32_1) = v2 & % 17.79/3.15 | | | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xl) = v0 & ( ~ (v3 = % 17.79/3.15 | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.15 | | | % 17.79/3.15 | | | DELTA: instantiating (58) with fresh symbols all_70_0, all_70_1, all_70_2, % 17.79/3.15 | | | all_70_3 gives: % 17.79/3.15 | | | (59) doDivides0(xn, all_32_1) = all_70_0 & aNaturalNumber0(all_32_1) = % 17.79/3.15 | | | all_70_1 & aNaturalNumber0(xn) = all_70_2 & aNaturalNumber0(xl) = % 17.79/3.15 | | | all_70_3 & ( ~ (all_70_0 = 0) | ~ (all_70_1 = 0) | ~ (all_70_2 = % 17.79/3.15 | | | 0) | ~ (all_70_3 = 0)) % 17.79/3.15 | | | % 17.79/3.15 | | | ALPHA: (59) implies: % 17.79/3.15 | | | (60) aNaturalNumber0(xl) = all_70_3 % 17.79/3.15 | | | (61) aNaturalNumber0(xn) = all_70_2 % 17.79/3.15 | | | (62) aNaturalNumber0(all_32_1) = all_70_1 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with 0, all_53_2, xl, simplifying with % 17.79/3.15 | | | (1), (42) gives: % 17.79/3.15 | | | (63) all_53_2 = 0 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_53_2, all_65_3, xl, simplifying % 17.79/3.15 | | | with (42), (53) gives: % 17.79/3.15 | | | (64) all_65_3 = all_53_2 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_65_3, all_70_3, xl, simplifying % 17.79/3.15 | | | with (53), (60) gives: % 17.79/3.15 | | | (65) all_70_3 = all_65_3 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_45_2, all_70_3, xl, simplifying % 17.79/3.15 | | | with (35), (60) gives: % 17.79/3.15 | | | (66) all_70_3 = all_45_2 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with 0, all_55_2, xm, simplifying with % 17.79/3.15 | | | (2), (45) gives: % 17.79/3.15 | | | (67) all_55_2 = 0 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_55_2, all_65_2, xm, simplifying % 17.79/3.15 | | | with (45), (54) gives: % 17.79/3.15 | | | (68) all_65_2 = all_55_2 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_49_2, all_65_2, xm, simplifying % 17.79/3.15 | | | with (37), (54) gives: % 17.79/3.15 | | | (69) all_65_2 = all_49_2 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_49_1, all_55_1, xn, simplifying % 17.79/3.15 | | | with (38), (46) gives: % 17.79/3.15 | | | (70) all_55_1 = all_49_1 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with 0, all_70_2, xn, simplifying with % 17.79/3.15 | | | (3), (61) gives: % 17.79/3.15 | | | (71) all_70_2 = 0 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_55_1, all_70_2, xn, simplifying % 17.79/3.15 | | | with (46), (61) gives: % 17.79/3.15 | | | (72) all_70_2 = all_55_1 % 17.79/3.15 | | | % 17.79/3.15 | | | GROUND_INST: instantiating (11) with all_65_1, all_70_1, all_32_1, % 17.79/3.16 | | | simplifying with (55), (62) gives: % 17.79/3.16 | | | (73) all_70_1 = all_65_1 % 17.79/3.16 | | | % 17.79/3.16 | | | GROUND_INST: instantiating (11) with all_49_0, all_70_1, all_32_1, % 17.79/3.16 | | | simplifying with (39), (62) gives: % 17.79/3.16 | | | (74) all_70_1 = all_49_0 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (73), (74) imply: % 17.79/3.16 | | | (75) all_65_1 = all_49_0 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (71), (72) imply: % 17.79/3.16 | | | (76) all_55_1 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | SIMP: (76) implies: % 17.79/3.16 | | | (77) all_55_1 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (65), (66) imply: % 17.79/3.16 | | | (78) all_65_3 = all_45_2 % 17.79/3.16 | | | % 17.79/3.16 | | | SIMP: (78) implies: % 17.79/3.16 | | | (79) all_65_3 = all_45_2 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (68), (69) imply: % 17.79/3.16 | | | (80) all_55_2 = all_49_2 % 17.79/3.16 | | | % 17.79/3.16 | | | SIMP: (80) implies: % 17.79/3.16 | | | (81) all_55_2 = all_49_2 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (64), (79) imply: % 17.79/3.16 | | | (82) all_53_2 = all_45_2 % 17.79/3.16 | | | % 17.79/3.16 | | | SIMP: (82) implies: % 17.79/3.16 | | | (83) all_53_2 = all_45_2 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (70), (77) imply: % 17.79/3.16 | | | (84) all_49_1 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | SIMP: (84) implies: % 17.79/3.16 | | | (85) all_49_1 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (67), (81) imply: % 17.79/3.16 | | | (86) all_49_2 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | COMBINE_EQS: (63), (83) imply: % 17.79/3.16 | | | (87) all_45_2 = 0 % 17.79/3.16 | | | % 17.79/3.16 | | | BETA: splitting (40) gives: % 17.79/3.16 | | | % 17.79/3.16 | | | Case 1: % 17.79/3.16 | | | | % 17.79/3.16 | | | | (88) ~ (all_49_1 = 0) % 17.79/3.16 | | | | % 17.79/3.16 | | | | REDUCE: (85), (88) imply: % 17.79/3.16 | | | | (89) $false % 17.79/3.16 | | | | % 17.79/3.16 | | | | CLOSE: (89) is inconsistent. % 17.79/3.16 | | | | % 17.79/3.16 | | | Case 2: % 17.79/3.16 | | | | % 17.79/3.16 | | | | (90) ~ (all_49_2 = 0) | all_49_0 = 0 % 17.79/3.16 | | | | % 17.79/3.16 | | | | BETA: splitting (30) gives: % 17.79/3.16 | | | | % 17.79/3.16 | | | | Case 1: % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | (91) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 17.79/3.16 | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | DELTA: instantiating (91) with fresh symbols all_82_0, all_82_1 gives: % 17.79/3.16 | | | | | (92) aNaturalNumber0(xn) = all_82_0 & aNaturalNumber0(xl) = % 17.79/3.16 | | | | | all_82_1 & ( ~ (all_82_0 = 0) | ~ (all_82_1 = 0)) % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | ALPHA: (92) implies: % 17.79/3.16 | | | | | (93) aNaturalNumber0(xl) = all_82_1 % 17.79/3.16 | | | | | (94) aNaturalNumber0(xn) = all_82_0 % 17.79/3.16 | | | | | (95) ~ (all_82_0 = 0) | ~ (all_82_1 = 0) % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | GROUND_INST: instantiating (11) with 0, all_82_1, xl, simplifying with % 17.79/3.16 | | | | | (1), (93) gives: % 17.79/3.16 | | | | | (96) all_82_1 = 0 % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | GROUND_INST: instantiating (11) with 0, all_82_0, xn, simplifying with % 17.79/3.16 | | | | | (3), (94) gives: % 17.79/3.16 | | | | | (97) all_82_0 = 0 % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | BETA: splitting (95) gives: % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | Case 1: % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | (98) ~ (all_82_0 = 0) % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | REDUCE: (97), (98) imply: % 17.79/3.16 | | | | | | (99) $false % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | CLOSE: (99) is inconsistent. % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | Case 2: % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | (100) ~ (all_82_1 = 0) % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | REDUCE: (96), (100) imply: % 17.79/3.16 | | | | | | (101) $false % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | CLOSE: (101) is inconsistent. % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | End of split % 17.79/3.16 | | | | | % 17.79/3.16 | | | | Case 2: % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | (102) ? [v0: $i] : (sdtasdt0(xl, v0) = xn & aNaturalNumber0(v0) = % 17.79/3.16 | | | | | 0 & $i(v0)) % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | DELTA: instantiating (102) with fresh symbol all_82_0 gives: % 17.79/3.16 | | | | | (103) sdtasdt0(xl, all_82_0) = xn & aNaturalNumber0(all_82_0) = 0 & % 17.79/3.16 | | | | | $i(all_82_0) % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | ALPHA: (103) implies: % 17.79/3.16 | | | | | (104) $i(all_82_0) % 17.79/3.16 | | | | | (105) aNaturalNumber0(all_82_0) = 0 % 17.79/3.16 | | | | | (106) sdtasdt0(xl, all_82_0) = xn % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | BETA: splitting (48) gives: % 17.79/3.16 | | | | | % 17.79/3.16 | | | | | Case 1: % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | (107) ~ (all_55_1 = 0) % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | REDUCE: (77), (107) imply: % 17.79/3.16 | | | | | | (108) $false % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | CLOSE: (108) is inconsistent. % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | Case 2: % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | (109) ~ (all_55_2 = 0) | all_55_0 = all_32_1 % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | BETA: splitting (29) gives: % 17.79/3.16 | | | | | | % 17.79/3.16 | | | | | | Case 1: % 17.79/3.16 | | | | | | | % 17.79/3.16 | | | | | | | (110) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 17.79/3.16 | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.16 | | | | | | | % 17.79/3.17 | | | | | | | DELTA: instantiating (110) with fresh symbols all_90_0, all_90_1 % 17.79/3.17 | | | | | | | gives: % 17.79/3.17 | | | | | | | (111) aNaturalNumber0(xm) = all_90_0 & aNaturalNumber0(xl) = % 17.79/3.17 | | | | | | | all_90_1 & ( ~ (all_90_0 = 0) | ~ (all_90_1 = 0)) % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | ALPHA: (111) implies: % 17.79/3.17 | | | | | | | (112) aNaturalNumber0(xl) = all_90_1 % 17.79/3.17 | | | | | | | (113) aNaturalNumber0(xm) = all_90_0 % 17.79/3.17 | | | | | | | (114) ~ (all_90_0 = 0) | ~ (all_90_1 = 0) % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | GROUND_INST: instantiating (11) with 0, all_90_1, xl, simplifying % 17.79/3.17 | | | | | | | with (1), (112) gives: % 17.79/3.17 | | | | | | | (115) all_90_1 = 0 % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | GROUND_INST: instantiating (11) with 0, all_90_0, xm, simplifying % 17.79/3.17 | | | | | | | with (2), (113) gives: % 17.79/3.17 | | | | | | | (116) all_90_0 = 0 % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | BETA: splitting (114) gives: % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | (117) ~ (all_90_0 = 0) % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | REDUCE: (116), (117) imply: % 17.79/3.17 | | | | | | | | (118) $false % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | CLOSE: (118) is inconsistent. % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | (119) ~ (all_90_1 = 0) % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | REDUCE: (115), (119) imply: % 17.79/3.17 | | | | | | | | (120) $false % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | CLOSE: (120) is inconsistent. % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | End of split % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | Case 2: % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | (121) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & % 17.79/3.17 | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | DELTA: instantiating (121) with fresh symbol all_90_0 gives: % 17.79/3.17 | | | | | | | (122) sdtasdt0(xl, all_90_0) = xm & aNaturalNumber0(all_90_0) = % 17.79/3.17 | | | | | | | 0 & $i(all_90_0) % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | ALPHA: (122) implies: % 17.79/3.17 | | | | | | | (123) $i(all_90_0) % 17.79/3.17 | | | | | | | (124) aNaturalNumber0(all_90_0) = 0 % 17.79/3.17 | | | | | | | (125) sdtasdt0(xl, all_90_0) = xm % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | BETA: splitting (90) gives: % 17.79/3.17 | | | | | | | % 17.79/3.17 | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | (126) ~ (all_49_2 = 0) % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | REDUCE: (86), (126) imply: % 17.79/3.17 | | | | | | | | (127) $false % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | CLOSE: (127) is inconsistent. % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | (128) all_49_0 = 0 % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | REDUCE: (39), (128) imply: % 17.79/3.17 | | | | | | | | (129) aNaturalNumber0(all_32_1) = 0 % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | BETA: splitting (33) gives: % 17.79/3.17 | | | | | | | | % 17.79/3.17 | | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | (130) ? [v0: any] : ? [v1: any] : % 17.79/3.17 | | | | | | | | | (aNaturalNumber0(all_32_1) = v1 & aNaturalNumber0(xl) % 17.79/3.17 | | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_106_0, % 17.79/3.17 | | | | | | | | | all_106_1 gives: % 17.79/3.17 | | | | | | | | | (131) aNaturalNumber0(all_32_1) = all_106_0 & % 17.79/3.17 | | | | | | | | | aNaturalNumber0(xl) = all_106_1 & ( ~ (all_106_0 = 0) % 17.79/3.17 | | | | | | | | | | ~ (all_106_1 = 0)) % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | ALPHA: (131) implies: % 17.79/3.17 | | | | | | | | | (132) aNaturalNumber0(xl) = all_106_1 % 17.79/3.17 | | | | | | | | | (133) aNaturalNumber0(all_32_1) = all_106_0 % 17.79/3.17 | | | | | | | | | (134) ~ (all_106_0 = 0) | ~ (all_106_1 = 0) % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_106_1, xl, % 17.79/3.17 | | | | | | | | | simplifying with (1), (132) gives: % 17.79/3.17 | | | | | | | | | (135) all_106_1 = 0 % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_106_0, all_32_1, % 17.79/3.17 | | | | | | | | | simplifying with (129), (133) gives: % 17.79/3.17 | | | | | | | | | (136) all_106_0 = 0 % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | BETA: splitting (134) gives: % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | (137) ~ (all_106_0 = 0) % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | REDUCE: (136), (137) imply: % 17.79/3.17 | | | | | | | | | | (138) $false % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | CLOSE: (138) is inconsistent. % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | (139) ~ (all_106_1 = 0) % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | REDUCE: (135), (139) imply: % 17.79/3.17 | | | | | | | | | | (140) $false % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | CLOSE: (140) is inconsistent. % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | End of split % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | (141) ( ~ (all_32_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) % 17.79/3.17 | | | | | | | | | = all_32_1 & aNaturalNumber0(v0) = 0 & $i(v0))) & % 17.79/3.17 | | | | | | | | | (all_32_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = % 17.79/3.17 | | | | | | | | | all_32_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 17.79/3.17 | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1))) % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | ALPHA: (141) implies: % 17.79/3.17 | | | | | | | | | (142) all_32_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = % 17.79/3.17 | | | | | | | | | all_32_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 17.79/3.17 | | | | | | | | | 0) & aNaturalNumber0(v0) = v1)) % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | BETA: splitting (109) gives: % 17.79/3.17 | | | | | | | | | % 17.79/3.17 | | | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | (143) ~ (all_55_2 = 0) % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | REDUCE: (67), (143) imply: % 17.79/3.17 | | | | | | | | | | (144) $false % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | CLOSE: (144) is inconsistent. % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | (145) all_55_0 = all_32_1 % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | REDUCE: (47), (145) imply: % 17.79/3.17 | | | | | | | | | | (146) sdtpldt0(xn, xm) = all_32_1 % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | BETA: splitting (142) gives: % 17.79/3.17 | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | Case 1: % 17.79/3.17 | | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | | (147) all_32_0 = 0 % 17.79/3.17 | | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | | REDUCE: (15), (147) imply: % 17.79/3.17 | | | | | | | | | | | (148) $false % 17.79/3.17 | | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | | CLOSE: (148) is inconsistent. % 17.79/3.17 | | | | | | | | | | | % 17.79/3.17 | | | | | | | | | | Case 2: % 17.79/3.17 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | (149) ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = all_32_1) | % 17.79/3.18 | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(v0) = v1)) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_82_0, xn, % 17.79/3.18 | | | | | | | | | | | simplifying with (7), (104), (106) gives: % 17.79/3.18 | | | | | | | | | | | (150) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 17.79/3.18 | | | | | | | | | | | (sdtasdt0(all_82_0, xl) = v2 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_82_0) = v1 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 17.79/3.18 | | | | | | | | | | | | ~ (v0 = 0) | v2 = xn)) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_90_0, % 17.79/3.18 | | | | | | | | | | | all_82_0, xm, xn, all_32_1, simplifying with (7), % 17.79/3.18 | | | | | | | | | | | (16), (104), (106), (123), (125) gives: % 17.79/3.18 | | | | | | | | | | | (151) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 17.79/3.18 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 17.79/3.18 | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) = % 17.79/3.18 | | | | | | | | | | | v5 & sdtasdt0(all_90_0, xl) = v6 & % 17.79/3.18 | | | | | | | | | | | sdtasdt0(all_82_0, xl) = v7 & sdtasdt0(xl, v3) = % 17.79/3.18 | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_90_0, % 17.79/3.18 | | | | | | | | | | | all_82_0) = v3 & aNaturalNumber0(all_90_0) = % 17.79/3.18 | | | | | | | | | | | v1 & aNaturalNumber0(all_82_0) = v2 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & % 17.79/3.18 | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) % 17.79/3.18 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 = % 17.79/3.18 | | | | | | | | | | | all_32_1))) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_82_0, % 17.79/3.18 | | | | | | | | | | | all_90_0, xn, xm, all_32_1, simplifying with (7), % 17.79/3.18 | | | | | | | | | | | (104), (106), (123), (125), (146) gives: % 17.79/3.18 | | | | | | | | | | | (152) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 17.79/3.18 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 17.79/3.18 | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) = % 17.79/3.18 | | | | | | | | | | | v5 & sdtasdt0(all_90_0, xl) = v7 & % 17.79/3.18 | | | | | | | | | | | sdtasdt0(all_82_0, xl) = v6 & sdtasdt0(xl, v3) = % 17.79/3.18 | | | | | | | | | | | v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(all_82_0, % 17.79/3.18 | | | | | | | | | | | all_90_0) = v3 & aNaturalNumber0(all_90_0) = % 17.79/3.18 | | | | | | | | | | | v2 & aNaturalNumber0(all_82_0) = v1 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & % 17.79/3.18 | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) % 17.79/3.18 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 = % 17.79/3.18 | | | | | | | | | | | all_32_1))) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_90_0, xm, % 17.79/3.18 | | | | | | | | | | | simplifying with (7), (123), (125) gives: % 17.79/3.18 | | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 17.79/3.18 | | | | | | | | | | | (sdtasdt0(all_90_0, xl) = v2 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_90_0) = v1 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 17.79/3.18 | | | | | | | | | | | | ~ (v0 = 0) | v2 = xm)) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_34_1, xl, % 17.79/3.18 | | | | | | | | | | | all_53_0, simplifying with (7), (20), (43) gives: % 17.79/3.18 | | | | | | | | | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 17.79/3.18 | | | | | | | | | | | (sdtasdt0(xl, all_34_1) = v2 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_34_1) = v0 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = 0) % 17.79/3.18 | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_53_0)) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_122_0, % 17.79/3.18 | | | | | | | | | | | all_122_1, all_122_2 gives: % 17.79/3.18 | | | | | | | | | | | (155) sdtasdt0(all_82_0, xl) = all_122_0 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_122_1 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = all_122_2 & $i(all_122_0) & % 17.79/3.18 | | | | | | | | | | | ( ~ (all_122_1 = 0) | ~ (all_122_2 = 0) | % 17.79/3.18 | | | | | | | | | | | all_122_0 = xn) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | ALPHA: (155) implies: % 17.79/3.18 | | | | | | | | | | | (156) aNaturalNumber0(xl) = all_122_2 % 17.79/3.18 | | | | | | | | | | | (157) aNaturalNumber0(all_82_0) = all_122_1 % 17.79/3.18 | | | | | | | | | | | (158) sdtasdt0(all_82_0, xl) = all_122_0 % 17.79/3.18 | | | | | | | | | | | (159) ~ (all_122_1 = 0) | ~ (all_122_2 = 0) | % 17.79/3.18 | | | | | | | | | | | all_122_0 = xn % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_126_0, % 17.79/3.18 | | | | | | | | | | | all_126_1, all_126_2 gives: % 17.79/3.18 | | | | | | | | | | | (160) sdtasdt0(xl, all_34_1) = all_126_0 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_34_1) = all_126_2 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = all_126_1 & $i(all_126_0) & % 17.79/3.18 | | | | | | | | | | | ( ~ (all_126_1 = 0) | ~ (all_126_2 = 0) | % 17.79/3.18 | | | | | | | | | | | all_126_0 = all_53_0) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | ALPHA: (160) implies: % 17.79/3.18 | | | | | | | | | | | (161) aNaturalNumber0(xl) = all_126_1 % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_128_0, % 17.79/3.18 | | | | | | | | | | | all_128_1, all_128_2 gives: % 17.79/3.18 | | | | | | | | | | | (162) sdtasdt0(all_90_0, xl) = all_128_0 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_128_1 & % 17.79/3.18 | | | | | | | | | | | aNaturalNumber0(xl) = all_128_2 & $i(all_128_0) & % 17.79/3.18 | | | | | | | | | | | ( ~ (all_128_1 = 0) | ~ (all_128_2 = 0) | % 17.79/3.18 | | | | | | | | | | | all_128_0 = xm) % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | ALPHA: (162) implies: % 17.79/3.18 | | | | | | | | | | | (163) aNaturalNumber0(xl) = all_128_2 % 17.79/3.18 | | | | | | | | | | | (164) aNaturalNumber0(all_90_0) = all_128_1 % 17.79/3.18 | | | | | | | | | | | (165) sdtasdt0(all_90_0, xl) = all_128_0 % 17.79/3.18 | | | | | | | | | | | (166) ~ (all_128_1 = 0) | ~ (all_128_2 = 0) | % 17.79/3.18 | | | | | | | | | | | all_128_0 = xm % 17.79/3.18 | | | | | | | | | | | % 17.79/3.18 | | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_130_0, % 17.79/3.18 | | | | | | | | | | | all_130_1, all_130_2, all_130_3, all_130_4, % 17.79/3.18 | | | | | | | | | | | all_130_5, all_130_6, all_130_7, all_130_8 gives: % 17.79/3.19 | | | | | | | | | | | (167) sdtasdt0(all_130_5, xl) = all_130_3 & % 17.79/3.19 | | | | | | | | | | | sdtasdt0(all_90_0, xl) = all_130_1 & % 17.79/3.19 | | | | | | | | | | | sdtasdt0(all_82_0, xl) = all_130_2 & sdtasdt0(xl, % 17.79/3.19 | | | | | | | | | | | all_130_5) = all_130_4 & sdtpldt0(all_130_2, % 17.79/3.19 | | | | | | | | | | | all_130_1) = all_130_0 & sdtpldt0(all_82_0, % 17.79/3.19 | | | | | | | | | | | all_90_0) = all_130_5 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_130_6 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_130_7 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(xl) = all_130_8 & $i(all_130_0) & % 17.79/3.19 | | | | | | | | | | | $i(all_130_1) & $i(all_130_2) & $i(all_130_3) & % 17.79/3.19 | | | | | | | | | | | $i(all_130_4) & $i(all_130_5) & ( ~ (all_130_6 = % 17.79/3.19 | | | | | | | | | | | 0) | ~ (all_130_7 = 0) | ~ (all_130_8 = 0) | % 17.79/3.19 | | | | | | | | | | | (all_130_0 = all_130_3 & all_130_4 = all_32_1)) % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | ALPHA: (167) implies: % 17.79/3.19 | | | | | | | | | | | (168) aNaturalNumber0(xl) = all_130_8 % 17.79/3.19 | | | | | | | | | | | (169) aNaturalNumber0(all_82_0) = all_130_7 % 17.79/3.19 | | | | | | | | | | | (170) aNaturalNumber0(all_90_0) = all_130_6 % 17.79/3.19 | | | | | | | | | | | (171) sdtpldt0(all_82_0, all_90_0) = all_130_5 % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | DELTA: instantiating (151) with fresh symbols all_132_0, % 17.79/3.19 | | | | | | | | | | | all_132_1, all_132_2, all_132_3, all_132_4, % 17.79/3.19 | | | | | | | | | | | all_132_5, all_132_6, all_132_7, all_132_8 gives: % 17.79/3.19 | | | | | | | | | | | (172) sdtasdt0(all_132_5, xl) = all_132_3 & % 17.79/3.19 | | | | | | | | | | | sdtasdt0(all_90_0, xl) = all_132_2 & % 17.79/3.19 | | | | | | | | | | | sdtasdt0(all_82_0, xl) = all_132_1 & sdtasdt0(xl, % 17.79/3.19 | | | | | | | | | | | all_132_5) = all_132_4 & sdtpldt0(all_132_2, % 17.79/3.19 | | | | | | | | | | | all_132_1) = all_132_0 & sdtpldt0(all_90_0, % 17.79/3.19 | | | | | | | | | | | all_82_0) = all_132_5 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_132_7 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_132_6 & % 17.79/3.19 | | | | | | | | | | | aNaturalNumber0(xl) = all_132_8 & $i(all_132_0) & % 17.79/3.19 | | | | | | | | | | | $i(all_132_1) & $i(all_132_2) & $i(all_132_3) & % 17.79/3.19 | | | | | | | | | | | $i(all_132_4) & $i(all_132_5) & ( ~ (all_132_6 = % 17.79/3.19 | | | | | | | | | | | 0) | ~ (all_132_7 = 0) | ~ (all_132_8 = 0) | % 17.79/3.19 | | | | | | | | | | | (all_132_0 = all_132_3 & all_132_4 = all_32_1)) % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | ALPHA: (172) implies: % 17.79/3.19 | | | | | | | | | | | (173) $i(all_132_5) % 17.79/3.19 | | | | | | | | | | | (174) aNaturalNumber0(xl) = all_132_8 % 17.79/3.19 | | | | | | | | | | | (175) aNaturalNumber0(all_82_0) = all_132_6 % 17.79/3.19 | | | | | | | | | | | (176) aNaturalNumber0(all_90_0) = all_132_7 % 17.79/3.19 | | | | | | | | | | | (177) sdtpldt0(all_90_0, all_82_0) = all_132_5 % 17.79/3.19 | | | | | | | | | | | (178) sdtpldt0(all_132_2, all_132_1) = all_132_0 % 17.79/3.19 | | | | | | | | | | | (179) sdtasdt0(xl, all_132_5) = all_132_4 % 17.79/3.19 | | | | | | | | | | | (180) sdtasdt0(all_82_0, xl) = all_132_1 % 17.79/3.19 | | | | | | | | | | | (181) sdtasdt0(all_90_0, xl) = all_132_2 % 17.79/3.19 | | | | | | | | | | | (182) sdtasdt0(all_132_5, xl) = all_132_3 % 17.79/3.19 | | | | | | | | | | | (183) ~ (all_132_6 = 0) | ~ (all_132_7 = 0) | ~ % 17.79/3.19 | | | | | | | | | | | (all_132_8 = 0) | (all_132_0 = all_132_3 & % 17.79/3.19 | | | | | | | | | | | all_132_4 = all_32_1) % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_130_8, xl, % 17.79/3.19 | | | | | | | | | | | simplifying with (1), (168) gives: % 17.79/3.19 | | | | | | | | | | | (184) all_130_8 = 0 % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_128_2, all_130_8, xl, % 17.79/3.19 | | | | | | | | | | | simplifying with (163), (168) gives: % 17.79/3.19 | | | | | | | | | | | (185) all_130_8 = all_128_2 % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_126_1, all_130_8, xl, % 17.79/3.19 | | | | | | | | | | | simplifying with (161), (168) gives: % 17.79/3.19 | | | | | | | | | | | (186) all_130_8 = all_126_1 % 17.79/3.19 | | | | | | | | | | | % 17.79/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_126_1, all_132_8, xl, % 17.79/3.19 | | | | | | | | | | | simplifying with (161), (174) gives: % 18.19/3.19 | | | | | | | | | | | (187) all_132_8 = all_126_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_122_2, all_132_8, xl, % 18.19/3.19 | | | | | | | | | | | simplifying with (156), (174) gives: % 18.19/3.19 | | | | | | | | | | | (188) all_132_8 = all_122_2 