%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM012+3 : 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 : Wed Aug 30 18:44:15 EDT 2023 % Result : Theorem 4.64s 1.38s % Output : Proof 7.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 13:46:11 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.50/1.01 Prover 4: Preprocessing ... % 2.50/1.01 Prover 1: Preprocessing ... % 2.50/1.05 Prover 2: Preprocessing ... % 2.50/1.05 Prover 0: Preprocessing ... % 2.50/1.05 Prover 6: Preprocessing ... % 2.50/1.05 Prover 5: Preprocessing ... % 2.50/1.05 Prover 3: Preprocessing ... % 3.87/1.21 Prover 5: Constructing countermodel ... % 3.94/1.23 Prover 2: Constructing countermodel ... % 3.94/1.28 Prover 1: Constructing countermodel ... % 4.64/1.32 Prover 3: Constructing countermodel ... % 4.64/1.33 Prover 6: Proving ... % 4.64/1.37 Prover 2: proved (745ms) % 4.64/1.38 % 4.64/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.64/1.38 % 4.64/1.38 Prover 5: stopped % 4.64/1.39 Prover 3: stopped % 4.64/1.40 Prover 6: stopped % 4.64/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.64/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.64/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.64/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.64/1.42 Prover 8: Preprocessing ... % 4.64/1.43 Prover 4: Constructing countermodel ... % 4.64/1.45 Prover 7: Preprocessing ... % 4.64/1.45 Prover 10: Preprocessing ... % 4.64/1.48 Prover 11: Preprocessing ... % 5.68/1.52 Prover 7: Constructing countermodel ... % 5.68/1.52 Prover 10: Constructing countermodel ... % 5.68/1.53 Prover 8: Warning: ignoring some quantifiers % 5.68/1.54 Prover 0: Proving ... % 5.68/1.54 Prover 8: Constructing countermodel ... % 5.68/1.54 Prover 0: stopped % 5.68/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.68/1.59 Prover 13: Preprocessing ... % 6.70/1.63 Prover 13: Constructing countermodel ... % 6.70/1.68 Prover 7: Found proof (size 16) % 6.70/1.68 Prover 7: proved (297ms) % 6.70/1.68 Prover 4: stopped % 6.70/1.68 Prover 1: stopped % 6.70/1.68 Prover 8: stopped % 6.70/1.68 Prover 10: Found proof (size 16) % 6.70/1.68 Prover 10: proved (279ms) % 6.70/1.68 Prover 13: stopped % 7.30/1.71 Prover 11: Constructing countermodel ... % 7.30/1.72 Prover 11: stopped % 7.30/1.72 % 7.30/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.30/1.72 % 7.30/1.73 % SZS output start Proof for theBenchmark % 7.30/1.73 Assumptions after simplification: % 7.30/1.73 --------------------------------- % 7.30/1.73 % 7.30/1.73 (mTCTrans) % 7.30/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 7.30/1.74 | ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v2, v1, v3) | ~ % 7.30/1.74 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) | % 7.30/1.74 ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3)) % 7.30/1.74 % 7.30/1.74 (m__) % 7.30/1.74 $i(xz) & $i(xy) & $i(xR) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ( ~ (xz = xx) % 7.30/1.74 & $i(v1) & $i(v0) & sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) % 7.30/1.74 & ~ sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~ % 7.30/1.74 aReductOfIn0(xz, xx, xR) & ! [v2: $i] : ( ~ $i(v2) | ~ sdtmndtplgtdt0(v2, % 7.30/1.74 xR, xz) | ~ aReductOfIn0(v2, xx, xR) | ~ aElement0(v2)) & (xz = xy | % 7.30/1.74 (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | % 7.30/1.74 (sdtmndtplgtdt0(v0, xR, xz) & aReductOfIn0(v0, xy, xR) & % 7.30/1.74 aElement0(v0))))) & (xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & % 7.30/1.74 (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(v1, xR, xy) & % 7.30/1.74 aReductOfIn0(v1, xx, xR) & aElement0(v1)))))) % 7.30/1.74 % 7.30/1.74 (m__349) % 7.30/1.74 $i(xz) & $i(xy) & $i(xR) & $i(xx) & aRewritingSystem0(xR) & aElement0(xz) & % 7.30/1.74 aElement0(xy) & aElement0(xx) % 7.30/1.74 % 7.30/1.74 Further assumptions not needed in the proof: % 7.30/1.74 -------------------------------------------- % 7.30/1.74 mElmSort, mReduct, mRelSort, mTCDef, mTCRDef, mTCbr, mWFOrd % 7.30/1.74 % 7.30/1.74 Those formulas are unsatisfiable: % 7.30/1.74 --------------------------------- % 7.30/1.74 % 7.30/1.74 Begin of proof % 7.30/1.74 | % 7.30/1.75 | ALPHA: (m__) implies: % 7.30/1.75 | (1) ? [v0: $i] : ? [v1: $i] : ( ~ (xz = xx) & $i(v1) & $i(v0) & % 7.30/1.75 | sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) & ~ % 7.30/1.75 | sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~ % 7.30/1.75 | aReductOfIn0(xz, xx, xR) & ! [v2: $i] : ( ~ $i(v2) | ~ % 7.30/1.75 | sdtmndtplgtdt0(v2, xR, xz) | ~ aReductOfIn0(v2, xx, xR) | ~ % 7.30/1.75 | aElement0(v2)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & % 7.30/1.75 | (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(v0, xR, xz) & % 7.30/1.75 | aReductOfIn0(v0, xy, xR) & aElement0(v0))))) & (xy = xx | % 7.30/1.75 | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | % 7.30/1.75 | (sdtmndtplgtdt0(v1, xR, xy) & aReductOfIn0(v1, xx, xR) & % 7.30/1.75 | aElement0(v1)))))) % 7.30/1.75 | % 7.30/1.75 | ALPHA: (m__349) implies: % 7.30/1.75 | (2) aElement0(xx) % 7.30/1.75 | (3) aElement0(xy) % 7.30/1.75 | (4) aElement0(xz) % 7.30/1.75 | (5) aRewritingSystem0(xR) % 7.30/1.75 | (6) $i(xx) % 7.30/1.75 | (7) $i(xR) % 7.30/1.75 | (8) $i(xy) % 7.30/1.75 | (9) $i(xz) % 7.30/1.75 | % 7.30/1.75 | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1 gives: % 7.30/1.75 | (10) ~ (xz = xx) & $i(all_7_0) & $i(all_7_1) & sdtmndtasgtdt0(xy, xR, xz) % 7.30/1.75 | & sdtmndtasgtdt0(xx, xR, xy) & ~ sdtmndtasgtdt0(xx, xR, xz) & ~ % 7.30/1.75 | sdtmndtplgtdt0(xx, xR, xz) & ~ aReductOfIn0(xz, xx, xR) & ! [v0: $i] % 7.30/1.75 | : ( ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, xz) | ~ aReductOfIn0(v0, xx, % 7.30/1.75 | xR) | ~ aElement0(v0)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & % 7.30/1.75 | (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_7_1, xR, xz) & % 7.30/1.75 | aReductOfIn0(all_7_1, xy, xR) & aElement0(all_7_1))))) & (xy = % 7.30/1.75 | xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | % 7.30/1.75 | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) % 7.30/1.75 | & aElement0(all_7_0))))) % 7.30/1.76 | % 7.30/1.76 | ALPHA: (10) implies: % 7.30/1.76 | (11) ~ sdtmndtplgtdt0(xx, xR, xz) % 7.30/1.76 | (12) ~ sdtmndtasgtdt0(xx, xR, xz) % 7.30/1.76 | (13) sdtmndtasgtdt0(xx, xR, xy) % 7.30/1.76 | (14) sdtmndtasgtdt0(xy, xR, xz) % 7.30/1.76 | (15) xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | % 7.30/1.76 | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) & % 7.30/1.76 | aElement0(all_7_0)))) % 7.30/1.76 | (16) xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | % 7.30/1.76 | (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR) & % 7.30/1.76 | aElement0(all_7_1)))) % 7.30/1.76 | % 7.30/1.76 | PRED_UNIFY: (12), (14) imply: % 7.30/1.76 | (17) ~ (xy = xx) % 7.30/1.76 | % 7.30/1.76 | PRED_UNIFY: (12), (13) imply: % 7.30/1.76 | (18) ~ (xz = xy) % 7.30/1.76 | % 7.30/1.76 | BETA: splitting (15) gives: % 7.30/1.76 | % 7.30/1.76 | Case 1: % 7.30/1.76 | | % 7.30/1.76 | | (19) xy = xx % 7.30/1.76 | | % 7.30/1.76 | | REDUCE: (17), (19) imply: % 7.30/1.76 | | (20) $false % 7.30/1.76 | | % 7.30/1.76 | | CLOSE: (20) is inconsistent. % 7.30/1.76 | | % 7.30/1.76 | Case 2: % 7.30/1.76 | | % 7.30/1.76 | | (21) sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) | % 7.30/1.76 | | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) & % 7.30/1.76 | | aElement0(all_7_0))) % 7.30/1.76 | | % 7.30/1.76 | | ALPHA: (21) implies: % 7.30/1.76 | | (22) sdtmndtplgtdt0(xx, xR, xy) % 7.30/1.76 | | % 7.30/1.76 | | BETA: splitting (16) gives: % 7.30/1.76 | | % 7.30/1.76 | | Case 1: % 7.30/1.76 | | | % 7.30/1.76 | | | (23) xz = xy % 7.30/1.76 | | | % 7.30/1.76 | | | REDUCE: (18), (23) imply: % 7.30/1.76 | | | (24) $false % 7.30/1.76 | | | % 7.30/1.76 | | | CLOSE: (24) is inconsistent. % 7.30/1.76 | | | % 7.30/1.76 | | Case 2: % 7.30/1.76 | | | % 7.30/1.76 | | | (25) sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) | % 7.30/1.76 | | | (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR) % 7.30/1.76 | | | & aElement0(all_7_1))) % 7.30/1.76 | | | % 7.30/1.76 | | | ALPHA: (25) implies: % 7.30/1.76 | | | (26) sdtmndtplgtdt0(xy, xR, xz) % 7.30/1.76 | | | % 7.30/1.77 | | | GROUND_INST: instantiating (mTCTrans) with xx, xR, xy, xz, simplifying % 7.30/1.77 | | | with (2), (3), (4), (5), (6), (7), (8), (9), (11), (22), (26) % 7.30/1.77 | | | gives: % 7.30/1.77 | | | (27) $false % 7.30/1.77 | | | % 7.30/1.77 | | | CLOSE: (27) is inconsistent. % 7.30/1.77 | | | % 7.30/1.77 | | End of split % 7.30/1.77 | | % 7.30/1.77 | End of split % 7.30/1.77 | % 7.30/1.77 End of proof % 7.30/1.77 % SZS output end Proof for theBenchmark % 7.30/1.77 % 7.30/1.77 1163ms %------------------------------------------------------------------------------