%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 00:20:28 EDT 2022 % Result : Theorem 2.98s 1.48s % Output : Proof 3.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.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 : 600 % 0.13/0.34 % DateTime : Mon Jul 11 07:37:57 EDT 2022 % 0.13/0.34 % CPUTime : % 0.52/0.62 ____ _ % 0.52/0.62 ___ / __ \_____(_)___ ________ __________ % 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.62 % 0.52/0.62 A Theorem Prover for First-Order Logic % 0.52/0.62 (ePrincess v.1.0) % 0.52/0.62 % 0.52/0.62 (c) Philipp Rümmer, 2009-2015 % 0.52/0.62 (c) Peter Backeman, 2014-2015 % 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.62 Bug reports to peter@backeman.se % 0.52/0.62 % 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.62 % 0.52/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.93 Prover 0: Preprocessing ... % 1.61/1.06 Prover 0: Warning: ignoring some quantifiers % 1.69/1.09 Prover 0: Constructing countermodel ... % 2.22/1.31 Prover 0: gave up % 2.22/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.41/1.33 Prover 1: Preprocessing ... % 2.62/1.39 Prover 1: Warning: ignoring some quantifiers % 2.62/1.40 Prover 1: Constructing countermodel ... % 2.98/1.48 Prover 1: proved (163ms) % 2.98/1.48 % 2.98/1.48 No countermodel exists, formula is valid % 2.98/1.48 % SZS status Theorem for theBenchmark % 2.98/1.48 % 2.98/1.48 Generating proof ... Warning: ignoring some quantifiers % 3.65/1.71 found it (size 29) % 3.65/1.71 % 3.65/1.71 % SZS output start Proof for theBenchmark % 3.65/1.71 Assumed formulas after preprocessing and simplification: % 3.65/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & intersection(v1, v2) = v4 & intersection(v0, v2) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection(v6, v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : (member(v8, v7) = v12 & member(v8, v6) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v7) = v9) | ~ (member(v8, v9) = 0) | (member(v8, v7) = 0 & member(v8, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | intersection(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : ? [v9] : ? [v10] : (member(v8, v7) = v10 & member(v8, v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = 0 | v9 = 0)))) % 3.65/1.74 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 3.65/1.74 | (1) ~ (all_0_0_0 = 0) & subset(all_0_2_2, all_0_1_1) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & intersection(all_0_4_4, all_0_3_3) = all_0_1_1 & intersection(all_0_5_5, all_0_3_3) = all_0_2_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)))) & ! [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))) % 3.65/1.74 | % 3.65/1.74 | Applying alpha-rule on (1) yields: % 3.65/1.74 | (2) intersection(all_0_5_5, all_0_3_3) = all_0_2_2 % 3.65/1.74 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 3.65/1.74 | (4) ! [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)))) % 3.65/1.75 | (5) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 3.65/1.75 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.65/1.75 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 3.65/1.75 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 3.65/1.75 | (9) subset(all_0_2_2, all_0_1_1) = all_0_0_0 % 3.65/1.75 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 3.65/1.75 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 3.65/1.75 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 3.65/1.75 | (13) subset(all_0_5_5, all_0_4_4) = 0 % 3.65/1.75 | (14) intersection(all_0_4_4, all_0_3_3) = all_0_1_1 % 3.65/1.75 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.65/1.75 | (16) ~ (all_0_0_0 = 0) % 3.65/1.75 | % 3.65/1.75 | Instantiating formula (8) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 3.65/1.75 | (17) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 3.65/1.75 | % 3.65/1.75 | Instantiating formula (10) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_1_1, yields: % 3.65/1.75 | (18) intersection(all_0_3_3, all_0_4_4) = all_0_1_1 % 3.65/1.75 | % 3.65/1.75 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms intersection(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 3.65/1.75 | (19) intersection(all_0_3_3, all_0_5_5) = all_0_2_2 % 3.65/1.75 | % 3.65/1.75 +-Applying beta-rule and splitting (17), into