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_130_7, all_82_0, % 18.19/3.19 | | | | | | | | | | | simplifying with (105), (169) gives: % 18.19/3.19 | | | | | | | | | | | (189) all_130_7 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_130_7, all_132_6, % 18.19/3.19 | | | | | | | | | | | all_82_0, simplifying with (169), (175) gives: % 18.19/3.19 | | | | | | | | | | | (190) all_132_6 = all_130_7 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_122_1, all_132_6, % 18.19/3.19 | | | | | | | | | | | all_82_0, simplifying with (157), (175) gives: % 18.19/3.19 | | | | | | | | | | | (191) all_132_6 = all_122_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_130_6, all_90_0, % 18.19/3.19 | | | | | | | | | | | simplifying with (124), (170) gives: % 18.19/3.19 | | | | | | | | | | | (192) all_130_6 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_130_6, all_132_7, % 18.19/3.19 | | | | | | | | | | | all_90_0, simplifying with (170), (176) gives: % 18.19/3.19 | | | | | | | | | | | (193) all_132_7 = all_130_6 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_128_1, all_132_7, % 18.19/3.19 | | | | | | | | | | | all_90_0, simplifying with (164), (176) gives: % 18.19/3.19 | | | | | | | | | | | (194) all_132_7 = all_128_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_122_0, all_132_1, xl, % 18.19/3.19 | | | | | | | | | | | all_82_0, simplifying with (158), (180) gives: % 18.19/3.19 | | | | | | | | | | | (195) all_132_1 = all_122_0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_128_0, all_132_2, xl, % 18.19/3.19 | | | | | | | | | | | all_90_0, simplifying with (165), (181) gives: % 18.19/3.19 | | | | | | | | | | | (196) all_132_2 = all_128_0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (190), (191) imply: % 18.19/3.19 | | | | | | | | | | | (197) all_130_7 = all_122_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (197) implies: % 18.19/3.19 | | | | | | | | | | | (198) all_130_7 = all_122_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (193), (194) imply: % 18.19/3.19 | | | | | | | | | | | (199) all_130_6 = all_128_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (199) implies: % 18.19/3.19 | | | | | | | | | | | (200) all_130_6 = all_128_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (187), (188) imply: % 18.19/3.19 | | | | | | | | | | | (201) all_126_1 = all_122_2 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (201) implies: % 18.19/3.19 | | | | | | | | | | | (202) all_126_1 = all_122_2 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (192), (200) imply: % 18.19/3.19 | | | | | | | | | | | (203) all_128_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (203) implies: % 18.19/3.19 | | | | | | | | | | | (204) all_128_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (189), (198) imply: % 18.19/3.19 | | | | | | | | | | | (205) all_122_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (205) implies: % 18.19/3.19 | | | | | | | | | | | (206) all_122_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (184), (185) imply: % 18.19/3.19 | | | | | | | | | | | (207) all_128_2 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (185), (186) imply: % 18.19/3.19 | | | | | | | | | | | (208) all_128_2 = all_126_1 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (207), (208) imply: % 18.19/3.19 | | | | | | | | | | | (209) all_126_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | SIMP: (209) implies: % 18.19/3.19 | | | | | | | | | | | (210) all_126_1 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (202), (210) imply: % 18.19/3.19 | | | | | | | | | | | (211) all_122_2 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (188), (211) imply: % 18.19/3.19 | | | | | | | | | | | (212) all_132_8 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (194), (204) imply: % 18.19/3.19 | | | | | | | | | | | (213) all_132_7 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | COMBINE_EQS: (191), (206) imply: % 18.19/3.19 | | | | | | | | | | | (214) all_132_6 = 0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | REDUCE: (178), (195), (196) imply: % 18.19/3.19 | | | | | | | | | | | (215) sdtpldt0(all_128_0, all_122_0) = all_132_0 % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | BETA: splitting (166) gives: % 18.19/3.19 | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | Case 1: % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | (216) ~ (all_128_1 = 0) % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | REDUCE: (204), (216) imply: % 18.19/3.19 | | | | | | | | | | | | (217) $false % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | Case 2: % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | (218) ~ (all_128_2 = 0) | all_128_0 = xm % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | BETA: splitting (183) gives: % 18.19/3.19 | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | Case 1: % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | (219) ~ (all_132_6 = 0) % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | REDUCE: (214), (219) imply: % 18.19/3.19 | | | | | | | | | | | | | (220) $false % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | Case 2: % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | (221) ~ (all_132_7 = 0) | ~ (all_132_8 = 0) | % 18.19/3.19 | | | | | | | | | | | | | (all_132_0 = all_132_3 & all_132_4 = all_32_1) % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | BETA: splitting (159) gives: % 18.19/3.19 | | | | | | | | | | | | | % 18.19/3.19 | | | | | | | | | | | | | Case 1: % 18.19/3.19 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | (222) ~ (all_122_1 = 0) % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | REDUCE: (206), (222) imply: % 18.19/3.20 | | | | | | | | | | | | | | (223) $false % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | Case 2: % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | (224) ~ (all_122_2 = 0) | all_122_0 = xn % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | BETA: splitting (224) gives: % 18.19/3.20 | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | Case 1: % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | (225) ~ (all_122_2 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | REDUCE: (211), (225) imply: % 18.19/3.20 | | | | | | | | | | | | | | | (226) $false % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | Case 2: % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | (227) all_122_0 = xn % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | REDUCE: (215), (227) imply: % 18.19/3.20 | | | | | | | | | | | | | | | (228) sdtpldt0(all_128_0, xn) = all_132_0 % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 18.19/3.20 | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | Case 1: % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | (229) ~ (all_128_2 