%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG093+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 : n011.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 13:57:49 EDT 2023 % Result : Theorem 62.99s 9.11s % Output : Proof 63.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : RNG093+1 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n011.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sun Aug 27 02:52:24 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.88/1.17 Prover 1: Preprocessing ... % 2.88/1.17 Prover 4: Preprocessing ... % 3.23/1.22 Prover 0: Preprocessing ... % 3.23/1.22 Prover 6: Preprocessing ... % 3.23/1.22 Prover 2: Preprocessing ... % 3.23/1.22 Prover 3: Preprocessing ... % 3.23/1.22 Prover 5: Preprocessing ... % 9.00/2.04 Prover 3: Constructing countermodel ... % 9.00/2.05 Prover 1: Constructing countermodel ... % 9.00/2.05 Prover 6: Proving ... % 9.00/2.06 Prover 5: Proving ... % 9.82/2.11 Prover 2: Proving ... % 9.96/2.16 Prover 4: Constructing countermodel ... % 11.22/2.32 Prover 0: Proving ... % 14.74/2.81 Prover 3: gave up % 14.74/2.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.74/2.90 Prover 7: Preprocessing ... % 15.85/2.95 Prover 1: gave up % 15.85/2.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.85/3.02 Prover 8: Preprocessing ... % 17.86/3.23 Prover 7: Constructing countermodel ... % 17.86/3.24 Prover 8: Warning: ignoring some quantifiers % 18.18/3.25 Prover 8: Constructing countermodel ... % 22.66/3.88 Prover 8: gave up % 22.66/3.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 23.52/4.00 Prover 9: Preprocessing ... % 27.73/4.60 Prover 9: Constructing countermodel ... % 59.84/8.71 Prover 2: stopped % 59.84/8.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 60.65/8.81 Prover 10: Preprocessing ... % 61.40/8.95 Prover 10: Constructing countermodel ... % 62.93/9.10 Prover 10: Found proof (size 34) % 62.93/9.10 Prover 10: proved (378ms) % 62.93/9.10 Prover 0: stopped % 62.93/9.10 Prover 5: stopped % 62.93/9.10 Prover 6: stopped % 62.99/9.10 Prover 9: stopped % 62.99/9.10 Prover 4: stopped % 62.99/9.11 Prover 7: stopped % 62.99/9.11 % 62.99/9.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 62.99/9.11 % 62.99/9.11 % SZS output start Proof for theBenchmark % 62.99/9.12 Assumptions after simplification: % 62.99/9.12 --------------------------------- % 62.99/9.12 % 62.99/9.12 (mAddComm) % 62.99/9.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 62.99/9.16 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 62.99/9.16 = v2 & $i(v2))) % 62.99/9.16 % 62.99/9.16 (mDefIdeal) % 62.99/9.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 62.99/9.16 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 62.99/9.16 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 62.99/9.16 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 62.99/9.16 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 62.99/9.16 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 62.99/9.16 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 62.99/9.16 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 62.99/9.16 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 62.99/9.16 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 62.99/9.16 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 62.99/9.16 aElementOf0(v5, v0))))) % 62.99/9.16 % 62.99/9.17 (mDefSInt) % 62.99/9.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 62.99/9.17 (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v3) % 62.99/9.17 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ aElementOf0(v4, % 62.99/9.17 v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & % 62.99/9.17 (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) & ! % 62.99/9.