%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG093+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 13:57:49 EDT 2023 % Result : Theorem 132.07s 18.29s % Output : Proof 132.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG093+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n015.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Sun Aug 27 01:44:08 EDT 2023 % 0.16/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.79/1.16 Prover 4: Preprocessing ... % 2.79/1.16 Prover 1: Preprocessing ... % 2.79/1.20 Prover 3: Preprocessing ... % 2.79/1.20 Prover 6: Preprocessing ... % 2.79/1.20 Prover 2: Preprocessing ... % 2.79/1.20 Prover 0: Preprocessing ... % 3.34/1.21 Prover 5: Preprocessing ... % 7.41/1.81 Prover 1: Constructing countermodel ... % 7.41/1.81 Prover 6: Proving ... % 7.82/1.82 Prover 3: Constructing countermodel ... % 8.09/1.88 Prover 5: Proving ... % 8.09/1.92 Prover 2: Proving ... % 8.65/1.95 Prover 4: Constructing countermodel ... % 9.47/2.05 Prover 0: Proving ... % 71.62/10.31 Prover 2: stopped % 71.62/10.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.62/10.37 Prover 7: Preprocessing ... % 72.84/10.49 Prover 7: Constructing countermodel ... % 99.74/13.97 Prover 5: stopped % 100.12/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.84/14.07 Prover 8: Preprocessing ... % 101.47/14.18 Prover 8: Warning: ignoring some quantifiers % 101.47/14.20 Prover 8: Constructing countermodel ... % 114.87/15.98 Prover 1: stopped % 114.87/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.52/16.01 Prover 9: Preprocessing ... % 117.00/16.19 Prover 9: Constructing countermodel ... % 128.89/17.90 Prover 6: stopped % 128.89/17.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 128.89/17.97 Prover 10: Preprocessing ... % 130.41/18.02 Prover 10: Constructing countermodel ... % 130.82/18.09 Prover 10: Found proof (size 26) % 130.82/18.09 Prover 10: proved (181ms) % 130.82/18.09 Prover 9: stopped % 130.82/18.09 Prover 7: stopped % 130.82/18.09 Prover 8: stopped % 130.82/18.09 Prover 3: stopped % 131.87/18.18 Prover 4: stopped % 132.07/18.28 Prover 0: stopped % 132.07/18.29 % 132.07/18.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 132.07/18.29 % 132.07/18.29 % SZS output start Proof for theBenchmark % 132.07/18.30 Assumptions after simplification: % 132.07/18.30 --------------------------------- % 132.07/18.30 % 132.07/18.30 (mAddComm) % 132.48/18.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 132.48/18.33 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 132.48/18.33 = v2 & $i(v2))) % 132.48/18.33 % 132.48/18.33 (mDefSInt) % 132.48/18.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 132.48/18.33 (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v3) % 132.48/18.33 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~ aElementOf0(v4, % 132.48/18.33 v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & % 132.48/18.33 (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) & ! % 132.48/18.33 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = % 132.48/18.33 v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, % 132.48/18.33 v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) & ! [v0: $i] : % 132.48/18.33 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ % 132.48/18.33 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 132.48/18.33 aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 132.48/18.33 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ % 132.48/18.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, % 132.48/18.33 v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : % 132.48/18.33 ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v2) | ~ % 132.48/18.33 $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 132.48/18.33 % 132.48/18.33 (mEOfElem) % 132.48/18.