%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 00:23:25 EDT 2022 % Result : Theorem 2.24s 1.23s % Output : Proof 2.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n017.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jul 9 17:00:32 EDT 2022 % 0.13/0.33 % CPUTime : % 0.49/0.62 ____ _ % 0.49/0.62 ___ / __ \_____(_)___ ________ __________ % 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.62 % 0.49/0.62 A Theorem Prover for First-Order Logic % 0.49/0.62 (ePrincess v.1.0) % 0.49/0.62 % 0.49/0.62 (c) Philipp Rümmer, 2009-2015 % 0.49/0.62 (c) Peter Backeman, 2014-2015 % 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.62 Bug reports to peter@backeman.se % 0.49/0.62 % 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.62 % 0.66/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.38/0.95 Prover 0: Preprocessing ... % 1.73/1.10 Prover 0: Constructing countermodel ... % 2.24/1.23 Prover 0: proved (553ms) % 2.24/1.23 % 2.24/1.23 No countermodel exists, formula is valid % 2.24/1.23 % SZS status Theorem for theBenchmark % 2.24/1.23 % 2.24/1.23 Generating proof ... found it (size 6) % 2.86/1.43 % 2.86/1.43 % SZS output start Proof for theBenchmark % 2.86/1.43 Assumed formulas after preprocessing and simplification: % 2.86/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v3, v2) = v7 & cartesian_product2(v2, v3) = v5 & ordered_pair(v1, v0) = v6 & ordered_pair(v0, v1) = v4 & empty(v9) & in(v4, v5) & ~ empty(v8) & ~ in(v6, v7) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v11, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v11, v13) | ~ in(v10, v12) | in(v14, v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11))) % 2.95/1.47 | 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, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 2.95/1.47 | (1) cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2 & cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4 & ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3 & ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5 & empty(all_0_0_0) & in(all_0_5_5, all_0_4_4) & ~ empty(all_0_1_1) & ~ in(all_0_3_3, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.95/1.48 | % 2.95/1.48 | Applying alpha-rule on (1) yields: % 2.95/1.48 | (2) ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3 % 2.95/1.48 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 2.95/1.48 | (4) ~ in(all_0_3_3, all_0_2_2) % 2.95/1.48 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 2.95/1.48 | (6) in(all_0_5_5, all_0_4_4) % 2.95/1.48 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 2.95/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 2.95/1.48 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.95/1.48 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 2.95/1.48 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 2.95/1.48 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 2.95/1.48 | (13) empty(all_0_0_0) % 2.95/1.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 2.95/1.48 | (15) ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5 % 2.95/1.48 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 2.95/1.48 | (17) cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4 % 2.95/1.48 | (18) ~ empty(all_0_1_1) % 2.95/1.48 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 2.95/1.48 | (20) cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2 % 2.95/1.48 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 2.95/1.48 | (22) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.95/1.48 | % 2.95/1.48 | Instantiating formula (14) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_4_4), yields: % 2.95/1.49 | (23) in(all_0_8_8, all_0_6_6) % 2.95/1.49 | % 2.95/1.49 | Instantiating formula (7) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_4_4), yields: % 2.95/1.49 | (24) in(all_0_9_9, all_0_7_7) % 2.95/1.49 | % 2.95/1.49 | Instantiating formula (19) with all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6, all_0_9_9, all_0_8_8 and discharging atoms cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2, ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3, in(all_0_8_8, all_0_6_6), in(all_0_9_9, all_0_7_7), ~ in(all_0_3_3, all_0_2_2), yields: % 2.95/1.49 | (25) $false % 2.95/1.49 | % 2.95/1.49 |-The branch is then unsatisfiable % 2.95/1.49 % SZS output end Proof for theBenchmark % 2.95/1.49 % 2.95/1.49 851ms %------------------------------------------------------------------------------