%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT027_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 22:18:55 EDT 2023 % Result : Theorem 4.74s 1.30s % Output : Proof 5.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : DAT027_1 : TPTP v8.1.2. Released v5.0.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Aug 24 14:34:57 EDT 2023 % 0.12/0.34 % CPUTime : % 0.57/0.54 ________ _____ % 0.57/0.54 ___ __ \_________(_)________________________________ % 0.57/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.54 % 0.57/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.54 (2023-06-19) % 0.57/0.54 % 0.57/0.54 (c) Philipp Rümmer, 2009-2023 % 0.57/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.54 Amanda Stjerna. % 0.57/0.54 Free software under BSD-3-Clause. % 0.57/0.54 % 0.57/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.54 % 0.57/0.54 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.56 Running up to 7 provers in parallel. % 0.61/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/0.95 Prover 1: Preprocessing ... % 2.44/0.95 Prover 4: Preprocessing ... % 2.69/1.00 Prover 5: Preprocessing ... % 2.69/1.00 Prover 2: Preprocessing ... % 2.69/1.00 Prover 6: Preprocessing ... % 2.69/1.00 Prover 3: Preprocessing ... % 2.69/1.00 Prover 0: Preprocessing ... % 3.84/1.16 Prover 1: Constructing countermodel ... % 3.84/1.16 Prover 4: Constructing countermodel ... % 3.84/1.16 Prover 3: Constructing countermodel ... % 3.84/1.16 Prover 6: Proving ... % 3.84/1.16 Prover 0: Proving ... % 3.84/1.16 Prover 2: Proving ... % 3.84/1.16 Prover 5: Proving ... % 4.74/1.30 Prover 3: proved (737ms) % 4.74/1.30 % 4.74/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.74/1.30 % 4.74/1.30 Prover 5: stopped % 4.74/1.30 Prover 2: stopped % 4.74/1.30 Prover 0: stopped % 4.74/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.74/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.74/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.74/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.17/1.33 Prover 6: stopped % 5.17/1.33 Prover 1: Found proof (size 18) % 5.17/1.33 Prover 1: proved (757ms) % 5.17/1.33 Prover 4: Found proof (size 15) % 5.17/1.33 Prover 4: proved (762ms) % 5.17/1.34 Prover 10: Preprocessing ... % 5.17/1.34 Prover 8: Preprocessing ... % 5.17/1.34 Prover 11: Preprocessing ... % 5.17/1.34 Prover 7: Preprocessing ... % 5.17/1.35 Prover 10: stopped % 5.17/1.35 Prover 7: stopped % 5.17/1.36 Prover 11: stopped % 5.45/1.38 Prover 8: Warning: ignoring some quantifiers % 5.45/1.39 Prover 8: Constructing countermodel ... % 5.45/1.39 Prover 8: stopped % 5.45/1.39 % 5.45/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.45/1.39 % 5.45/1.40 % SZS output start Proof for theBenchmark % 5.45/1.40 Assumptions after simplification: % 5.45/1.40 --------------------------------- % 5.45/1.40 % 5.45/1.40 (ax4) % 5.45/1.42 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 5.45/1.42 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 5.45/1.42 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = % 5.45/1.42 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 5.45/1.42 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 5.45/1.42 collection(v1) | in(v0, v1) = 0) % 5.45/1.42 % 5.45/1.42 (ax5) % 5.45/1.43 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 5.45/1.43 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = % 5.45/1.43 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 5.45/1.43 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ( % 5.45/1.43 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | ( ~ (v2 % 5.45/1.43 = v0) & in(v0, v1) = 0)) % 5.45/1.43 % 5.45/1.43 (co1) % 5.45/1.43 ? [v0: collection] : ? [v1: collection] : ? [v2: int] : ? [v3: int] : ? % 5.45/1.43 [v4: collection] : ($lesseq(0, v3) & remove(v2, v1) = v4 & add($sum(v3, v2), % 5.45/1.43 v4) = v0 & in(v2, v1) = 0 & collection(v4) & collection(v1) & % 5.45/1.43 collection(v0) & ! [v5: int] : ( ~ ($lesseq(v5, 0) | ~ (in(v5, v1) = 0)) & % 5.45/1.43 ? [v5: int] : ($lesseq(v5, 