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | REDUCE: (207), (229) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | (230) $false % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | Case 2: % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | (231) all_128_0 = xm % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | REDUCE: (228), (231) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | (232) sdtpldt0(xm, xn) = all_132_0 % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 18.19/3.20 | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | Case 1: % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | (233) ~ (all_132_7 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | REDUCE: (213), (233) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | | (234) $false % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | Case 2: % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | (235) ~ (all_132_8 = 0) | (all_132_0 = all_132_3 & % 18.19/3.20 | | | | | | | | | | | | | | | | | all_132_4 = all_32_1) % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | Case 1: % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | (236) ~ (all_132_8 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | REDUCE: (212), (236) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (237) $false % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent. % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | Case 2: % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | (238) all_132_0 = all_132_3 & all_132_4 = all_32_1 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (239) all_132_4 = all_32_1 % 18.19/3.20 | | | | | | | | | | | | | | | | | | (240) all_132_0 = all_132_3 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | REDUCE: (179), (239) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (241) sdtasdt0(xl, all_132_5) = all_32_1 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | REDUCE: (232), (240) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (242) sdtpldt0(xm, xn) = all_132_3 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_32_1, all_132_3, xn, % 18.19/3.20 | | | | | | | | | | | | | | | | | | xm, simplifying with (16), (242) gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (243) all_132_3 = all_32_1 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | REDUCE: (182), (243) imply: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (244) sdtasdt0(all_132_5, xl) = all_32_1 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_82_0, all_90_0, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_130_5, simplifying with (104), (123), (171) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (245) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (sdtpldt0(all_90_0, all_82_0) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = v1 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = v0 & $i(v2) & ( ~ % 18.19/3.20 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = all_130_5)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_82_0, all_90_0, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_130_5, simplifying with (104), (123), (171) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (246) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_130_5) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = v1 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = v0 & ( ~ (v1 = 0) | % 18.19/3.20 | | | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with all_90_0, all_82_0, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (104), (123), (177) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (sdtpldt0(all_82_0, all_90_0) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = v0 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = v1 & $i(v2) & ( ~ % 18.19/3.20 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v2 = all_132_5)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with all_90_0, all_82_0, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (104), (123), (177) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (248) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_132_5) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = v0 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = v1 & ( ~ (v1 = 0) | % 18.19/3.20 | | | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (149) with all_132_5, simplifying % 18.19/3.20 | | | | | | | | | | | | | | | | | | with (173), (241) gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (249) ? [v0: int] : ( ~ (v0 = 0) & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_132_5) = v0) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_132_5, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_32_1, simplifying with (7), (173), (241) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (250) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (sdtasdt0(all_132_5, xl) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_132_5) = v1 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_32_1)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xl, all_132_5, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_32_1, simplifying with (7), (173), (241) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (251) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_132_5) = v1 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_32_1) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 % 18.19/3.20 | | | | | | | | | | | | | | | | | | = 0) | v2 = 0)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_132_5, xl, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_32_1, simplifying with (7), (173), (244) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (252) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (sdtasdt0(xl, all_132_5) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_132_5) = v0 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_32_1)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_132_5, xl, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_32_1, simplifying with (7), (173), (244) % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (253) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.19/3.20 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_132_5) = v0 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_32_1) = v2 & % 18.19/3.20 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = v1 & ( ~ (v1 = 0) | ~ (v0 % 18.19/3.20 | | | | | | | | | | | | | | | | | | = 0) | v2 = 0)) % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | DELTA: instantiating (249) with fresh symbol all_199_0 % 18.19/3.20 | | | | | | | | | | | | | | | | | | gives: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (254) ~ (all_199_0 = 0) & aNaturalNumber0(all_132_5) = % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_199_0 