%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET597+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 00:20:35 EDT 2022 % Result : Theorem 2.24s 1.18s % Output : Proof 3.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n012.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 : Sun Jul 10 15:41:13 EDT 2022 % 0.13/0.34 % CPUTime : % 0.21/0.60 ____ _ % 0.21/0.60 ___ / __ \_____(_)___ ________ __________ % 0.21/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.21/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.21/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic % 0.64/0.61 (ePrincess v.1.0) % 0.64/0.61 % 0.64/0.61 (c) Philipp Rümmer, 2009-2015 % 0.64/0.61 (c) Peter Backeman, 2014-2015 % 0.64/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.64/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.64/0.61 Bug reports to peter@backeman.se % 0.64/0.61 % 0.64/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.64/0.61 % 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.44/0.90 Prover 0: Preprocessing ... % 1.72/1.03 Prover 0: Warning: ignoring some quantifiers % 1.72/1.05 Prover 0: Constructing countermodel ... % 2.24/1.18 Prover 0: proved (500ms) % 2.24/1.18 % 2.24/1.18 No countermodel exists, formula is valid % 2.24/1.18 % SZS status Theorem for theBenchmark % 2.24/1.18 % 2.24/1.18 Generating proof ... Warning: ignoring some quantifiers % 2.83/1.43 found it (size 25) % 2.83/1.43 % 2.83/1.43 % SZS output start Proof for theBenchmark % 2.83/1.44 Assumed formulas after preprocessing and simplification: % 2.83/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (union(v1, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v7) = v8) | ~ subset(v7, v6) | ~ subset(v5, v6) | subset(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v8) | member(v7, v6) | member(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v6) | member(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v5) | member(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v6, v5) = v7) | union(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v5) | ~ subset(v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ subset(v6, v5) | ~ subset(v5, v6)) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : (( ~ member(v7, v6) | ~ member(v7, v5)) & (member(v7, v6) | member(v7, v5)))) & ? [v5] : ? [v6] : (subset(v5, v6) | ? [v7] : (member(v7, v5) & ~ member(v7, v6))) & ? [v5] : subset(v5, v5) & ((v3 = v0 & ( ~ subset(v2, v0) | ~ subset(v1, v0) | (subset(v2, v4) & subset(v1, v4) & ~ subset(v0, v4)))) | ( ~ (v3 = v0) & subset(v2, v0) & subset(v1, v0) & ! [v5] : ( ~ subset(v2, v5) | ~ subset(v1, v5) | subset(v0, v5))))) % 3.08/1.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.08/1.47 | (1) union(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : subset(v0, v0) & ((all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)))) | ( ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0)))) % 3.08/1.48 | % 3.08/1.48 | Applying alpha-rule on (1) yields: % 3.08/1.48 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 3.08/1.48 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.08/1.48 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 3.08/1.48 | (5) ? [v0] : subset(v0, v0) % 3.08/1.48 | (6) union(all_0_3_3, all_0_2_2) = all_0_1_1 % 3.08/1.48 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 3.08/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 3.08/1.48 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 3.08/1.48 | (10) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 3.08/1.48 | (11) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 3.08/1.48 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) % 3.08/1.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.08/1.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 3.08/1.48 | (15) (all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)))) | ( ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0))) % 3.08/1.