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = % 62.99/9.17 v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, % 62.99/9.17 v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) & ! [v0: $i] : % 62.99/9.17 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 62.99/9.17 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 62.99/9.17 aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 62.99/9.17 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ % 62.99/9.17 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, % 62.99/9.17 v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : % 62.99/9.17 ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v2) | ~ % 62.99/9.17 $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 62.99/9.17 % 62.99/9.17 (mEOfElem) % 62.99/9.18 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 62.99/9.18 ~ aSet0(v0) | aElement0(v1)) % 62.99/9.18 % 62.99/9.18 (mMulComm) % 62.99/9.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 62.99/9.18 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 62.99/9.18 = v2 & $i(v2))) % 62.99/9.18 % 62.99/9.18 (m__) % 62.99/9.18 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v0) & ~ % 62.99/9.18 aIdeal0(v0)) % 62.99/9.18 % 62.99/9.18 (m__1150) % 62.99/9.18 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) % 62.99/9.18 % 62.99/9.18 Further assumptions not needed in the proof: % 62.99/9.18 -------------------------------------------- % 62.99/9.18 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mDefSSum, mElmSort, mIdeSum, % 62.99/9.18 mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, % 62.99/9.18 mSortsC, mSortsC_01, mSortsU, mUnNeZr % 62.99/9.18 % 62.99/9.18 Those formulas are unsatisfiable: % 62.99/9.18 --------------------------------- % 62.99/9.18 % 62.99/9.18 Begin of proof % 62.99/9.18 | % 62.99/9.18 | ALPHA: (mDefSInt) implies: % 62.99/9.18 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) % 62.99/9.18 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 62.99/9.18 | aSet0(v2)) % 62.99/9.18 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.99/9.18 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 62.99/9.18 | $i(v0) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~ % 62.99/9.18 | aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 62.99/9.19 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.99/9.19 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 62.99/9.19 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 62.99/9.19 | aElementOf0(v3, v0)) % 62.99/9.19 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.99/9.19 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 62.99/9.19 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 62.99/9.19 | aElementOf0(v3, v1)) % 62.99/9.19 | % 62.99/9.19 | ALPHA: (mDefIdeal) implies: % 62.99/9.19 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | aIdeal0(v0) | ? [v1: $i] : % 62.99/9.19 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & % 62.99/9.19 | $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & % 62.99/9.19 | $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 62.99/9.19 | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 62.99/9.19 | aElementOf0(v5, v0))))) % 62.99/9.19 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0)) % 62.99/9.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.99/9.19 | (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 62.99/9.19 | aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | % 62.99/9.19 | aElementOf0(v3, v0)) % 62.99/9.