%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:47:03 EDT 2022 % Result : Theorem 3.19s 1.49s % Output : Proof 4.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n008.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sat Jun 18 21:18:52 EDT 2022 % 0.14/0.36 % CPUTime : % 0.57/0.61 ____ _ % 0.57/0.61 ___ / __ \_____(_)___ ________ __________ % 0.57/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.61 % 0.57/0.61 A Theorem Prover for First-Order Logic % 0.57/0.61 (ePrincess v.1.0) % 0.57/0.61 % 0.57/0.61 (c) Philipp Rümmer, 2009-2015 % 0.57/0.61 (c) Peter Backeman, 2014-2015 % 0.57/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.61 Bug reports to peter@backeman.se % 0.57/0.61 % 0.57/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.61 % 0.57/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/0.95 Prover 0: Preprocessing ... % 1.82/1.13 Prover 0: Warning: ignoring some quantifiers % 1.82/1.14 Prover 0: Constructing countermodel ... % 2.26/1.30 Prover 0: gave up % 2.26/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.48/1.32 Prover 1: Preprocessing ... % 2.75/1.40 Prover 1: Warning: ignoring some quantifiers % 2.75/1.41 Prover 1: Constructing countermodel ... % 3.19/1.49 Prover 1: proved (190ms) % 3.19/1.49 % 3.19/1.49 No countermodel exists, formula is valid % 3.19/1.49 % SZS status Theorem for theBenchmark % 3.19/1.49 % 3.19/1.49 Generating proof ... Warning: ignoring some quantifiers % 4.00/1.75 found it (size 21) % 4.00/1.75 % 4.00/1.75 % SZS output start Proof for theBenchmark % 4.00/1.75 Assumed formulas after preprocessing and simplification: % 4.00/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & empty(v5) = 0 & empty(v3) = v4 & empty(empty_set) = 0 & disjoint(v2, v1) = 0 & singleton(v0) = v2 & in(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v6) = v10) | ? [v11] : ? [v12] : (in(v9, v8) = v11 & in(v9, v7) = v12 & ( ~ (v11 = 0) | (v12 = 0 & v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (disjoint(v9, v8) = v7) | ~ (disjoint(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_intersection2(v9, v8) = v7) | ~ (set_intersection2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (in(v9, v8) = v7) | ~ (in(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) | ~ (in(v9, v6) = 0) | ? [v10] : ? [v11] : (in(v9, v8) = v11 & in(v9, v7) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ? [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (in(v10, v8) = v13 & in(v10, v7) = v12 & in(v10, v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)) & (v11 = 0 | (v13 = 0 & v12 = 0)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v6) = v7) | ~ (in(v8, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (disjoint(v6, v7) = v8) | ? [v9] : ( ~ (v9 = empty_set) & set_intersection2(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v6) = v7) | ~ (in(v6, v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (empty(v8) = v7) | ~ (empty(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) | set_intersection2(v7, v6) = v8) & ? [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v7) = v8) | ? [v9] : ? [v10] : (in(v9, v6) = v10 & ( ~ (v10 = 0) | ~ (v9 = v7)) & (v10 = 0 | v9 = v7))) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_intersection2(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (disjoint(v6, v7) = 0) | disjoint(v7, v6) = 0) & ! [v6] : ! [v7] : ( ~ (disjoint(v6, v7) = 0) | set_intersection2(v6, v7) = empty_set) & ! [v6] : ! [v7] : ( ~ (in(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v7, v6) = v8)) & ! [v6] : ~ (in(v6, empty_set) = 0) & ? [v6] : (v6 = empty_set | ? [v7] : in(v7, v6) = 0)) % 4.42/1.78 | 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: % 4.42/1.78 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & disjoint(all_0_3_3, all_0_4_4) = 0 & singleton(all_0_5_5) = all_0_3_3 & in(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 4.42/1.79 | % 4.42/1.79 | Applying alpha-rule on (1) yields: % 4.42/1.79 | (2) singleton(all_0_5_5) = all_0_3_3 % 4.42/1.79 | (3) disjoint(all_0_3_3, all_0_4_4) = 0 % 4.42/1.79 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.42/1.79 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 4.42/1.79 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 4.42/1.79 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.42/1.79 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 4.42/1.79 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 4.42/1.79 | (10) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 4.42/1.79 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.42/1.79 