%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : PUZ130_1 : TPTP v8.1.2. Released v5.5.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 13:23:13 EDT 2023 % Result : Theorem 3.88s 1.34s % Output : Proof 5.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : PUZ130_1 : TPTP v8.1.2. Released v5.5.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 23:06:35 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.64 ________ _____ % 0.21/0.64 ___ __ \_________(_)________________________________ % 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.64 % 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.64 (2023-06-19) % 0.21/0.64 % 0.21/0.64 (c) Philipp Rümmer, 2009-2023 % 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.64 Amanda Stjerna. % 0.21/0.64 Free software under BSD-3-Clause. % 0.21/0.64 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.23/1.02 Prover 4: Preprocessing ... % 2.23/1.02 Prover 1: Preprocessing ... % 2.45/1.06 Prover 0: Preprocessing ... % 2.45/1.06 Prover 6: Preprocessing ... % 2.45/1.06 Prover 2: Preprocessing ... % 2.45/1.06 Prover 3: Preprocessing ... % 2.45/1.06 Prover 5: Preprocessing ... % 3.43/1.22 Prover 6: Constructing countermodel ... % 3.43/1.22 Prover 4: Constructing countermodel ... % 3.43/1.22 Prover 1: Constructing countermodel ... % 3.43/1.22 Prover 3: Constructing countermodel ... % 3.43/1.23 Prover 0: Proving ... % 3.43/1.23 Prover 2: Proving ... % 3.43/1.23 Prover 5: Proving ... % 3.88/1.34 Prover 0: proved (675ms) % 3.88/1.34 % 3.88/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.88/1.34 % 3.88/1.34 Prover 6: stopped % 3.88/1.34 Prover 3: stopped % 3.88/1.34 Prover 2: proved (671ms) % 3.88/1.34 % 3.88/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.88/1.34 % 3.88/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.88/1.35 Prover 5: stopped % 3.88/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.88/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.88/1.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.88/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.88/1.37 Prover 7: Preprocessing ... % 3.88/1.37 Prover 13: Preprocessing ... % 3.88/1.38 Prover 10: Preprocessing ... % 3.88/1.39 Prover 8: Preprocessing ... % 3.88/1.39 Prover 11: Preprocessing ... % 4.55/1.42 Prover 1: Found proof (size 27) % 4.55/1.42 Prover 10: Constructing countermodel ... % 4.55/1.42 Prover 1: proved (758ms) % 4.55/1.42 Prover 7: Constructing countermodel ... % 4.55/1.42 Prover 4: stopped % 4.55/1.42 Prover 13: stopped % 4.55/1.42 Prover 10: stopped % 4.55/1.42 Prover 8: Warning: ignoring some quantifiers % 4.55/1.43 Prover 7: stopped % 4.55/1.43 Prover 8: Constructing countermodel ... % 4.55/1.43 Prover 8: stopped % 4.55/1.44 Prover 11: Constructing countermodel ... % 5.03/1.45 Prover 11: stopped % 5.03/1.45 % 5.03/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.03/1.45 % 5.03/1.45 % SZS output start Proof for theBenchmark % 5.03/1.46 Assumptions after simplification: % 5.03/1.46 --------------------------------- % 5.03/1.46 % 5.03/1.46 (dog_chase_cat) % 5.03/1.49 ! [v0: cat] : ! [v1: dog] : ! [v2: animal] : ! [v3: human] : ! [v4: % 5.03/1.49 animal] : ! [v5: human] : ! [v6: int] : (v6 = 0 | ~ (hates(v3, v5) = v6) % 5.03/1.49 | ~ (dog_to_animal(v1) = v4) | ~ (cat_to_animal(v0) = v2) | ~ % 5.03/1.49 (owner_of(v4) = v5) | ~ (owner_of(v2) = v3) | ~ dog(v1) | ~ cat(v0) | ? % 5.03/1.49 [v7: int] : ( ~ (v7 = 0) & chased(v1, v0) = v7)) % 