%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM466+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:47:56 EDT 2023 % Result : Theorem 9.37s 2.13s % Output : Proof 14.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM466+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 : n019.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 14:13:43 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.61/1.14 Prover 1: Preprocessing ... % 2.61/1.14 Prover 4: Preprocessing ... % 3.19/1.18 Prover 2: Preprocessing ... % 3.19/1.18 Prover 0: Preprocessing ... % 3.19/1.18 Prover 6: Preprocessing ... % 3.19/1.18 Prover 3: Preprocessing ... % 3.48/1.19 Prover 5: Preprocessing ... % 7.66/1.77 Prover 1: Constructing countermodel ... % 7.66/1.78 Prover 3: Constructing countermodel ... % 8.24/1.87 Prover 6: Proving ... % 8.44/1.89 Prover 5: Constructing countermodel ... % 9.37/2.05 Prover 2: Proving ... % 9.37/2.13 Prover 3: proved (1502ms) % 9.37/2.13 % 9.37/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.37/2.13 % 9.37/2.14 Prover 4: Constructing countermodel ... % 9.37/2.14 Prover 5: stopped % 9.37/2.15 Prover 6: stopped % 9.37/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.37/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.37/2.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.37/2.19 Prover 2: stopped % 9.37/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.61/2.25 Prover 7: Preprocessing ... % 10.61/2.25 Prover 10: Preprocessing ... % 10.61/2.26 Prover 11: Preprocessing ... % 10.61/2.27 Prover 8: Preprocessing ... % 10.61/2.28 Prover 0: Proving ... % 10.61/2.28 Prover 0: stopped % 10.61/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.52/2.33 Prover 13: Preprocessing ... % 11.75/2.38 Prover 10: Constructing countermodel ... % 11.75/2.38 Prover 8: Warning: ignoring some quantifiers % 11.75/2.39 Prover 8: Constructing countermodel ... % 12.89/2.55 Prover 7: Constructing countermodel ... % 13.45/2.56 Prover 13: Constructing countermodel ... % 13.54/2.58 Prover 1: Found proof (size 133) % 13.54/2.58 Prover 1: proved (1959ms) % 13.54/2.58 Prover 4: stopped % 13.54/2.58 Prover 8: stopped % 13.54/2.59 Prover 7: stopped % 13.54/2.59 Prover 10: stopped % 13.54/2.60 Prover 13: stopped % 13.90/2.66 Prover 11: Constructing countermodel ... % 13.90/2.67 Prover 11: stopped % 13.90/2.67 % 13.90/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.90/2.67 % 13.90/2.69 % SZS output start Proof for theBenchmark % 13.90/2.69 Assumptions after simplification: % 13.90/2.69 --------------------------------- % 13.90/2.69 % 13.90/2.69 (mDefDiv) % 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 13.90/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 13.90/2.72 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 13.90/2.72 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 13.90/2.72 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 13.90/2.72 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 13.90/2.72 % 13.90/2.72 (mMulAsso) % 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.90/2.72 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 13.90/2.72 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 13.90/2.72 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 13.90/2.72 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 13.90/2.72 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 13.90/2.72 v4))) % 13.90/2.72 % 13.90/2.72 (mMulComm) % 13.90/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 13.90/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 13.90/2.72 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 13.90/2.72 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 13.90/2.72 % 13.90/2.72 (mSortsB_02) % 14.31/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 14.31/2.72 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 14.31/2.72 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 14.31/2.72 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 14.31/2.72 % 14.31/2.72 (m__) % 14.31/2.72 $i(xn) & $i(xm) & $i(xl) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xm, xn) = % 14.31/2.72 0 & doDivides0(xl, xn) = v0 & doDivides0(xl, xm) = 0) % 14.31/2.72 % 14.31/2.72 (m__1218) % 14.31/2.73 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & % 14.31/2.73 $i(xn) & $i(xm) & $i(xl) % 14.31/2.73 % 14.31/2.73 (function-axioms) % 14.31/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.31/2.73 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 14.31/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.31/2.73 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 14.31/2.