%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG089+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 13:57:47 EDT 2023 % Result : Theorem 11.77s 2.38s % Output : Proof 15.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG089+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sun Aug 27 02:17:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 3.02/1.15 Prover 1: Preprocessing ... % 3.02/1.15 Prover 4: Preprocessing ... % 3.44/1.19 Prover 5: Preprocessing ... % 3.44/1.19 Prover 2: Preprocessing ... % 3.44/1.19 Prover 0: Preprocessing ... % 3.44/1.19 Prover 3: Preprocessing ... % 3.44/1.19 Prover 6: Preprocessing ... % 8.13/1.88 Prover 3: Constructing countermodel ... % 8.25/1.88 Prover 1: Constructing countermodel ... % 8.25/1.90 Prover 6: Proving ... % 8.25/1.91 Prover 5: Proving ... % 8.46/2.01 Prover 4: Constructing countermodel ... % 8.46/2.05 Prover 2: Proving ... % 8.94/2.09 Prover 0: Proving ... % 11.77/2.38 Prover 3: proved (1736ms) % 11.77/2.38 % 11.77/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.77/2.38 % 11.77/2.38 Prover 2: stopped % 11.77/2.38 Prover 5: stopped % 11.77/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.77/2.39 Prover 0: stopped % 11.77/2.40 Prover 6: stopped % 11.77/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.77/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.77/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.77/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.19/2.44 Prover 8: Preprocessing ... % 12.44/2.46 Prover 7: Preprocessing ... % 12.44/2.48 Prover 10: Preprocessing ... % 12.44/2.49 Prover 13: Preprocessing ... % 12.44/2.52 Prover 11: Preprocessing ... % 13.29/2.63 Prover 7: Constructing countermodel ... % 13.79/2.64 Prover 10: Constructing countermodel ... % 13.79/2.65 Prover 8: Warning: ignoring some quantifiers % 13.79/2.66 Prover 8: Constructing countermodel ... % 13.79/2.74 Prover 13: Warning: ignoring some quantifiers % 13.79/2.75 Prover 13: Constructing countermodel ... % 13.79/2.79 Prover 11: Constructing countermodel ... % 15.40/2.88 Prover 10: Found proof (size 14) % 15.40/2.88 Prover 1: Found proof (size 55) % 15.40/2.88 Prover 10: proved (488ms) % 15.40/2.88 Prover 1: proved (2254ms) % 15.40/2.89 Prover 11: stopped % 15.40/2.89 Prover 13: stopped % 15.40/2.89 Prover 7: stopped % 15.40/2.89 Prover 4: stopped % 15.40/2.89 Prover 8: stopped % 15.40/2.89 % 15.40/2.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.40/2.89 % 15.62/2.90 % SZS output start Proof for theBenchmark % 15.62/2.91 Assumptions after simplification: % 15.62/2.91 --------------------------------- % 15.62/2.91 % 15.62/2.91 (mMulComm) % 15.80/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 15.80/2.93 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 15.80/2.93 (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) & % 15.80/2.93 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 15.80/2.93 % 15.80/2.93 (m__) % 15.80/2.93 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: any] : ? % 15.80/2.93 [v2: $i] : ? [v3: any] : (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 % 15.80/2.93 & sdtasdt0(xz, xl) = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3 % 15.80/2.93 = 0) | ~ (v1 = 0))) % 15.80/2.93 % 15.80/2.93 (m__870) % 15.80/2.94 aIdeal0(xJ) = 0 & aIdeal0(xI) = 0 & aSet0(xJ) = 0 & aSet0(xI) = 0 & $i(xJ) & % 15.80/2.94 $i(xI) & ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: % 15.80/2.94 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: % 15.80/2.94 any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1) = v3 & % 15.80/2.94 ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ (aElementOf0(v1, xJ) = 0) % 15.80/2.94 | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1) % 