%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG090+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 : 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 13:57:48 EDT 2023 % Result : Theorem 12.32s 2.46s % Output : Proof 16.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : RNG090+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n027.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Aug 27 02:22:50 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.82/1.03 Prover 4: Preprocessing ... % 2.82/1.03 Prover 1: Preprocessing ... % 2.82/1.06 Prover 0: Preprocessing ... % 2.82/1.06 Prover 5: Preprocessing ... % 2.82/1.06 Prover 3: Preprocessing ... % 2.82/1.06 Prover 2: Preprocessing ... % 2.82/1.06 Prover 6: Preprocessing ... % 6.87/1.67 Prover 1: Constructing countermodel ... % 6.87/1.69 Prover 6: Proving ... % 6.87/1.70 Prover 3: Constructing countermodel ... % 7.48/1.75 Prover 5: Proving ... % 8.01/1.83 Prover 4: Constructing countermodel ... % 8.69/1.89 Prover 2: Proving ... % 9.03/1.95 Prover 0: Proving ... % 12.32/2.46 Prover 3: proved (1842ms) % 12.32/2.46 % 12.32/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.32/2.46 % 12.32/2.46 Prover 2: stopped % 12.32/2.46 Prover 6: stopped % 13.08/2.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.08/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.08/2.48 Prover 0: stopped % 13.08/2.48 Prover 5: stopped % 13.08/2.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.08/2.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.08/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.37/2.52 Prover 7: Preprocessing ... % 13.37/2.54 Prover 11: Preprocessing ... % 13.37/2.55 Prover 10: Preprocessing ... % 13.37/2.55 Prover 13: Preprocessing ... % 13.37/2.56 Prover 8: Preprocessing ... % 14.00/2.67 Prover 10: Constructing countermodel ... % 14.69/2.73 Prover 7: Constructing countermodel ... % 14.69/2.74 Prover 8: Warning: ignoring some quantifiers % 14.69/2.74 Prover 8: Constructing countermodel ... % 14.69/2.77 Prover 13: Warning: ignoring some quantifiers % 15.45/2.79 Prover 13: Constructing countermodel ... % 15.45/2.91 Prover 11: Constructing countermodel ... % 15.45/2.93 Prover 10: Found proof (size 53) % 16.00/2.93 Prover 10: proved (450ms) % 16.00/2.93 Prover 7: stopped % 16.00/2.93 Prover 13: stopped % 16.00/2.93 Prover 4: stopped % 16.00/2.93 Prover 1: stopped % 16.00/2.93 Prover 8: stopped % 16.00/2.93 Prover 11: stopped % 16.00/2.93 % 16.00/2.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.00/2.93 % 16.47/2.95 % SZS output start Proof for theBenchmark % 16.47/2.95 Assumptions after simplification: % 16.47/2.95 --------------------------------- % 16.47/2.95 % 16.47/2.95 (mAddAsso) % 16.47/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.47/2.97 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 16.47/2.97 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 16.47/2.97 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) & % 16.47/2.97 $i(v4))) % 16.47/2.97 % 16.47/2.97 (mAddComm) % 16.47/2.