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 18.19/3.20 | | | | | | | | | | | | | | | | | | (255) ~ (all_199_0 = 0) % 18.19/3.20 | | | | | | | | | | | | | | | | | | (256) aNaturalNumber0(all_132_5) = all_199_0 % 18.19/3.20 | | | | | | | | | | | | | | | | | | % 18.19/3.20 | | | | | | | | | | | | | | | | | | DELTA: instantiating (248) with fresh symbols all_205_0, % 18.19/3.20 | | | | | | | | | | | | | | | | | | all_205_1, all_205_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (257) aNaturalNumber0(all_132_5) = all_205_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_205_2 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_205_1 & ( ~ % 18.19/3.21 | | | | | | | | | | | | | | | | | | (all_205_1 = 0) | ~ (all_205_2 = 0) | all_205_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (257) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (258) aNaturalNumber0(all_82_0) = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (259) aNaturalNumber0(all_90_0) = all_205_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (260) aNaturalNumber0(all_132_5) = all_205_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (261) ~ (all_205_1 = 0) | ~ (all_205_2 = 0) | % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_205_0 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (246) with fresh symbols all_207_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_207_1, all_207_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (262) aNaturalNumber0(all_130_5) = all_207_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_207_1 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_207_2 & ( ~ % 18.19/3.21 | | | | | | | | | | | | | | | | | | (all_207_1 = 0) | ~ (all_207_2 = 0) | all_207_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (263) aNaturalNumber0(all_82_0) = all_207_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (264) aNaturalNumber0(all_90_0) = all_207_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (253) with fresh symbols all_209_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_209_1, all_209_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (265) aNaturalNumber0(all_132_5) = all_209_2 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_32_1) = all_209_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_209_1 & ( ~ (all_209_1 = % 18.19/3.21 | | | | | | | | | | | | | | | | | | 0) | ~ (all_209_2 = 0) | all_209_0 = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (266) aNaturalNumber0(all_132_5) = all_209_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (251) with fresh symbols all_213_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_213_1, all_213_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (267) aNaturalNumber0(all_132_5) = all_213_1 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_32_1) = all_213_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_213_2 & ( ~ (all_213_1 = % 18.19/3.21 | | | | | | | | | | | | | | | | | | 0) | ~ (all_213_2 = 0) | all_213_0 = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (268) aNaturalNumber0(all_132_5) = all_213_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (252) with fresh symbols all_215_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_215_1, all_215_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (269) sdtasdt0(xl, all_132_5) = all_215_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_132_5) = all_215_2 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_215_1 & $i(all_215_0) & % 18.19/3.21 | | | | | | | | | | | | | | | | | | ( ~ (all_215_1 = 0) | ~ (all_215_2 = 0) | % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_215_0 = all_32_1) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (270) aNaturalNumber0(all_132_5) = all_215_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (250) with fresh symbols all_219_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_219_1, all_219_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (271) sdtasdt0(all_132_5, xl) = all_219_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_132_5) = all_219_1 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xl) = all_219_2 & $i(all_219_0) & % 18.19/3.21 | | | | | | | | | | | | | | | | | | ( ~ (all_219_1 = 0) | ~ (all_219_2 = 0) | % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_219_0 = all_32_1) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (271) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (272) aNaturalNumber0(all_132_5) = all_219_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (245) with fresh symbols all_221_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_221_1, all_221_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (273) sdtpldt0(all_90_0, all_82_0) = all_221_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_221_1 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_221_2 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | $i(all_221_0) & ( ~ (all_221_1 = 0) | ~ % 18.19/3.21 | | | | | | | | | | | | | | | | | | (all_221_2 = 0) | all_221_0 = all_130_5) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (274) aNaturalNumber0(all_82_0) = all_221_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (275) aNaturalNumber0(all_90_0) = all_221_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_223_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_223_1, all_223_2 gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (276) sdtpldt0(all_82_0, all_90_0) = all_223_0 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_90_0) = all_223_2 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_82_0) = all_223_1 & % 18.19/3.21 | | | | | | | | | | | | | | | | | | $i(all_223_0) & ( ~ (all_223_1 = 0) | ~ % 18.19/3.21 | | | | | | | | | | | | | | | | | | (all_223_2 = 0) | all_223_0 = all_132_5) % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (277) aNaturalNumber0(all_82_0) = all_223_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | (278) aNaturalNumber0(all_90_0) = all_223_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_207_2, all_82_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | simplifying with (105), (263) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (279) all_207_2 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_2, all_221_2, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_82_0, simplifying with (263), (274) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (280) all_221_2 = all_207_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_221_2, all_223_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_82_0, simplifying with (274), (277) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (281) all_223_1 = all_221_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_205_1, all_223_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_82_0, simplifying