%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET196+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 00:18:19 EDT 2022 % Result : Theorem 2.57s 1.35s % Output : Proof 3.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET196+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 05:05:28 EDT 2022 % 0.13/0.34 % CPUTime : % 0.66/0.63 ____ _ % 0.66/0.63 ___ / __ \_____(_)___ ________ __________ % 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic % 0.66/0.63 (ePrincess v.1.0) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2015 % 0.66/0.63 (c) Peter Backeman, 2014-2015 % 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.63 Bug reports to peter@backeman.se % 0.66/0.63 % 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.63 % 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.43/0.98 Prover 0: Preprocessing ... % 1.74/1.10 Prover 0: Warning: ignoring some quantifiers % 1.74/1.12 Prover 0: Constructing countermodel ... % 2.22/1.24 Prover 0: gave up % 2.22/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.22/1.26 Prover 1: Preprocessing ... % 2.22/1.32 Prover 1: Warning: ignoring some quantifiers % 2.22/1.32 Prover 1: Constructing countermodel ... % 2.57/1.35 Prover 1: proved (113ms) % 2.57/1.35 % 2.57/1.35 No countermodel exists, formula is valid % 2.57/1.35 % SZS status Theorem for theBenchmark % 2.57/1.35 % 2.57/1.35 Generating proof ... Warning: ignoring some quantifiers % 3.16/1.53 found it (size 17) % 3.16/1.53 % 3.16/1.53 % SZS output start Proof for theBenchmark % 3.16/1.53 Assumed formulas after preprocessing and simplification: % 3.16/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & intersection(v0, v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection(v4, v5) = v7) | ~ (member(v6, v7) = v8) | ? [v9] : ? [v10] : (member(v6, v5) = v10 & member(v6, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v4, v5) = v7) | ~ (member(v6, v7) = 0) | (member(v6, v5) = 0 & member(v6, v4) = 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] : ( ~ (intersection(v4, v5) = v6) | intersection(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)))) % 3.16/1.56 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 3.16/1.56 | (1) ~ (all_0_0_0 = 0) & subset(all_0_1_1, all_0_3_3) = all_0_0_0 & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 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] : ( ~ (intersection(v0, v1) = v2) | intersection(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))) % 3.16/1.57 | % 3.16/1.57 | Applying alpha-rule on (1) yields: % 3.16/1.57 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 3.16/1.57 | (3) intersection(all_0_3_3, all_0_2_2) = all_0_1_1 % 3.16/1.57 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 3.16/1.57 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 3.16/1.57 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.16/1.57 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 3.16/1.57 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 3.16/1.57 | (9) ~ (all_0_0_0 = 0) % 3.16/1.57 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 3.16/1.57 | (11) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 3.16/1.57 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.16/1.57 | (13) subset(all_0_1_1, all_0_3_3) = all_0_0_0 % 3.16/1.57 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 3.16/1.57 | % 3.16/1.57 | Instantiating formula (8) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_0_0_0, yields: % 3.16/1.58 | (15) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 3.16/1.58 | % 3.16/1.58 | Instantiating formula (4) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 3.16/1.58 | (16) intersection(all_0_2_2, all_0_3_3) = all_0_1_1 % 3.16/1.58 | % 3.16/1.58 +-Applying beta-rule and splitting (15), into two cases. % 3.16/1.58 |-Branch one: % 3.16/1.58 | (17) all_0_0_0 = 0 % 3.16/1.58 | % 3.16/1.58 | Equations (17) can reduce 9 to: % 3.16/1.58 | (18) $false % 3.16/1.58 | % 3.16/1.58 |-The branch is then unsatisfiable % 3.16/1.58 |-Branch two: % 3.16/1.58 | (9) ~ (all_0_0_0 = 0) % 3.16/1.58 | (20) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 3.16/1.58 | % 3.16/1.58 | Instantiating (20) with all_18_0_6, all_18_1_7 yields: % 3.16/1.58 | (21) ~ (all_18_0_6 = 0) & member(all_18_1_7, all_0_1_1) = 0 & member(all_18_1_7, all_0_3_3) = all_18_0_6 % 3.16/1.58 | % 3.16/1.58 | Applying alpha-rule on (21) yields: % 3.16/1.58 | (22) ~ (all_18_0_6 = 0) % 3.16/1.58 | (23) member(all_18_1_7, all_0_1_1) = 0 % 3.16/1.58 | (24) member(all_18_1_7, all_0_3_3) = all_18_0_6 % 3.16/1.58 | % 3.16/1.58 | Instantiating formula (14) with all_18_1_7, all_0_3_3, all_18_0_6, 0 and discharging atoms member(all_18_1_7, all_0_3_3) = all_18_0_6, yields: % 3.16/1.58 | (25) all_18_0_6 = 0 | ~ (member(all_18_1_7, all_0_3_3) = 0) % 3.16/1.58 | % 3.16/1.58 | Instantiating formula (5) with all_0_1_1, all_18_1_7, all_0_3_3, all_0_2_2 and discharging atoms intersection(all_0_2_2, all_0_3_3) = all_0_1_1, member(all_18_1_7, all_0_1_1) = 0, yields: % 3.16/1.58 | (26) member(all_18_1_7, all_0_2_2) = 0 & member(all_18_1_7, all_0_3_3) = 0 % 3.16/1.58 | % 3.16/1.58 | Applying alpha-rule on (26) yields: % 3.16/1.58 | (27) member(all_18_1_7, all_0_2_2) = 0 % 3.16/1.58 | (28) member(all_18_1_7, all_0_3_3) = 0 % 3.16/1.58 | % 3.16/1.58 +-Applying beta-rule and splitting (25), into two cases. % 3.16/1.58 |-Branch one: % 3.16/1.58 | (29) ~ (member(all_18_1_7, all_0_3_3) = 0) % 3.16/1.58 | % 3.16/1.58 | Using (28) and (29) yields: % 3.16/1.58 | (30) $false % 3.16/1.58 | % 3.16/1.58 |-The branch is then unsatisfiable % 3.16/1.58 |-Branch two: % 3.16/1.58 | (28) member(all_18_1_7, all_0_3_3) = 0 % 3.16/1.58 | (32) all_18_0_6 = 0 % 3.16/1.58 | % 3.16/1.58 | Equations (32) can reduce 22 to: % 3.16/1.58 | (18) $false % 3.16/1.58 | % 3.16/1.58 |-The branch is then unsatisfiable % 3.16/1.58 % SZS output end Proof for theBenchmark % 3.16/1.58 % 3.16/1.58 932ms %------------------------------------------------------------------------------