%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 : 600s % DateTime : Tue Jul 19 00:18:18 EDT 2022 % Result : Theorem 2.66s 1.34s % Output : Proof 3.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n020.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 : 600 % 0.12/0.34 % DateTime : Sun Jul 10 13:23:13 EDT 2022 % 0.12/0.34 % CPUTime : % 0.50/0.59 ____ _ % 0.50/0.59 ___ / __ \_____(_)___ ________ __________ % 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.59 % 0.50/0.59 A Theorem Prover for First-Order Logic % 0.50/0.59 (ePrincess v.1.0) % 0.50/0.59 % 0.50/0.59 (c) Philipp Rümmer, 2009-2015 % 0.50/0.59 (c) Peter Backeman, 2014-2015 % 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.59 Bug reports to peter@backeman.se % 0.50/0.59 % 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.59 % 0.50/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.28/0.92 Prover 0: Preprocessing ... % 1.68/1.05 Prover 0: Warning: ignoring some quantifiers % 1.68/1.07 Prover 0: Constructing countermodel ... % 2.09/1.20 Prover 0: gave up % 2.09/1.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.09/1.22 Prover 1: Preprocessing ... % 2.51/1.29 Prover 1: Warning: ignoring some quantifiers % 2.51/1.30 Prover 1: Constructing countermodel ... % 2.66/1.34 Prover 1: proved (132ms) % 2.66/1.34 % 2.66/1.34 No countermodel exists, formula is valid % 2.66/1.34 % SZS status Theorem for theBenchmark % 2.66/1.34 % 2.66/1.34 Generating proof ... Warning: ignoring some quantifiers % 3.23/1.55 found it (size 18) % 3.23/1.55 % 3.23/1.55 % SZS output start Proof for theBenchmark % 3.23/1.55 Assumed formulas after preprocessing and simplification: % 3.23/1.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v0, v2) = v3 & union(v0, v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (union(v4, v5) = v7) | ~ (member(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & member(v6, v5) = v10 & member(v6, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ (member(v6, v7) = 0) | ? [v8] : ? [v9] : (member(v6, v5) = v9 & member(v6, v4) = v8 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | union(v5, v4) = v6) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v4, v4) = v5)) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : ? [v7] : ? [v8] : (member(v6, v5) = v8 & member(v6, v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0)))) % 3.38/1.58 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 3.38/1.58 | (1) ~ (all_0_0_0 = 0) & subset(all_0_3_3, all_0_1_1) = all_0_0_0 & union(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 3.38/1.58 | % 3.38/1.58 | Applying alpha-rule on (1) yields: % 3.38/1.59 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) % 3.38/1.59 | (3) subset(all_0_3_3, all_0_1_1) = all_0_0_0 % 3.38/1.59 | (4) union(all_0_3_3, all_0_2_2) = all_0_1_1 % 3.38/1.59 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.38/1.59 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.38/1.59 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 3.38/1.59 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 3.38/1.59 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 3.38/1.59 | (10) ~ (all_0_0_0 = 0) % 3.38/1.59 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.38/1.59 | (12) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 3.38/1.59 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.38/1.59 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 3.38/1.59 | % 3.38/1.59 | Instantiating formula (8) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 3.38/1.59 | (15) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 3.38/1.59 | % 3.38/1.59 | Instantiating formula (5) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 3.38/1.59 | (16) union(all_0_2_2, all_0_3_3) = all_0_1_1 % 3.38/1.59 | % 3.38/1.59 +-Applying beta-rule and splitting (15), into two cases. % 3.38/1.59 |-Branch one: % 3.38/1.59 | (17) all_0_0_0 = 0 % 3.38/1.59 | % 3.38/1.59 | Equations (17) can reduce 10 to: % 3.38/1.59 | (18) $false % 3.38/1.59 | % 3.38/1.59 |-The branch is then unsatisfiable % 3.38/1.59 |-Branch two: % 3.38/1.59 | (10) ~ (all_0_0_0 = 0) % 3.38/1.59 | (20) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 3.38/1.59 | % 3.38/1.59 | Instantiating (20) with all_18_0_6, all_18_1_7 yields: % 3.38/1.59 | (21) ~ (all_18_0_6 = 0) & member(all_18_1_7, all_0_1_1) = all_18_0_6 & member(all_18_1_7, all_0_3_3) = 0 % 3.38/1.59 | % 3.38/1.59 | Applying alpha-rule on (21) yields: % 3.38/1.59 | (22) ~ (all_18_0_6 = 0) % 3.38/1.60 | (23) member(all_18_1_7, all_0_1_1) = all_18_0_6 % 3.38/1.60 | (24) member(all_18_1_7, all_0_3_3) = 0 % 3.38/1.60 | % 3.38/1.60 | Instantiating formula (2) with all_18_0_6, all_0_1_1, all_18_1_7, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_1_1, member(all_18_1_7, all_0_1_1) = all_18_0_6, yields: % 3.38/1.60 | (25) all_18_0_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_7, all_0_2_2) = v0 & member(all_18_1_7, all_0_3_3) = v1) % 3.38/1.60 | % 3.38/1.60 +-Applying beta-rule and splitting (25), into two cases. % 3.38/1.60 |-Branch one: % 3.38/1.60 | (26) all_18_0_6 = 0 % 3.38/1.60 | % 3.38/1.60 | Equations (26) can reduce 22 to: % 3.38/1.60 | (18) $false % 3.38/1.60 | % 3.38/1.60 |-The branch is then unsatisfiable % 3.38/1.60 |-Branch two: % 3.38/1.60 | (22) ~ (all_18_0_6 = 0) % 3.38/1.60 | (29) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_7, all_0_2_2) = v0 & member(all_18_1_7, all_0_3_3) = v1) % 3.38/1.60 | % 3.38/1.60 | Instantiating (29) with all_35_0_8, all_35_1_9 yields: % 3.38/1.60 | (30) ~ (all_35_0_8 = 0) & ~ (all_35_1_9 = 0) & member(all_18_1_7, all_0_2_2) = all_35_1_9 & member(all_18_1_7, all_0_3_3) = all_35_0_8 % 3.38/1.60 | % 3.38/1.60 | Applying alpha-rule on (30) yields: % 3.38/1.60 | (31) ~ (all_35_0_8 = 0) % 3.38/1.60 | (32) ~ (all_35_1_9 = 0) % 3.38/1.60 | (33) member(all_18_1_7, all_0_2_2) = all_35_1_9 % 3.38/1.60 | (34) member(all_18_1_7, all_0_3_3) = all_35_0_8 % 3.38/1.60 | % 3.38/1.60 | Instantiating formula (14) with all_18_1_7, all_0_3_3, all_35_0_8, 0 and discharging atoms member(all_18_1_7, all_0_3_3) = all_35_0_8, member(all_18_1_7, all_0_3_3) = 0, yields: % 3.38/1.60 | (35) all_35_0_8 = 0 % 3.38/1.60 | % 3.38/1.60 | Equations (35) can reduce 31 to: % 3.38/1.60 | (18) $false % 3.38/1.60 | % 3.38/1.60 |-The branch is then unsatisfiable % 3.38/1.60 % SZS output end Proof for theBenchmark % 3.38/1.60 % 3.38/1.60 1001ms %------------------------------------------------------------------------------