%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM434+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 11:47:44 EDT 2023 % Result : Theorem 10.03s 2.23s % Output : Proof 15.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM434+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n027.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 10:45:18 EDT 2023 % 0.14/0.35 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.62 (c) Philipp Rümmer, 2009-2023 % 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.62 Amanda Stjerna. % 0.18/0.62 Free software under BSD-3-Clause. % 0.18/0.62 % 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.62 % 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.63 Running up to 7 provers in parallel. % 0.18/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.63/1.15 Prover 4: Preprocessing ... % 2.63/1.15 Prover 1: Preprocessing ... % 3.29/1.22 Prover 0: Preprocessing ... % 3.29/1.22 Prover 2: Preprocessing ... % 3.29/1.22 Prover 5: Preprocessing ... % 3.29/1.22 Prover 6: Preprocessing ... % 3.29/1.22 Prover 3: Preprocessing ... % 7.17/1.85 Prover 1: Constructing countermodel ... % 7.17/1.85 Prover 3: Constructing countermodel ... % 8.22/1.94 Prover 6: Proving ... % 8.98/2.05 Prover 5: Constructing countermodel ... % 8.98/2.11 Prover 4: Constructing countermodel ... % 10.03/2.20 Prover 2: Proving ... % 10.03/2.23 Prover 3: proved (1573ms) % 10.03/2.23 % 10.03/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.03/2.23 % 10.03/2.23 Prover 6: stopped % 10.03/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.03/2.24 Prover 5: stopped % 10.03/2.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.03/2.25 Prover 2: stopped % 10.03/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.03/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.68/2.30 Prover 0: Proving ... % 10.68/2.30 Prover 0: stopped % 10.68/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.91/2.31 Prover 7: Preprocessing ... % 11.04/2.36 Prover 8: Preprocessing ... % 11.04/2.37 Prover 10: Preprocessing ... % 11.04/2.38 Prover 11: Preprocessing ... % 11.04/2.40 Prover 13: Preprocessing ... % 12.17/2.52 Prover 8: Warning: ignoring some quantifiers % 12.17/2.54 Prover 8: Constructing countermodel ... % 12.17/2.54 Prover 10: Constructing countermodel ... % 12.75/2.57 Prover 7: Constructing countermodel ... % 12.80/2.68 Prover 13: Constructing countermodel ... % 14.07/2.80 Prover 1: Found proof (size 42) % 14.07/2.80 Prover 1: proved (2151ms) % 14.07/2.80 Prover 4: stopped % 14.07/2.80 Prover 7: stopped % 14.07/2.80 Prover 10: stopped % 14.07/2.80 Prover 8: stopped % 14.07/2.80 Prover 13: stopped % 14.07/2.81 Prover 11: Constructing countermodel ... % 14.07/2.83 Prover 11: stopped % 14.07/2.83 % 14.07/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.07/2.83 % 14.07/2.84 % SZS output start Proof for theBenchmark % 14.07/2.84 Assumptions after simplification: % 14.07/2.84 --------------------------------- % 14.07/2.84 % 14.07/2.84 (mIntMult) % 14.62/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 14.62/2.87 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 14.62/2.87 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0) % 14.62/2.87 | ~ (v3 = 0) | v5 = 0))) % 14.62/2.87 % 14.62/2.87 (mMulAsso) % 14.62/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.62/2.88 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 14.62/2.88 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 14.62/2.88 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aInteger0(v2) = % 14.62/2.88 v7 & aInteger0(v1) = v6 & aInteger0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = % 14.62/2.88 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) % 14.62/2.88 % 14.62/2.88 (mMulComm) % 14.62/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 14.62/2.88 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 