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 132.48/18.34 ~ aSet0(v0) | aElement0(v1)) % 132.48/18.34 % 132.48/18.34 (mMulComm) % 132.48/18.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 132.48/18.34 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 132.48/18.34 = v2 & $i(v2))) % 132.48/18.34 % 132.48/18.34 (m__) % 132.48/18.34 $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 132.48/18.34 [v4: $i] : ? [v5: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v4) & $i(v2) & $i(v1) & % 132.48/18.34 $i(v0) & aElementOf0(v1, v0) & aSet0(v0) & ~ aIdeal0(v0) & ! [v6: $i] : ( % 132.48/18.34 ~ $i(v6) | ~ aElementOf0(v6, v0) | aElementOf0(v6, xJ)) & ! [v6: $i] : ( % 132.48/18.34 ~ $i(v6) | ~ aElementOf0(v6, v0) | aElementOf0(v6, xI)) & ! [v6: $i] : ( % 132.48/18.34 ~ $i(v6) | ~ aElementOf0(v6, xJ) | ~ aElementOf0(v6, xI) | % 132.48/18.34 aElementOf0(v6, v0)) & ((sdtasdt0(v2, v1) = v3 & $i(v3) & aElement0(v2) & % 132.48/18.34 ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v4) = v5 & $i(v5) & % 132.48/18.34 aElementOf0(v4, v0) & ~ aElementOf0(v5, v0)))) % 132.48/18.34 % 132.48/18.34 (m__1150) % 132.48/18.34 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0: % 132.48/18.34 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | % 132.48/18.34 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) % 132.48/18.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 132.48/18.34 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 132.48/18.34 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 132.48/18.34 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | % 132.48/18.34 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] : % 132.48/18.34 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 132.48/18.34 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 132.48/18.34 % 132.48/18.34 Further assumptions not needed in the proof: % 132.48/18.34 -------------------------------------------- % 132.48/18.34 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSSum, mElmSort, % 132.48/18.34 mIdeSum, mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, % 132.48/18.34 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 132.48/18.34 % 132.48/18.34 Those formulas are unsatisfiable: % 132.48/18.34 --------------------------------- % 132.48/18.34 % 132.48/18.34 Begin of proof % 132.48/18.34 | % 132.48/18.35 | ALPHA: (mDefSInt) implies: % 132.48/18.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 132.48/18.35 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 132.48/18.35 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 132.48/18.35 | aElementOf0(v3, v0)) % 132.48/18.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 132.48/18.35 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 132.48/18.35 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 132.48/18.35 | aElementOf0(v3, v1)) % 132.48/18.35 | % 132.48/18.35 | ALPHA: (m__1150) implies: % 132.48/18.35 | (3) aSet0(xI) % 132.48/18.35 | (4) aSet0(xJ) % 132.48/18.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 132.48/18.35 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, % 132.48/18.35 | xI) | aElementOf0(v2, xI)) % 132.48/18.