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 16.47/2.97 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 16.47/2.97 = v2 & $i(v2))) % 16.47/2.97 % 16.47/2.97 (mDefIdeal) % 16.47/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 16.47/2.98 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 16.47/2.98 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 16.47/2.98 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 16.47/2.98 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 16.47/2.98 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 16.47/2.98 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 16.47/2.98 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 16.47/2.98 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 16.47/2.98 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 16.47/2.98 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 16.47/2.98 aElementOf0(v5, v0))))) % 16.47/2.98 % 16.47/2.98 (mDefSSum) % 16.47/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.47/2.98 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 16.47/2.98 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.47/2.98 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 16.47/2.98 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 16.47/2.98 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 16.47/2.98 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 16.47/2.98 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 16.47/2.98 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 16.47/2.98 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 16.47/2.98 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 16.47/2.98 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 16.47/2.98 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 16.47/2.98 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 16.47/2.98 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 16.47/2.98 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 16.47/2.98 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.47/2.98 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 16.47/2.98 % 16.47/2.98 (mEOfElem) % 16.47/2.98 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 16.47/2.98 ~ aSet0(v0) | aElement0(v1)) % 16.47/2.98 % 16.47/2.98 (m__) % 16.47/2.99 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: % 16.47/2.99 $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v0) & sdtpldt0(v1, v2) = v3 & % 16.47/2.99 sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0 & % 16.47/2.99 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.47/2.99 % 16.47/2.99 (m__1021) % 16.47/2.99 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : % 16.47/2.99 (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) = v0 & $i(v1) & $i(v0) & % 16.47/2.99 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 16.47/2.99 % 16.47/2.99 (m__870) % 16.47/2.99 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) % 16.47/2.99 % 16.47/2.99 (m__901) % 16.47/2.99 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = % 16.47/2.99 v0 & $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz)) % 16.47/2.99 % 16.47/2.99 (m__934) % 16.47/2.99 sdtpldt0(xk, xl) = xx & $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) & % 16.47/2.99 aElementOf0(xl, xJ) & aElementOf0(xk, xI) % 16.47/2.99 % 16.47/2.99 (m__967) % 16.47/2.99 sdtpldt0(xm, xn) = xy & $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI) & % 16.47/2.99 aElementOf0(xn, xJ) & aElementOf0(xm, xI) % 16.47/2.99 % 16.47/2.99 (m__994) % 16.47/2.99 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: % 16.47/2.99 $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) = v0 & $i(v1) & $i(v0) & % 16.47/2.99 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 16.47/2.99 % 16.47/2.99 (function-axioms) % 16.47/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.47/2.99 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.47/2.