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.31/2.73 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 14.31/2.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.31/2.73 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 14.31/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.31/2.73 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 14.31/2.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.31/2.73 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 14.31/2.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 14.31/2.73 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.31/2.73 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 14.31/2.73 | ~ (aNaturalNumber0(v2) = v0)) % 14.31/2.73 % 14.31/2.73 Further assumptions not needed in the proof: % 14.31/2.73 -------------------------------------------- % 14.31/2.73 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefQuot, mIH, mIH_03, % 14.31/2.73 mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, % 14.31/2.73 mMulCanc, mNatSort, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, % 14.31/2.73 m_MulUnit, m_MulZero % 14.31/2.73 % 14.31/2.73 Those formulas are unsatisfiable: % 14.31/2.73 --------------------------------- % 14.31/2.73 % 14.31/2.73 Begin of proof % 14.31/2.73 | % 14.31/2.73 | ALPHA: (m__1218) implies: % 14.31/2.73 | (1) aNaturalNumber0(xl) = 0 % 14.31/2.73 | (2) aNaturalNumber0(xm) = 0 % 14.31/2.73 | (3) aNaturalNumber0(xn) = 0 % 14.31/2.73 | % 14.31/2.73 | ALPHA: (m__) implies: % 14.31/2.73 | (4) $i(xl) % 14.31/2.73 | (5) $i(xm) % 14.31/2.73 | (6) $i(xn) % 14.31/2.73 | (7) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xm, xn) = 0 & doDivides0(xl, % 14.31/2.73 | xn) = v0 & doDivides0(xl, xm) = 0) % 14.31/2.73 | % 14.31/2.73 | ALPHA: (function-axioms) implies: % 14.31/2.74 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.31/2.74 | (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 14.31/2.74 | v0)) % 14.31/2.74 | % 14.31/2.74 | DELTA: instantiating (7) with fresh symbol all_31_0 gives: % 14.31/2.74 | (9) ~ (all_31_0 = 0) & doDivides0(xm, xn) = 0 & doDivides0(xl, xn) = % 14.31/2.74 | all_31_0 & doDivides0(xl, xm) = 0 % 14.31/2.74 | % 14.31/2.74 | ALPHA: (9) implies: % 14.31/2.74 | (10) ~ (all_31_0 = 0) % 14.31/2.74 | (11) doDivides0(xl, xm) = 0 % 14.31/2.74 | (12) doDivides0(xl, xn) = all_31_0 % 14.31/2.74 | (13) doDivides0(xm, xn) = 0 % 14.31/2.74 | % 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (4), % 14.31/2.74 | (5), (11) gives: % 14.31/2.74 | (14) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 14.31/2.74 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 14.31/2.74 | $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0)) % 14.31/2.74 | % 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xl, xn, all_31_0, simplifying with % 14.31/2.74 | (4), (6), (12) gives: % 14.31/2.74 | (15) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 14.31/2.74 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~ % 14.31/2.74 | (all_31_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) = xn & % 14.31/2.74 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_31_0 = 0 | ! [v0: $i] % 14.31/2.74 | : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 14.31/2.74 | = 0) & aNaturalNumber0(v0) = v1)))) % 14.31/2.74 | % 14.31/2.74 | GROUND_INST: instantiating (mDefDiv) with xm, xn, 0, simplifying with (5), % 14.31/2.74 | (6), (13) gives: % 14.31/2.74 | (16) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 14.31/2.74 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 14.31/2.74 | $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 14.31/2.74 | % 14.31/2.74 | BETA: splitting (16) gives: % 14.31/2.74 | % 14.31/2.74 | Case 1: % 14.31/2.74 | | % 14.31/2.74 | | (17) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 14.31/2.74 | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.31/2.74 | | % 14.31/2.74 | | DELTA: instantiating (17) with fresh symbols all_39_0, all_39_1 gives: % 14.31/2.74 | | (18) aNaturalNumber0(xn) = all_39_0 & aNaturalNumber0(xm) = all_39_1 & ( % 14.31/2.74 | | ~ (all_39_0 = 0) | ~ (all_39_1 = 0)) % 14.31/2.74 | | % 14.31/2.74 | | ALPHA: (18) implies: % 14.31/2.74 | | (19) aNaturalNumber0(xm) = all_39_1 % 14.31/2.74 | | (20) aNaturalNumber0(xn) = all_39_0 % 14.31/2.74 | | (21) ~ (all_39_0 = 0) | ~ (all_39_1 = 0) % 14.31/2.74 | | % 14.31/2.75 | | GROUND_INST: instantiating (8) with 0, all_39_1, xm, simplifying with (2), % 14.31/2.75 | | (19) gives: % 14.31/2.75 | | (22) all_39_1 = 0 % 