%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM022+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 : n014.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 : Wed Aug 30 18:44:18 EDT 2023 % Result : Theorem 21.96s 3.74s % Output : Proof 39.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM022+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n014.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Aug 29 13:28:45 EDT 2023 % 0.17/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.90/1.11 Prover 1: Preprocessing ... % 2.90/1.11 Prover 4: Preprocessing ... % 2.90/1.16 Prover 2: Preprocessing ... % 2.90/1.16 Prover 0: Preprocessing ... % 2.90/1.16 Prover 3: Preprocessing ... % 2.90/1.16 Prover 6: Preprocessing ... % 2.90/1.16 Prover 5: Preprocessing ... % 5.49/1.51 Prover 5: Constructing countermodel ... % 5.49/1.51 Prover 2: Constructing countermodel ... % 6.15/1.61 Prover 1: Constructing countermodel ... % 6.82/1.68 Prover 3: Constructing countermodel ... % 6.82/1.70 Prover 6: Proving ... % 9.37/2.04 Prover 4: Constructing countermodel ... % 9.37/2.16 Prover 0: Proving ... % 21.96/3.74 Prover 2: proved (3101ms) % 21.96/3.74 % 21.96/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.96/3.74 % 21.96/3.74 Prover 5: stopped % 21.96/3.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.96/3.74 Prover 6: stopped % 21.96/3.74 Prover 0: stopped % 21.96/3.75 Prover 3: stopped % 21.96/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.23/3.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.23/3.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.23/3.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.23/3.81 Prover 7: Preprocessing ... % 22.23/3.81 Prover 8: Preprocessing ... % 22.23/3.82 Prover 10: Preprocessing ... % 22.81/3.83 Prover 13: Preprocessing ... % 22.81/3.84 Prover 11: Preprocessing ... % 22.81/3.87 Prover 7: Constructing countermodel ... % 22.81/3.88 Prover 10: Constructing countermodel ... % 23.16/3.90 Prover 13: Constructing countermodel ... % 23.16/3.91 Prover 8: Warning: ignoring some quantifiers % 23.16/3.91 Prover 8: Constructing countermodel ... % 25.41/4.24 Prover 11: Constructing countermodel ... % 38.73/5.97 Prover 7: Found proof (size 32) % 38.73/5.97 Prover 7: proved (2235ms) % 38.73/5.97 Prover 1: stopped % 38.73/5.97 Prover 13: stopped % 38.73/5.98 Prover 8: stopped % 38.73/5.98 Prover 10: stopped % 38.73/5.98 Prover 4: stopped % 38.73/5.98 Prover 11: stopped % 38.73/5.98 % 38.73/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 38.73/5.98 % 38.73/5.98 % SZS output start Proof for theBenchmark % 38.73/5.98 Assumptions after simplification: % 38.73/5.98 --------------------------------- % 38.73/5.99 % 38.73/5.99 (mNFRDef) % 38.73/5.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 38.73/5.99 | ~ $i(v1) | ~ $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~ % 38.73/5.99 aReductOfIn0(v3, v2, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0)) & ! % 38.73/5.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 38.73/5.99 aNormalFormOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | % 38.73/5.99 sdtmndtasgtdt0(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 38.73/5.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~ % 38.73/5.99 aRewritingSystem0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0: $i] : ! % 38.73/5.99 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 38.73/5.99 sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | % 38.73/5.99 ~ aElement0(v0) | aNormalFormOfIn0(v2, v0, v1) | ? [v3: $i] : ($i(v3) & % 38.73/5.99 aReductOfIn0(v3, v2, v1))) % 38.73/5.99 % 38.73/5.99 (mTCRDef) % 38.73/6.