%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%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 : 600s % DateTime : Tue Jul 19 00:20:52 EDT 2022 % Result : Theorem 2.10s 1.22s % Output : Proof 3.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 06:47:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.67/0.63 ____ _ % 0.67/0.63 ___ / __ \_____(_)___ ________ __________ % 0.67/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.67/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.67/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.67/0.63 % 0.67/0.63 A Theorem Prover for First-Order Logic % 0.67/0.63 (ePrincess v.1.0) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2015 % 0.67/0.63 (c) Peter Backeman, 2014-2015 % 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.67/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.67/0.63 Bug reports to peter@backeman.se % 0.67/0.63 % 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.67/0.63 % 0.67/0.64 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 % 1.52/0.93 Prover 0: Preprocessing ... % 1.92/1.11 Prover 0: Warning: ignoring some quantifiers % 2.01/1.12 Prover 0: Constructing countermodel ... % 2.10/1.22 Prover 0: proved (533ms) % 2.10/1.22 % 2.10/1.22 No countermodel exists, formula is valid % 2.10/1.22 % SZS status Theorem for theBenchmark % 2.10/1.22 % 2.10/1.22 Generating proof ... Warning: ignoring some quantifiers % 2.83/1.42 found it (size 13) % 2.83/1.42 % 2.83/1.42 % SZS output start Proof for theBenchmark % 2.83/1.42 Assumed formulas after preprocessing and simplification: % 2.83/1.42 | (0) ? [v0] : ? [v1] : ( ~ (v1 = empty_set) & symmetric_difference(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v3, v2) = v5) | ~ (difference(v2, v3) = v4) | ~ (union(v4, v5) = v6) | symmetric_difference(v2, v3) = v6) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (difference(v5, v4) = v3) | ~ (difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (union(v5, v4) = v3) | ~ (union(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (symmetric_difference(v5, v4) = v3) | ~ (symmetric_difference(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v3, v2) = v4) | union(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v2, v3) = v4) | union(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v3, v2) = v4) | symmetric_difference(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v2, v3) = v4) | symmetric_difference(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (symmetric_difference(v2, v3) = v4) | ? [v5] : ? [v6] : (difference(v3, v2) = v6 & difference(v2, v3) = v5 & union(v5, v6) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ subset(v2, v3) | ~ member(v4, v2) | member(v4, v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (union(v2, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ subset(v3, v2) | ~ subset(v2, v3)) & ! [v2] : ! [v3] : (v3 = empty_set | ~ (difference(v2, v2) = v3)) & ! [v2] : ! [v3] : ( ~ empty(v2) | ~ member(v3, v2)) & ! [v2] : ~ member(v2, empty_set) & ? [v2] : ? [v3] : (v3 = v2 | ? [v4] : (( ~ member(v4, v3) | ~ member(v4, v2)) & (member(v4, v3) | member(v4, v2)))) & ? [v2] : ? [v3] : (subset(v2, v3) | ? [v4] : (member(v4, v2) & ~ member(v4, v3))) & ? [v2] : (empty(v2) | ? [v3] : member(v3, v2)) & ? [v2] : subset(v2, v2)) % 3.03/1.46 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 3.03/1.46 | (1) ~ (all_0_0_0 = empty_set) & symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [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] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) & ! [v0] : ~ member(v0, empty_set) & ? [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] : (empty(v0) | ? [v1] : member(v1, v0)) & ? [v0] : subset(v0, v0) % 3.03/1.46 | % 3.03/1.46 | Applying alpha-rule on (1) yields: % 3.03/1.46 | (2) ! [v0] : ~ member(v0, empty_set) % 3.03/1.46 | (3) ? [v0] : (empty(v0) | ? [v1] : member(v1, v0)) % 3.03/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.03/1.46 | (5) ! [v0] : ! [v1] : (v1 = empty_set | ~ (difference(v0, v0) = v1)) % 3.03/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 3.03/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.03/1.47 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 3.03/1.47 | (9) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0)) % 3.03/1.47 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 3.03/1.47 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 3.03/1.47 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 3.03/1.47 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 3.03/1.47 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 3.03/1.47 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0, v0) = v1)) % 3.03/1.47 | (16) symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0 % 3.03/1.47 | (17) ? [v0] : subset(v0, v0) % 3.03/1.47 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) % 3.03/1.47 | (19) ~ (all_0_0_0 = empty_set) % 3.03/1.47 | (20) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 3.03/1.47 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 3.03/1.47 | (22) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 3.03/1.47 | % 3.03/1.47 | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms symmetric_difference(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 3.03/1.47 | (23) ? [v0] : ? [v1] : (difference(all_0_1_1, all_0_1_1) = v1 & difference(all_0_1_1, all_0_1_1) = v0 & union(v0, v1) = all_0_0_0) % 3.03/1.47 | % 3.03/1.47 | Instantiating (23) with all_13_0_8, all_13_1_9 yields: % 3.03/1.47 | (24) difference(all_0_1_1, all_0_1_1) = all_13_0_8 & difference(all_0_1_1, all_0_1_1) = all_13_1_9 & union(all_13_1_9, all_13_0_8) = all_0_0_0 % 3.03/1.47 | % 3.03/1.47 | Applying alpha-rule on (24) yields: % 3.03/1.47 | (25) difference(all_0_1_1, all_0_1_1) = all_13_0_8 % 3.03/1.47 | (26) difference(all_0_1_1, all_0_1_1) = all_13_1_9 % 3.03/1.47 | (27) union(all_13_1_9, all_13_0_8) = all_0_0_0 % 3.03/1.47 | % 3.03/1.47 | Instantiating formula (5) with all_13_0_8, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_1_1) = all_13_0_8, yields: % 3.03/1.47 | (28) all_13_0_8 = empty_set % 3.03/1.47 | % 3.03/1.47 | Instantiating formula (21) with all_0_1_1, all_0_1_1, all_13_1_9, all_13_0_8 and discharging atoms difference(all_0_1_1, all_0_1_1) = all_13_0_8, difference(all_0_1_1, all_0_1_1) = all_13_1_9, yields: % 3.03/1.47 | (29) all_13_0_8 = all_13_1_9 % 3.03/1.47 | % 3.03/1.47 | Combining equations (28,29) yields a new equation: % 3.03/1.47 | (30) all_13_1_9 = empty_set % 3.03/1.47 | % 3.03/1.47 | Combining equations (30,29) yields a new equation: % 3.03/1.47 | (28) all_13_0_8 = empty_set % 3.03/1.47 | % 3.03/1.47 | From (30)(28) and (27) follows: % 3.03/1.48 | (32) union(empty_set, empty_set) = all_0_0_0 % 3.03/1.48 | % 3.03/1.48 | Instantiating formula (15) with all_0_0_0, empty_set and discharging atoms union(empty_set, empty_set) = all_0_0_0, yields: % 3.03/1.48 | (33) all_0_0_0 = empty_set % 3.03/1.48 | % 3.03/1.48 | Equations (33) can reduce 19 to: % 3.03/1.48 | (34) $false % 3.03/1.48 | % 3.03/1.48 |-The branch is then unsatisfiable % 3.03/1.48 % SZS output end Proof for theBenchmark % 3.03/1.48 % 3.03/1.48 833ms %------------------------------------------------------------------------------