with (258), (277) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (282) all_223_1 = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_205_2, all_207_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_90_0, simplifying with (259), (264) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (283) all_207_1 = all_205_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_1, all_221_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_90_0, simplifying with (264), (275) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (284) all_221_1 = all_207_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_223_2, all_90_0, % 18.19/3.21 | | | | | | | | | | | | | | | | | | simplifying with (124), (278) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (285) all_223_2 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_221_1, all_223_2, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_90_0, simplifying with (275), (278) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (286) all_223_2 = all_221_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_205_0, all_209_2, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (260), (266) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (287) all_209_2 = all_205_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_213_1, all_215_2, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (268), (270) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (288) all_215_2 = all_213_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_209_2, all_215_2, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (266), (270) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (289) all_215_2 = all_209_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_215_2, all_219_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (270), (272) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (290) all_219_1 = all_215_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_199_0, all_219_1, % 18.19/3.21 | | | | | | | | | | | | | | | | | | all_132_5, simplifying with (256), (272) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (291) all_219_1 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (282) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (292) all_221_2 = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (292) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (293) all_221_2 = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (286) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (294) all_221_1 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (294) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (295) all_221_1 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (295) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (296) all_207_1 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (297) all_207_1 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (293) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (298) all_207_2 = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (299) all_207_2 = all_205_1 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (291) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (300) all_215_2 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (301) all_215_2 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (301) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (302) all_213_1 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (289) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (303) all_213_1 = all_209_2 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (303) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (304) all_209_2 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (304) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (305) all_209_2 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (305) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (306) all_205_0 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (307) all_205_0 = all_199_0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (297) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (308) all_205_2 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (309) all_205_2 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (299) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | (310) all_205_1 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | Case 1: % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | (311) ~ (all_205_1 = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | REDUCE: (310), (311) imply: % 18.19/3.21 | | | | | | | | | | | | | | | | | | | (312) $false % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | Case 2: % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | (313) ~ (all_205_2 = 0) | all_205_0 = 0 % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 18.19/3.21 | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | Case 1: % 18.19/3.21 | | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | | (314) ~ (all_205_2 = 0) % 18.19/3.21 | | | | | | | | | | | | | | | | | | | | % 18.19/3.21 | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (314) imply: % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | (315) $false % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent. % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | Case 2: % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | (316) all_205_0 = 0 % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (316) imply: % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | (317) all_199_0 = 0 % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | SIMP: (317) implies: % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | (318) all_199_0 = 0 % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (318) imply: % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | (319) $false % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 18.19/3.22 | | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | | % 18.19/3.22 | | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | | % 18.19/3.22 | | | | | | | | | End of split % 18.19/3.22 | | | | | | | | | % 18.19/3.22 | | | | | | | | End of split % 18.19/3.22 | | | | | | | | % 18.19/3.22 | | | | | | | End of split % 18.19/3.22 | | | | | | | % 18.19/3.22 | | | | | | End of split % 18.19/3.22 | | | | | | % 18.19/3.22 | | | | | End of split % 18.19/3.22 | | | | | % 18.19/3.22 | | | | End of split % 18.19/3.22 | | | | % 18.19/3.22 | | | End of split % 18.19/3.22 | | | % 18.19/3.22 | | End of split % 18.19/3.22 | | % 18.19/3.22 | End of split % 18.19/3.22 | % 18.19/3.22 End of proof % 18.19/3.22 % SZS output end Proof for theBenchmark % 18.19/3.22 % 18.19/3.22 2595ms %------------------------------------------------------------------------------