%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO081+1 : TPTP v8.1.2. Released v2.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 23:21:18 EDT 2023 % Result : Theorem 6.52s 2.83s % Output : Proof 9.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.20 % Problem : GEO081+1 : TPTP v8.1.2. Released v2.4.0. % 0.04/0.21 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.44 % Computer : n008.cluster.edu % 0.13/0.44 % Model : x86_64 x86_64 % 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.44 % Memory : 8042.1875MB % 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.44 % CPULimit : 300 % 0.13/0.44 % WCLimit : 300 % 0.13/0.44 % DateTime : Tue Aug 29 20:48:32 EDT 2023 % 0.13/0.44 % CPUTime : % 0.16/0.78 ________ _____ % 0.16/0.78 ___ __ \_________(_)________________________________ % 0.16/0.78 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.78 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.78 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.78 % 0.16/0.78 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.78 (2023-06-19) % 0.16/0.78 % 0.16/0.78 (c) Philipp Rümmer, 2009-2023 % 0.16/0.78 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.78 Amanda Stjerna. % 0.16/0.78 Free software under BSD-3-Clause. % 0.16/0.78 % 0.16/0.78 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.78 % 0.16/0.78 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.80 Running up to 7 provers in parallel. % 0.66/0.89 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.89 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.89 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.89 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.89 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.89 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.41/1.47 Prover 1: Preprocessing ... % 1.41/1.49 Prover 4: Preprocessing ... % 2.06/1.57 Prover 6: Preprocessing ... % 2.06/1.57 Prover 3: Preprocessing ... % 2.06/1.57 Prover 2: Preprocessing ... % 2.06/1.57 Prover 5: Preprocessing ... % 2.06/1.57 Prover 0: Preprocessing ... % 4.33/2.36 Prover 5: Proving ... % 4.71/2.40 Prover 2: Proving ... % 5.10/2.45 Prover 1: Warning: ignoring some quantifiers % 5.10/2.47 Prover 3: Warning: ignoring some quantifiers % 5.10/2.47 Prover 6: Proving ... % 5.44/2.52 Prover 3: Constructing countermodel ... % 5.44/2.53 Prover 1: Constructing countermodel ... % 6.52/2.83 Prover 3: proved (1977ms) % 6.52/2.83 % 6.52/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.52/2.83 % 6.52/2.86 Prover 2: stopped % 6.52/2.87 Prover 6: stopped % 6.52/2.88 Prover 5: stopped % 6.77/2.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.77/2.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.77/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.77/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.77/3.04 Prover 8: Preprocessing ... % 6.77/3.06 Prover 11: Preprocessing ... % 6.77/3.06 Prover 7: Preprocessing ... % 6.77/3.07 Prover 10: Preprocessing ... % 6.77/3.12 Prover 1: Found proof (size 29) % 6.77/3.12 Prover 1: proved (2284ms) % 6.77/3.12 Prover 10: stopped % 6.77/3.20 Prover 7: Warning: ignoring some quantifiers % 6.77/3.24 Prover 7: Constructing countermodel ... % 6.77/3.24 Prover 11: stopped % 6.77/3.25 Prover 7: stopped % 8.37/3.31 Prover 8: Warning: ignoring some quantifiers % 8.42/3.34 Prover 8: Constructing countermodel ... % 8.42/3.35 Prover 8: stopped % 8.74/3.45 Prover 4: Warning: ignoring some quantifiers % 9.01/3.55 Prover 4: Constructing countermodel ... % 9.01/3.57 Prover 4: stopped % 9.42/3.64 Prover 0: Proving ... % 9.42/3.67 Prover 0: stopped % 9.42/3.67 % 9.42/3.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.42/3.67 % 9.42/3.67 % SZS output start Proof for theBenchmark % 9.42/3.68 Assumptions after simplification: % 9.42/3.68 --------------------------------- % 9.42/3.68 % 9.42/3.68 (part_of_defn) % 9.63/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2) % 9.63/3.