5.03/1.49 % 5.03/1.49 (jon_hates_jon) % 5.03/1.49 human(jon) & ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0) % 5.03/1.49 % 5.03/1.49 (jon_owns_garfield) % 5.03/1.49 human(jon) & cat(garfield) & ? [v0: animal] : (cat_to_animal(garfield) = v0 & % 5.03/1.49 owner_of(v0) = jon & animal(v0)) % 5.03/1.49 % 5.03/1.49 (jon_owns_odie) % 5.03/1.49 human(jon) & dog(odie) & ? [v0: animal] : (dog_to_animal(odie) = v0 & % 5.03/1.49 owner_of(v0) = jon & animal(v0)) % 5.03/1.49 % 5.03/1.49 (jon_owns_only) % 5.03/1.49 human(jon) & dog(odie) & cat(garfield) & ? [v0: animal] : ? [v1: animal] : % 5.03/1.49 (dog_to_animal(odie) = v1 & cat_to_animal(garfield) = v0 & animal(v1) & % 5.03/1.49 animal(v0) & ! [v2: animal] : (v2 = v1 | v2 = v0 | ~ (owner_of(v2) = jon) % 5.03/1.49 | ~ animal(v2))) % 5.03/1.49 % 5.03/1.49 (odie_chased_garfield) % 5.03/1.49 chased(odie, garfield) = 0 & dog(odie) & cat(garfield) % 5.03/1.49 % 5.03/1.49 (function-axioms) % 5.03/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: human] : ! % 5.03/1.50 [v3: human] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2) = v0)) & % 5.03/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: cat] : ! % 5.03/1.50 [v3: dog] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, v2) = v0)) & % 5.03/1.50 ! [v0: animal] : ! [v1: animal] : ! [v2: dog] : (v1 = v0 | ~ % 5.03/1.50 (dog_to_animal(v2) = v1) | ~ (dog_to_animal(v2) = v0)) & ! [v0: animal] : % 5.03/1.50 ! [v1: animal] : ! [v2: cat] : (v1 = v0 | ~ (cat_to_animal(v2) = v1) | ~ % 5.03/1.50 (cat_to_animal(v2) = v0)) & ! [v0: human] : ! [v1: human] : ! [v2: % 5.03/1.50 animal] : (v1 = v0 | ~ (owner_of(v2) = v1) | ~ (owner_of(v2) = v0)) % 5.03/1.50 % 5.03/1.50 Further assumptions not needed in the proof: % 5.03/1.50 -------------------------------------------- % 5.03/1.50 human_owner % 5.03/1.50 % 5.03/1.50 Those formulas are unsatisfiable: % 5.03/1.50 --------------------------------- % 5.03/1.50 % 5.03/1.50 Begin of proof % 5.03/1.50 | % 5.03/1.50 | ALPHA: (jon_owns_garfield) implies: % 5.03/1.50 | (1) ? [v0: animal] : (cat_to_animal(garfield) = v0 & owner_of(v0) = jon & % 5.03/1.50 | animal(v0)) % 5.03/1.50 | % 5.03/1.50 | ALPHA: (jon_owns_odie) implies: % 5.03/1.50 | (2) ? [v0: animal] : (dog_to_animal(odie) = v0 & owner_of(v0) = jon & % 5.03/1.50 | animal(v0)) % 5.03/1.50 | % 5.03/1.50 | ALPHA: (jon_owns_only) implies: % 5.03/1.50 | (3) ? [v0: animal] : ? [v1: animal] : (dog_to_animal(odie) = v1 & % 5.03/1.50 | cat_to_animal(garfield) = v0 & animal(v1) & animal(v0) & ! [v2: % 5.03/1.50 | animal] : (v2 = v1 | v2 = v0 | ~ (owner_of(v2) = jon) | ~ % 5.03/1.50 | animal(v2))) % 5.03/1.50 | % 5.03/1.50 | ALPHA: (odie_chased_garfield) implies: % 5.03/1.51 | (4) cat(garfield) % 5.03/1.51 | (5) dog(odie) % 5.03/1.51 | (6) chased(odie, garfield) = 0 % 5.03/1.51 | % 5.03/1.51 | ALPHA: (jon_hates_jon) implies: % 5.03/1.51 | (7) ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0) % 5.03/1.51 | % 5.03/1.51 | ALPHA: (function-axioms) implies: % 5.03/1.51 | (8) ! [v0: animal] : ! [v1: animal] : ! [v2: cat] : (v1 = v0 | ~ % 5.03/1.51 | (cat_to_animal(v2) = v1) | ~ (cat_to_animal(v2) = v0)) % 5.03/1.51 | (9) ! [v0: animal] : ! [v1: animal] : ! [v2: dog] : (v1 = v0 | ~ % 5.03/1.51 | (dog_to_animal(v2) = v1) | ~ (dog_to_animal(v2) = v0)) % 5.03/1.51 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: cat] % 5.03/1.51 | : ! [v3: dog] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, % 5.03/1.51 | v2) = v0)) % 5.03/1.51 | % 5.03/1.51 | DELTA: instantiating (7) with fresh symbol all_14_0 gives: % 5.03/1.51 | (11) ~ (all_14_0 = 0) & hates(jon, jon) = all_14_0 % 5.03/1.51 | % 5.03/1.51 | ALPHA: (11) implies: % 5.03/1.51 | (12) ~ (all_14_0 = 0) % 5.03/1.51 | (13) hates(jon, jon) = all_14_0 % 5.03/1.51 | % 5.03/1.51 | DELTA: instantiating (1) with fresh symbol all_16_0 gives: % 5.03/1.51 | (14) cat_to_animal(garfield) = all_16_0 & owner_of(all_16_0) = jon & % 5.03/1.51 | animal(all_16_0) % 5.03/1.51 | % 5.03/1.51 | ALPHA: (14) implies: % 5.03/1.51 | (15) owner_of(all_16_0) = jon % 5.03/1.51 | (16) cat_to_animal(garfield) = all_16_0 % 5.03/1.51 | % 5.03/1.51 | DELTA: instantiating (2) with fresh symbol all_18_0 gives: % 5.03/1.51 | (17) dog_to_animal(odie) = all_18_0 & owner_of(all_18_0) = jon & % 5.03/1.51 | animal(all_18_0) % 5.03/1.51 | % 5.03/1.51 | ALPHA: (17) implies: % 5.03/1.51 | (18) owner_of(all_18_0) = jon % 5.03/1.51 | (19) dog_to_animal(odie) = all_18_0 % 5.03/1.51 | % 5.03/1.51 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1 gives: % 5.03/1.52 | (20) dog_to_animal(odie) = all_20_0 & cat_to_animal(garfield) = all_20_1 & % 5.03/1.52 | animal(all_20_0) & animal(all_20_1) & ! [v0: any] : (v0 = all_20_0 | % 5.03/1.52 | v0 = all_20_1 | ~ (owner_of(v0) = jon) | ~ animal(v0)) % 5.03/1.52 | % 5.03/1.52 | ALPHA: (20) implies: % 5.03/1.52 | (21) cat_to_animal(garfield) = all_20_1 % 5.03/1.52 | (22) dog_to_animal(odie) = all_20_0 % 5.03/1.52 | % 5.03/1.52 | GROUND_INST: instantiating (8) with all_16_0, all_20_1, garfield, simplifying % 5.03/1.52 | with (16), (21) gives: % 5.03/1.52 | (23) all_20_1 = all_16_0 % 5.03/1.52 | % 5.03/1.52 | GROUND_INST: instantiating (9) with all_18_0, all_20_0, odie, simplifying with % 5.03/1.52 | (19), (22) gives: % 5.03/1.52 | (24) all_20_0 = all_18_0 % 5.03/1.52 | % 5.03/1.52 | GROUND_INST: instantiating (dog_chase_cat) with garfield, odie, all_16_0, jon, % 5.03/1.52 | all_18_0, jon, all_14_0, simplifying with (4), (5), (13), (15), % 5.03/1.52 | (16), (18), (19) gives: % 5.03/1.52 | (25) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & chased(odie, garfield) = % 5.03/1.52 | v0) % 5.03/1.52 | % 5.03/1.52 | BETA: splitting (25) gives: % 5.03/1.52 | % 5.03/1.52 | Case 1: % 5.03/1.52 | | % 5.03/1.52 | | (26) all_14_0 = 0 % 5.03/1.52 | | % 5.03/1.52 | | REDUCE: (12), (26) imply: % 5.03/1.52 | | (27) $false % 5.03/1.52 | | % 5.03/1.52 | | CLOSE: (27) is inconsistent. % 5.03/1.52 | | % 5.03/1.52 | Case 2: % 5.03/1.52 | | % 5.03/1.52 | | (28) ? [v0: int] : ( ~ (v0 = 0) & chased(odie, garfield) = v0) % 5.03/1.52 | | % 5.03/1.52 | | DELTA: instantiating (28) with fresh symbol all_34_0 gives: % 5.03/1.52 | | (29) ~ (all_34_0 = 0) & chased(odie, garfield) = all_34_0 % 5.03/1.52 | | % 5.03/1.52 | | ALPHA: (29) implies: % 5.03/1.52 | | (30) ~ (all_34_0 = 0) % 5.03/1.52 | | (31) chased(odie, garfield) = all_34_0 % 5.03/1.52 | | % 5.03/1.52 | | GROUND_INST: instantiating (10) with 0, all_34_0, garfield, odie, % 5.03/1.52 | | simplifying with (6), (31) gives: % 5.03/1.52 | | (32) all_34_0 = 0 % 5.03/1.52 | | % 5.03/1.52 | | REDUCE: (30), (32) imply: % 5.03/1.52 | | (33) $false % 5.03/1.52 | | % 5.03/1.52 | | CLOSE: (33) is inconsistent. % 5.03/1.52 | | % 5.03/1.52 | End of split % 5.03/1.52 | % 5.03/1.52 End of proof % 5.03/1.52 % SZS output end Proof for theBenchmark % 5.03/1.53 % 5.03/1.53 882ms %------------------------------------------------------------------------------