14.62/2.88 (sdtasdt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) & % 14.62/2.88 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 14.62/2.88 % 14.62/2.88 (m__) % 14.62/2.88 $i(xq) & $i(xp) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 14.62/2.88 (sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v1) = v2 & smndt0(xb) = v1 & $i(v2) & % 14.62/2.88 $i(v1) & $i(v0) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ? % 14.62/2.88 [v4: int] : ( ~ (v4 = 0) & aInteger0(v3) = v4))) % 14.62/2.88 % 14.62/2.88 (m__1003) % 14.62/2.89 $i(xq) & $i(xp) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? % 14.62/2.89 [v2: $i] : ( ~ (v0 = sz00) & sdteqdtlpzmzozddtrp0(xa, xb, v0) = 0 & % 14.62/2.89 aDivisorOf0(v0, v2) = 0 & sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v1) = v2 & % 14.62/2.89 smndt0(xb) = v1 & $i(v2) & $i(v1) & $i(v0) & ? [v3: $i] : (sdtasdt0(v0, v3) % 14.62/2.89 = v2 & aInteger0(v3) = 0 & $i(v3))) % 14.81/2.89 % 14.81/2.89 (function-axioms) % 14.81/2.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.81/2.89 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) % 14.81/2.89 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 14.81/2.89 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.81/2.89 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] : % 14.81/2.89 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 14.81/2.89 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.81/2.89 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.81/2.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | % 14.81/2.89 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.81/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ % 14.81/2.89 (aInteger0(v2) = v0)) % 14.81/2.89 % 14.81/2.89 Further assumptions not needed in the proof: % 14.81/2.89 -------------------------------------------- % 14.81/2.89 mAddAsso, mAddComm, mAddNeg, mAddZero, mDistrib, mDivisor, mEquMod, mEquModRef, % 14.81/2.89 mEquModSym, mEquModTrn, mIntNeg, mIntOne, mIntPlus, mIntZero, mIntegers, % 14.81/2.89 mMulMinOne, mMulOne, mMulZero, mZeroDiv, m__979 % 14.81/2.89 % 14.81/2.89 Those formulas are unsatisfiable: % 14.81/2.89 --------------------------------- % 14.81/2.89 % 14.81/2.89 Begin of proof % 14.81/2.89 | % 14.81/2.89 | ALPHA: (m__1003) implies: % 14.81/2.90 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = sz00) & % 14.81/2.90 | sdteqdtlpzmzozddtrp0(xa, xb, v0) = 0 & aDivisorOf0(v0, v2) = 0 & % 14.81/2.90 | sdtasdt0(xp, xq) = v0 & sdtpldt0(xa, v1) = v2 & smndt0(xb) = v1 & % 14.81/2.90 | $i(v2) & $i(v1) & $i(v0) & ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & % 14.81/2.90 | aInteger0(v3) = 0 & $i(v3))) % 14.81/2.90 | % 14.81/2.90 | ALPHA: (m__) implies: % 14.81/2.90 | (2) $i(xp) % 14.81/2.90 | (3) $i(xq) % 14.81/2.90 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xp, xq) = v0 & % 14.81/2.90 | sdtpldt0(xa, v1) = v2 & smndt0(xb) = v1 & $i(v2) & $i(v1) & $i(v0) & % 14.81/2.90 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ? [v4: int] : % 14.81/2.90 | ( ~ (v4 = 0) & aInteger0(v3) = v4))) % 14.81/2.90 | % 14.81/2.90 | ALPHA: (function-axioms) implies: % 14.81/2.90 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.81/2.90 | (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0)) % 14.81/2.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 14.81/2.90 | v1) | ~ (smndt0(v2) = v0)) % 14.81/2.