%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS195+1 : TPTP v8.1.2. Bugfixed v5.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.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 05:51:36 EDT 2023 % Result : Theorem 10.20s 2.22s % Output : Proof 13.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS195+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n016.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 : Mon Aug 28 01:55:44 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.55/1.21 Prover 4: Preprocessing ... % 3.55/1.21 Prover 1: Preprocessing ... % 3.55/1.25 Prover 3: Preprocessing ... % 3.55/1.25 Prover 0: Preprocessing ... % 3.55/1.25 Prover 6: Preprocessing ... % 3.55/1.25 Prover 5: Preprocessing ... % 3.55/1.25 Prover 2: Preprocessing ... % 7.63/1.84 Prover 5: Proving ... % 7.63/1.84 Prover 2: Proving ... % 8.99/1.99 Prover 6: Proving ... % 9.47/2.06 Prover 1: Constructing countermodel ... % 9.47/2.07 Prover 3: Constructing countermodel ... % 9.47/2.09 Prover 4: Constructing countermodel ... % 10.20/2.20 Prover 0: Proving ... % 10.20/2.22 Prover 3: proved (1578ms) % 10.20/2.22 % 10.20/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.20/2.22 % 10.20/2.22 Prover 0: stopped % 10.20/2.22 Prover 2: stopped % 10.20/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.20/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.20/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.20/2.22 Prover 6: stopped % 10.20/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.20/2.22 Prover 5: stopped % 10.20/2.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.23/2.28 Prover 13: Preprocessing ... % 11.23/2.28 Prover 8: Preprocessing ... % 11.44/2.30 Prover 7: Preprocessing ... % 11.44/2.30 Prover 10: Preprocessing ... % 11.44/2.30 Prover 11: Preprocessing ... % 12.22/2.41 Prover 1: Found proof (size 23) % 12.22/2.41 Prover 1: proved (1773ms) % 12.22/2.41 Prover 4: stopped % 12.22/2.41 Prover 11: stopped % 12.22/2.41 Prover 7: Warning: ignoring some quantifiers % 12.22/2.42 Prover 10: Warning: ignoring some quantifiers % 12.22/2.44 Prover 13: Warning: ignoring some quantifiers % 12.22/2.44 Prover 7: Constructing countermodel ... % 12.22/2.44 Prover 10: Constructing countermodel ... % 12.22/2.45 Prover 7: stopped % 12.22/2.46 Prover 10: stopped % 12.22/2.46 Prover 13: Constructing countermodel ... % 12.69/2.47 Prover 13: stopped % 12.69/2.52 Prover 8: Warning: ignoring some quantifiers % 12.69/2.53 Prover 8: Constructing countermodel ... % 12.69/2.54 Prover 8: stopped % 12.69/2.54 % 12.69/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.69/2.54 % 12.69/2.54 % SZS output start Proof for theBenchmark % 12.69/2.54 Assumptions after simplification: % 12.69/2.54 --------------------------------- % 12.69/2.54 % 12.69/2.54 (isa) % 13.18/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) = v2) | % 13.18/2.57 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 13.18/2.57 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0 & $i(v4) & % 13.18/2.57 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (isa(v0, v1) = 0) | ~ $i(v1) | % 13.18/2.57 ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (status(v2, v3, v0) = 0) | ~ % 13.18/2.57 $i(v3) | ~ $i(v2) | status(v2, v3, v1) = 0)) % 13.18/2.57 % 13.18/2.57 (isa_tca_thm) % 13.18/2.57 $i(tca) & $i(thm) & ? [v0: int] : ( ~ (v0 = 0) & isa(tca, thm) = v0) % 13.18/2.57 % 13.18/2.57 (tca) % 13.18/2.57 $i(tca) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, % 13.18/2.57 v1, tca) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( % 13.18/2.57 ~ (v4 = 0) & model(v3, v1) = v4 & $i(v3)) | ? [v3: $i] : (model(v3, v0) = % 13.18/2.57 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, tca) = 0) | % 13.18/2.57 ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.18/2.57 (model(v2, v1) = v3) | ~ $i(v2)) & ! [v2: $i] : ( ~ (model(v2, v0) = % 13.18/2.57 0) | ~ $i(v2)))) % 13.18/2.57 % 13.18/2.57 (thm) % 13.18/2.57 $i(thm) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, % 13.18/2.57 v1, thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( % 13.18/2.57 ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) & ! [v0: % 13.18/2.57 $i] : ! [v1: $i] : ( ~ (status(v0, v1, thm) = 0) | ~ $i(v1) | ~ $i(v0) | % 13.18/2.57 ! [v2: $i] : ( ~ (model(v2, v0) = 0) | ~ $i(v2) | model(v2, v1) = 0)) % 13.18/2.57 % 13.18/2.57 Further assumptions not needed in the proof: % 13.18/2.57 -------------------------------------------- % 13.18/2.57 cax, completeness, contradiction, csa, eqv, esa, eth, mighta, mixed_pair, % 13.18/2.57 nevera, noc, non_thm_spt, not, nota, sap, sat, sat_non_taut_pair, satisfiable, % 13.18/2.57 sca, tac, tau, tautology, unp, uns, wca, wec, wtc, wth, xora % 13.18/2.57 % 13.18/2.57 Those formulas are unsatisfiable: % 13.18/2.57 --------------------------------- % 13.18/2.57 % 13.18/2.57 Begin of proof % 13.18/2.58 | % 13.18/2.58 | ALPHA: (thm) implies: % 13.18/2.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1, % 13.18/2.58 | thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 13.18/2.58 | ( ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) % 13.18/2.58 | % 13.18/2.58 | ALPHA: (tca) implies: % 13.18/2.58 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, tca) = 0) | ~ $i(v1) | % 13.18/2.58 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (model(v2, v1) % 13.18/2.58 | = v3) | ~ $i(v2)) & ! [v2: $i] : ( ~ (model(v2, v0) = 0) | ~ % 13.18/2.58 | $i(v2)))) % 13.18/2.58 | % 13.18/2.58 | ALPHA: (isa) implies: % 13.18/2.58 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) = % 13.18/2.58 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.18/2.58 | int] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) % 13.18/2.58 | = 0 & $i(v4) & $i(v3))) % 13.18/2.58 | % 13.18/2.58 | ALPHA: (isa_tca_thm) implies: % 13.18/2.58 | (4) $i(thm) % 13.18/2.58 | (5) $i(tca) % 13.18/2.58 | (6) ? [v0: int] : ( ~ (v0 = 0) & isa(tca, thm) = v0) % 13.18/2.58 | % 13.18/2.58 | DELTA: instantiating (6) with fresh symbol all_30_0 gives: % 13.18/2.58 | (7) ~ (all_30_0 = 0) & isa(tca, thm) = all_30_0 % 13.18/2.58 | % 13.18/2.58 | ALPHA: (7) implies: % 13.18/2.58 | (8) ~ (all_30_0 = 0) % 13.18/2.58 | (9) isa(tca, thm) = all_30_0 % 13.18/2.58 | % 13.18/2.58 | GROUND_INST: instantiating (3) with tca, thm, all_30_0, simplifying with (4), % 13.18/2.58 | (5), (9) gives: % 13.18/2.58 | (10) all_30_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 13.18/2.58 | & status(v0, v1, tca) = 0 & status(v0, v1, thm) = v2 & $i(v1) & % 13.18/2.58 | $i(v0)) % 13.18/2.58 | % 13.18/2.58 | BETA: splitting (10) gives: % 13.18/2.58 | % 13.18/2.58 | Case 1: % 13.18/2.58 | | % 13.18/2.58 | | (11) all_30_0 = 0 % 13.18/2.58 | | % 13.18/2.59 | | REDUCE: (8), (11) imply: % 13.18/2.59 | | (12) $false % 13.18/2.59 | | % 13.18/2.59 | | CLOSE: (12) is inconsistent. % 13.18/2.59 | | % 13.18/2.59 | Case 2: % 13.18/2.59 | | % 13.18/2.59 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & status(v0, % 13.18/2.59 | | v1, tca) = 0 & status(v0, v1, thm) = v2 & $i(v1) & $i(v0)) % 13.18/2.59 | | % 13.18/2.59 | | DELTA: instantiating (13) with fresh symbols all_73_0, all_73_1, all_73_2 % 13.18/2.59 | | gives: % 13.18/2.59 | | (14) ~ (all_73_0 = 0) & status(all_73_2, all_73_1, tca) = 0 & % 13.18/2.59 | | status(all_73_2, all_73_1, thm) = all_73_0 & $i(all_73_1) & % 13.18/2.59 | | $i(all_73_2) % 13.18/2.59 | | % 13.18/2.59 | | ALPHA: (14) implies: % 13.18/2.59 | | (15) ~ (all_73_0 = 0) % 13.18/2.59 | | (16) $i(all_73_2) % 13.18/2.59 | | (17) $i(all_73_1) % 13.18/2.59 | | (18) status(all_73_2, all_73_1, thm) = all_73_0 % 13.18/2.59 | | (19) status(all_73_2, all_73_1, tca) = 0 % 13.18/2.59 | | % 13.18/2.59 | | GROUND_INST: instantiating (1) with all_73_2, all_73_1, all_73_0, % 13.18/2.59 | | simplifying with (16), (17), (18) gives: % 13.18/2.59 | | (20) all_73_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0, % 13.18/2.59 | | all_73_1) = v1 & model(v0, all_73_2) = 0 & $i(v0)) % 13.18/2.59 | | % 13.18/2.59 | | GROUND_INST: instantiating (2) with all_73_2, all_73_1, simplifying with % 13.18/2.59 | | (16), (17), (19) gives: % 13.18/2.59 | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (model(v0, all_73_1) = v1) % 13.18/2.59 | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) | ~ % 13.18/2.59 | | $i(v0)) % 13.18/2.59 | | % 13.18/2.59 | | ALPHA: (21) implies: % 13.18/2.59 | | (22) ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) | ~ $i(v0)) % 13.18/2.59 | | % 13.18/2.59 | | BETA: splitting (20) gives: % 13.18/2.59 | | % 13.18/2.59 | | Case 1: % 13.18/2.59 | | | % 13.18/2.59 | | | (23) all_73_0 = 0 % 13.18/2.59 | | | % 13.18/2.59 | | | REDUCE: (15), (23) imply: % 13.18/2.59 | | | (24) $false % 13.18/2.59 | | | % 13.18/2.59 | | | CLOSE: (24) is inconsistent. % 13.18/2.59 | | | % 13.18/2.59 | | Case 2: % 13.18/2.59 | | | % 13.18/2.59 | | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_73_1) = % 13.18/2.59 | | | v1 & model(v0, all_73_2) = 0 & $i(v0)) % 13.18/2.59 | | | % 13.18/2.59 | | | DELTA: instantiating (25) with fresh symbols all_89_0, all_89_1 gives: % 13.18/2.59 | | | (26) ~ (all_89_0 = 0) & model(all_89_1, all_73_1) = all_89_0 & % 13.18/2.59 | | | model(all_89_1, all_73_2) = 0 & $i(all_89_1) % 13.18/2.59 | | | % 13.18/2.59 | | | ALPHA: (26) implies: % 13.18/2.59 | | | (27) $i(all_89_1) % 13.18/2.59 | | | (28) model(all_89_1, all_73_2) = 0 % 13.18/2.59 | | | % 13.18/2.59 | | | GROUND_INST: instantiating (22) with all_89_1, simplifying with (27), (28) % 13.18/2.59 | | | gives: % 13.18/2.59 | | | (29) $false % 13.18/2.59 | | | % 13.18/2.59 | | | CLOSE: (29) is inconsistent. % 13.18/2.59 | | | % 13.18/2.59 | | End of split % 13.18/2.59 | | % 13.18/2.59 | End of split % 13.18/2.59 | % 13.18/2.59 End of proof % 13.18/2.59 % SZS output end Proof for theBenchmark % 13.34/2.59 % 13.34/2.59 1975ms %------------------------------------------------------------------------------