%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 08:48:19 EDT 2022 % Result : Theorem 1.79s 0.98s % Output : Proof 2.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.08 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.08 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.27 % Computer : n032.cluster.edu % 0.08/0.27 % Model : x86_64 x86_64 % 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.27 % Memory : 8042.1875MB % 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.27 % CPULimit : 300 % 0.08/0.27 % WCLimit : 600 % 0.08/0.27 % DateTime : Sun Jun 19 10:02:02 EDT 2022 % 0.08/0.27 % CPUTime : % 0.12/0.46 ____ _ % 0.12/0.46 ___ / __ \_____(_)___ ________ __________ % 0.12/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.12/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.12/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.12/0.46 % 0.12/0.46 A Theorem Prover for First-Order Logic % 0.12/0.46 (ePrincess v.1.0) % 0.12/0.46 % 0.12/0.46 (c) Philipp Rümmer, 2009-2015 % 0.12/0.46 (c) Peter Backeman, 2014-2015 % 0.12/0.46 (contributions by Angelo Brillout, Peter Baumgartner) % 0.12/0.46 Free software under GNU Lesser General Public License (LGPL). % 0.12/0.46 Bug reports to peter@backeman.se % 0.12/0.46 % 0.12/0.46 For more information, visit http://user.uu.se/~petba168/breu/ % 0.12/0.46 % 0.12/0.46 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.12/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.01/0.73 Prover 0: Preprocessing ... % 1.40/0.87 Prover 0: Warning: ignoring some quantifiers % 1.40/0.89 Prover 0: Constructing countermodel ... % 1.79/0.98 Prover 0: proved (473ms) % 1.79/0.98 % 1.79/0.98 No countermodel exists, formula is valid % 1.79/0.98 % SZS status Theorem for theBenchmark % 1.79/0.98 % 1.79/0.98 Generating proof ... Warning: ignoring some quantifiers % 2.30/1.16 found it (size 9) % 2.30/1.16 % 2.30/1.16 % SZS output start Proof for theBenchmark % 2.30/1.16 Assumed formulas after preprocessing and simplification: % 2.30/1.16 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (pair_second(v2) = v4 & pair_first(v2) = v3 & ordered_pair(v0, v1) = v2 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (pair_second(v7) = v8) | ~ (ordered_pair(v11, v12) = v7) | ~ (ordered_pair(v9, v10) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (pair_first(v7) = v8) | ~ (ordered_pair(v11, v12) = v7) | ~ (ordered_pair(v9, v10) = v7)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v7 | ~ (pair_second(v8) = v9) | ~ (ordered_pair(v10, v11) = v8) | ? [v12] : ? [v13] : ( ~ (v13 = v7) & ordered_pair(v12, v13) = v8)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v7 | ~ (pair_first(v8) = v9) | ~ (ordered_pair(v10, v11) = v8) | ? [v12] : ? [v13] : ( ~ (v12 = v7) & ordered_pair(v12, v13) = v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (pair_second(v9) = v8) | ~ (pair_second(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (pair_first(v9) = v8) | ~ (pair_first(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | in(v7, v8) | empty(v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ( ~ (v4 = v1) | ~ (v3 = v0))) % 2.30/1.20 | 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: % 2.30/1.20 | (1) pair_second(all_0_4_4) = all_0_2_2 & pair_first(all_0_4_4) = all_0_3_3 & ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_second(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ordered_pair(v5, v6) = v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_first(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v5 = v0) & ordered_pair(v5, v6) = v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ( ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_3_3 = all_0_6_6)) % 2.30/1.20 | % 2.30/1.20 | Applying alpha-rule on (1) yields: % 2.30/1.20 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.30/1.20 | (3) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_first(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v5 = v0) & ordered_pair(v5, v6) = v1)) % 2.30/1.21 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) % 2.30/1.21 | (5) ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 % 2.30/1.21 | (6) pair_second(all_0_4_4) = all_0_2_2 % 2.30/1.21 | (7) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 2.30/1.21 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) % 2.30/1.21 | (9) ~ empty(all_0_1_1) % 2.30/1.21 | (10) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_second(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ordered_pair(v5, v6) = v1)) % 2.30/1.21 | (11) pair_first(all_0_4_4) = all_0_3_3 % 2.30/1.21 | (12) ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_3_3 = all_0_6_6) % 2.30/1.21 | (13) ? [v0] : ? [v1] : element(v1, v0) % 2.30/1.21 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 2.30/1.21 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 2.30/1.21 | (16) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 2.30/1.21 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 2.30/1.21 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 2.30/1.21 | (19) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 2.30/1.21 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 2.30/1.21 | (21) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 2.30/1.21 | (22) empty(all_0_0_0) % 2.30/1.21 | (23) empty(empty_set) % 2.30/1.21 | % 2.30/1.21 | Instantiating formula (20) with all_0_5_5, all_0_6_6, all_0_5_5, all_0_6_6, all_0_2_2, all_0_4_4 and discharging atoms pair_second(all_0_4_4) = all_0_2_2, ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 2.30/1.21 | (24) all_0_2_2 = all_0_5_5 % 2.30/1.21 | % 2.30/1.21 | Instantiating formula (17) with all_0_5_5, all_0_6_6, all_0_5_5, all_0_6_6, all_0_3_3, all_0_4_4 and discharging atoms pair_first(all_0_4_4) = all_0_3_3, ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 2.30/1.21 | (25) all_0_3_3 = all_0_6_6 % 2.30/1.21 | % 2.30/1.21 +-Applying beta-rule and splitting (12), into two cases. % 2.30/1.21 |-Branch one: % 2.30/1.21 | (26) ~ (all_0_2_2 = all_0_5_5) % 2.30/1.21 | % 2.30/1.21 | Equations (24) can reduce 26 to: % 2.30/1.21 | (27) $false % 2.30/1.21 | % 2.30/1.21 |-The branch is then unsatisfiable % 2.30/1.21 |-Branch two: % 2.30/1.21 | (24) all_0_2_2 = all_0_5_5 % 2.30/1.21 | (29) ~ (all_0_3_3 = all_0_6_6) % 2.30/1.21 | % 2.30/1.21 | Equations (25) can reduce 29 to: % 2.30/1.21 | (27) $false % 2.30/1.21 | % 2.30/1.21 |-The branch is then unsatisfiable % 2.30/1.21 % SZS output end Proof for theBenchmark % 2.30/1.21 % 2.30/1.21 742ms %------------------------------------------------------------------------------