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 9.63/3.75 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i] % 9.63/3.75 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: % 9.63/3.75 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) | % 9.63/3.75 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))) % 9.63/3.75 % 9.63/3.75 (part_of_transitivity) % 9.63/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.63/3.75 part_of(v1, v2) = 0 & part_of(v0, v2) = v3 & part_of(v0, v1) = 0 & $i(v2) & % 9.63/3.75 $i(v1) & $i(v0)) % 9.63/3.75 % 9.63/3.75 (function-axioms) % 9.63/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.63/3.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, % 9.63/3.76 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 9.63/3.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~ % 9.63/3.76 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.63/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.63/3.76 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : ! % 9.63/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ % 9.63/3.76 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.63/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, % 9.63/3.76 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.63/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.63/3.76 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0: % 9.63/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.63/3.76 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.63/3.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~ % 9.63/3.76 (closed(v2) = v0)) % 9.63/3.76 % 9.63/3.76 Further assumptions not needed in the proof: % 9.63/3.76 -------------------------------------------- % 9.63/3.76 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, % 9.63/3.76 inner_point_defn, meet_defn, open_defn, sum_defn % 9.63/3.76 % 9.63/3.76 Those formulas are unsatisfiable: % 9.63/3.76 --------------------------------- % 9.63/3.76 % 9.63/3.76 Begin of proof % 9.63/3.76 | % 9.63/3.76 | ALPHA: (part_of_defn) implies: % 9.63/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ % 9.63/3.77 | $i(v0) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, % 9.63/3.77 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & % 9.63/3.77 | incident_c(v2, v1) = v4))) % 9.63/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, % 9.63/3.77 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 9.63/3.77 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & % 9.63/3.77 | $i(v3))) % 9.63/3.77 | % 9.63/3.77 | ALPHA: (function-axioms) implies: % 9.63/3.77 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.63/3.77 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~ % 9.63/3.77 | (incident_c(v3, v2) = v0)) % 9.63/3.77 | % 9.63/3.77 | DELTA: instantiating (part_of_transitivity) with fresh symbols all_18_0, % 9.63/3.77 | all_18_1, all_18_2, all_18_3 gives: % 9.63/3.78 | (4) ~ (all_18_0 = 0) & part_of(all_18_2, all_18_1) = 0 & part_of(all_18_3, % 9.63/3.78 | all_18_1) = all_18_0 & part_of(all_18_3, all_18_2) = 0 & $i(all_18_1) % 9.63/3.78 | & $i(all_18_2) & $i(all_18_3) % 9.63/3.78 | % 9.63/3.78 | ALPHA: (4) implies: % 9.63/3.78 | (5) ~ (all_18_0 = 0) % 9.63/3.78 | (6) $i(all_18_3) % 9.63/3.78 | (7) $i(all_18_2) % 9.63/3.78 | (8) $i(all_18_1) % 9.63/3.78 | (9) part_of(all_18_3, all_18_2) = 0 % 9.63/3.78 | (10) part_of(all_18_3, all_18_1) = all_18_0 % 9.63/3.78 | (11) part_of(all_18_2, all_18_1) = 0 % 9.63/3.78 | % 9.63/3.78 | GROUND_INST: instantiating (1) with all_18_2, all_18_3, simplifying with (6), % 9.63/3.78 | (7), (9) gives: % 9.63/3.79 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_18_2) = % 9.63/3.79 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0, % 9.63/3.79 | all_18_3) = v2)) % 9.63/3.79 | % 9.63/3.79 | GROUND_INST: instantiating (2) with all_18_1, all_18_3, all_18_0, simplifying % 9.63/3.79 | with (6), (8), (10) gives: % 9.63/3.80 | (13) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.63/3.80 | incident_c(v0, all_18_1) = v1 & incident_c(v0, all_18_3) = 0 & % 9.63/3.80 | $i(v0)) % 9.63/3.80 | % 9.63/3.80 | GROUND_INST: instantiating (1) with all_18_1, all_18_2, simplifying with (7), % 9.63/3.80 | (8), (11) gives: % 9.63/3.80 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_18_1) = % 9.63/3.80 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0, % 9.63/3.80 | all_18_2) = v2)) % 9.63/3.80 | % 9.63/3.80 | BETA: splitting (13) gives: % 9.63/3.80 | % 9.63/3.80 | Case 1: % 9.63/3.80 | | % 9.63/3.80 | | (15) all_18_0 = 0 % 9.63/3.80 | | % 9.63/3.80 | | REDUCE: (5), (15) imply: % 9.63/3.80 | | (16) $false % 9.63/3.80 | | % 9.63/3.80 | | CLOSE: (16) is inconsistent. % 9.63/3.80 | | % 9.63/3.80 | Case 2: % 9.63/3.80 | | % 9.63/3.80 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_18_1) % 9.63/3.80 | | = v1 & incident_c(v0, all_18_3) = 0 & $i(v0)) % 9.63/3.80 | | % 9.63/3.80 | | DELTA: instantiating (17) with fresh symbols all_33_0, all_33_1 gives: % 9.63/3.80 | | (18) ~ (all_33_0 = 0) & incident_c(all_33_1, all_18_1) = all_33_0 & % 9.63/3.80 | | incident_c(all_33_1, all_18_3) = 0 & $i(all_33_1) % 9.63/3.80 | | % 9.63/3.80 | | ALPHA: (18) implies: % 9.63/3.80 | | (19) ~ (all_33_0 = 0) % 9.63/3.81 | | (20) $i(all_33_1) % 9.63/3.81 | | (21) incident_c(all_33_1, all_18_3) = 0 % 9.63/3.81 | | (22) incident_c(all_33_1, all_18_1) = all_33_0 % 9.63/3.81 | | % 9.63/3.81 | | GROUND_INST: instantiating (14) with all_33_1, all_33_0, simplifying with % 9.63/3.81 | | (20), (22) gives: % 9.63/3.81 | | (23) all_33_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, % 9.63/3.81 | | all_18_2) = v0) % 9.63/3.81 | | % 9.63/3.81 | | BETA: splitting (23) gives: % 9.63/3.81 | | % 9.63/3.81 | | Case 1: % 9.63/3.81 | | | % 9.63/3.81 | | | (24) all_33_0 = 0 % 9.63/3.81 | | | % 9.63/3.81 | | | REDUCE: (19), (24) imply: % 9.63/3.81 | | | (25) $false % 9.63/3.81 | | | % 9.63/3.81 | | | CLOSE: (25) is inconsistent. % 9.63/3.81 | | | % 9.63/3.81 | | Case 2: % 9.63/3.81 | | | % 9.63/3.81 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, all_18_2) = v0) % 9.63/3.81 | | | % 9.63/3.81 | | | DELTA: instantiating (26) with fresh symbol all_46_0 gives: % 9.63/3.81 | | | (27) ~ (all_46_0 = 0) & incident_c(all_33_1, all_18_2) = all_46_0 % 9.63/3.81 | | | % 9.63/3.81 | | | ALPHA: (27) implies: % 9.63/3.81 | | | (28) ~ (all_46_0 = 0) % 9.63/3.84 | | | (29) incident_c(all_33_1, all_18_2) = all_46_0 % 9.63/3.84 | | | % 9.63/3.84 | | | GROUND_INST: instantiating (12) with all_33_1, all_46_0, simplifying with % 9.63/3.84 | | | (20), (29) gives: % 9.63/3.84 | | | (30) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, % 9.63/3.84 | | | all_18_3) = v0) % 9.63/3.84 | | | % 9.63/3.84 | | | BETA: splitting (30) gives: % 9.63/3.84 | | | % 9.63/3.84 | | | Case 1: % 9.63/3.84 | | | | % 9.63/3.84 | | | | (31) all_46_0 = 0 % 9.63/3.84 | | | | % 9.63/3.84 | | | | REDUCE: (28), (31) imply: % 9.63/3.84 | | | | (32) $false % 9.63/3.84 | | | | % 9.63/3.84 | | | | CLOSE: (32) is inconsistent. % 9.63/3.84 | | | | % 9.63/3.84 | | | Case 2: % 9.63/3.84 | | | | % 9.63/3.84 | | | | (33) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, all_18_3) = % 9.63/3.84 | | | | v0) % 9.63/3.84 | | | | % 9.63/3.84 | | | | DELTA: instantiating (33) with fresh symbol all_59_0 gives: % 9.63/3.84 | | | | (34) ~ (all_59_0 = 0) & incident_c(all_33_1, all_18_3) = all_59_0 % 9.63/3.84 | | | | % 9.63/3.84 | | | | ALPHA: (34) implies: % 9.63/3.84 | | | | (35) ~ (all_59_0 = 0) % 9.63/3.84 | | | | (36) incident_c(all_33_1, all_18_3) = all_59_0 % 9.63/3.84 | | | | % 9.63/3.84 | | | | GROUND_INST: instantiating (3) with 0, all_59_0, all_18_3, all_33_1, % 9.63/3.84 | | | | simplifying with (21), (36) gives: % 9.63/3.84 | | | | (37) all_59_0 = 0 % 9.63/3.84 | | | | % 9.63/3.84 | | | | REDUCE: (35), (37) imply: % 9.63/3.84 | | | | (38) $false % 9.63/3.84 | | | | % 9.63/3.84 | | | | CLOSE: (38) is inconsistent. % 9.63/3.84 | | | | % 9.63/3.84 | | | End of split % 9.63/3.84 | | | % 9.63/3.84 | | End of split % 9.63/3.84 | | % 9.63/3.84 | End of split % 9.63/3.84 | % 9.63/3.84 End of proof % 9.63/3.84 % SZS output end Proof for theBenchmark % 9.63/3.84 % 9.63/3.84 3061ms %------------------------------------------------------------------------------