14.31/2.75 | | % 14.31/2.75 | | GROUND_INST: instantiating (8) with 0, all_39_0, xn, simplifying with (3), % 14.31/2.75 | | (20) gives: % 14.31/2.75 | | (23) all_39_0 = 0 % 14.31/2.75 | | % 14.31/2.75 | | BETA: splitting (21) gives: % 14.31/2.75 | | % 14.31/2.75 | | Case 1: % 14.31/2.75 | | | % 14.31/2.75 | | | (24) ~ (all_39_0 = 0) % 14.31/2.75 | | | % 14.31/2.75 | | | REDUCE: (23), (24) imply: % 14.31/2.75 | | | (25) $false % 14.31/2.75 | | | % 14.31/2.75 | | | CLOSE: (25) is inconsistent. % 14.31/2.75 | | | % 14.31/2.75 | | Case 2: % 14.31/2.75 | | | % 14.31/2.75 | | | (26) ~ (all_39_1 = 0) % 14.31/2.75 | | | % 14.31/2.75 | | | REDUCE: (22), (26) imply: % 14.31/2.75 | | | (27) $false % 14.31/2.75 | | | % 14.31/2.75 | | | CLOSE: (27) is inconsistent. % 14.31/2.75 | | | % 14.31/2.75 | | End of split % 14.31/2.75 | | % 14.31/2.75 | Case 2: % 14.31/2.75 | | % 14.31/2.75 | | (28) ? [v0: $i] : (sdtasdt0(xm, v0) = xn & aNaturalNumber0(v0) = 0 & % 14.31/2.75 | | $i(v0)) % 14.31/2.75 | | % 14.31/2.75 | | DELTA: instantiating (28) with fresh symbol all_39_0 gives: % 14.31/2.75 | | (29) sdtasdt0(xm, all_39_0) = xn & aNaturalNumber0(all_39_0) = 0 & % 14.31/2.75 | | $i(all_39_0) % 14.31/2.75 | | % 14.31/2.75 | | ALPHA: (29) implies: % 14.31/2.75 | | (30) $i(all_39_0) % 14.31/2.75 | | (31) aNaturalNumber0(all_39_0) = 0 % 14.31/2.75 | | (32) sdtasdt0(xm, all_39_0) = xn % 14.31/2.75 | | % 14.31/2.75 | | BETA: splitting (15) gives: % 14.31/2.75 | | % 14.31/2.75 | | Case 1: % 14.31/2.75 | | | % 14.31/2.75 | | | (33) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xn) = v1 & % 14.31/2.75 | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.31/2.75 | | | % 14.31/2.75 | | | DELTA: instantiating (33) with fresh symbols all_47_0, all_47_1 gives: % 14.31/2.75 | | | (34) aNaturalNumber0(xn) = all_47_0 & aNaturalNumber0(xl) = all_47_1 & % 14.31/2.75 | | | ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0)) % 14.31/2.75 | | | % 14.31/2.75 | | | ALPHA: (34) implies: % 14.31/2.75 | | | (35) aNaturalNumber0(xl) = all_47_1 % 14.31/2.75 | | | (36) aNaturalNumber0(xn) = all_47_0 % 14.31/2.75 | | | (37) ~ (all_47_0 = 0) | ~ (all_47_1 = 0) % 14.31/2.75 | | | % 14.31/2.75 | | | GROUND_INST: instantiating (8) with 0, all_47_1, xl, simplifying with (1), % 14.31/2.75 | | | (35) gives: % 14.31/2.75 | | | (38) all_47_1 = 0 % 14.31/2.75 | | | % 14.31/2.75 | | | GROUND_INST: instantiating (8) with 0, all_47_0, xn, simplifying with (3), % 14.31/2.75 | | | (36) gives: % 14.31/2.75 | | | (39) all_47_0 = 0 % 14.31/2.75 | | | % 14.31/2.75 | | | BETA: splitting (37) gives: % 14.31/2.75 | | | % 14.31/2.75 | | | Case 1: % 14.31/2.75 | | | | % 14.31/2.75 | | | | (40) ~ (all_47_0 = 0) % 14.31/2.75 | | | | % 14.31/2.75 | | | | REDUCE: (39), (40) imply: % 14.31/2.75 | | | | (41) $false % 14.31/2.75 | | | | % 14.31/2.75 | | | | CLOSE: (41) is inconsistent. % 14.31/2.75 | | | | % 14.31/2.75 | | | Case 2: % 14.31/2.75 | | | | % 14.31/2.75 | | | | (42) ~ (all_47_1 = 0) % 14.31/2.75 | | | | % 14.31/2.75 | | | | REDUCE: (38), (42) imply: % 14.31/2.75 | | | | (43) $false % 14.31/2.75 | | | | % 14.31/2.75 | | | | CLOSE: (43) is inconsistent. % 14.31/2.75 | | | | % 14.31/2.75 | | | End of split % 14.31/2.75 | | | % 14.31/2.75 | | Case 2: % 14.31/2.75 | | | % 14.31/2.75 | | | (44) ( ~ (all_31_0 = 0) | ? [v0: $i] : (sdtasdt0(xl, v0) = xn & % 14.31/2.75 | | | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_31_0 = 0 | ! [v0: % 14.31/2.75 | | | $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ? [v1: int] : % 14.31/2.75 | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))) % 14.31/2.75 | | | % 14.31/2.75 | | | ALPHA: (44) implies: % 14.31/2.75 | | | (45) all_31_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~ % 14.31/2.75 | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 14.31/2.75 | | | v1)) % 14.31/2.75 | | | % 14.31/2.75 | | | BETA: splitting (14) gives: % 14.31/2.75 | | | % 14.31/2.75 | | | Case 1: % 14.31/2.75 | | | | % 14.31/2.76 | | | | (46) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 14.31/2.76 | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.31/2.76 | | | | % 14.31/2.76 | | | | DELTA: instantiating (46) with fresh symbols all_49_0, all_49_1 gives: % 14.31/2.76 | | | | (47) aNaturalNumber0(xm) = all_49_0 & aNaturalNumber0(xl) = all_49_1 % 14.31/2.76 | | | | & ( ~ (all_49_0 = 0) | ~ (all_49_1 = 0)) % 14.31/2.76 | | | | % 14.31/2.76 | | | | ALPHA: (47) implies: % 14.31/2.76 | | | | (48) aNaturalNumber0(xl) = all_49_1 % 14.31/2.76 | | | | (49) aNaturalNumber0(xm) = all_49_0 % 14.31/2.76 | | | | (50) ~ (all_49_0 = 0) | ~ (all_49_1 = 0) % 14.31/2.76 | | | | % 14.31/2.76 | | | | GROUND_INST: instantiating (8) with 0, all_49_1, xl, simplifying with % 14.31/2.76 | | | | (1), (48) gives: % 14.31/2.76 | | | | (51) all_49_1 = 0 % 14.31/2.76 | | | | % 14.31/2.76 | | | | GROUND_INST: instantiating (8) with 0, all_49_0, xm, simplifying with % 14.31/2.76 | | | | (2), (49) gives: % 14.31/2.76 | | | | (52) all_49_0 = 0 % 14.31/2.76 | | | | % 14.31/2.76 | | | | BETA: splitting (50) gives: % 14.31/2.76 | | | | % 14.31/2.76 | | | | Case 1: % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | (53) ~ (all_49_0 = 0) % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | REDUCE: (52), (53) imply: % 14.31/2.76 | | | | | (54) $false % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | CLOSE: (54) is inconsistent. % 14.31/2.76 | | | | | % 14.31/2.76 | | | | Case 2: % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | (55) ~ (all_49_1 = 0) % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | REDUCE: (51), (55) imply: % 14.31/2.76 | | | | | (56) $false % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | CLOSE: (56) is inconsistent. % 14.31/2.76 | | | | | % 14.31/2.76 | | | | End of split % 14.31/2.76 | | | | % 14.31/2.76 | | | Case 2: % 14.31/2.76 | | | | % 14.31/2.76 | | | | (57) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & % 14.31/2.76 | | | | $i(v0)) % 14.31/2.76 | | | | % 14.31/2.76 | | | | DELTA: instantiating (57) with fresh symbol all_49_0 gives: % 14.31/2.76 | | | | (58) sdtasdt0(xl, all_49_0) = xm & aNaturalNumber0(all_49_0) = 0 & % 14.31/2.76 | | | | $i(all_49_0) % 14.31/2.76 | | | | % 14.31/2.76 | | | | ALPHA: (58) implies: % 14.31/2.76 | | | | (59) $i(all_49_0) % 14.31/2.76 | | | | (60) aNaturalNumber0(all_49_0) = 0 % 14.31/2.76 | | | | (61) sdtasdt0(xl, all_49_0) = xm % 14.31/2.76 | | | | % 14.31/2.76 | | | | BETA: splitting (45) gives: % 14.31/2.76 | | | | % 14.31/2.76 | | | | Case 1: % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | (62) all_31_0 = 0 % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | REDUCE: (10), (62) imply: % 14.31/2.76 | | | | | (63) $false % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | CLOSE: (63) is inconsistent. % 14.31/2.76 | | | | | % 14.31/2.76 | | | | Case 2: % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | (64) ! [v0: $i] : ( ~ (sdtasdt0(xl, v0) = xn) | ~ $i(v0) | ? % 14.31/2.76 | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_49_0, xm, % 14.31/2.76 | | | | | simplifying with (4), (59), (61) gives: % 14.31/2.76 | | | | | (65) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 14.31/2.76 | | | | | (sdtasdt0(all_49_0, xl) = v2 & aNaturalNumber0(all_49_0) = v1 % 14.31/2.76 | | | | | & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 % 14.31/2.76 | | | | | = 0) | v2 = xm)) % 14.31/2.76 | | | | | % 14.31/2.76 | | | | | GROUND_INST: instantiating (mMulAsso) with xl, all_49_0, all_39_0, xm, % 14.31/2.76 | | | | | xn, simplifying with (4), (30), (32), (59), (61) gives: % 14.31/2.77 | | | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 14.31/2.77 | | | | | [v4: $i] : (sdtasdt0(all_49_0, all_39_0) = v3 & sdtasdt0(xl, % 14.31/2.77 | | | | | v3) = v4 & aNaturalNumber0(all_49_0) = v1 & % 14.31/2.77 | | | | | aNaturalNumber0(all_39_0) = v2 & aNaturalNumber0(xl) = v0 & % 14.31/2.77 | | | | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | % 14.31/2.77 | | | | | v4 = xn)) % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (mMulComm) with xm, all_39_0, xn, % 14.31/2.77 | | | | | simplifying with (5), (30), (32) gives: % 14.31/2.77 | | | | | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 14.31/2.77 | | | | | (sdtasdt0(all_39_0, xm) = v2 & aNaturalNumber0(all_39_0) = v1 % 14.31/2.77 | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 % 14.31/2.77 | | | | | = 0) | v2 = xn)) % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | DELTA: instantiating (67) with fresh symbols all_61_0, all_61_1, % 14.31/2.77 | | | | | all_61_2 gives: % 14.31/2.77 | | | | | (68) sdtasdt0(all_39_0, xm) = all_61_0 & aNaturalNumber0(all_39_0) % 14.31/2.77 | | | | | = all_61_1 & aNaturalNumber0(xm) = all_61_2 & $i(all_61_0) & ( % 14.31/2.77 | | | | | ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | all_61_0 = xn) % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | ALPHA: (68) implies: % 14.31/2.77 | | | | | (69) aNaturalNumber0(all_39_0) = all_61_1 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | DELTA: instantiating (65) with fresh symbols all_63_0, all_63_1, % 14.31/2.77 | | | | | all_63_2 gives: % 14.31/2.77 | | | | | (70) sdtasdt0(all_49_0, xl) = all_63_0 & aNaturalNumber0(all_49_0) % 14.31/2.77 | | | | | = all_63_1 & aNaturalNumber0(xl) = all_63_2 & $i(all_63_0) & ( % 14.31/2.77 | | | | | ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = xm) % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | ALPHA: (70) implies: % 14.31/2.77 | | | | | (71) aNaturalNumber0(xl) = all_63_2 % 14.31/2.77 | | | | | (72) aNaturalNumber0(all_49_0) = all_63_1 % 14.31/2.77 | | | | | (73) sdtasdt0(all_49_0, xl) = all_63_0 % 14.31/2.77 | | | | | (74) ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | all_63_0 = xm % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | DELTA: instantiating (66) with fresh symbols all_65_0, all_65_1, % 14.31/2.77 | | | | | all_65_2, all_65_3, all_65_4 gives: % 14.31/2.77 | | | | | (75) sdtasdt0(all_49_0, all_39_0) = all_65_1 & sdtasdt0(xl, % 14.31/2.77 | | | | | all_65_1) = all_65_0 & aNaturalNumber0(all_49_0) = all_65_3 % 14.31/2.77 | | | | | & aNaturalNumber0(all_39_0) = all_65_2 & aNaturalNumber0(xl) = % 14.31/2.77 | | | | | all_65_4 & $i(all_65_0) & $i(all_65_1) & ( ~ (all_65_2 = 0) | % 14.31/2.77 | | | | | ~ (all_65_3 = 0) | ~ (all_65_4 = 0) | all_65_0 = xn) % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | ALPHA: (75) implies: % 14.31/2.77 | | | | | (76) $i(all_65_1) % 14.31/2.77 | | | | | (77) aNaturalNumber0(xl) = all_65_4 % 14.31/2.77 | | | | | (78) aNaturalNumber0(all_39_0) = all_65_2 % 14.31/2.77 | | | | | (79) aNaturalNumber0(all_49_0) = all_65_3 % 14.31/2.77 | | | | | (80) sdtasdt0(xl, all_65_1) = all_65_0 % 14.31/2.77 | | | | | (81) sdtasdt0(all_49_0, all_39_0) = all_65_1 % 14.31/2.77 | | | | | (82) ~ (all_65_2 = 0) | ~ (all_65_3 = 0) | ~ (all_65_4 = 0) | % 14.31/2.77 | | | | | all_65_0 = xn % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_4, xl, simplifying with % 14.31/2.77 | | | | | (1), (77) gives: % 14.31/2.77 | | | | | (83) all_65_4 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_63_2, all_65_4, xl, % 14.31/2.77 | | | | | simplifying with (71), (77) gives: % 14.31/2.77 | | | | | (84) all_65_4 = all_63_2 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_2, all_39_0, simplifying % 14.31/2.77 | | | | | with (31), (78) gives: % 14.31/2.77 | | | | | (85) all_65_2 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_61_1, all_65_2, all_39_0, % 14.31/2.77 | | | | | simplifying with (69), (78) gives: % 14.31/2.77 | | | | | (86) all_65_2 = all_61_1 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with 0, all_65_3, all_49_0, simplifying % 14.31/2.77 | | | | | with (60), (79) gives: % 14.31/2.77 | | | | | (87) all_65_3 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | GROUND_INST: instantiating (8) with all_63_1, all_65_3, all_49_0, % 14.31/2.77 | | | | | simplifying with (72), (79) gives: % 14.31/2.77 | | | | | (88) all_65_3 = all_63_1 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | COMBINE_EQS: (85), (86) imply: % 14.31/2.77 | | | | | (89) all_61_1 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | SIMP: (89) implies: % 14.31/2.77 | | | | | (90) all_61_1 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | COMBINE_EQS: (87), (88) imply: % 14.31/2.77 | | | | | (91) all_63_1 = 0 % 14.31/2.77 | | | | | % 14.31/2.77 | | | | | SIMP: (91) implies: % 14.31/2.78 | | | | | (92) all_63_1 = 0 % 14.31/2.78 | | | | | % 14.31/2.78 | | | | | COMBINE_EQS: (83), (84) imply: % 14.31/2.78 | | | | | (93) all_63_2 = 0 % 14.31/2.78 | | | | | % 14.31/2.78 | | | | | SIMP: (93) implies: % 14.31/2.78 | | | | | (94) all_63_2 = 0 % 14.31/2.78 | | | | | % 14.31/2.78 | | | | | BETA: splitting (82) gives: % 14.31/2.78 | | | | | % 14.31/2.78 | | | | | Case 1: % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | (95) ~ (all_65_2 = 0) % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | REDUCE: (85), (95) imply: % 14.31/2.78 | | | | | | (96) $false % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | CLOSE: (96) is inconsistent. % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | Case 2: % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | (97) ~ (all_65_3 = 0) | ~ (all_65_4 = 0) | all_65_0 = xn % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | BETA: splitting (97) gives: % 14.31/2.78 | | | | | | % 14.31/2.78 | | | | | | Case 1: % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | (98) ~ (all_65_3 = 0) % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | REDUCE: (87), (98) imply: % 14.31/2.78 | | | | | | | (99) $false % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | CLOSE: (99) is