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 132.48/18.35 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, % 132.48/18.35 | xJ) | aElementOf0(v2, xJ)) % 132.48/18.35 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 132.48/18.35 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 132.48/18.35 | aElementOf0(v2, xI)) % 132.48/18.35 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 132.48/18.35 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | % 132.48/18.35 | aElementOf0(v2, xJ)) % 132.48/18.35 | % 132.48/18.35 | ALPHA: (m__) implies: % 132.48/18.35 | (9) $i(xI) % 132.48/18.35 | (10) $i(xJ) % 132.48/18.35 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 132.48/18.35 | ? [v5: $i] : (sdtasasdt0(xI, xJ) = v0 & $i(v4) & $i(v2) & $i(v1) & % 132.48/18.35 | $i(v0) & aElementOf0(v1, v0) & aSet0(v0) & ~ aIdeal0(v0) & ! [v6: % 132.48/18.35 | $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | aElementOf0(v6, xJ)) & % 132.48/18.35 | ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v0) | aElementOf0(v6, % 132.48/18.35 | xI)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, xJ) | ~ % 132.48/18.35 | aElementOf0(v6, xI) | aElementOf0(v6, v0)) & ((sdtasdt0(v2, v1) = % 132.48/18.35 | v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 132.48/18.35 | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 132.48/18.35 | aElementOf0(v5, v0)))) % 132.48/18.35 | % 132.48/18.35 | DELTA: instantiating (11) with fresh symbols all_27_0, all_27_1, all_27_2, % 132.48/18.35 | all_27_3, all_27_4, all_27_5 gives: % 132.48/18.36 | (12) sdtasasdt0(xI, xJ) = all_27_5 & $i(all_27_1) & $i(all_27_3) & % 132.48/18.36 | $i(all_27_4) & $i(all_27_5) & aElementOf0(all_27_4, all_27_5) & % 132.48/18.36 | aSet0(all_27_5) & ~ aIdeal0(all_27_5) & ! [v0: $i] : ( ~ $i(v0) | ~ % 132.48/18.36 | aElementOf0(v0, all_27_5) | aElementOf0(v0, xJ)) & ! [v0: $i] : ( ~ % 132.48/18.36 | $i(v0) | ~ aElementOf0(v0, all_27_5) | aElementOf0(v0, xI)) & ! % 132.48/18.36 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElementOf0(v0, % 132.48/18.36 | xI) | aElementOf0(v0, all_27_5)) & ((sdtasdt0(all_27_3, all_27_4) % 132.48/18.36 | = all_27_2 & $i(all_27_2) & aElement0(all_27_3) & ~ % 132.48/18.36 | aElementOf0(all_27_2, all_27_5)) | (sdtpldt0(all_27_4, all_27_1) = % 132.48/18.36 | all_27_0 & $i(all_27_0) & aElementOf0(all_27_1, all_27_5) & ~ % 132.48/18.36 | aElementOf0(all_27_0, all_27_5))) % 132.48/18.36 | % 132.48/18.36 | ALPHA: (12) implies: % 132.48/18.36 | (13) aSet0(all_27_5) % 132.48/18.36 | (14) aElementOf0(all_27_4, all_27_5) % 132.48/18.36 | (15) $i(all_27_5) % 132.48/18.36 | (16) $i(all_27_4) % 132.48/18.36 | (17) $i(all_27_3) % 132.48/18.36 | (18) $i(all_27_1) % 132.48/18.36 | (19) sdtasasdt0(xI, xJ) = all_27_5 % 132.48/18.36 | (20) (sdtasdt0(all_27_3, all_27_4) = all_27_2 & $i(all_27_2) & % 132.48/18.36 | aElement0(all_27_3) & ~ aElementOf0(all_27_2, all_27_5)) | % 132.48/18.36 | (sdtpldt0(all_27_4, all_27_1) = all_27_0 & $i(all_27_0) & % 132.48/18.36 | aElementOf0(all_27_1, all_27_5) & ~ aElementOf0(all_27_0, % 132.48/18.36 | all_27_5)) % 132.48/18.36 | (21) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElementOf0(v0, % 132.48/18.36 | xI) | aElementOf0(v0, all_27_5)) % 132.48/18.36 | (22) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_27_5) | % 132.48/18.36 | aElementOf0(v0, xI)) % 132.48/18.36 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_27_5) | % 132.48/18.36 | aElementOf0(v0, xJ)) % 132.48/18.36 | % 132.48/18.36 | GROUND_INST: instantiating (mEOfElem) with all_27_5, all_27_4, simplifying % 132.48/18.36 | with (13), (14), (15), (16) gives: % 132.48/18.36 | (24) aElement0(all_27_4) % 132.48/18.36 | % 132.48/18.36 | GROUND_INST: instantiating (2) with xI, xJ, all_27_5, all_27_4, simplifying % 132.48/18.36 | with (3), (4), (9), (10), (14), (15), (16), (19) gives: % 132.48/18.36 | (25) aElementOf0(all_27_4, xJ) % 132.48/18.36 | % 132.48/18.36 | GROUND_INST: instantiating (1) with xI, xJ, all_27_5, all_27_4, simplifying % 132.48/18.36 | with (3), (4), (9), (10), (14), (15), (16), (19) gives: % 132.48/18.36 | (26) aElementOf0(all_27_4, xI) % 132.48/18.36 | % 132.48/18.36 | BETA: splitting (20) gives: % 132.48/18.36 | % 132.48/18.36 | Case 1: % 