15.80/2.94 = v2 & $i(v2))))) & ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ % 15.80/2.94 $i(v0) | ( ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 15.80/2.94 $i(v1) | ? [v3: any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 & % 15.80/2.94 aElement0(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ % 15.80/2.94 (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : (aElementOf0(v2, % 15.80/2.94 xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2))))) % 15.80/2.94 % 15.80/2.94 (m__901) % 15.80/2.94 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = % 15.80/2.94 v0 & aElementOf0(xy, v0) = 0 & aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & % 15.80/2.94 $i(v0) & ? [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & % 15.80/2.94 aElementOf0(v1, xI) = 0 & sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ? % 15.80/2.94 [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 % 15.80/2.94 & sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1))) % 15.80/2.94 % 15.80/2.94 (m__934) % 15.80/2.94 aElementOf0(xl, xJ) = 0 & aElementOf0(xk, xI) = 0 & sdtpldt0(xk, xl) = xx & % 15.80/2.94 $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) % 15.80/2.94 % 15.80/2.94 (function-axioms) % 15.80/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.80/2.95 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 15.80/2.95 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 15.80/2.95 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.80/2.95 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.80/2.95 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 15.80/2.95 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 15.80/2.95 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.80/2.95 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.80/2.95 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 15.80/2.95 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: % 15.80/2.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.80/2.95 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.80/2.95 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 15.80/2.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.80/2.95 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 15.80/2.95 % 15.80/2.95 Further assumptions not needed in the proof: % 15.80/2.95 -------------------------------------------- % 15.80/2.95 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, % 15.80/2.95 mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, % 15.80/2.95 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__967, % 15.80/2.95 m__994 % 15.80/2.95 % 15.80/2.95 Those formulas are unsatisfiable: % 15.80/2.95 --------------------------------- % 15.80/2.95 % 15.80/2.95 Begin of proof % 15.80/2.95 | % 15.80/2.95 | ALPHA: (m__870) implies: % 15.80/2.95 | (1) ! [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ( ! [v1: $i] % 15.80/2.95 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: % 15.80/2.95 | any] : ? [v4: any] : (aElementOf0(v2, xI) = v4 & aElement0(v1) % 15.80/2.95 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ % 15.80/2.95 | (aElementOf0(v1, xI) = 0) | ~ $i(v1) | ? [v2: $i] : % 15.80/2.95 | (aElementOf0(v2, xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2))))) % 15.80/2.95 | (2) ! [v0: $i] : ( ~ (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ( ! [v1: $i] % 15.80/2.95 | : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: % 15.80/2.95 | any] : ? [v4: any] : (aElementOf0(v2, xJ) = v4 & aElement0(v1) % 15.80/2.95 | = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v1: $i] : ( ~ % 15.80/2.95 | (aElementOf0(v1, xJ) = 0) | ~ $i(v1) | ? [v2: $i] : % 15.80/2.95 | (aElementOf0(v2, xJ) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2))))) % 15.80/2.95 | % 15.80/2.95 | ALPHA: (m__901) implies: % 15.80/2.95 | (3) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & aElementOf0(xy, v0) = 0 & % 15.80/2.95 | aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & $i(v0) & ? [v1: $i] : % 15.80/2.95 | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 & % 15.80/2.96 | sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ? [v1: $i] : ? [v2: % 15.80/2.96 | $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 & % 15.80/2.96 | sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1))) % 15.80/2.96 | % 15.80/2.96 | ALPHA: (m__934) implies: % 15.80/2.96 | (4) aElementOf0(xk, xI) = 0 % 15.80/2.96 | (5) aElementOf0(xl, xJ) = 0 % 15.80/2.96 | % 15.80/2.96 | ALPHA: (m__) implies: % 15.80/2.96 | (6) $i(xz) % 15.80/2.96 | (7) $i(xk) % 15.80/2.96 | (8) $i(xl) % 15.80/2.96 | (9) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.80/2.96 | (aElementOf0(v2, xJ) = v3 & aElementOf0(v0, xI) = v1 & sdtasdt0(xz, xl) % 15.80/2.96 | = v2 & sdtasdt0(xz, xk) = v0 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ % 15.80/2.96 | (v1 = 0))) % 15.80/2.96 | % 15.80/2.96 | ALPHA: (function-axioms) implies: % 15.80/2.96 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.80/2.96 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 15.80/2.96 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.80/2.96 | : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ % 15.80/2.96 | (aElementOf0(v3, v2) = v0)) % 15.80/2.96 | % 15.80/2.96 | DELTA: instantiating (9) with fresh symbols all_25_0, all_25_1, all_25_2, % 15.80/2.96 | all_25_3 gives: % 15.80/2.96 | (12) aElementOf0(all_25_1, xJ) = all_25_0 & aElementOf0(all_25_3, xI) = % 15.80/2.96 | all_25_2 & sdtasdt0(xz, xl) = all_25_1 & sdtasdt0(xz, xk) = all_25_3 & % 15.80/2.96 | $i(all_25_1) & $i(all_25_3) & ( ~ (all_25_0 = 0) | ~ (all_25_2 = 0)) % 15.80/2.96 | % 15.80/2.96 | ALPHA: (12) implies: % 15.80/2.96 | (13) sdtasdt0(xz, xk) = all_25_3 % 15.80/2.96 | (14) sdtasdt0(xz, xl) = all_25_1 % 15.80/2.96 | (15) aElementOf0(all_25_3, xI) = all_25_2 % 15.80/2.96 | (16) aElementOf0(all_25_1, xJ) = all_25_0 % 15.80/2.96 | (17) ~ (all_25_0 = 0) | ~ (all_25_2 = 0) % 15.80/2.96 | % 15.80/2.96 | DELTA: instantiating (3) with fresh symbol all_30_0 gives: % 15.80/2.96 | (18) sdtpldt1(xI, xJ) = all_30_0 & aElementOf0(xy, all_30_0) = 0 & % 15.80/2.96 | aElementOf0(xx, all_30_0) = 0 & aElement0(xz) = 0 & $i(all_30_0) & ? % 15.80/2.96 | [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, % 15.80/2.96 | xI) = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0)) & ? [v0: $i] : % 15.80/2.96 | ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI) = 0 & % 15.80/2.96 | sdtpldt0(v0, v1) = xx & $i(v1) & $i(v0)) % 15.80/2.96 | % 15.80/2.96 | ALPHA: (18) implies: % 15.80/2.96 | (19) aElement0(xz) = 0 % 15.80/2.96 | % 15.80/2.96 | GROUND_INST: instantiating (mMulComm) with xz, xk, all_25_3, simplifying with % 15.80/2.96 | (6), (7), (13) gives: % 15.80/2.96 | (20) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xz) = v2 & % 15.80/2.96 | aElement0(xk) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 15.80/2.96 | (v0 = 0) | v2 = all_25_3)) % 15.80/2.96 | % 15.80/2.96 | GROUND_INST: instantiating (mMulComm) with xz, xl, all_25_1, simplifying with % 15.80/2.96 | (6), (8), (14) gives: % 15.80/2.97 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xl, xz) = v2 & % 15.80/2.97 | aElement0(xl) = v1 & aElement0(xz) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ % 15.80/2.97 | (v0 = 0) | v2 = all_25_1)) % 15.80/2.97 | % 15.80/2.97 | GROUND_INST: instantiating (1) with xk, simplifying with (4), (7) gives: % 15.80/2.97 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 & % 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 15.80/2.97 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.80/2.97 | (aElementOf0(v1, xI) = 0 & sdtpldt0(xk, v0) = v1 & $i(v1))) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (22) implies: % 15.80/2.97 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xI) = v3 & % 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 15.80/2.97 | % 15.80/2.97 | GROUND_INST: instantiating (2) with xl, simplifying with (5), (8) gives: % 15.80/2.97 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) | % 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 & % 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 15.80/2.97 | (aElementOf0(v0, xJ) = 0) | ~ $i(v0) | ? [v1: $i] : % 15.80/2.97 | (aElementOf0(v1, xJ) = 0 & sdtpldt0(xl, v0) = v1 & $i(v1))) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (24) implies: % 15.80/2.97 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, xl) = v1) | ~ $i(v0) | % 15.80/2.97 | ? [v2: any] : ? [v3: any] : (aElementOf0(v1, xJ) = v3 & % 15.80/2.97 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 15.80/2.97 | % 15.80/2.97 | GROUND_INST: instantiating (25) with xz, all_25_1, simplifying with (6), (14) % 15.80/2.97 | gives: % 15.80/2.97 | (26) ? [v0: any] : ? [v1: any] : (aElementOf0(all_25_1, xJ) = v1 & % 15.80/2.97 | aElement0(xz) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 15.80/2.97 | % 15.80/2.97 | GROUND_INST: instantiating (23) with xz, all_25_3, simplifying with (6), (13) % 15.80/2.97 | gives: % 15.80/2.97 | (27) ? [v0: any] : ? [v1: any] : (aElementOf0(all_25_3, xI) = v1 & % 15.80/2.97 | aElement0(xz) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 15.80/2.97 | % 15.80/2.97 | DELTA: instantiating (21) with fresh symbols all_86_0, all_86_1, all_86_2 % 15.80/2.97 | gives: % 15.80/2.97 | (28) sdtasdt0(xl, xz) = all_86_0 & aElement0(xl) = all_86_1 & aElement0(xz) % 15.80/2.97 | = all_86_2 & $i(all_86_0) & ( ~ (all_86_1 = 0) | ~ (all_86_2 = 0) | % 15.80/2.97 | all_86_0 = all_25_1) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (28) implies: % 15.80/2.97 | (29) aElement0(xz) = all_86_2 % 15.80/2.97 | % 15.80/2.97 | DELTA: instantiating (20) with fresh symbols all_96_0, all_96_1, all_96_2 % 15.80/2.97 | gives: % 15.80/2.97 | (30) sdtasdt0(xk, xz) = all_96_0 & aElement0(xk) = all_96_1 & aElement0(xz) % 15.80/2.97 | = all_96_2 & $i(all_96_0) & ( ~ (all_96_1 = 0) | ~ (all_96_2 = 0) | % 15.80/2.97 | all_96_0 = all_25_3) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (30) implies: % 15.80/2.97 | (31) aElement0(xz) = all_96_2 % 15.80/2.97 | % 15.80/2.97 | DELTA: instantiating (26) with fresh symbols all_174_0, all_174_1 gives: % 15.80/2.97 | (32) aElementOf0(all_25_1, xJ) = all_174_0 & aElement0(xz) = all_174_1 & ( % 15.80/2.97 | ~ (all_174_1 = 0) | all_174_0 = 0) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (32) implies: % 15.80/2.97 | (33) aElement0(xz) = all_174_1 % 15.80/2.97 | (34) aElementOf0(all_25_1, xJ) = all_174_0 % 15.80/2.97 | (35) ~ (all_174_1 = 0) | all_174_0 = 0 % 15.80/2.97 | % 15.80/2.97 | DELTA: instantiating (27) with fresh symbols all_198_0, all_198_1 gives: % 15.80/2.97 | (36) aElementOf0(all_25_3, xI) = all_198_0 & aElement0(xz) = all_198_1 & ( % 15.80/2.97 | ~ (all_198_1 = 0) | all_198_0 = 0) % 15.80/2.97 | % 15.80/2.97 | ALPHA: (36) implies: % 15.80/2.97 | (37) aElement0(xz) = all_198_1 % 15.80/2.97 | (38) aElementOf0(all_25_3, xI) = all_198_0 % 15.80/2.97 | (39) ~ (all_198_1 = 0) | all_198_0 = 0 % 15.80/2.97 | % 15.80/2.98 | GROUND_INST: instantiating (10) with 0, all_96_2, xz, simplifying with (19), % 15.80/2.98 | (31) gives: % 15.80/2.98 | (40) all_96_2 = 0 % 15.80/2.98 | % 15.80/2.98 | GROUND_INST: instantiating (10) with all_174_1, all_198_1, xz, simplifying % 15.80/2.98 | with (33), (37) gives: % 15.80/2.98 | (41) all_198_1 = all_174_1 % 15.80/2.98 | % 15.80/2.98 | GROUND_INST: instantiating (10) with all_96_2, all_198_1, xz, simplifying with % 15.80/2.98 | (31), (37) gives: % 15.80/2.98 | (42) all_198_1 = all_96_2 % 15.80/2.98 | % 15.80/2.98 | GROUND_INST: instantiating (10) with all_86_2, all_198_1, xz, simplifying with % 15.80/2.98 | (29), (37) gives: % 15.80/2.98 | (43) all_198_1 = all_86_2 % 15.80/2.98 | % 15.80/2.98 | GROUND_INST: instantiating (11) with all_25_2, all_198_0, xI, all_25_3, % 15.80/2.98 | simplifying with (15), (38) gives: % 15.80/2.98 | (44) all_198_0 = all_25_2 % 15.80/2.98 | % 15.80/2.98 | GROUND_INST: instantiating (11) with all_25_0, all_174_0, xJ, all_25_1, % 15.80/2.98 | simplifying with (16), (34) gives: % 15.80/2.98 | (45) all_174_0 = all_25_0 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (41), (43) imply: % 15.80/2.98 | (46) all_174_1 = all_86_2 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (41), (42) imply: % 15.80/2.98 | (47) all_174_1 = all_96_2 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (46), (47) imply: % 15.80/2.98 | (48) all_96_2 = all_86_2 % 15.80/2.98 | % 15.80/2.98 | SIMP: (48) implies: % 15.80/2.98 | (49) all_96_2 = all_86_2 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (40), (49) imply: % 15.80/2.98 | (50) all_86_2 = 0 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (46), (50) imply: % 15.80/2.98 | (51) all_174_1 = 0 % 15.80/2.98 | % 15.80/2.98 | COMBINE_EQS: (41), (51) imply: % 15.80/2.98 | (52) all_198_1 = 0 % 15.80/2.98 | % 15.80/2.98 | BETA: splitting (35) gives: % 15.80/2.98 | % 15.80/2.98 | Case 1: % 15.80/2.98 | | % 15.80/2.98 | | (53) ~ (all_174_1 = 0) % 15.80/2.98 | | % 15.80/2.98 | | REDUCE: (51), (53) imply: % 15.80/2.98 | | (54) $false % 15.80/2.98 | | % 15.80/2.98 | | CLOSE: (54) is inconsistent. % 15.80/2.98 | | % 15.80/2.98 | Case 2: % 15.80/2.98 | | % 15.80/2.98 | | (55) all_174_0 = 0 % 15.80/2.98 | | % 15.80/2.98 | | COMBINE_EQS: (45), (55) imply: % 15.80/2.98 | | (56) all_25_0 = 0 % 15.80/2.98 | | % 15.80/2.98 | | SIMP: (56) implies: % 15.80/2.98 | | (57) all_25_0 = 0 % 15.80/2.98 | | % 15.80/2.98 | | BETA: splitting (17) gives: % 15.80/2.98 | | % 15.80/2.98 | | Case 1: % 15.80/2.98 | | | % 15.80/2.98 | | | (58) ~ (all_25_0 = 0) % 15.80/2.98 | | | % 15.80/2.98 | | | REDUCE: (57), (58) imply: % 15.80/2.98 | | | (59) $false % 15.80/2.98 | | | % 15.80/2.98 | | | CLOSE: (59) is inconsistent. % 15.80/2.98 | | | % 15.80/2.98 | | Case 2: % 15.80/2.98 | | | % 15.80/2.98 | | | (60) ~ (all_25_2 = 0) % 15.80/2.98 | | | % 15.80/2.98 | | | BETA: splitting (39) gives: % 15.80/2.98 | | | % 15.80/2.98 | | | Case 1: % 15.80/2.98 | | | | % 15.80/2.98 | | | | (61) ~ (all_198_1 = 0) % 15.80/2.98 | | | | % 15.80/2.98 | | | | REDUCE: (52), (61) imply: % 15.80/2.98 | | | | (62) $false % 15.80/2.98 | | | | % 15.80/2.98 | | | | CLOSE: (62) is inconsistent. % 15.80/2.98 | | | | % 15.80/2.98 | | | Case 2: % 15.80/2.98 | | | | % 15.80/2.98 | | | | (63) all_198_0 = 0 % 15.80/2.98 | | | | % 15.80/2.98 | | | | COMBINE_EQS: (44), (63) imply: % 15.80/2.98 | | | | (64) all_25_2 = 0 % 15.80/2.98 | | | | % 15.80/2.98 | | | | REDUCE: (60), (64) imply: % 15.80/2.98 | | | | (65) $false % 15.80/2.98 | | | | % 15.80/2.98 | | | | CLOSE: (65) is inconsistent. % 15.80/2.98 | | | | % 15.80/2.98 | | | End of split % 15.80/2.98 | | | % 15.80/2.98 | | End of split % 15.80/2.98 | | % 15.80/2.98 | End of split % 15.80/2.98 | % 15.80/2.98 End of proof % 15.80/2.98 % SZS output end Proof for theBenchmark % 15.80/2.98 % 15.80/2.98 2372ms %------------------------------------------------------------------------------