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ $i(v2) | ~ $i(v1) | % 38.73/6.00 ~ $i(v0) | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ % 38.73/6.00 aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0: $i] % 38.73/6.00 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 38.73/6.00 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) | % 38.73/6.00 ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : % 38.73/6.00 ( ~ $i(v1) | ~ $i(v0) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) | % 38.73/6.00 sdtmndtasgtdt0(v0, v1, v0)) % 38.73/6.00 % 38.73/6.00 (m__) % 38.73/6.00 $i(xc) & $i(xb) & $i(xa) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 38.73/6.00 ? [v3: $i] : ($i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtmndtasgtdt0(xa, xR, xc) & % 38.73/6.00 sdtmndtasgtdt0(xa, xR, xb) & ! [v4: $i] : ( ~ $i(v4) | ~ % 38.73/6.00 sdtmndtasgtdt0(xc, xR, v4) | ~ sdtmndtasgtdt0(xb, xR, v4) | ~ % 38.73/6.00 aElement0(v4)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~ sdtmndtplgtdt0(xa, % 38.73/6.00 xR, xb) | (aNormalFormOfIn0(v3, v2, xR) & sdtmndtasgtdt0(v1, xR, v2) & % 38.73/6.00 sdtmndtasgtdt0(v1, xR, xc) & sdtmndtasgtdt0(v0, xR, v2) & % 38.73/6.00 sdtmndtasgtdt0(v0, xR, xb) & sdtmndtasgtdt0(xc, xR, v3) & % 38.73/6.00 sdtmndtasgtdt0(xb, xR, v3) & aReductOfIn0(v1, xa, xR) & aReductOfIn0(v0, % 38.73/6.00 xa, xR) & aElement0(v2) & aElement0(v1) & aElement0(v0)))) % 38.73/6.00 % 38.73/6.00 (m__656) % 38.73/6.00 $i(xR) & aRewritingSystem0(xR) % 38.73/6.00 % 38.73/6.00 (m__731) % 38.73/6.00 $i(xc) & $i(xb) & $i(xa) & aElement0(xc) & aElement0(xb) & aElement0(xa) % 38.73/6.00 % 38.73/6.00 Further assumptions not needed in the proof: % 38.73/6.00 -------------------------------------------- % 38.73/6.00 mCRDef, mElmSort, mReduct, mRelSort, mTCDef, mTCRTrans, mTCTrans, mTCbr, % 38.73/6.00 mTermNF, mTermin, mWCRDef, mWFOrd, m__656_01, m__715 % 38.73/6.00 % 38.73/6.00 Those formulas are unsatisfiable: % 38.73/6.00 --------------------------------- % 38.73/6.00 % 38.73/6.00 Begin of proof % 38.73/6.00 | % 38.73/6.00 | ALPHA: (m__) implies: % 39.08/6.00 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 39.08/6.00 | $i(v2) & $i(v1) & $i(v0) & sdtmndtasgtdt0(xa, xR, xc) & % 39.08/6.00 | sdtmndtasgtdt0(xa, xR, xb) & ! [v4: $i] : ( ~ $i(v4) | ~ % 39.08/6.00 | sdtmndtasgtdt0(xc, xR, v4) | ~ sdtmndtasgtdt0(xb, xR, v4) | ~ % 39.08/6.00 | aElement0(v4)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~ % 39.08/6.00 | sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(v3, v2, xR) & % 39.08/6.00 | sdtmndtasgtdt0(v1, xR, v2) & sdtmndtasgtdt0(v1, xR, xc) & % 39.08/6.00 | sdtmndtasgtdt0(v0, xR, v2) & sdtmndtasgtdt0(v0, xR, xb) & % 39.08/6.00 | sdtmndtasgtdt0(xc, xR, v3) & sdtmndtasgtdt0(xb, xR, v3) & % 39.08/6.00 | aReductOfIn0(v1, xa, xR) & aReductOfIn0(v0, xa, xR) & % 39.08/6.00 | aElement0(v2) & aElement0(v1) & aElement0(v0)))) % 39.08/6.00 | % 39.08/6.00 | ALPHA: (m__731) implies: % 39.08/6.00 | (2) aElement0(xa) % 39.08/6.00 | (3) aElement0(xb) % 39.08/6.00 | (4) aElement0(xc) % 39.08/6.00 | (5) $i(xa) % 39.08/6.00 | (6) $i(xb) % 39.08/6.00 | (7) $i(xc) % 39.08/6.00 | % 39.08/6.00 | ALPHA: (m__656) implies: % 39.08/6.01 | (8) aRewritingSystem0(xR) % 39.08/6.01 | (9) $i(xR) % 39.08/6.01 | % 39.08/6.01 | ALPHA: (mNFRDef) implies: % 39.08/6.01 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 39.08/6.01 | $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) % 39.08/6.01 | | ~ aElement0(v0) | aElement0(v2)) % 39.08/6.01 | % 39.08/6.01 | ALPHA: (mTCRDef) implies: % 39.08/6.01 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 39.08/6.01 | aRewritingSystem0(v1) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, % 39.08/6.01 | v0)) % 39.08/6.01 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ $i(v2) | ~ % 39.08/6.01 | $i(v1) | ~ $i(v0) | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ % 39.08/6.01 | aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) | % 