%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG091+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 26.58s 4.54s % Output : Proof 31.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG091+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 01:51:53 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.32/1.24 Prover 1: Preprocessing ... % 3.32/1.25 Prover 4: Preprocessing ... % 3.81/1.31 Prover 2: Preprocessing ... % 3.81/1.31 Prover 0: Preprocessing ... % 3.81/1.31 Prover 3: Preprocessing ... % 3.81/1.31 Prover 6: Preprocessing ... % 3.81/1.33 Prover 5: Preprocessing ... % 10.51/2.31 Prover 3: Constructing countermodel ... % 10.51/2.31 Prover 1: Constructing countermodel ... % 11.02/2.33 Prover 6: Proving ... % 11.02/2.33 Prover 5: Proving ... % 11.84/2.47 Prover 2: Proving ... % 11.84/2.49 Prover 4: Constructing countermodel ... % 13.09/2.64 Prover 0: Proving ... % 26.58/4.53 Prover 2: proved (3842ms) % 26.58/4.53 % 26.58/4.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.58/4.54 % 26.58/4.54 Prover 6: stopped % 26.96/4.54 Prover 3: stopped % 26.96/4.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.96/4.55 Prover 5: stopped % 26.96/4.55 Prover 0: stopped % 26.96/4.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.96/4.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.96/4.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.96/4.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.76/4.67 Prover 7: Preprocessing ... % 27.76/4.67 Prover 13: Preprocessing ... % 27.76/4.68 Prover 11: Preprocessing ... % 27.76/4.68 Prover 8: Preprocessing ... % 27.76/4.70 Prover 10: Preprocessing ... % 29.13/4.85 Prover 10: Constructing countermodel ... % 29.25/4.88 Prover 8: Warning: ignoring some quantifiers % 29.25/4.88 Prover 7: Constructing countermodel ... % 29.25/4.88 Prover 8: Constructing countermodel ... % 29.25/4.88 Prover 13: Warning: ignoring some quantifiers % 29.25/4.91 Prover 13: Constructing countermodel ... % 29.25/4.98 Prover 11: Constructing countermodel ... % 29.25/5.02 Prover 10: Found proof (size 49) % 29.25/5.02 Prover 10: proved (468ms) % 29.25/5.03 Prover 11: stopped % 29.25/5.03 Prover 13: stopped % 29.25/5.03 Prover 8: stopped % 29.25/5.03 Prover 1: stopped % 29.25/5.03 Prover 7: stopped % 29.25/5.04 Prover 4: stopped % 29.25/5.04 % 29.25/5.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 29.25/5.04 % 29.25/5.05 % SZS output start Proof for theBenchmark % 29.25/5.06 Assumptions after simplification: % 29.25/5.06 --------------------------------- % 29.25/5.06 % 29.25/5.06 (mDefSSum) % 30.03/5.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 30.03/5.10 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 30.03/5.10 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.03/5.10 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 30.03/5.10 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 30.03/5.10 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 30.03/5.10 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 30.03/5.10 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 30.03/5.10 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 30.03/5.10 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 30.03/5.10 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 30.03/5.10 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 30.03/5.10 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 30.03/5.10 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 30.03/5.10 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 30.03/5.10 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 30.03/5.10 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 30.03/5.10 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 30.03/5.11 % 30.03/5.11 (m__) % 30.03/5.11 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : ? % 30.03/5.11 [v2: $i] : (sdtpldt1(xI, xJ) = v1 & $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2) % 30.03/5.11 & ~ aElementOf0(v2, v1) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, % 30.03/5.11 v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, xJ) | ~ % 30.03/5.11 aElementOf0(v3, xI))) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ % 30.03/5.11 aElementOf0(v0, v1) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v4) % 30.03/5.11 = v0) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, xJ) | ~ % 30.03/5.11 aElementOf0(v3, xI))))) % 30.03/5.11 % 30.03/5.11 (m__1021) % 30.03/5.11 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : % 30.03/5.11 (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) = v0 & $i(v1) & $i(v0) & % 30.03/5.11 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 30.03/5.11 % 30.03/5.11 (m__1061) % 30.03/5.11 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: % 30.03/5.11 $i] : ? [v2: $i] : (sdtpldt0(v1, v2) = v0 & sdtpldt0(xl, xn) = v2 & % 30.03/5.11 sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0 & $i(v2) & $i(v1) & $i(v0)) % 30.03/5.11 % 30.03/5.11 (m__1098) % 30.03/5.11 $i(xl) & $i(xk) & $i(xz) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 30.03/5.11 (sdtasdt0(xz, xl) = v2 & sdtasdt0(xz, xk) = v1 & sdtasdt0(xz, xx) = v0 & % 30.03/5.11 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 30.03/5.11 % 30.03/5.11 (m__870) % 30.03/5.12 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0: % 30.03/5.12 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | % 30.03/5.12 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) % 30.03/5.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 30.03/5.12 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 30.03/5.12 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 30.03/5.12 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | % 30.03/5.12 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] : % 30.03/5.12 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.03/5.12 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 30.03/5.12 % 30.03/5.12 (m__901) % 30.03/5.12 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : ? % 30.03/5.12 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtpldt1(xI, xJ) = v0 & sdtpldt0(v3, % 30.03/5.12 v4) = xx & sdtpldt0(v1, v2) = xy & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 30.03/5.12 $i(v0) & aElementOf0(v4, xJ) & aElementOf0(v3, xI) & aElementOf0(v2, xJ) & % 30.03/5.12 aElementOf0(v1, xI) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & % 30.03/5.12 aElement0(xz)) % 30.03/5.12 % 30.03/5.12 (m__994) % 30.03/5.12 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: % 30.03/5.12 $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) = v0 & $i(v1) & $i(v0) & % 30.03/5.12 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 30.03/5.12 % 30.03/5.12 (function-axioms) % 30.03/5.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.03/5.12 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.03/5.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 30.03/5.12 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 30.03/5.12 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.03/5.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.03/5.12 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.03/5.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 30.03/5.12 v0)) % 30.03/5.12 % 30.03/5.12 Further assumptions not needed in the proof: % 30.03/5.12 -------------------------------------------- % 30.03/5.12 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, % 30.03/5.12 mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, % 30.03/5.12 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__934, % 30.03/5.12 m__967 % 30.03/5.12 % 30.03/5.12 Those formulas are unsatisfiable: % 30.03/5.12 --------------------------------- % 30.03/5.12 % 30.03/5.12 Begin of proof % 30.03/5.12 | % 30.03/5.13 | ALPHA: (mDefSSum) implies: % 30.03/5.