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 62.99/9.19 | (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 62.99/9.19 | aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | % 62.99/9.19 | aElementOf0(v3, v0)) % 62.99/9.19 | % 62.99/9.19 | ALPHA: (m__1150) implies: % 62.99/9.19 | (9) aIdeal0(xI) % 62.99/9.19 | (10) aIdeal0(xJ) % 62.99/9.19 | % 62.99/9.19 | ALPHA: (m__) implies: % 62.99/9.19 | (11) $i(xI) % 62.99/9.19 | (12) $i(xJ) % 62.99/9.19 | (13) ? [v0: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v0) & ~ aIdeal0(v0)) % 62.99/9.19 | % 62.99/9.20 | DELTA: instantiating (13) with fresh symbol all_23_0 gives: % 62.99/9.20 | (14) sdtasasdt0(xI, xJ) = all_23_0 & $i(all_23_0) & ~ aIdeal0(all_23_0) % 62.99/9.20 | % 62.99/9.20 | ALPHA: (14) implies: % 62.99/9.20 | (15) ~ aIdeal0(all_23_0) % 62.99/9.20 | (16) $i(all_23_0) % 62.99/9.20 | (17) sdtasasdt0(xI, xJ) = all_23_0 % 62.99/9.20 | % 62.99/9.20 | GROUND_INST: instantiating (6) with xI, simplifying with (9), (11) gives: % 62.99/9.20 | (18) aSet0(xI) % 62.99/9.20 | % 62.99/9.20 | GROUND_INST: instantiating (6) with xJ, simplifying with (10), (12) gives: % 62.99/9.20 | (19) aSet0(xJ) % 62.99/9.20 | % 62.99/9.20 | GROUND_INST: instantiating (1) with xI, xJ, all_23_0, simplifying with (11), % 62.99/9.20 | (12), (16), (17), (18), (19) gives: % 62.99/9.20 | (20) aSet0(all_23_0) % 62.99/9.20 | % 62.99/9.20 | GROUND_INST: instantiating (5) with all_23_0, simplifying with (15), (16), % 62.99/9.20 | (20) gives: % 62.99/9.20 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 62.99/9.20 | ($i(v3) & $i(v1) & $i(v0) & aElementOf0(v0, all_23_0) & ((sdtasdt0(v1, % 62.99/9.20 | v0) = v2 & $i(v2) & aElement0(v1) & ~ aElementOf0(v2, % 62.99/9.20 | all_23_0)) | (sdtpldt0(v0, v3) = v4 & $i(v4) & aElementOf0(v3, % 62.99/9.20 | all_23_0) & ~ aElementOf0(v4, all_23_0)))) % 62.99/9.20 | % 62.99/9.20 | DELTA: instantiating (21) with fresh symbols all_45_0, all_45_1, all_45_2, % 62.99/9.20 | all_45_3, all_45_4 gives: % 62.99/9.20 | (22) $i(all_45_1) & $i(all_45_3) & $i(all_45_4) & aElementOf0(all_45_4, % 62.99/9.20 | all_23_0) & ((sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2) % 62.99/9.20 | & aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0)) | % 62.99/9.20 | (sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) & % 62.99/9.20 | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0, % 62.99/9.20 | all_23_0))) % 62.99/9.20 | % 62.99/9.20 | ALPHA: (22) implies: % 63.46/9.20 | (23) aElementOf0(all_45_4, all_23_0) % 63.46/9.20 | (24) $i(all_45_4) % 63.46/9.20 | (25) $i(all_45_3) % 63.46/9.20 | (26) $i(all_45_1) % 63.46/9.20 | (27) (sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2) & % 63.46/9.20 | aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0)) | % 63.46/9.20 | (sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) & % 63.46/9.20 | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0, % 63.46/9.20 | all_23_0)) % 63.46/9.20 | % 63.46/9.21 | GROUND_INST: instantiating (4) with xI, xJ, all_23_0, all_45_4, simplifying % 63.46/9.21 | with (11), (12), (16), (17), (18), (19), (23), (24) gives: % 63.46/9.21 | (28) aElementOf0(all_45_4, xJ) % 63.46/9.21 | % 63.46/9.21 | GROUND_INST: instantiating (3) with xI, xJ, all_23_0, all_45_4, simplifying % 63.46/9.21 | with (11), (12), (16), (17), (18), (19), (23), (24) gives: % 63.46/9.21 | (29) aElementOf0(all_45_4, xI) % 63.46/9.21 | % 63.46/9.21 | GROUND_INST: instantiating (mEOfElem) with all_23_0, all_45_4, simplifying % 63.46/9.21 | with (16), (20), (23), (24) gives: % 63.46/9.21 | (30) aElement0(all_45_4) % 63.46/9.21 | % 63.46/9.21 | BETA: splitting (27) gives: % 63.46/9.21 | % 63.46/9.21 | Case 1: % 63.46/9.21 | | % 63.46/9.21 | | (31) sdtasdt0(all_45_3, all_45_4) = all_45_2 & $i(all_45_2) & % 63.46/9.21 | | aElement0(all_45_3) & ~ aElementOf0(all_45_2, all_23_0) % 63.46/9.21 | | % 63.46/9.21 | | ALPHA: (31) implies: % 63.46/9.21 | | (32) ~ aElementOf0(all_45_2, all_23_0) % 