39.08/6.01 | sdtmndtplgtdt0(v0, v1, v2)) % 39.08/6.01 | % 39.08/6.01 | DELTA: instantiating (1) with fresh symbols all_14_0, all_14_1, all_14_2, % 39.08/6.01 | all_14_3 gives: % 39.08/6.01 | (13) $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & % 39.08/6.01 | sdtmndtasgtdt0(xa, xR, xc) & sdtmndtasgtdt0(xa, xR, xb) & ! [v0: $i] % 39.08/6.01 | : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xc, xR, v0) | ~ sdtmndtasgtdt0(xb, % 39.08/6.01 | xR, v0) | ~ aElement0(v0)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~ % 39.08/6.01 | sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(all_14_0, all_14_1, % 39.08/6.01 | xR) & sdtmndtasgtdt0(all_14_2, xR, all_14_1) & % 39.08/6.01 | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3, xR, % 39.08/6.01 | all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) & % 39.08/6.01 | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR, % 39.08/6.01 | all_14_0) & aReductOfIn0(all_14_2, xa, xR) & % 39.08/6.01 | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) & % 39.08/6.01 | aElement0(all_14_2) & aElement0(all_14_3))) % 39.08/6.01 | % 39.08/6.01 | ALPHA: (13) implies: % 39.08/6.01 | (14) sdtmndtasgtdt0(xa, xR, xb) % 39.08/6.01 | (15) sdtmndtasgtdt0(xa, xR, xc) % 39.08/6.01 | (16) $i(all_14_1) % 39.08/6.01 | (17) $i(all_14_0) % 39.08/6.01 | (18) ~ sdtmndtplgtdt0(xa, xR, xc) | ~ sdtmndtplgtdt0(xa, xR, xb) | % 39.08/6.01 | (aNormalFormOfIn0(all_14_0, all_14_1, xR) & sdtmndtasgtdt0(all_14_2, % 39.08/6.01 | xR, all_14_1) & sdtmndtasgtdt0(all_14_2, xR, xc) & % 39.08/6.01 | sdtmndtasgtdt0(all_14_3, xR, all_14_1) & sdtmndtasgtdt0(all_14_3, % 39.08/6.01 | xR, xb) & sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, % 39.08/6.01 | xR, all_14_0) & aReductOfIn0(all_14_2, xa, xR) & % 39.08/6.01 | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) & % 39.08/6.01 | aElement0(all_14_2) & aElement0(all_14_3)) % 39.08/6.01 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xc, xR, v0) | ~ % 39.08/6.01 | sdtmndtasgtdt0(xb, xR, v0) | ~ aElement0(v0)) % 39.08/6.01 | % 39.08/6.01 | GROUND_INST: instantiating (11) with xc, xR, simplifying with (4), (7), (8), % 39.08/6.01 | (9) gives: % 39.08/6.01 | (20) sdtmndtasgtdt0(xc, xR, xc) % 39.08/6.01 | % 39.08/6.01 | GROUND_INST: instantiating (11) with xb, xR, simplifying with (3), (6), (8), % 39.08/6.01 | (9) gives: % 39.08/6.01 | (21) sdtmndtasgtdt0(xb, xR, xb) % 39.08/6.01 | % 39.08/6.01 | GROUND_INST: instantiating (12) with xa, xR, xb, simplifying with (2), (3), % 39.08/6.01 | (5), (6), (8), (9), (14) gives: % 39.08/6.01 | (22) xb = xa | sdtmndtplgtdt0(xa, xR, xb) % 39.08/6.01 | % 39.08/6.01 | GROUND_INST: instantiating (12) with xa, xR, xc, simplifying with (2), (4), % 39.08/6.01 | (5), (7), (8), (9), (15) gives: % 39.08/6.01 | (23) xc = xa | sdtmndtplgtdt0(xa, xR, xc) % 39.08/6.01 | % 39.08/6.02 | GROUND_INST: instantiating (19) with xb, simplifying with (3), (6), (21) % 39.08/6.02 | gives: % 39.08/6.02 | (24) ~ sdtmndtasgtdt0(xc, xR, xb) % 39.08/6.02 | % 39.08/6.02 | GROUND_INST: instantiating (19) with xc, simplifying with (4), (7), (20) % 39.08/6.02 | gives: % 39.08/6.02 | (25) ~ sdtmndtasgtdt0(xb, xR, xc) % 39.08/6.02 | % 39.08/6.02 | PRED_UNIFY: (15), (25) imply: % 39.08/6.02 | (26) ~ (xb = xa) % 39.08/6.02 | % 39.08/6.02 | PRED_UNIFY: (14), (24) imply: % 39.08/6.02 | (27) ~ (xc = xa) % 39.08/6.02 | % 39.08/6.02 | BETA: splitting (23) gives: % 39.08/6.02 | % 39.08/6.02 | Case 1: % 39.08/6.02 | | % 39.08/6.02 | | (28) sdtmndtplgtdt0(xa, xR, xc) % 39.08/6.02 | | % 39.08/6.02 | | BETA: splitting (22) gives: % 39.08/6.02 | | % 39.08/6.02 | | Case 1: % 39.08/6.02 | | | % 39.08/6.02 | | | (29) sdtmndtplgtdt0(xa, xR, xb) % 39.08/6.02 | | | % 39.08/6.02 | | | BETA: splitting (18) gives: % 39.08/6.02 | | | % 