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 30.03/5.13 | ! [v5: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | % 30.03/5.13 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 30.03/5.13 | | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ % 30.03/5.13 | aSet0(v0) | aElementOf0(v3, v2)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__870) implies: % 30.03/5.13 | (2) aSet0(xI) % 30.03/5.13 | (3) aSet0(xJ) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__901) implies: % 30.03/5.13 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 30.03/5.13 | (sdtpldt1(xI, xJ) = v0 & sdtpldt0(v3, v4) = xx & sdtpldt0(v1, v2) = xy % 30.03/5.13 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v4, xJ) & % 30.03/5.13 | aElementOf0(v3, xI) & aElementOf0(v2, xJ) & aElementOf0(v1, xI) & % 30.03/5.13 | aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__994) implies: % 30.03/5.13 | (5) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) = % 30.03/5.13 | v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__1021) implies: % 30.03/5.13 | (6) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) = % 30.03/5.13 | v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__1061) implies: % 30.03/5.13 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v2) = v0 & % 30.03/5.13 | sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0 % 30.03/5.13 | & $i(v2) & $i(v1) & $i(v0)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__1098) implies: % 30.03/5.13 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xz, xl) = v2 & % 30.03/5.13 | sdtasdt0(xz, xk) = v1 & sdtasdt0(xz, xx) = v0 & sdtpldt0(v1, v2) = v0 % 30.03/5.13 | & $i(v2) & $i(v1) & $i(v0)) % 30.03/5.13 | % 30.03/5.13 | ALPHA: (m__) implies: % 30.03/5.13 | (9) $i(xI) % 30.03/5.14 | (10) $i(xJ) % 30.03/5.14 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtpldt1(xI, xJ) = v1 & % 30.03/5.14 | $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ aElementOf0(v2, v1) & % 30.03/5.14 | ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v4) = v2) | ~ % 31.03/5.14 | $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, xJ) | ~ % 31.03/5.14 | aElementOf0(v3, xI))) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ % 31.03/5.14 | aElementOf0(v0, v1) & ! [v3: $i] : ! [v4: $i] : ( ~ % 31.03/5.14 | (sdtpldt0(v3, v4) = v0) | ~ $i(v4) | ~ $i(v3) | ~ % 31.03/5.14 | aElementOf0(v4, xJ) | ~ aElementOf0(v3, xI))))) % 31.03/5.14 | % 31.03/5.14 | ALPHA: (function-axioms) implies: % 31.03/5.14 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.03/5.14 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 31.03/5.14 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.03/5.14 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 31.03/5.14 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 31.03/5.14 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 31.03/5.14 | % 31.03/5.14 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1 gives: % 31.03/5.14 | (15) sdtpldt0(xl, xn) = all_23_0 & sdtpldt0(xk, xm) = all_23_1 & % 31.03/5.14 | $i(all_23_0) & $i(all_23_1) & aElementOf0(all_23_0, xJ) & % 31.03/5.14 | aElementOf0(all_23_1, xI) % 31.03/5.14 | % 31.03/5.14 | ALPHA: (15) implies: % 31.03/5.14 | (16) aElementOf0(all_23_1, xI) % 31.03/5.14 | (17) aElementOf0(all_23_0, xJ) % 31.03/5.14 | (18) sdtpldt0(xk, xm) = all_23_1 % 31.03/5.14 | (19) sdtpldt0(xl, xn) = all_23_0 % 31.03/5.14 | % 31.03/5.14 | DELTA: instantiating (6) with fresh symbols all_25_0, all_25_1 gives: % 31.03/5.14 | (20) sdtasdt0(xz, xl) = all_25_0 & sdtasdt0(xz, xk) = all_25_1 & % 31.03/5.14 | $i(all_25_0) & $i(all_25_1) & aElementOf0(all_25_0, xJ) & % 31.03/5.14 | aElementOf0(all_25_1, xI) % 31.03/5.14 | % 31.03/5.14 | ALPHA: (20) implies: % 31.03/5.14 | (21) aElementOf0(all_25_1, xI) % 31.03/5.14 | (22) aElementOf0(all_25_0, xJ) % 31.03/5.14 | (23) sdtasdt0(xz, xk) = all_25_1 % 31.03/5.14 | (24) sdtasdt0(xz, xl) = all_25_0 % 31.03/5.14 | % 31.03/5.14 | DELTA: instantiating (8) with fresh symbols all_27_0, all_27_1, all_27_2 % 31.03/5.14 | gives: % 31.03/5.14 | (25) sdtasdt0(xz, xl) = all_27_0 & sdtasdt0(xz, xk) = all_27_1 & % 31.03/5.14 | sdtasdt0(xz, xx) = all_27_2 & sdtpldt0(all_27_1, all_27_0) = all_27_2 % 31.03/5.14 | & $i(all_27_0) & $i(all_27_1) & $i(all_27_2) % 31.03/5.15 | % 31.03/5.15 | ALPHA: (25) implies: % 31.03/5.15 | (26) $i(all_27_2) % 31.03/5.15 | (27) $i(all_27_1) % 31.03/5.15 | (28) $i(all_27_0) % 31.03/5.15 | (29) sdtpldt0(all_27_1, all_27_0) = all_27_2 % 31.03/5.15 | (30) sdtasdt0(xz, xx) = all_27_2 % 31.03/5.15 | (31) sdtasdt0(xz, xk) = all_27_1 % 31.03/5.15 | (32) sdtasdt0(xz, xl) = all_27_0 % 31.03/5.15 | % 31.03/5.15 | DELTA: instantiating (7) with fresh symbols all_29_0, all_29_1, all_29_2 % 31.03/5.15 | gives: % 31.03/5.15 | (33) sdtpldt0(all_29_1, all_29_0) = all_29_2 & sdtpldt0(xl, xn) = all_29_0 % 31.03/5.15 | & sdtpldt0(xk, xm) = all_29_1 & sdtpldt0(xx, xy) = all_29_2 & % 31.03/5.15 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) % 31.03/5.15 | % 31.03/5.15 | ALPHA: (33) implies: % 31.03/5.15 | (34) $i(all_29_2) % 31.03/5.15 | (35) $i(all_29_1) % 31.03/5.15 | (36) $i(all_29_0) % 31.03/5.15 | (37) sdtpldt0(xx, xy) = all_29_2 % 31.03/5.15 | (38) sdtpldt0(xk, xm) = all_29_1 % 31.03/5.15 | (39) sdtpldt0(xl, xn) = all_29_0 % 31.03/5.15 | (40) sdtpldt0(all_29_1, all_29_0) = all_29_2 % 31.03/5.15 | % 31.03/5.15 | DELTA: instantiating (4) with fresh symbols all_34_0, all_34_1, all_34_2, % 31.03/5.15 | all_34_3, all_34_4 gives: % 31.03/5.15 | (41) sdtpldt1(xI, xJ) = all_34_4 & sdtpldt0(all_34_1, all_34_0) = xx & % 31.03/5.15 | sdtpldt0(all_34_3, all_34_2) = xy & $i(all_34_0) & $i(all_34_1) & % 31.03/5.15 | $i(all_34_2) & $i(all_34_3) & $i(all_34_4) & aElementOf0(all_34_0, xJ) % 31.03/5.15 | & aElementOf0(all_34_1, xI) & aElementOf0(all_34_2, xJ) & % 31.03/5.15 | aElementOf0(all_34_3, xI) & aElementOf0(xy, all_34_4) & % 31.03/5.15 | aElementOf0(xx, all_34_4) & aElement0(xz) % 31.03/5.15 | % 31.03/5.15 | ALPHA: (41) implies: % 31.03/5.15 | (42) sdtpldt1(xI, xJ) = all_34_4 % 31.03/5.15 | % 31.03/5.15 | DELTA: instantiating (11) with fresh symbols all_36_0, all_36_1, all_36_2 % 31.03/5.15 | gives: % 31.03/5.15 | (43) sdtpldt1(xI, xJ) = all_36_1 & $i(all_36_1) & ((sdtasdt0(xz, xx) = % 31.03/5.15 | all_36_0 & $i(all_36_0) & ~ aElementOf0(all_36_0, all_36_1) & ! % 31.03/5.15 | [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = all_36_0) | ~ % 31.03/5.15 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, % 31.03/5.15 | xI))) | (sdtpldt0(xx, xy) = all_36_2 & $i(all_36_2) & ~ % 31.03/5.15 | aElementOf0(all_36_2, all_36_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 31.03/5.15 | (sdtpldt0(v0, v1) = all_36_2) | ~ $i(v1) | ~ $i(v0) | ~ % 31.03/5.15 | aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI)))) % 31.03/5.15 | % 31.03/5.15 | ALPHA: (43) implies: % 31.03/5.15 | (44) $i(all_36_1) % 31.03/5.15 | (45) sdtpldt1(xI, xJ) = all_36_1 % 31.03/5.16 | (46) (sdtasdt0(xz, xx) = all_36_0 & $i(all_36_0) & ~ aElementOf0(all_36_0, % 31.03/5.16 | all_36_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = % 31.03/5.16 | all_36_0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ % 31.03/5.16 | aElementOf0(v0, xI))) | (sdtpldt0(xx, xy) = all_36_2 & % 31.03/5.16 | $i(all_36_2) & ~ aElementOf0(all_36_2, all_36_1) & ! [v0: $i] : ! % 31.03/5.16 | [v1: $i] : ( ~ (sdtpldt0(v0, v1) = all_36_2) | ~ $i(v1) | ~ $i(v0) % 31.03/5.16 | | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI))) % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (12) with all_23_1, all_29_1, xm, xk, simplifying % 31.03/5.16 | with (18), (38) gives: % 31.03/5.16 | (47) all_29_1 = all_23_1 % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (12) with all_23_0, all_29_0, xn, xl, simplifying % 31.03/5.16 | with (19), (39) gives: % 31.03/5.16 | (48) all_29_0 = all_23_0 % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (13) with all_25_1, all_27_1, xk, xz, simplifying % 31.03/5.16 | with (23), (31) gives: % 31.03/5.16 | (49) all_27_1 = all_25_1 % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (13) with all_25_0, all_27_0, xl, xz, simplifying % 31.03/5.16 | with (24), (32) gives: % 31.03/5.16 | (50) all_27_0 = all_25_0 % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (14) with all_34_4, all_36_1, xJ, xI, simplifying % 31.03/5.16 | with (42), (45) gives: % 31.03/5.16 | (51) all_36_1 = all_34_4 % 31.03/5.16 | % 31.03/5.16 | REDUCE: (40), (47), (48) imply: % 31.03/5.16 | (52) sdtpldt0(all_23_1, all_23_0) = all_29_2 % 31.03/5.16 | % 31.03/5.16 | REDUCE: (29), (49), (50) imply: % 31.03/5.16 | (53) sdtpldt0(all_25_1, all_25_0) = all_27_2 % 31.03/5.16 | % 31.03/5.16 | REDUCE: (44), (51) imply: % 31.03/5.16 | (54) $i(all_34_4) % 31.03/5.16 | % 31.03/5.16 | REDUCE: (36), (48) imply: % 31.03/5.16 | (55) $i(all_23_0) % 31.03/5.16 | % 31.03/5.16 | REDUCE: (35), (47) imply: % 31.03/5.16 | (56) $i(all_23_1) % 31.03/5.16 | % 31.03/5.16 | REDUCE: (28), (50) imply: % 31.03/5.16 | (57) $i(all_25_0) % 31.03/5.16 | % 31.03/5.16 | REDUCE: (27), (49) imply: % 31.03/5.16 | (58) $i(all_25_1) % 31.03/5.16 | % 31.03/5.16 | GROUND_INST: instantiating (1) with xI, xJ, all_34_4, all_27_2, all_25_1, % 31.03/5.16 | all_25_0, simplifying with (2), (3), (9), (10), (21), (22), (26), % 31.03/5.16 | (42), (53), (54), (57), (58) gives: % 31.03/5.17 | (59) aElementOf0(all_27_2, all_34_4) % 31.03/5.17 | % 31.03/5.17 | GROUND_INST: instantiating (1) with xI, xJ, all_34_4, all_29_2, all_23_1, % 31.03/5.17 | all_23_0, simplifying with (2), (3), (9), (10), (16), (17), (34), % 31.03/5.17 | (42), (52), (54), (55), (56) gives: % 31.03/5.17 | (60) aElementOf0(all_29_2, all_34_4) % 31.03/5.17 | % 31.03/5.17 | BETA: splitting (46) gives: % 31.03/5.17 | % 31.03/5.17 | Case 1: % 31.03/5.17 | | % 31.03/5.17 | | (61) sdtasdt0(xz, xx) = all_36_0 & $i(all_36_0) & ~ % 31.03/5.17 | | aElementOf0(all_36_0, all_36_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 31.03/5.17 | | (sdtpldt0(v0, v1) = all_36_0) | ~ $i(v1) | ~ $i(v0) | ~ % 31.03/5.17 | | aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI)) % 31.03/5.17 | | % 31.03/5.17 | | ALPHA: (61) implies: % 31.03/5.17 | | (62) ~ aElementOf0(all_36_0, all_36_1) % 31.03/5.17 | | (63) sdtasdt0(xz, xx) = all_36_0 % 31.03/5.17 | | % 31.03/5.17 | | REDUCE: (51), (62) imply: % 31.03/5.17 | | (64) ~ aElementOf0(all_36_0, all_34_4) % 31.03/5.17 | | % 31.03/5.17 | | GROUND_INST: instantiating (13) with all_27_2, all_36_0, xx, xz, simplifying % 31.03/5.17 | | with (30), (63) gives: % 31.03/5.17 | | (65) all_36_0 = all_27_2 % 31.03/5.17 | | % 31.03/5.17 | | REDUCE: (64), (65) imply: % 31.03/5.17 | | (66) ~ aElementOf0(all_27_2, all_34_4) % 31.03/5.17 | | % 31.03/5.17 | | PRED_UNIFY: (59), (66) imply: % 31.03/5.17 | | (67) $false % 31.03/5.17 | | % 31.03/5.17 | | CLOSE: (67) is inconsistent. % 31.03/5.17 | | % 31.03/5.17 | Case 2: % 31.03/5.17 | | % 31.03/5.17 | | (68) sdtpldt0(xx, xy) = all_36_2 & $i(all_36_2) & ~ % 31.03/5.17 | | aElementOf0(all_36_2, all_36_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 31.03/5.17 | | (sdtpldt0(v0, v1) = all_36_2) | ~ $i(v1) | ~ $i(v0) | ~ % 31.03/5.17 | | aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI)) % 31.03/5.17 | | % 31.03/5.17 | | ALPHA: (68) implies: % 31.03/5.17 | | (69) ~ aElementOf0(all_36_2, all_36_1) % 31.03/5.17 | | (70) sdtpldt0(xx, xy) = all_36_2 % 31.03/5.17 | | % 31.03/5.17 | | REDUCE: (51), (69) imply: % 31.03/5.17 | | (71) ~ aElementOf0(all_36_2, all_34_4) % 31.03/5.17 | | % 31.03/5.17 | | GROUND_INST: instantiating (12) with all_29_2, all_36_2, xy, xx, simplifying % 31.03/5.17 | | with (37), (70) gives: % 31.03/5.17 | | (72) all_36_2 = all_29_2 % 31.03/5.17 | | % 31.03/5.17 | | REDUCE: (71), (72) imply: % 31.03/5.17 | | (73) ~ aElementOf0(all_29_2, all_34_4) % 31.03/5.17 | | % 31.03/5.17 | | PRED_UNIFY: (60), (73) imply: % 31.03/5.17 | | (74) $false % 31.03/5.17 | | % 31.03/5.17 | | CLOSE: (74) is inconsistent. % 31.03/5.17 | | % 31.03/5.17 | End of split % 31.03/5.17 | % 31.03/5.17 End of proof % 31.03/5.17 % SZS output end Proof for theBenchmark % 31.03/5.18 % 31.03/5.18 4519ms %------------------------------------------------------------------------------