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 16.47/2.99 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.47/2.99 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.47/2.99 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.47/2.99 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.47/2.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 16.47/2.99 v0)) % 16.47/2.99 % 16.47/2.99 Further assumptions not needed in the proof: % 16.47/2.99 -------------------------------------------- % 16.47/2.99 mAMDistr, mAddInvr, mAddZero, mCancel, mDefSInt, mElmSort, mMulAsso, mMulComm, % 16.47/2.99 mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, % 16.47/2.99 mSortsC_01, mSortsU, mUnNeZr % 16.47/2.99 % 16.47/2.99 Those formulas are unsatisfiable: % 16.47/2.99 --------------------------------- % 16.47/2.99 % 16.47/2.99 Begin of proof % 16.47/2.99 | % 16.47/2.99 | ALPHA: (mDefSSum) implies: % 16.47/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | % 16.47/2.99 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 16.47/2.99 | aSet0(v2)) % 16.47/2.99 | % 16.47/2.99 | ALPHA: (mDefIdeal) implies: % 16.47/2.99 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0)) % 16.47/2.99 | % 16.47/2.99 | ALPHA: (m__870) implies: % 16.47/2.99 | (3) aIdeal0(xI) % 16.47/2.99 | (4) aIdeal0(xJ) % 16.47/2.99 | % 16.47/2.99 | ALPHA: (m__901) implies: % 16.47/3.00 | (5) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & aElementOf0(xy, v0) & % 16.47/3.00 | aElementOf0(xx, v0) & aElement0(xz)) % 16.47/3.00 | % 16.47/3.00 | ALPHA: (m__934) implies: % 16.47/3.00 | (6) aElementOf0(xk, xI) % 16.47/3.00 | (7) aElementOf0(xl, xJ) % 16.47/3.00 | (8) sdtpldt0(xk, xl) = xx % 16.47/3.00 | % 16.47/3.00 | ALPHA: (m__967) implies: % 16.47/3.00 | (9) aElementOf0(xm, xI) % 16.47/3.00 | (10) aElementOf0(xn, xJ) % 16.47/3.00 | (11) sdtpldt0(xm, xn) = xy % 16.47/3.00 | % 16.47/3.00 | ALPHA: (m__994) implies: % 16.47/3.00 | (12) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) % 16.47/3.00 | = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 16.47/3.00 | % 16.47/3.00 | ALPHA: (m__1021) implies: % 16.47/3.00 | (13) $i(xI) % 16.47/3.00 | (14) $i(xJ) % 16.47/3.00 | % 16.47/3.00 | ALPHA: (m__) implies: % 16.74/3.00 | (15) $i(xk) % 16.74/3.00 | (16) $i(xl) % 16.74/3.00 | (17) $i(xm) % 16.74/3.00 | (18) $i(xn) % 16.74/3.00 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v0) % 16.74/3.00 | & sdtpldt0(v1, v2) = v3 & sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = % 16.74/3.00 | v1 & sdtpldt0(xx, xy) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (function-axioms) implies: % 16.74/3.00 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.74/3.00 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (5) with fresh symbol all_22_0 gives: % 16.74/3.00 | (21) sdtpldt1(xI, xJ) = all_22_0 & $i(all_22_0) & aElementOf0(xy, all_22_0) % 16.74/3.00 | & aElementOf0(xx, all_22_0) & aElement0(xz) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (21) implies: % 16.74/3.00 | (22) aElementOf0(xy, all_22_0) % 16.74/3.00 | (23) $i(all_22_0) % 16.74/3.00 | (24) sdtpldt1(xI, xJ) = all_22_0 % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1 gives: % 16.74/3.00 | (25) sdtpldt0(xl, xn) = all_26_0 & sdtpldt0(xk, xm) = all_26_1 & % 16.74/3.00 | $i(all_26_0) & $i(all_26_1) & aElementOf0(all_26_0, xJ) & % 16.74/3.00 | aElementOf0(all_26_1, xI) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (25) implies: % 16.74/3.00 | (26) aElementOf0(all_26_0, xJ) % 