132.48/18.36 | | % 132.48/18.36 | | (27) sdtasdt0(all_27_3, all_27_4) = all_27_2 & $i(all_27_2) & % 132.48/18.36 | | aElement0(all_27_3) & ~ aElementOf0(all_27_2, all_27_5) % 132.48/18.36 | | % 132.48/18.36 | | ALPHA: (27) implies: % 132.48/18.36 | | (28) ~ aElementOf0(all_27_2, all_27_5) % 132.48/18.36 | | (29) aElement0(all_27_3) % 132.48/18.36 | | (30) sdtasdt0(all_27_3, all_27_4) = all_27_2 % 132.48/18.36 | | % 132.48/18.36 | | GROUND_INST: instantiating (8) with all_27_4, all_27_3, all_27_2, % 132.48/18.36 | | simplifying with (16), (17), (25), (29), (30) gives: % 132.48/18.36 | | (31) aElementOf0(all_27_2, xJ) % 132.48/18.36 | | % 132.48/18.36 | | GROUND_INST: instantiating (7) with all_27_4, all_27_3, all_27_2, % 132.48/18.36 | | simplifying with (16), (17), (26), (29), (30) gives: % 132.48/18.36 | | (32) aElementOf0(all_27_2, xI) % 132.48/18.36 | | % 132.48/18.37 | | GROUND_INST: instantiating (mMulComm) with all_27_3, all_27_4, all_27_2, % 132.48/18.37 | | simplifying with (16), (17), (24), (29), (30) gives: % 132.48/18.37 | | (33) sdtasdt0(all_27_4, all_27_3) = all_27_2 & $i(all_27_2) % 132.48/18.37 | | % 132.48/18.37 | | ALPHA: (33) implies: % 132.48/18.37 | | (34) $i(all_27_2) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (21) with all_27_2, simplifying with (28), (31), % 132.48/18.37 | | (32), (34) gives: % 132.48/18.37 | | (35) $false % 132.48/18.37 | | % 132.48/18.37 | | CLOSE: (35) is inconsistent. % 132.48/18.37 | | % 132.48/18.37 | Case 2: % 132.48/18.37 | | % 132.48/18.37 | | (36) sdtpldt0(all_27_4, all_27_1) = all_27_0 & $i(all_27_0) & % 132.48/18.37 | | aElementOf0(all_27_1, all_27_5) & ~ aElementOf0(all_27_0, all_27_5) % 132.48/18.37 | | % 132.48/18.37 | | ALPHA: (36) implies: % 132.48/18.37 | | (37) ~ aElementOf0(all_27_0, all_27_5) % 132.48/18.37 | | (38) aElementOf0(all_27_1, all_27_5) % 132.48/18.37 | | (39) sdtpldt0(all_27_4, all_27_1) = all_27_0 % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (mEOfElem) with all_27_5, all_27_1, simplifying % 132.48/18.37 | | with (13), (15), (18), (38) gives: % 132.48/18.37 | | (40) aElement0(all_27_1) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (23) with all_27_1, simplifying with (18), (38) % 132.48/18.37 | | gives: % 132.48/18.37 | | (41) aElementOf0(all_27_1, xJ) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (22) with all_27_1, simplifying with (18), (38) % 132.48/18.37 | | gives: % 132.48/18.37 | | (42) aElementOf0(all_27_1, xI) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (mAddComm) with all_27_4, all_27_1, all_27_0, % 132.48/18.37 | | simplifying with (16), (18), (24), (39), (40) gives: % 132.48/18.37 | | (43) sdtpldt0(all_27_1, all_27_4) = all_27_0 & $i(all_27_0) % 132.48/18.37 | | % 132.48/18.37 | | ALPHA: (43) implies: % 132.48/18.37 | | (44) $i(all_27_0) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (5) with all_27_4, all_27_1, all_27_0, % 132.48/18.37 | | simplifying with (16), (18), (26), (39), (42) gives: % 132.48/18.37 | | (45) aElementOf0(all_27_0, xI) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (6) with all_27_4, all_27_1, all_27_0, % 132.48/18.37 | | simplifying with (16), (18), (25), (39), (41) gives: % 132.48/18.37 | | (46) aElementOf0(all_27_0, xJ) % 132.48/18.37 | | % 132.48/18.37 | | GROUND_INST: instantiating (21) with all_27_0, simplifying with (37), (44), % 132.48/18.37 | | (45), (46) gives: % 132.48/18.37 | | (47) $false % 132.48/18.37 | | % 132.48/18.37 | | CLOSE: (47) is inconsistent. % 132.48/18.37 | | % 132.48/18.37 | End of split % 132.48/18.37 | % 132.48/18.37 End of proof % 132.48/18.37 % SZS output end Proof for theBenchmark % 132.48/18.37 % 132.48/18.37 17757ms %------------------------------------------------------------------------------