39.08/6.02 | | | Case 1: % 39.08/6.02 | | | | % 39.08/6.02 | | | | (30) ~ sdtmndtplgtdt0(xa, xR, xc) % 39.08/6.02 | | | | % 39.08/6.02 | | | | PRED_UNIFY: (28), (30) imply: % 39.08/6.02 | | | | (31) $false % 39.08/6.02 | | | | % 39.08/6.02 | | | | CLOSE: (31) is inconsistent. % 39.08/6.02 | | | | % 39.08/6.02 | | | Case 2: % 39.08/6.02 | | | | % 39.08/6.02 | | | | (32) ~ sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(all_14_0, % 39.08/6.02 | | | | all_14_1, xR) & sdtmndtasgtdt0(all_14_2, xR, all_14_1) & % 39.08/6.02 | | | | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3, % 39.08/6.02 | | | | xR, all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) & % 39.08/6.02 | | | | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR, % 39.08/6.02 | | | | all_14_0) & aReductOfIn0(all_14_2, xa, xR) & % 39.08/6.02 | | | | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) & % 39.08/6.02 | | | | aElement0(all_14_2) & aElement0(all_14_3)) % 39.08/6.02 | | | | % 39.08/6.02 | | | | BETA: splitting (32) gives: % 39.08/6.02 | | | | % 39.08/6.02 | | | | Case 1: % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | (33) ~ sdtmndtplgtdt0(xa, xR, xb) % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | PRED_UNIFY: (29), (33) imply: % 39.08/6.02 | | | | | (34) $false % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | CLOSE: (34) is inconsistent. % 39.08/6.02 | | | | | % 39.08/6.02 | | | | Case 2: % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | (35) aNormalFormOfIn0(all_14_0, all_14_1, xR) & % 39.08/6.02 | | | | | sdtmndtasgtdt0(all_14_2, xR, all_14_1) & % 39.08/6.02 | | | | | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3, % 39.08/6.02 | | | | | xR, all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) & % 39.08/6.02 | | | | | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR, % 39.08/6.02 | | | | | all_14_0) & aReductOfIn0(all_14_2, xa, xR) & % 39.08/6.02 | | | | | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) & % 39.08/6.02 | | | | | aElement0(all_14_2) & aElement0(all_14_3) % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | ALPHA: (35) implies: % 39.08/6.02 | | | | | (36) aElement0(all_14_1) % 39.08/6.02 | | | | | (37) sdtmndtasgtdt0(xb, xR, all_14_0) % 39.08/6.02 | | | | | (38) sdtmndtasgtdt0(xc, xR, all_14_0) % 39.08/6.02 | | | | | (39) aNormalFormOfIn0(all_14_0, all_14_1, xR) % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | GROUND_INST: instantiating (10) with all_14_1, xR, all_14_0, % 39.08/6.02 | | | | | simplifying with (8), (9), (16), (17), (36), (39) gives: % 39.08/6.02 | | | | | (40) aElement0(all_14_0) % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | GROUND_INST: instantiating (19) with all_14_0, simplifying with (17), % 39.08/6.02 | | | | | (37), (38), (40) gives: % 39.08/6.02 | | | | | (41) $false % 39.08/6.02 | | | | | % 39.08/6.02 | | | | | CLOSE: (41) is inconsistent. % 39.08/6.02 | | | | | % 39.08/6.02 | | | | End of split % 39.08/6.02 | | | | % 39.08/6.02 | | | End of split % 39.08/6.02 | | | % 39.08/6.02 | | Case 2: % 39.08/6.02 | | | % 39.08/6.02 | | | (42) xb = xa % 39.08/6.02 | | | % 39.08/6.02 | | | REDUCE: (26), (42) imply: % 39.08/6.02 | | | (43) $false % 39.08/6.02 | | | % 39.08/6.02 | | | CLOSE: (43) is inconsistent. % 39.08/6.02 | | | % 39.08/6.02 | | End of split % 39.08/6.02 | | % 39.08/6.02 | Case 2: % 39.08/6.02 | | % 39.08/6.02 | | (44) xc = xa % 39.08/6.02 | | % 39.08/6.02 | | REDUCE: (27), (44) imply: % 39.08/6.02 | | (45) $false % 39.08/6.02 | | % 39.08/6.02 | | CLOSE: (45) is inconsistent. % 39.08/6.02 | | % 39.08/6.02 | End of split % 39.08/6.02 | % 39.08/6.02 End of proof % 39.08/6.02 % SZS output end Proof for theBenchmark % 39.08/6.02 % 39.08/6.02 5416ms %------------------------------------------------------------------------------