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) % 4.42/1.79 | (13) in(all_0_5_5, all_0_4_4) = 0 % 4.42/1.79 | (14) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 4.42/1.79 | (15) empty(all_0_0_0) = 0 % 4.42/1.79 | (16) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 4.42/1.79 | (17) empty(empty_set) = 0 % 4.42/1.79 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.42/1.79 | (19) ~ (all_0_1_1 = 0) % 4.42/1.80 | (20) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.42/1.80 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.42/1.80 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 4.42/1.80 | (23) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 4.42/1.80 | (24) ! [v0] : ~ (in(v0, empty_set) = 0) % 4.42/1.80 | (25) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 4.42/1.80 | (26) empty(all_0_2_2) = all_0_1_1 % 4.42/1.80 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (24) with all_0_5_5 yields: % 4.42/1.80 | (28) ~ (in(all_0_5_5, empty_set) = 0) % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (25) with all_0_4_4, all_0_3_3 and discharging atoms disjoint(all_0_3_3, all_0_4_4) = 0, yields: % 4.42/1.80 | (29) set_intersection2(all_0_3_3, all_0_4_4) = empty_set % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (7) with empty_set, all_0_4_4, all_0_3_3 and discharging atoms set_intersection2(all_0_3_3, all_0_4_4) = empty_set, yields: % 4.42/1.80 | (30) set_intersection2(all_0_4_4, all_0_3_3) = empty_set % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (5) with all_0_5_5, empty_set, all_0_3_3, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_3_3) = empty_set, in(all_0_5_5, all_0_4_4) = 0, yields: % 4.42/1.80 | (31) ? [v0] : ? [v1] : (in(all_0_5_5, all_0_3_3) = v0 & in(all_0_5_5, empty_set) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (12) with 0, all_0_5_5, empty_set, all_0_3_3, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_3_3) = empty_set, in(all_0_5_5, all_0_4_4) = 0, yields: % 4.42/1.80 | (32) ? [v0] : ? [v1] : (in(all_0_5_5, all_0_3_3) = v1 & in(all_0_5_5, empty_set) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.42/1.80 | % 4.42/1.80 | Instantiating (32) with all_43_0_10, all_43_1_11 yields: % 4.42/1.80 | (33) in(all_0_5_5, all_0_3_3) = all_43_0_10 & in(all_0_5_5, empty_set) = all_43_1_11 & ( ~ (all_43_1_11 = 0) | all_43_0_10 = 0) % 4.42/1.80 | % 4.42/1.80 | Applying alpha-rule on (33) yields: % 4.42/1.80 | (34) in(all_0_5_5, all_0_3_3) = all_43_0_10 % 4.42/1.80 | (35) in(all_0_5_5, empty_set) = all_43_1_11 % 4.42/1.80 | (36) ~ (all_43_1_11 = 0) | all_43_0_10 = 0 % 4.42/1.80 | % 4.42/1.80 | Instantiating (31) with all_45_0_12, all_45_1_13 yields: % 4.42/1.80 | (37) in(all_0_5_5, all_0_3_3) = all_45_1_13 & in(all_0_5_5, empty_set) = all_45_0_12 & ( ~ (all_45_1_13 = 0) | all_45_0_12 = 0) % 4.42/1.80 | % 4.42/1.80 | Applying alpha-rule on (37) yields: % 4.42/1.80 | (38) in(all_0_5_5, all_0_3_3) = all_45_1_13 % 4.42/1.80 | (39) in(all_0_5_5, empty_set) = all_45_0_12 % 4.42/1.80 | (40) ~ (all_45_1_13 = 0) | all_45_0_12 = 0 % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (6) with all_45_1_13, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, in(all_0_5_5, all_0_3_3) = all_45_1_13, yields: % 4.42/1.80 | (41) all_45_1_13 = 0 % 4.42/1.80 | % 4.42/1.80 | Using (39) and (28) yields: % 4.42/1.80 | (42) ~ (all_45_0_12 = 0) % 4.42/1.80 | % 4.42/1.80 | Instantiating formula (27) with all_0_5_5, empty_set, all_43_1_11, all_45_0_12 and discharging atoms in(all_0_5_5, empty_set) = all_45_0_12, in(all_0_5_5, empty_set) = all_43_1_11, yields: % 4.42/1.80 | (43) all_45_0_12 = all_43_1_11 % 4.42/1.80 | % 4.42/1.80 | Equations (43) can reduce 42 to: % 4.42/1.80 | (44) ~ (all_43_1_11 = 0) % 4.42/1.80 | % 4.42/1.80 +-Applying beta-rule and splitting (40), into two cases. % 4.42/1.80 |-Branch one: % 4.42/1.80 | (45) ~ (all_45_1_13 = 0) % 4.42/1.80 | % 4.42/1.80 | Equations (41) can reduce 45 to: % 4.42/1.80 | (46) $false % 4.42/1.80 | % 4.42/1.81 |-The branch is then unsatisfiable % 4.42/1.81 |-Branch two: % 4.42/1.81 | (41) all_45_1_13 = 0 % 4.42/1.81 | (48) all_45_0_12 = 0 % 4.42/1.81 | % 4.42/1.81 | Combining equations (48,43) yields a new equation: % 4.42/1.81 | (49) all_43_1_11 = 0 % 4.42/1.81 | % 4.42/1.81 | Equations (49) can reduce 44 to: % 4.42/1.81 | (46) $false % 4.42/1.81 | % 4.42/1.81 |-The branch is then unsatisfiable % 4.42/1.81 % SZS output end Proof for theBenchmark % 4.42/1.81 % 4.42/1.81 1189ms %------------------------------------------------------------------------------