inconsistent. % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | Case 2: % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | (100) ~ (all_65_4 = 0) | all_65_0 = xn % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | BETA: splitting (74) gives: % 14.31/2.78 | | | | | | | % 14.31/2.78 | | | | | | | Case 1: % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | (101) ~ (all_63_1 = 0) % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | REDUCE: (92), (101) imply: % 14.31/2.78 | | | | | | | | (102) $false % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | CLOSE: (102) is inconsistent. % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | Case 2: % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | (103) ~ (all_63_2 = 0) | all_63_0 = xm % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | BETA: splitting (103) gives: % 14.31/2.78 | | | | | | | | % 14.31/2.78 | | | | | | | | Case 1: % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | (104) ~ (all_63_2 = 0) % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | REDUCE: (94), (104) imply: % 14.31/2.78 | | | | | | | | | (105) $false % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | CLOSE: (105) is inconsistent. % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | Case 2: % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | (106) all_63_0 = xm % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | REDUCE: (73), (106) imply: % 14.31/2.78 | | | | | | | | | (107) sdtasdt0(all_49_0, xl) = xm % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | BETA: splitting (100) gives: % 14.31/2.78 | | | | | | | | | % 14.31/2.78 | | | | | | | | | Case 1: % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | (108) ~ (all_65_4 = 0) % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | REDUCE: (83), (108) imply: % 14.31/2.78 | | | | | | | | | | (109) $false % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | CLOSE: (109) is inconsistent. % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | Case 2: % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | (110) all_65_0 = xn % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | REDUCE: (80), (110) imply: % 14.31/2.78 | | | | | | | | | | (111) sdtasdt0(xl, all_65_1) = xn % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (64) with all_65_1, simplifying with % 14.31/2.78 | | | | | | | | | | (76), (111) gives: % 14.31/2.78 | | | | | | | | | | (112) ? [v0: int] : ( ~ (v0 = 0) & % 14.31/2.78 | | | | | | | | | | aNaturalNumber0(all_65_1) = v0) % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_65_1, xn, % 14.31/2.78 | | | | | | | | | | simplifying with (4), (76), (111) gives: % 14.31/2.78 | | | | | | | | | | (113) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 14.31/2.78 | | | | | | | | | | (sdtasdt0(all_65_1, xl) = v2 & % 14.31/2.78 | | | | | | | | | | aNaturalNumber0(all_65_1) = v1 & % 14.31/2.78 | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 14.31/2.78 | | | | | | | | | | | ~ (v0 = 0) | v2 = xn)) % 14.31/2.78 | | | | | | | | | | % 14.31/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with all_49_0, xl, % 14.31/2.78 | | | | | | | | | | all_39_0, xm, xn, simplifying with (4), (30), % 14.31/2.78 | | | | | | | | | | (32), (59), (107) gives: % 14.60/2.78 | | | | | | | | | | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 14.60/2.78 | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_49_0, v3) = % 14.60/2.78 | | | | | | | | | | v4 & sdtasdt0(xl, all_39_0) = v3 & % 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 & % 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_39_0) = v2 & % 14.60/2.78 | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v4) & $i(v3) & ( ~ % 14.60/2.78 | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 14.60/2.78 | | | | | | | | | | xn)) % 14.60/2.78 | | | | | | | | | | % 14.60/2.78 | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_49_0, all_39_0, % 14.60/2.78 | | | | | | | | | | all_65_1, simplifying with (30), (59), (81) gives: % 14.60/2.78 | | | | | | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 14.60/2.78 | | | | | | | | | | (sdtasdt0(all_39_0, all_49_0) = v2 & % 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 & % 14.60/2.78 | | | | | | | | | | aNaturalNumber0(all_39_0) = v1 & $i(v2) & ( ~ (v1 % 14.60/2.78 | | | | | | | | | | = 0) | ~ (v0 = 0) | v2 = all_65_1)) % 14.60/2.78 | | | | | | | | | | % 14.60/2.78 | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_49_0, % 14.60/2.78 | | | | | | | | | | all_39_0, all_65_1, simplifying with (30), (59), % 14.60/2.78 | | | | | | | | | | (81) gives: % 14.60/2.79 | | | | | | | | | | (116) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 14.60/2.79 | | | | | | | | | | (aNaturalNumber0(all_65_1) = v2 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = v0 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = v1 & ( ~ (v1 = 0) | % 14.60/2.79 | | | | | | | | | | ~ (v0 = 0) | v2 = 0)) % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | DELTA: instantiating (112) with fresh symbol all_104_0 % 14.60/2.79 | | | | | | | | | | gives: % 14.60/2.79 | | | | | | | | | | (117) ~ (all_104_0 = 0) & aNaturalNumber0(all_65_1) = % 14.60/2.79 | | | | | | | | | | all_104_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | ALPHA: (117) implies: % 14.60/2.79 | | | | | | | | | | (118) ~ (all_104_0 = 0) % 14.60/2.79 | | | | | | | | | | (119) aNaturalNumber0(all_65_1) = all_104_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_108_0, % 14.60/2.79 | | | | | | | | | | all_108_1, all_108_2 gives: % 14.60/2.79 | | | | | | | | | | (120) aNaturalNumber0(all_65_1) = all_108_0 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_108_2 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_108_1 & ( ~ % 14.60/2.79 | | | | | | | | | | (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0 % 14.60/2.79 | | | | | | | | | | = 0) % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | ALPHA: (120) implies: % 14.60/2.79 | | | | | | | | | | (121) aNaturalNumber0(all_39_0) = all_108_1 % 14.60/2.79 | | | | | | | | | | (122) aNaturalNumber0(all_49_0) = all_108_2 % 14.60/2.79 | | | | | | | | | | (123) aNaturalNumber0(all_65_1) = all_108_0 % 14.60/2.79 | | | | | | | | | | (124) ~ (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0 % 14.60/2.79 | | | | | | | | | | = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_110_0, % 14.60/2.79 | | | | | | | | | | all_110_1, all_110_2 gives: % 14.60/2.79 | | | | | | | | | | (125) sdtasdt0(all_39_0, all_49_0) = all_110_0 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_110_2 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_110_1 & % 14.60/2.79 | | | | | | | | | | $i(all_110_0) & ( ~ (all_110_1 = 0) | ~ (all_110_2 % 14.60/2.79 | | | | | | | | | | = 0) | all_110_0 = all_65_1) % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | ALPHA: (125) implies: % 14.60/2.79 | | | | | | | | | | (126) aNaturalNumber0(all_39_0) = all_110_1 % 14.60/2.79 | | | | | | | | | | (127) aNaturalNumber0(all_49_0) = all_110_2 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_112_0, % 14.60/2.79 | | | | | | | | | | all_112_1, all_112_2 gives: % 14.60/2.79 | | | | | | | | | | (128) sdtasdt0(all_65_1, xl) = all_112_0 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_65_1) = all_112_1 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(xl) = all_112_2 & $i(all_112_0) & ( % 14.60/2.79 | | | | | | | | | | ~ (all_112_1 = 0) | ~ (all_112_2 = 0) | % 14.60/2.79 | | | | | | | | | | all_112_0 = xn) % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | ALPHA: (128) implies: % 14.60/2.79 | | | | | | | | | | (129) aNaturalNumber0(all_65_1) = all_112_1 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_114_0, % 14.60/2.79 | | | | | | | | | | all_114_1, all_114_2, all_114_3, all_114_4 gives: % 14.60/2.79 | | | | | | | | | | (130) sdtasdt0(all_49_0, all_114_1) = all_114_0 & % 14.60/2.79 | | | | | | | | | | sdtasdt0(xl, all_39_0) = all_114_1 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_49_0) = all_114_4 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(all_39_0) = all_114_2 & % 14.60/2.79 | | | | | | | | | | aNaturalNumber0(xl) = all_114_3 & $i(all_114_0) & % 14.60/2.79 | | | | | | | | | | $i(all_114_1) & ( ~ (all_114_2 = 0) | ~ (all_114_3 % 14.60/2.79 | | | | | | | | | | = 0) | ~ (all_114_4 = 0) | all_114_0 = xn) % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | ALPHA: (130) implies: % 14.60/2.79 | | | | | | | | | | (131) aNaturalNumber0(all_39_0) = all_114_2 % 14.60/2.79 | | | | | | | | | | (132) aNaturalNumber0(all_49_0) = all_114_4 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_114_2, all_39_0, % 14.60/2.79 | | | | | | | | | | simplifying with (31), (131) gives: % 14.60/2.79 | | | | | | | | | | (133) all_114_2 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_110_1, all_114_2, % 14.60/2.79 | | | | | | | | | | all_39_0, simplifying with (126), (131) gives: % 14.60/2.79 | | | | | | | | | | (134) all_114_2 = all_110_1 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_1, all_114_2, % 14.60/2.79 | | | | | | | | | | all_39_0, simplifying with (121), (131) gives: % 14.60/2.79 | | | | | | | | | | (135) all_114_2 = all_108_1 