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 3.08/1.49 | % 3.08/1.49 | Instantiating formula (4) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 3.08/1.49 | (17) union(all_0_2_2, all_0_3_3) = all_0_1_1 % 3.08/1.49 | % 3.08/1.49 | Instantiating formula (12) 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: % 3.08/1.49 | (18) subset(all_0_3_3, all_0_1_1) % 3.08/1.49 | % 3.08/1.49 | Instantiating formula (12) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 3.08/1.49 | (19) subset(all_0_2_2, all_0_1_1) % 3.08/1.49 | % 3.08/1.49 +-Applying beta-rule and splitting (15), into two cases. % 3.08/1.49 |-Branch one: % 3.08/1.49 | (20) all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0))) % 3.08/1.49 | % 3.08/1.49 | Applying alpha-rule on (20) yields: % 3.08/1.49 | (21) all_0_1_1 = all_0_4_4 % 3.08/1.49 | (22) ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)) % 3.08/1.49 | % 3.08/1.49 | From (21) and (6) follows: % 3.08/1.49 | (23) union(all_0_3_3, all_0_2_2) = all_0_4_4 % 3.08/1.49 | % 3.08/1.49 | From (21) and (19) follows: % 3.08/1.49 | (24) subset(all_0_2_2, all_0_4_4) % 3.08/1.49 | % 3.08/1.49 | From (21) and (18) follows: % 3.08/1.49 | (25) subset(all_0_3_3, all_0_4_4) % 3.08/1.49 | % 3.08/1.49 +-Applying beta-rule and splitting (22), into two cases. % 3.08/1.49 |-Branch one: % 3.08/1.49 | (26) ~ subset(all_0_2_2, all_0_4_4) % 3.08/1.49 | % 3.08/1.49 | Using (24) and (26) yields: % 3.08/1.49 | (27) $false % 3.08/1.49 | % 3.08/1.49 |-The branch is then unsatisfiable % 3.08/1.49 |-Branch two: % 3.08/1.49 | (24) subset(all_0_2_2, all_0_4_4) % 3.08/1.49 | (29) ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)) % 3.08/1.49 | % 3.08/1.49 +-Applying beta-rule and splitting (29), into two cases. % 3.08/1.49 |-Branch one: % 3.08/1.49 | (30) ~ subset(all_0_3_3, all_0_4_4) % 3.08/1.49 | % 3.08/1.49 | Using (25) and (30) yields: % 3.08/1.49 | (27) $false % 3.08/1.49 | % 3.08/1.49 |-The branch is then unsatisfiable % 3.08/1.49 |-Branch two: % 3.08/1.49 | (25) subset(all_0_3_3, all_0_4_4) % 3.08/1.49 | (33) subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0) % 3.08/1.49 | % 3.08/1.49 | Applying alpha-rule on (33) yields: % 3.08/1.49 | (34) subset(all_0_2_2, all_0_0_0) % 3.08/1.49 | (35) subset(all_0_3_3, all_0_0_0) % 3.08/1.49 | (36) ~ subset(all_0_4_4, all_0_0_0) % 3.08/1.49 | % 3.08/1.49 | Instantiating formula (16) with all_0_4_4, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_4_4, subset(all_0_2_2, all_0_0_0), subset(all_0_3_3, all_0_0_0), ~ subset(all_0_4_4, all_0_0_0), yields: % 3.08/1.49 | (27) $false % 3.08/1.49 | % 3.08/1.49 |-The branch is then unsatisfiable % 3.08/1.49 |-Branch two: % 3.08/1.49 | (38) ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0)) % 3.08/1.50 | % 3.08/1.50 | Applying alpha-rule on (38) yields: % 3.08/1.50 | (39) ~ (all_0_1_1 = all_0_4_4) % 3.08/1.50 | (24) subset(all_0_2_2, all_0_4_4) % 3.08/1.50 | (25) subset(all_0_3_3, all_0_4_4) % 3.08/1.50 | (42) ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0)) % 3.08/1.50 | % 3.08/1.50 | Instantiating formula (42) with all_0_1_1 and discharging atoms subset(all_0_2_2, all_0_1_1), subset(all_0_3_3, all_0_1_1), yields: % 3.08/1.50 | (43) subset(all_0_4_4, all_0_1_1) % 3.08/1.50 | % 3.08/1.50 | Instantiating formula (16) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, subset(all_0_2_2, all_0_4_4), subset(all_0_3_3, all_0_4_4), yields: % 3.08/1.50 | (44) subset(all_0_1_1, all_0_4_4) % 3.08/1.50 | % 3.08/1.50 | Instantiating formula (2) with all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_1_1, all_0_4_4), subset(all_0_4_4, all_0_1_1), yields: % 3.08/1.50 | (21) all_0_1_1 = all_0_4_4 % 3.08/1.50 | % 3.08/1.50 | Equations (21) can reduce 39 to: % 3.08/1.50 | (46) $false % 3.08/1.50 | % 3.08/1.50 |-The branch is then unsatisfiable % 3.08/1.50 % SZS output end Proof for theBenchmark % 3.08/1.50 % 3.08/1.50 877ms %------------------------------------------------------------------------------