%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 00:21:02 EDT 2022 % Result : Theorem 2.24s 1.20s % Output : Proof 3.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET633+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.33 % Computer : n023.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 600 % 0.14/0.33 % DateTime : Sat Jul 9 22:22:10 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.41/0.91 Prover 0: Preprocessing ... % 1.87/1.08 Prover 0: Warning: ignoring some quantifiers % 1.87/1.10 Prover 0: Constructing countermodel ... % 2.24/1.20 Prover 0: proved (556ms) % 2.24/1.20 % 2.24/1.20 No countermodel exists, formula is valid % 2.24/1.20 % SZS status Theorem for theBenchmark % 2.24/1.20 % 2.24/1.20 Generating proof ... Warning: ignoring some quantifiers % 2.90/1.39 found it (size 10) % 2.90/1.39 % 2.90/1.39 % SZS output start Proof for theBenchmark % 2.90/1.40 Assumed formulas after preprocessing and simplification: % 2.90/1.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & symmetric_difference(v0, v1) = v5 & subset(v4, v2) & subset(v3, v2) & ~ subset(v5, v2) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v7, v6) = v9) | ~ (difference(v6, v7) = v8) | ~ (union(v8, v9) = v10) | symmetric_difference(v6, v7) = v10) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (symmetric_difference(v9, v8) = v7) | ~ (symmetric_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | ~ member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v6) | member(v8, v9) | member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v8) = v9) | ~ subset(v8, v7) | ~ subset(v6, v7) | subset(v9, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v7, v6) = v8) | union(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | union(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v7, v6) = v8) | symmetric_difference(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | symmetric_difference(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | ? [v9] : ? [v10] : (difference(v7, v6) = v10 & difference(v6, v7) = v9 & union(v9, v10) = v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ member(v8, v6) | ~ subset(v6, v7) | member(v8, v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : (( ~ member(v8, v7) | ~ member(v8, v6)) & (member(v8, v7) | member(v8, v6)))) & ? [v6] : ? [v7] : (subset(v6, v7) | ? [v8] : (member(v8, v6) & ~ member(v8, v7))) & ? [v6] : subset(v6, v6)) % 2.90/1.43 | 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: % 2.90/1.43 | (1) difference(all_0_4_4, all_0_5_5) = all_0_1_1 & difference(all_0_5_5, all_0_4_4) = all_0_2_2 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0 & subset(all_0_1_1, all_0_3_3) & subset(all_0_2_2, all_0_3_3) & ~ subset(all_0_0_0, all_0_3_3) & ! [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] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [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] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, 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) % 2.90/1.44 | % 2.90/1.44 | Applying alpha-rule on (1) yields: % 2.90/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 2.90/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 2.90/1.44 | (4) ~ subset(all_0_0_0, all_0_3_3) % 2.90/1.44 | (5) ? [v0] : subset(v0, v0) % 2.90/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 2.90/1.44 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 2.90/1.44 | (8) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 2.90/1.44 | (9) subset(all_0_1_1, all_0_3_3) % 2.90/1.44 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 2.90/1.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 2.90/1.45 | (12) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0 % 2.90/1.45 | (13) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 2.90/1.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 2.90/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 2.90/1.45 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 2.90/1.45 | (17) subset(all_0_2_2, all_0_3_3) % 2.90/1.45 | (18) difference(all_0_5_5, all_0_4_4) = all_0_2_2 % 2.90/1.45 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 2.90/1.45 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 2.90/1.45 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 2.90/1.45 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 2.90/1.45 | (23) difference(all_0_4_4, all_0_5_5) = all_0_1_1 % 2.90/1.45 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 2.90/1.45 | % 2.90/1.45 | Instantiating formula (20) with all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0, yields: % 2.90/1.45 | (25) ? [v0] : ? [v1] : (difference(all_0_4_4, all_0_5_5) = v1 & difference(all_0_5_5, all_0_4_4) = v0 & union(v0, v1) = all_0_0_0) % 2.90/1.45 | % 2.90/1.45 | Instantiating (25) with all_13_0_11, all_13_1_12 yields: % 2.90/1.45 | (26) difference(all_0_4_4, all_0_5_5) = all_13_0_11 & difference(all_0_5_5, all_0_4_4) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_0_0 % 2.90/1.45 | % 2.90/1.45 | Applying alpha-rule on (26) yields: % 2.90/1.45 | (27) difference(all_0_4_4, all_0_5_5) = all_13_0_11 % 2.90/1.45 | (28) difference(all_0_5_5, all_0_4_4) = all_13_1_12 % 2.90/1.45 | (29) union(all_13_1_12, all_13_0_11) = all_0_0_0 % 2.90/1.45 | % 2.90/1.45 | Instantiating formula (14) with all_0_4_4, all_0_5_5, all_13_0_11, all_0_1_1 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_13_0_11, difference(all_0_4_4, all_0_5_5) = all_0_1_1, yields: % 2.90/1.45 | (30) all_13_0_11 = all_0_1_1 % 2.90/1.45 | % 2.90/1.45 | Instantiating formula (14) with all_0_5_5, all_0_4_4, all_13_1_12, all_0_2_2 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_13_1_12, difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 2.90/1.45 | (31) all_13_1_12 = all_0_2_2 % 2.90/1.45 | % 3.11/1.45 | From (31)(30) and (29) follows: % 3.11/1.46 | (32) union(all_0_2_2, all_0_1_1) = all_0_0_0 % 3.11/1.46 | % 3.11/1.46 | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, subset(all_0_1_1, all_0_3_3), subset(all_0_2_2, all_0_3_3), ~ subset(all_0_0_0, all_0_3_3), yields: % 3.11/1.46 | (33) $false % 3.11/1.46 | % 3.11/1.46 |-The branch is then unsatisfiable % 3.11/1.46 % SZS output end Proof for theBenchmark % 3.11/1.46 % 3.11/1.46 854ms %------------------------------------------------------------------------------