%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU165+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 08:47:13 EDT 2022 % Result : Theorem 2.03s 1.21s % Output : Proof 3.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU165+3 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.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 : Mon Jun 20 07:32:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.58 ____ _ % 0.48/0.58 ___ / __ \_____(_)___ ________ __________ % 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic % 0.48/0.58 (ePrincess v.1.0) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2015 % 0.48/0.58 (c) Peter Backeman, 2014-2015 % 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.58 Bug reports to peter@backeman.se % 0.48/0.58 % 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.21/0.90 Prover 0: Preprocessing ... % 1.73/1.07 Prover 0: Constructing countermodel ... % 2.03/1.21 Prover 0: proved (580ms) % 2.03/1.21 % 2.03/1.21 No countermodel exists, formula is valid % 2.03/1.21 % SZS status Theorem for theBenchmark % 2.03/1.21 % 2.03/1.21 Generating proof ... found it (size 14) % 2.66/1.41 % 2.66/1.41 % SZS output start Proof for theBenchmark % 2.66/1.41 Assumed formulas after preprocessing and simplification: % 2.66/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (cartesian_product2(v2, v3) = v5 & ordered_pair(v0, v1) = v4 & empty(v7) & ~ empty(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v9, v11) | ~ in(v8, v10) | in(v12, v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ((in(v4, v5) & ( ~ in(v1, v3) | ~ in(v0, v2))) | (in(v1, v3) & in(v0, v2) & ~ in(v4, v5)))) % 2.88/1.45 | 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 yields: % 2.88/1.45 | (1) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [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)) & ((in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2))) % 3.00/1.45 | % 3.00/1.45 | Applying alpha-rule on (1) yields: % 3.00/1.45 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.00/1.46 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.00/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 3.00/1.46 | (5) ~ empty(all_0_1_1) % 3.00/1.46 | (6) (in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)) % 3.00/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.00/1.46 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 3.00/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.00/1.46 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.00/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.00/1.46 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.00/1.46 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.00/1.46 | (14) ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 % 3.00/1.46 | (15) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 % 3.00/1.46 | (16) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.00/1.46 | (17) empty(all_0_0_0) % 3.00/1.46 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.00/1.46 | (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)) % 3.00/1.46 | % 3.00/1.46 +-Applying beta-rule and splitting (6), into two cases. % 3.00/1.46 |-Branch one: % 3.00/1.46 | (20) in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5)) % 3.00/1.46 | % 3.00/1.46 | Applying alpha-rule on (20) yields: % 3.00/1.46 | (21) in(all_0_3_3, all_0_2_2) % 3.00/1.46 | (22) ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5) % 3.00/1.46 | % 3.00/1.46 | Instantiating formula (8) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_3_3, all_0_2_2), yields: % 3.00/1.46 | (23) in(all_0_6_6, all_0_4_4) % 3.00/1.46 | % 3.00/1.46 | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_3_3, all_0_2_2), yields: % 3.00/1.46 | (24) in(all_0_7_7, all_0_5_5) % 3.00/1.46 | % 3.00/1.46 +-Applying beta-rule and splitting (22), into two cases. % 3.00/1.46 |-Branch one: % 3.00/1.46 | (25) ~ in(all_0_6_6, all_0_4_4) % 3.00/1.46 | % 3.00/1.47 | Using (23) and (25) yields: % 3.00/1.47 | (26) $false % 3.00/1.47 | % 3.00/1.47 |-The branch is then unsatisfiable % 3.00/1.47 |-Branch two: % 3.00/1.47 | (23) in(all_0_6_6, all_0_4_4) % 3.00/1.47 | (28) ~ in(all_0_7_7, all_0_5_5) % 3.00/1.47 | % 3.00/1.47 | Using (24) and (28) yields: % 3.00/1.47 | (26) $false % 3.00/1.47 | % 3.00/1.47 |-The branch is then unsatisfiable % 3.00/1.47 |-Branch two: % 3.00/1.47 | (30) in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2) % 3.00/1.47 | % 3.00/1.47 | Applying alpha-rule on (30) yields: % 3.00/1.47 | (23) in(all_0_6_6, all_0_4_4) % 3.00/1.47 | (24) in(all_0_7_7, all_0_5_5) % 3.00/1.47 | (33) ~ in(all_0_3_3, all_0_2_2) % 3.00/1.47 | % 3.00/1.47 | Instantiating formula (19) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_6_6, all_0_4_4), in(all_0_7_7, all_0_5_5), ~ in(all_0_3_3, all_0_2_2), yields: % 3.00/1.47 | (26) $false % 3.00/1.47 | % 3.00/1.47 |-The branch is then unsatisfiable % 3.00/1.47 % SZS output end Proof for theBenchmark % 3.00/1.47 % 3.00/1.47 881ms %------------------------------------------------------------------------------