16.74/3.00 | (27) sdtpldt0(xk, xm) = all_26_1 % 16.74/3.00 | (28) sdtpldt0(xl, xn) = all_26_0 % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (19) with fresh symbols all_31_0, all_31_1, all_31_2, % 16.74/3.00 | all_31_3 gives: % 16.74/3.00 | (29) ~ (all_31_0 = all_31_3) & sdtpldt0(all_31_2, all_31_1) = all_31_0 & % 16.74/3.00 | sdtpldt0(xl, xn) = all_31_1 & sdtpldt0(xk, xm) = all_31_2 & % 16.74/3.00 | sdtpldt0(xx, xy) = all_31_3 & $i(all_31_0) & $i(all_31_1) & % 16.74/3.00 | $i(all_31_2) & $i(all_31_3) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (29) implies: % 16.74/3.00 | (30) ~ (all_31_0 = all_31_3) % 16.74/3.00 | (31) $i(all_31_1) % 16.74/3.00 | (32) sdtpldt0(xx, xy) = all_31_3 % 16.74/3.00 | (33) sdtpldt0(xk, xm) = all_31_2 % 16.74/3.00 | (34) sdtpldt0(xl, xn) = all_31_1 % 16.74/3.00 | (35) sdtpldt0(all_31_2, all_31_1) = all_31_0 % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (20) with all_26_1, all_31_2, xm, xk, simplifying % 16.74/3.00 | with (27), (33) gives: % 16.74/3.00 | (36) all_31_2 = all_26_1 % 16.74/3.00 | % 16.74/3.01 | GROUND_INST: instantiating (20) with all_26_0, all_31_1, xn, xl, simplifying % 16.74/3.01 | with (28), (34) gives: % 16.74/3.01 | (37) all_31_1 = all_26_0 % 16.74/3.01 | % 16.74/3.01 | REDUCE: (35), (36), (37) imply: % 16.74/3.01 | (38) sdtpldt0(all_26_1, all_26_0) = all_31_0 % 16.74/3.01 | % 16.74/3.01 | REDUCE: (31), (37) imply: % 16.74/3.01 | (39) $i(all_26_0) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (2) with xI, simplifying with (3), (13) gives: % 16.74/3.01 | (40) aSet0(xI) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (2) with xJ, simplifying with (4), (14) gives: % 16.74/3.01 | (41) aSet0(xJ) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with xI, xm, simplifying with (9), (13), % 16.74/3.01 | (17), (40) gives: % 16.74/3.01 | (42) aElement0(xm) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with xI, xk, simplifying with (6), (13), % 16.74/3.01 | (15), (40) gives: % 16.74/3.01 | (43) aElement0(xk) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (1) with xI, xJ, all_22_0, simplifying with (13), % 16.74/3.01 | (14), (23), (24), (40), (41) gives: % 16.74/3.01 | (44) aSet0(all_22_0) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with xJ, all_26_0, simplifying with % 16.74/3.01 | (14), (26), (39), (41) gives: % 16.74/3.01 | (45) aElement0(all_26_0) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with xJ, xn, simplifying with (10), % 16.74/3.01 | (14), (18), (41) gives: % 16.74/3.01 | (46) aElement0(xn) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with xJ, xl, simplifying with (7), (14), % 16.74/3.01 | (16), (41) gives: % 16.74/3.01 | (47) aElement0(xl) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mAddComm) with xm, xn, xy, simplifying with (11), % 16.74/3.01 | (17), (18), (42), (46) gives: % 16.74/3.01 | (48) sdtpldt0(xn, xm) = xy & $i(xy) % 16.74/3.01 | % 16.74/3.01 | ALPHA: (48) implies: % 16.74/3.01 | (49) $i(xy) % 16.74/3.01 | (50) sdtpldt0(xn, xm) = xy % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mAddComm) with xl, xn, all_26_0, simplifying with % 16.74/3.01 | (16), (18), (28), (46), (47) gives: % 16.74/3.01 | (51) sdtpldt0(xn, xl) = all_26_0 & $i(all_26_0) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mAddAsso) with xk, xm, all_26_0, all_26_1, % 16.74/3.01 | all_31_0, simplifying with (15), (17), (27), (38), (39), (42), % 16.74/3.01 | (43), (45) gives: % 16.74/3.01 | (52) ? [v0: $i] : (sdtpldt0(xm, all_26_0) = v0 & sdtpldt0(xk, v0) = % 16.74/3.01 | all_31_0 & $i(v0) & $i(all_31_0)) % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mEOfElem) with all_22_0, xy, simplifying with % 16.74/3.01 | (22), (23), (44), (49) gives: % 16.74/3.01 | (53) aElement0(xy) % 16.74/3.01 | % 16.74/3.01 | DELTA: instantiating (52) with fresh symbol all_59_0 gives: % 16.74/3.01 | (54) sdtpldt0(xm, all_26_0) = all_59_0 & sdtpldt0(xk, all_59_0) = all_31_0 % 16.74/3.01 | & $i(all_59_0) & $i(all_31_0) % 16.74/3.01 | % 16.74/3.01 | ALPHA: (54) implies: % 16.74/3.01 | (55) sdtpldt0(xk, all_59_0) = all_31_0 % 16.74/3.01 | (56) sdtpldt0(xm, all_26_0) = all_59_0 % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (mAddAsso) with xk, xl, xy, xx, all_31_3, % 16.74/3.01 | simplifying with (8), (15), (16), (32), (43), (47), (49), (53) % 16.74/3.02 | gives: % 16.74/3.02 | (57) ? [v0: $i] : (sdtpldt0(xl, xy) = v0 & sdtpldt0(xk, v0) = all_31_3 & % 16.74/3.02 | $i(v0) & $i(all_31_3)) % 16.74/3.02 | % 16.74/3.02 | GROUND_INST: instantiating (mAddComm) with xm, all_26_0, all_59_0, simplifying % 16.74/3.02 | with (17), (39), (42), (45), (56) gives: % 16.74/3.02 | (58) sdtpldt0(all_26_0, xm) = all_59_0 & $i(all_59_0) % 16.74/3.02 | % 16.74/3.02 | ALPHA: (58) implies: % 16.74/3.02 | (59) sdtpldt0(all_26_0, xm) = all_59_0 % 16.74/3.02 | % 16.74/3.02 | DELTA: instantiating (57) with fresh symbol all_71_0 gives: % 16.74/3.02 | (60) sdtpldt0(xl, xy) = all_71_0 & sdtpldt0(xk, all_71_0) = all_31_3 & % 16.74/3.02 | $i(all_71_0) & $i(all_31_3) % 16.74/3.02 | % 16.74/3.02 | ALPHA: (60) implies: % 16.74/3.02 | (61) sdtpldt0(xk, all_71_0) = all_31_3 % 16.74/3.02 | (62) sdtpldt0(xl, xy) = all_71_0 % 16.74/3.02 | % 16.74/3.02 | GROUND_INST: instantiating (mAddAsso) with xl, xn, xm, all_26_0, all_59_0, % 16.74/3.02 | simplifying with (16), (17), (18), (28), (42), (46), (47), (59) % 16.74/3.02 | gives: % 16.74/3.02 | (63) ? [v0: $i] : (sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, v0) = all_59_0 & % 16.74/3.02 | $i(v0) & $i(all_59_0)) % 16.74/3.02 | % 16.74/3.02 | DELTA: instantiating (63) with fresh symbol all_93_0 gives: % 16.74/3.02 | (64) sdtpldt0(xn, xm) = all_93_0 & sdtpldt0(xl, all_93_0) = all_59_0 & % 16.74/3.02 | $i(all_93_0) & $i(all_59_0) % 16.74/3.02 | % 16.74/3.02 | ALPHA: (64) implies: % 16.74/3.02 | (65) sdtpldt0(xl, all_93_0) = all_59_0 % 16.74/3.02 | (66) sdtpldt0(xn, xm) = all_93_0 % 16.74/3.02 | % 16.74/3.02 | GROUND_INST: instantiating (20) with xy, all_93_0, xm, xn, simplifying with % 16.74/3.02 | (50), (66) gives: % 16.74/3.02 | (67) all_93_0 = xy % 16.74/3.02 | % 16.74/3.02 | REDUCE: (65), (67) imply: % 16.74/3.02 | (68) sdtpldt0(xl, xy) = all_59_0 % 16.74/3.02 | % 16.74/3.02 | GROUND_INST: instantiating (20) with all_71_0, all_59_0, xy, xl, simplifying % 16.74/3.02 | with (62), (68) gives: % 16.74/3.02 | (69) all_71_0 = all_59_0 % 16.74/3.02 | % 16.74/3.02 | REDUCE: (61), (69) imply: % 16.74/3.02 | (70) sdtpldt0(xk, all_59_0) = all_31_3 % 16.74/3.02 | % 16.74/3.02 | GROUND_INST: instantiating (20) with all_31_0, all_31_3, all_59_0, xk, % 16.74/3.02 | simplifying with (55), (70) gives: % 16.74/3.02 | (71) all_31_0 = all_31_3 % 16.74/3.02 | % 16.74/3.02 | REDUCE: (30), (71) imply: % 16.74/3.02 | (72) $false % 16.74/3.02 | % 16.74/3.02 | CLOSE: (72) is inconsistent. % 16.74/3.02 | % 16.74/3.02 End of proof % 16.74/3.02 % SZS output end Proof for theBenchmark % 16.74/3.02 % 16.74/3.02 2432ms %------------------------------------------------------------------------------