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.81/2.90 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 14.81/2.91 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.81/2.91 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 14.81/2.91 | % 14.81/2.91 | DELTA: instantiating (4) with fresh symbols all_22_0, all_22_1, all_22_2 % 14.81/2.91 | gives: % 14.81/2.91 | (9) sdtasdt0(xp, xq) = all_22_2 & sdtpldt0(xa, all_22_1) = all_22_0 & % 14.81/2.91 | smndt0(xb) = all_22_1 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & ! % 14.81/2.91 | [v0: $i] : ( ~ (sdtasdt0(all_22_2, v0) = all_22_0) | ~ $i(v0) | ? % 14.81/2.91 | [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)) % 14.81/2.91 | % 14.81/2.91 | ALPHA: (9) implies: % 14.81/2.91 | (10) smndt0(xb) = all_22_1 % 14.81/2.91 | (11) sdtpldt0(xa, all_22_1) = all_22_0 % 14.81/2.91 | (12) sdtasdt0(xp, xq) = all_22_2 % 14.81/2.91 | (13) ! [v0: $i] : ( ~ (sdtasdt0(all_22_2, v0) = all_22_0) | ~ $i(v0) | ? % 14.81/2.91 | [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)) % 14.81/2.91 | % 14.81/2.91 | DELTA: instantiating (1) with fresh symbols all_25_0, all_25_1, all_25_2 % 14.81/2.91 | gives: % 14.81/2.91 | (14) ~ (all_25_2 = sz00) & sdteqdtlpzmzozddtrp0(xa, xb, all_25_2) = 0 & % 14.81/2.91 | aDivisorOf0(all_25_2, all_25_0) = 0 & sdtasdt0(xp, xq) = all_25_2 & % 14.81/2.91 | sdtpldt0(xa, all_25_1) = all_25_0 & smndt0(xb) = all_25_1 & % 14.81/2.91 | $i(all_25_0) & $i(all_25_1) & $i(all_25_2) & ? [v0: $i] : % 14.81/2.91 | (sdtasdt0(all_25_2, v0) = all_25_0 & aInteger0(v0) = 0 & $i(v0)) % 14.81/2.91 | % 14.81/2.91 | ALPHA: (14) implies: % 14.81/2.91 | (15) $i(all_25_2) % 14.81/2.91 | (16) smndt0(xb) = all_25_1 % 14.81/2.91 | (17) sdtpldt0(xa, all_25_1) = all_25_0 % 14.81/2.91 | (18) sdtasdt0(xp, xq) = all_25_2 % 14.81/2.91 | (19) ? [v0: $i] : (sdtasdt0(all_25_2, v0) = all_25_0 & aInteger0(v0) = 0 & % 14.81/2.91 | $i(v0)) % 14.81/2.91 | % 14.81/2.91 | DELTA: instantiating (19) with fresh symbol all_30_0 gives: % 14.81/2.91 | (20) sdtasdt0(all_25_2, all_30_0) = all_25_0 & aInteger0(all_30_0) = 0 & % 14.81/2.91 | $i(all_30_0) % 14.81/2.91 | % 14.81/2.91 | ALPHA: (20) implies: % 14.81/2.91 | (21) $i(all_30_0) % 14.81/2.91 | (22) aInteger0(all_30_0) = 0 % 14.81/2.91 | (23) sdtasdt0(all_25_2, all_30_0) = all_25_0 % 14.81/2.91 | % 14.81/2.92 | GROUND_INST: instantiating (6) with all_22_1, all_25_1, xb, simplifying with % 14.81/2.92 | (10), (16) gives: % 14.81/2.92 | (24) all_25_1 = all_22_1 % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (8) with all_22_2, all_25_2, xq, xp, simplifying % 14.81/2.92 | with (12), (18) gives: % 14.81/2.92 | (25) all_25_2 = all_22_2 % 14.81/2.92 | % 14.81/2.92 | REDUCE: (23), (25) imply: % 14.81/2.92 | (26) sdtasdt0(all_22_2, all_30_0) = all_25_0 % 14.81/2.92 | % 14.81/2.92 | REDUCE: (17), (24) imply: % 14.81/2.92 | (27) sdtpldt0(xa, all_22_1) = all_25_0 % 14.81/2.92 | % 14.81/2.92 | REDUCE: (15), (25) imply: % 14.81/2.92 | (28) $i(all_22_2) % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (7) with all_22_0, all_25_0, all_22_1, xa, % 14.81/2.92 | simplifying with (11), (27) gives: % 14.81/2.92 | (29) all_25_0 = all_22_0 % 14.81/2.92 | % 14.81/2.92 | REDUCE: (26), (29) imply: % 14.81/2.92 | (30) sdtasdt0(all_22_2, all_30_0) = all_22_0 % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (mMulAsso) with xp, xq, all_30_0, all_22_2, % 14.81/2.92 | all_22_0, simplifying with (2), (3), (12), (21), (30) gives: % 14.81/2.92 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 14.81/2.92 | : (sdtasdt0(xq, all_30_0) = v3 & sdtasdt0(xp, v3) = v4 & % 14.81/2.92 | aInteger0(all_30_0) = v2 & aInteger0(xq) = v1 & aInteger0(xp) = v0 & % 14.81/2.92 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 14.81/2.92 | all_22_0)) % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (13) with all_30_0, simplifying with (21), (30) % 14.81/2.92 | gives: % 14.81/2.92 | (32) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_30_0) = v0) % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (mMulComm) with all_22_2, all_30_0, all_22_0, % 14.81/2.92 | simplifying with (21), (28), (30) gives: % 14.81/2.92 | (33) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_30_0, % 14.81/2.92 | all_22_2) = v2 & aInteger0(all_30_0) = v1 & aInteger0(all_22_2) = % 14.81/2.92 | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_22_0)) % 14.81/2.92 | % 14.81/2.92 | GROUND_INST: instantiating (mIntMult) with all_22_2, all_30_0, all_22_0, % 14.81/2.92 | simplifying with (21), (28), (30) gives: % 14.81/2.93 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_30_0) = v1 % 14.81/2.93 | & aInteger0(all_22_0) = v2 & aInteger0(all_22_2) = v0 & ( ~ (v1 = 0) % 14.81/2.93 | | ~ (v0 = 0) | v2 = 0)) % 14.81/2.93 | % 14.81/2.93 | DELTA: instantiating (32) with fresh symbol all_52_0 gives: % 14.81/2.93 | (35) ~ (all_52_0 = 0) & aInteger0(all_30_0) = all_52_0 % 14.81/2.93 | % 14.81/2.93 | ALPHA: (35) implies: % 14.81/2.93 | (36) ~ (all_52_0 = 0) % 14.81/2.93 | (37) aInteger0(all_30_0) = all_52_0 % 14.81/2.93 | % 14.81/2.93 | DELTA: instantiating (34) with fresh symbols all_62_0, all_62_1, all_62_2 % 14.81/2.93 | gives: % 14.81/2.93 | (38) aInteger0(all_30_0) = all_62_1 & aInteger0(all_22_0) = all_62_0 & % 14.81/2.93 | aInteger0(all_22_2) = all_62_2 & ( ~ (all_62_1 = 0) | ~ (all_62_2 = % 14.81/2.93 | 0) | all_62_0 = 0) % 14.81/2.93 | % 14.81/2.93 | ALPHA: (38) implies: % 14.81/2.93 | (39) aInteger0(all_30_0) = all_62_1 % 14.81/2.93 | % 14.81/2.93 | DELTA: instantiating (33) with fresh symbols all_66_0, all_66_1, all_66_2 % 14.81/2.93 | gives: % 14.81/2.93 | (40) sdtasdt0(all_30_0, all_22_2) = all_66_0 & aInteger0(all_30_0) = % 14.81/2.93 | all_66_1 & aInteger0(all_22_2) = all_66_2 & $i(all_66_0) & ( ~ % 14.81/2.93 | (all_66_1 = 0) | ~ (all_66_2 = 0) | all_66_0 = all_22_0) % 14.81/2.93 | % 14.81/2.93 | ALPHA: (40) implies: % 14.81/2.93 | (41) aInteger0(all_30_0) = all_66_1 % 14.81/2.93 | % 14.81/2.93 | DELTA: instantiating (31) with fresh symbols all_70_0, all_70_1, all_70_2, % 14.81/2.93 | all_70_3, all_70_4 gives: % 14.81/2.93 | (42) sdtasdt0(xq, all_30_0) = all_70_1 & sdtasdt0(xp, all_70_1) = all_70_0 % 14.81/2.93 | & aInteger0(all_30_0) = all_70_2 & aInteger0(xq) = all_70_3 & % 14.81/2.93 | aInteger0(xp) = all_70_4 & $i(all_70_0) & $i(all_70_1) & ( ~ (all_70_2 % 14.81/2.93 | = 0) | ~ (all_70_3 = 0) | ~ (all_70_4 = 0) | all_70_0 = % 14.81/2.93 | all_22_0) % 14.81/2.93 | % 14.81/2.93 | ALPHA: (42) implies: % 14.81/2.93 | (43) aInteger0(all_30_0) = all_70_2 % 14.81/2.93 | % 14.81/2.93 | GROUND_INST: instantiating (5) with all_52_0, all_66_1, all_30_0, simplifying % 14.81/2.93 | with (37), (41) gives: % 14.81/2.93 | (44) all_66_1 = all_52_0 % 14.81/2.93 | % 14.81/2.93 | GROUND_INST: instantiating (5) with 0, all_70_2, all_30_0, simplifying with % 14.81/2.93 | (22), (43) gives: % 14.81/2.93 | (45) all_70_2 = 0 % 15.03/2.93 | % 15.03/2.93 | GROUND_INST: instantiating (5) with all_66_1, all_70_2, all_30_0, simplifying % 15.03/2.93 | with (41), (43) gives: % 15.03/2.93 | (46) all_70_2 = all_66_1 % 15.03/2.93 | % 15.03/2.93 | GROUND_INST: instantiating (5) with all_62_1, all_70_2, all_30_0, simplifying % 15.03/2.93 | with (39), (43) gives: % 15.03/2.93 | (47) all_70_2 = all_62_1 % 15.03/2.93 | % 15.03/2.93 | COMBINE_EQS: (45), (47) imply: % 15.03/2.93 | (48) all_62_1 = 0 % 15.03/2.93 | % 15.03/2.93 | COMBINE_EQS: (46), (47) imply: % 15.03/2.93 | (49) all_66_1 = all_62_1 % 15.03/2.93 | % 15.03/2.93 | SIMP: (49) implies: % 15.03/2.93 | (50) all_66_1 = all_62_1 % 15.03/2.93 | % 15.03/2.94 | COMBINE_EQS: (44), (50) imply: % 15.03/2.94 | (51) all_62_1 = all_52_0 % 15.03/2.94 | % 15.03/2.94 | SIMP: (51) implies: % 15.03/2.94 | (52) all_62_1 = all_52_0 % 15.03/2.94 | % 15.03/2.94 | COMBINE_EQS: (48), (52) imply: % 15.03/2.94 | (53) all_52_0 = 0 % 15.03/2.94 | % 15.03/2.94 | REDUCE: (36), (53) imply: % 15.03/2.94 | (54) $false % 15.03/2.94 | % 15.03/2.94 | CLOSE: (54) is inconsistent. % 15.03/2.94 | % 15.03/2.94 End of proof % 15.03/2.94 % SZS output end Proof for theBenchmark % 15.03/2.94 % 15.03/2.94 2321ms %------------------------------------------------------------------------------