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_114_4, all_49_0, % 14.60/2.79 | | | | | | | | | | simplifying with (60), (132) gives: % 14.60/2.79 | | | | | | | | | | (136) all_114_4 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_110_2, all_114_4, % 14.60/2.79 | | | | | | | | | | all_49_0, simplifying with (127), (132) gives: % 14.60/2.79 | | | | | | | | | | (137) all_114_4 = all_110_2 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_2, all_114_4, % 14.60/2.79 | | | | | | | | | | all_49_0, simplifying with (122), (132) gives: % 14.60/2.79 | | | | | | | | | | (138) all_114_4 = all_108_2 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_108_0, all_112_1, % 14.60/2.79 | | | | | | | | | | all_65_1, simplifying with (123), (129) gives: % 14.60/2.79 | | | | | | | | | | (139) all_112_1 = all_108_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | GROUND_INST: instantiating (8) with all_104_0, all_112_1, % 14.60/2.79 | | | | | | | | | | all_65_1, simplifying with (119), (129) gives: % 14.60/2.79 | | | | | | | | | | (140) all_112_1 = all_104_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (134), (135) imply: % 14.60/2.79 | | | | | | | | | | (141) all_110_1 = all_108_1 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (133), (134) imply: % 14.60/2.79 | | | | | | | | | | (142) all_110_1 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (136), (137) imply: % 14.60/2.79 | | | | | | | | | | (143) all_110_2 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 14.60/2.79 | | | | | | | | | | (144) all_110_2 = all_108_2 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (139), (140) imply: % 14.60/2.79 | | | | | | | | | | (145) all_108_0 = all_104_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | SIMP: (145) implies: % 14.60/2.79 | | | | | | | | | | (146) all_108_0 = all_104_0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (141), (142) imply: % 14.60/2.79 | | | | | | | | | | (147) all_108_1 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 14.60/2.79 | | | | | | | | | | (148) all_108_2 = 0 % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | BETA: splitting (124) gives: % 14.60/2.79 | | | | | | | | | | % 14.60/2.79 | | | | | | | | | | Case 1: % 14.60/2.79 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | (149) ~ (all_108_1 = 0) % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | REDUCE: (147), (149) imply: % 14.60/2.80 | | | | | | | | | | | (150) $false % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | CLOSE: (150) is inconsistent. % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | Case 2: % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | (151) ~ (all_108_2 = 0) | all_108_0 = 0 % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | BETA: splitting (151) gives: % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | Case 1: % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | (152) ~ (all_108_2 = 0) % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | REDUCE: (148), (152) imply: % 14.60/2.80 | | | | | | | | | | | | (153) $false % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | Case 2: % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | (154) all_108_0 = 0 % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | COMBINE_EQS: (146), (154) imply: % 14.60/2.80 | | | | | | | | | | | | (155) all_104_0 = 0 % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | SIMP: (155) implies: % 14.60/2.80 | | | | | | | | | | | | (156) all_104_0 = 0 % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | REDUCE: (118), (156) imply: % 14.60/2.80 | | | | | | | | | | | | (157) $false % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 14.60/2.80 | | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | | End of split % 14.60/2.80 | | | | | | | | | | | % 14.60/2.80 | | | | | | | | | | End of split % 14.60/2.80 | | | | | | | | | | % 14.60/2.80 | | | | | | | | | End of split % 14.60/2.80 | | | | | | | | | % 14.60/2.80 | | | | | | | | End of split % 14.60/2.80 | | | | | | | | % 14.60/2.80 | | | | | | | End of split % 14.60/2.80 | | | | | | | % 14.60/2.80 | | | | | | End of split % 14.60/2.80 | | | | | | % 14.60/2.80 | | | | | End of split % 14.60/2.80 | | | | | % 14.60/2.80 | | | | End of split % 14.60/2.80 | | | | % 14.60/2.80 | | | End of split % 14.60/2.80 | | | % 14.60/2.80 | | End of split % 14.60/2.80 | | % 14.60/2.80 | End of split % 14.60/2.80 | % 14.60/2.80 End of proof % 14.60/2.80 % SZS output end Proof for theBenchmark % 14.60/2.80 % 14.60/2.80 2191ms %------------------------------------------------------------------------------