two cases. % 3.65/1.75 |-Branch one: % 3.65/1.75 | (20) all_0_0_0 = 0 % 3.65/1.75 | % 3.65/1.75 | Equations (20) can reduce 16 to: % 3.65/1.75 | (21) $false % 3.65/1.75 | % 3.65/1.75 |-The branch is then unsatisfiable % 3.65/1.75 |-Branch two: % 3.65/1.75 | (16) ~ (all_0_0_0 = 0) % 3.65/1.75 | (23) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 3.65/1.75 | % 3.65/1.75 | Instantiating (23) with all_18_0_8, all_18_1_9 yields: % 3.65/1.75 | (24) ~ (all_18_0_8 = 0) & member(all_18_1_9, all_0_1_1) = all_18_0_8 & member(all_18_1_9, all_0_2_2) = 0 % 3.65/1.75 | % 3.65/1.75 | Applying alpha-rule on (24) yields: % 3.65/1.75 | (25) ~ (all_18_0_8 = 0) % 3.65/1.75 | (26) member(all_18_1_9, all_0_1_1) = all_18_0_8 % 3.65/1.75 | (27) member(all_18_1_9, all_0_2_2) = 0 % 3.65/1.75 | % 3.65/1.75 | Instantiating formula (4) with all_18_0_8, all_0_1_1, all_18_1_9, all_0_4_4, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_18_1_9, all_0_1_1) = all_18_0_8, yields: % 3.65/1.75 | (28) all_18_0_8 = 0 | ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 3.65/1.76 | % 3.65/1.76 | Instantiating formula (3) with all_0_2_2, all_18_1_9, all_0_5_5, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_5_5) = all_0_2_2, member(all_18_1_9, all_0_2_2) = 0, yields: % 3.65/1.76 | (29) member(all_18_1_9, all_0_3_3) = 0 & member(all_18_1_9, all_0_5_5) = 0 % 3.65/1.76 | % 3.65/1.76 | Applying alpha-rule on (29) yields: % 3.65/1.76 | (30) member(all_18_1_9, all_0_3_3) = 0 % 3.65/1.76 | (31) member(all_18_1_9, all_0_5_5) = 0 % 3.65/1.76 | % 3.65/1.76 | Instantiating formula (11) with all_18_1_9, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields: % 3.65/1.76 | (32) ~ (member(all_18_1_9, all_0_5_5) = 0) | member(all_18_1_9, all_0_4_4) = 0 % 3.65/1.76 | % 3.65/1.76 +-Applying beta-rule and splitting (32), into two cases. % 3.65/1.76 |-Branch one: % 3.65/1.76 | (33) ~ (member(all_18_1_9, all_0_5_5) = 0) % 3.65/1.76 | % 3.65/1.76 | Using (31) and (33) yields: % 3.65/1.76 | (34) $false % 3.65/1.76 | % 3.65/1.76 |-The branch is then unsatisfiable % 3.65/1.76 |-Branch two: % 3.65/1.76 | (31) member(all_18_1_9, all_0_5_5) = 0 % 3.65/1.76 | (36) member(all_18_1_9, all_0_4_4) = 0 % 3.65/1.76 | % 3.65/1.76 +-Applying beta-rule and splitting (28), into two cases. % 3.65/1.76 |-Branch one: % 3.65/1.76 | (37) all_18_0_8 = 0 % 3.65/1.76 | % 3.65/1.76 | Equations (37) can reduce 25 to: % 3.65/1.76 | (21) $false % 3.65/1.76 | % 3.65/1.76 |-The branch is then unsatisfiable % 3.65/1.76 |-Branch two: % 3.65/1.76 | (25) ~ (all_18_0_8 = 0) % 3.65/1.76 | (40) ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 3.65/1.76 | % 3.65/1.76 | Instantiating (40) with all_38_0_10, all_38_1_11 yields: % 3.65/1.76 | (41) member(all_18_1_9, all_0_3_3) = all_38_1_11 & member(all_18_1_9, all_0_4_4) = all_38_0_10 & ( ~ (all_38_0_10 = 0) | ~ (all_38_1_11 = 0)) % 3.65/1.76 | % 3.65/1.76 | Applying alpha-rule on (41) yields: % 3.65/1.76 | (42) member(all_18_1_9, all_0_3_3) = all_38_1_11 % 3.65/1.76 | (43) member(all_18_1_9, all_0_4_4) = all_38_0_10 % 3.65/1.76 | (44) ~ (all_38_0_10 = 0) | ~ (all_38_1_11 = 0) % 3.65/1.76 | % 3.65/1.76 | Instantiating formula (7) with all_18_1_9, all_0_3_3, all_38_1_11, 0 and discharging atoms member(all_18_1_9, all_0_3_3) = all_38_1_11, member(all_18_1_9, all_0_3_3) = 0, yields: % 3.65/1.76 | (45) all_38_1_11 = 0 % 3.65/1.76 | % 3.65/1.76 | Instantiating formula (7) with all_18_1_9, all_0_4_4, all_38_0_10, 0 and discharging atoms member(all_18_1_9, all_0_4_4) = all_38_0_10, member(all_18_1_9, all_0_4_4) = 0, yields: % 3.65/1.76 | (46) all_38_0_10 = 0 % 3.89/1.76 | % 3.89/1.76 +-Applying beta-rule and splitting (44), into two cases. % 3.89/1.76 |-Branch one: % 3.89/1.76 | (47) ~ (all_38_0_10 = 0) % 3.89/1.76 | % 3.89/1.76 | Equations (46) can reduce 47 to: % 3.89/1.76 | (21) $false % 3.89/1.76 | % 3.89/1.76 |-The branch is then unsatisfiable % 3.89/1.76 |-Branch two: % 3.89/1.76 | (46) all_38_0_10 = 0 % 3.89/1.76 | (50) ~ (all_38_1_11 = 0) % 3.89/1.76 | % 3.89/1.76 | Equations (45) can reduce 50 to: % 3.89/1.76 | (21) $false % 3.89/1.76 | % 3.89/1.76 |-The branch is then unsatisfiable % 3.89/1.76 % SZS output end Proof for theBenchmark % 3.89/1.76 % 3.89/1.76 1122ms %------------------------------------------------------------------------------