%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU133+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:46:49 EDT 2022 % Result : Theorem 2.71s 1.36s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU133+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.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 Jun 19 12:51:23 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.57 (ePrincess v.1.0) % 0.54/0.57 % 0.54/0.57 (c) Philipp Rümmer, 2009-2015 % 0.54/0.57 (c) Peter Backeman, 2014-2015 % 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.57 Bug reports to peter@backeman.se % 0.54/0.57 % 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.57 % 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.54/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.31/0.90 Prover 0: Preprocessing ... % 1.59/1.03 Prover 0: Warning: ignoring some quantifiers % 1.73/1.05 Prover 0: Constructing countermodel ... % 2.21/1.21 Prover 0: gave up % 2.21/1.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.21/1.23 Prover 1: Preprocessing ... % 2.52/1.30 Prover 1: Warning: ignoring some quantifiers % 2.52/1.31 Prover 1: Constructing countermodel ... % 2.71/1.36 Prover 1: proved (148ms) % 2.71/1.36 % 2.71/1.36 No countermodel exists, formula is valid % 2.71/1.36 % SZS status Theorem for theBenchmark % 2.71/1.36 % 2.71/1.36 Generating proof ... Warning: ignoring some quantifiers % 3.58/1.59 found it (size 18) % 3.58/1.59 % 3.58/1.59 % SZS output start Proof for theBenchmark % 3.58/1.59 Assumed formulas after preprocessing and simplification: % 3.58/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & set_difference(v0, v1) = v2 & subset(v2, v0) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v11 = 0 & ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & (v12 = 0 | v11 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0) & (v12 = 0 | (v13 = 0 & ~ (v14 = 0))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0))) % 3.58/1.62 | 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, all_0_6_6 yields: % 3.58/1.62 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & set_difference(all_0_6_6, all_0_5_5) = all_0_4_4 & subset(all_0_4_4, all_0_6_6) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 3.58/1.63 | % 3.58/1.63 | Applying alpha-rule on (1) yields: % 3.58/1.63 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 3.58/1.63 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 3.58/1.63 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) % 3.58/1.63 | (5) empty(all_0_2_2) = all_0_1_1 % 3.58/1.63 | (6) set_difference(all_0_6_6, all_0_5_5) = all_0_4_4 % 3.58/1.63 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 3.58/1.63 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 3.58/1.63 | (9) empty(all_0_0_0) = 0 % 3.58/1.63 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 3.58/1.63 | (11) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 3.58/1.63 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 3.58/1.64 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 3.58/1.64 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 3.58/1.64 | (15) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 3.58/1.64 | (16) ~ (all_0_1_1 = 0) % 3.58/1.64 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 3.58/1.64 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 3.58/1.64 | (19) ~ (all_0_3_3 = 0) % 3.58/1.64 | (20) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) % 3.58/1.64 | (21) subset(all_0_4_4, all_0_6_6) = all_0_3_3 % 3.58/1.64 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 3.58/1.64 | (23) empty(empty_set) = 0 % 3.58/1.64 | (24) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 3.58/1.64 | % 3.58/1.64 | Instantiating formula (7) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_0_3_3, yields: % 3.58/1.64 | (25) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1) % 3.58/1.64 | % 3.58/1.64 +-Applying beta-rule and splitting (25), into two cases. % 3.58/1.64 |-Branch one: % 3.58/1.64 | (26) all_0_3_3 = 0 % 3.58/1.64 | % 3.58/1.64 | Equations (26) can reduce 19 to: % 3.58/1.64 | (27) $false % 3.58/1.64 | % 3.58/1.64 |-The branch is then unsatisfiable % 3.58/1.64 |-Branch two: % 3.58/1.64 | (19) ~ (all_0_3_3 = 0) % 3.58/1.64 | (29) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1) % 3.58/1.64 | % 3.58/1.64 | Instantiating (29) with all_36_0_8, all_36_1_9 yields: % 3.93/1.64 | (30) ~ (all_36_0_8 = 0) & in(all_36_1_9, all_0_4_4) = 0 & in(all_36_1_9, all_0_6_6) = all_36_0_8 % 3.93/1.64 | % 3.93/1.64 | Applying alpha-rule on (30) yields: % 3.93/1.64 | (31) ~ (all_36_0_8 = 0) % 3.93/1.64 | (32) in(all_36_1_9, all_0_4_4) = 0 % 3.93/1.64 | (33) in(all_36_1_9, all_0_6_6) = all_36_0_8 % 3.93/1.64 | % 3.93/1.64 | Instantiating formula (4) with all_36_0_8, all_36_1_9, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_36_1_9, all_0_6_6) = all_36_0_8, yields: % 3.93/1.64 | (34) ? [v0] : ? [v1] : (in(all_36_1_9, all_0_4_4) = v0 & in(all_36_1_9, all_0_5_5) = v1 & ( ~ (v0 = 0) | (all_36_0_8 = 0 & ~ (v1 = 0)))) % 3.93/1.64 | % 3.93/1.64 | Instantiating (34) with all_47_0_10, all_47_1_11 yields: % 3.93/1.64 | (35) in(all_36_1_9, all_0_4_4) = all_47_1_11 & in(all_36_1_9, all_0_5_5) = all_47_0_10 & ( ~ (all_47_1_11 = 0) | (all_36_0_8 = 0 & ~ (all_47_0_10 = 0))) % 3.93/1.64 | % 3.93/1.64 | Applying alpha-rule on (35) yields: % 3.93/1.65 | (36) in(all_36_1_9, all_0_4_4) = all_47_1_11 % 3.93/1.65 | (37) in(all_36_1_9, all_0_5_5) = all_47_0_10 % 3.93/1.65 | (38) ~ (all_47_1_11 = 0) | (all_36_0_8 = 0 & ~ (all_47_0_10 = 0)) % 3.93/1.65 | % 3.93/1.65 +-Applying beta-rule and splitting (38), into two cases. % 3.93/1.65 |-Branch one: % 3.93/1.65 | (39) ~ (all_47_1_11 = 0) % 3.93/1.65 | % 3.93/1.65 | Instantiating formula (17) with all_36_1_9, all_0_4_4, all_47_1_11, 0 and discharging atoms in(all_36_1_9, all_0_4_4) = all_47_1_11, in(all_36_1_9, all_0_4_4) = 0, yields: % 3.93/1.65 | (40) all_47_1_11 = 0 % 3.93/1.65 | % 3.93/1.65 | Equations (40) can reduce 39 to: % 3.93/1.65 | (27) $false % 3.93/1.65 | % 3.93/1.65 |-The branch is then unsatisfiable % 3.93/1.65 |-Branch two: % 3.93/1.65 | (40) all_47_1_11 = 0 % 3.93/1.65 | (43) all_36_0_8 = 0 & ~ (all_47_0_10 = 0) % 3.93/1.65 | % 3.93/1.65 | Applying alpha-rule on (43) yields: % 3.93/1.65 | (44) all_36_0_8 = 0 % 3.93/1.65 | (45) ~ (all_47_0_10 = 0) % 3.93/1.65 | % 3.93/1.65 | Equations (44) can reduce 31 to: % 3.93/1.65 | (27) $false % 3.93/1.65 | % 3.93/1.65 |-The branch is then unsatisfiable % 3.93/1.65 % SZS output end Proof for theBenchmark % 3.93/1.65 % 3.93/1.65 1064ms %------------------------------------------------------------------------------