0)in(v5, v0) = 0)) % 5.45/1.43 % 5.45/1.43 Further assumptions not needed in the proof: % 5.45/1.43 -------------------------------------------- % 5.45/1.43 ax1, ax2, ax3 % 5.45/1.43 % 5.45/1.43 Those formulas are unsatisfiable: % 5.45/1.43 --------------------------------- % 5.45/1.43 % 5.45/1.43 Begin of proof % 5.45/1.43 | % 5.45/1.43 | ALPHA: (ax4) implies: % 5.76/1.43 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 5.76/1.43 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 5.76/1.43 | collection(v1) | in(v0, v1) = 0) % 5.76/1.44 | % 5.76/1.44 | ALPHA: (ax5) implies: % 5.76/1.44 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 5.76/1.44 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | % 5.76/1.44 | ( ~ (v2 = v0) & in(v0, v1) = 0)) % 5.76/1.44 | % 5.76/1.44 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2, % 5.76/1.44 | all_11_3, all_11_4 gives: % 5.76/1.44 | (3) $lesseq(0, all_11_1) & remove(all_11_2, all_11_3) = all_11_0 & % 5.76/1.44 | add($sum(all_11_1, all_11_2), all_11_0) = all_11_4 & in(all_11_2, % 5.76/1.44 | all_11_3) = 0 & collection(all_11_0) & collection(all_11_3) & % 5.76/1.44 | collection(all_11_4) & ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, % 5.76/1.44 | all_11_3) = 0)) & ? [v0: int] : ($lesseq(v0, 0)in(v0, % 5.76/1.44 | all_11_4) = 0) % 5.76/1.44 | % 5.76/1.44 | ALPHA: (3) implies: % 5.76/1.44 | (4) $lesseq(0, all_11_1) % 5.76/1.44 | (5) collection(all_11_3) % 5.76/1.44 | (6) collection(all_11_0) % 5.76/1.44 | (7) in(all_11_2, all_11_3) = 0 % 5.76/1.44 | (8) add($sum(all_11_1, all_11_2), all_11_0) = all_11_4 % 5.76/1.44 | (9) remove(all_11_2, all_11_3) = all_11_0 % 5.76/1.44 | (10) ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_3) = 0)) % 5.76/1.44 | (11) ? [v0: int] : ($lesseq(v0, 0)in(v0, all_11_4) = 0) % 5.76/1.44 | % 5.76/1.44 | DELTA: instantiating (11) with fresh symbol all_15_0 gives: % 5.76/1.44 | (12) $lesseq(all_15_0, 0)in(all_15_0, all_11_4) = 0 % 5.76/1.44 | % 5.76/1.44 | ALPHA: (12) implies: % 5.76/1.44 | (13) $lesseq(all_15_0, 0) % 5.76/1.45 | (14) in(all_15_0, all_11_4) = 0 % 5.76/1.45 | % 5.76/1.45 | GROUND_INST: instantiating (10) with all_11_2, simplifying with (7) gives: % 5.76/1.45 | (15) $lesseq(1, all_11_2) % 5.76/1.45 | % 5.76/1.45 | GROUND_INST: instantiating (1) with all_15_0, all_11_0, $sum(all_11_1, % 5.76/1.45 | all_11_2), all_11_4, simplifying with (6), (8), (14) gives: % 5.76/1.45 | (16) $difference(all_15_0, all_11_1) = all_11_2 | in(all_15_0, all_11_0) = % 5.76/1.45 | 0 % 5.76/1.45 | % 5.76/1.45 | BETA: splitting (16) gives: % 5.76/1.45 | % 5.76/1.45 | Case 1: % 5.76/1.45 | | % 5.76/1.45 | | (17) in(all_15_0, all_11_0) = 0 % 5.76/1.45 | | % 5.76/1.45 | | GROUND_INST: instantiating (2) with all_15_0, all_11_3, all_11_2, all_11_0, % 5.76/1.45 | | simplifying with (5), (9), (17) gives: % 5.76/1.45 | | (18) ~ (all_15_0 = all_11_2) & in(all_15_0, all_11_3) = 0 % 5.76/1.45 | | % 5.76/1.45 | | ALPHA: (18) implies: % 5.76/1.45 | | (19) in(all_15_0, all_11_3) = 0 % 5.76/1.45 | | % 5.76/1.45 | | GROUND_INST: instantiating (10) with all_15_0, simplifying with (19) gives: % 5.76/1.45 | | (20) $lesseq(1, all_15_0) % 5.76/1.45 | | % 5.76/1.45 | | COMBINE_INEQS: (13), (20) imply: % 5.76/1.45 | | (21) $false % 5.76/1.45 | | % 5.76/1.45 | | CLOSE: (21) is inconsistent. % 5.76/1.45 | | % 5.76/1.45 | Case 2: % 5.76/1.45 | | % 5.76/1.45 | | (22) $difference(all_15_0, all_11_1) = all_11_2 % 5.76/1.45 | | % 5.76/1.45 | | REDUCE: (13), (22) imply: % 5.76/1.45 | | (23) $lesseq(all_11_2, $product(-1, all_11_1)) % 5.76/1.45 | | % 5.76/1.45 | | COMBINE_INEQS: (4), (23) imply: % 5.76/1.45 | | (24) $lesseq(all_11_2, 0) % 5.76/1.45 | | % 5.76/1.45 | | COMBINE_INEQS: (15), (24) imply: % 5.76/1.45 | | (25) $false % 5.76/1.45 | | % 5.76/1.45 | | CLOSE: (25) is inconsistent. % 5.76/1.45 | | % 5.76/1.45 | End of split % 5.76/1.45 | % 5.76/1.45 End of proof % 5.76/1.45 % SZS output end Proof for theBenchmark % 5.76/1.45 % 5.76/1.45 909ms %------------------------------------------------------------------------------