63.46/9.21 | | (33) aElement0(all_45_3) % 63.46/9.21 | | (34) sdtasdt0(all_45_3, all_45_4) = all_45_2 % 63.46/9.21 | | % 63.46/9.21 | | GROUND_INST: instantiating (8) with xJ, all_45_4, all_45_3, all_45_2, % 63.46/9.21 | | simplifying with (10), (12), (24), (25), (28), (33), (34) % 63.46/9.21 | | gives: % 63.46/9.21 | | (35) aElementOf0(all_45_2, xJ) % 63.46/9.21 | | % 63.46/9.21 | | GROUND_INST: instantiating (8) with xI, all_45_4, all_45_3, all_45_2, % 63.46/9.21 | | simplifying with (9), (11), (24), (25), (29), (33), (34) gives: % 63.46/9.21 | | (36) aElementOf0(all_45_2, xI) % 63.46/9.21 | | % 63.46/9.21 | | GROUND_INST: instantiating (mMulComm) with all_45_3, all_45_4, all_45_2, % 63.46/9.21 | | simplifying with (24), (25), (30), (33), (34) gives: % 63.46/9.21 | | (37) sdtasdt0(all_45_4, all_45_3) = all_45_2 & $i(all_45_2) % 63.46/9.21 | | % 63.46/9.22 | | ALPHA: (37) implies: % 63.46/9.22 | | (38) $i(all_45_2) % 63.46/9.22 | | % 63.46/9.22 | | GROUND_INST: instantiating (2) with xI, xJ, all_23_0, all_45_2, simplifying % 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (32), (35), (36), (38) % 63.46/9.22 | | gives: % 63.46/9.22 | | (39) $false % 63.46/9.22 | | % 63.46/9.22 | | CLOSE: (39) is inconsistent. % 63.46/9.22 | | % 63.46/9.22 | Case 2: % 63.46/9.22 | | % 63.46/9.22 | | (40) sdtpldt0(all_45_4, all_45_1) = all_45_0 & $i(all_45_0) & % 63.46/9.22 | | aElementOf0(all_45_1, all_23_0) & ~ aElementOf0(all_45_0, all_23_0) % 63.46/9.22 | | % 63.46/9.22 | | ALPHA: (40) implies: % 63.46/9.22 | | (41) ~ aElementOf0(all_45_0, all_23_0) % 63.46/9.22 | | (42) aElementOf0(all_45_1, all_23_0) % 63.46/9.22 | | (43) sdtpldt0(all_45_4, all_45_1) = all_45_0 % 63.46/9.22 | | % 63.46/9.22 | | GROUND_INST: instantiating (4) with xI, xJ, all_23_0, all_45_1, simplifying % 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (26), (42) gives: % 63.46/9.22 | | (44) aElementOf0(all_45_1, xJ) % 63.46/9.22 | | % 63.46/9.22 | | GROUND_INST: instantiating (3) with xI, xJ, all_23_0, all_45_1, simplifying % 63.46/9.22 | | with (11), (12), (16), (17), (18), (19), (26), (42) gives: % 63.46/9.22 | | (45) aElementOf0(all_45_1, xI) % 63.46/9.22 | | % 63.46/9.22 | | GROUND_INST: instantiating (mEOfElem) with all_23_0, all_45_1, simplifying % 63.46/9.22 | | with (16), (20), (26), (42) gives: % 63.46/9.22 | | (46) aElement0(all_45_1) % 63.46/9.22 | | % 63.46/9.22 | | GROUND_INST: instantiating (mAddComm) with all_45_4, all_45_1, all_45_0, % 63.46/9.22 | | simplifying with (24), (26), (30), (43), (46) gives: % 63.46/9.23 | | (47) sdtpldt0(all_45_1, all_45_4) = all_45_0 & $i(all_45_0) % 63.46/9.23 | | % 63.46/9.23 | | ALPHA: (47) implies: % 63.46/9.23 | | (48) $i(all_45_0) % 63.46/9.23 | | % 63.46/9.23 | | GROUND_INST: instantiating (7) with xI, all_45_4, all_45_1, all_45_0, % 63.46/9.23 | | simplifying with (9), (11), (24), (26), (29), (43), (45) gives: % 63.46/9.23 | | (49) aElementOf0(all_45_0, xI) % 63.46/9.23 | | % 63.46/9.23 | | GROUND_INST: instantiating (7) with xJ, all_45_4, all_45_1, all_45_0, % 63.46/9.23 | | simplifying with (10), (12), (24), (26), (28), (43), (44) % 63.46/9.23 | | gives: % 63.46/9.23 | | (50) aElementOf0(all_45_0, xJ) % 63.46/9.23 | | % 63.46/9.23 | | GROUND_INST: instantiating (2) with xI, xJ, all_23_0, all_45_0, simplifying % 63.46/9.23 | | with (11), (12), (16), (17), (18), (19), (41), (48), (49), (50) % 63.46/9.23 | | gives: % 63.46/9.23 | | (51) $false % 63.46/9.23 | | % 63.46/9.23 | | CLOSE: (51) is inconsistent. % 63.46/9.23 | | % 63.46/9.23 | End of split % 63.46/9.23 | % 63.46/9.23 End of proof % 63.46/9.23 % SZS output end Proof for theBenchmark % 63.46/9.23 % 63.46/9.23 8617ms %------------------------------------------------------------------------------