%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU177+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 08:47:20 EDT 2022 % Result : Theorem 2.58s 1.25s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n008.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jun 19 07:10:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.56 ____ _ % 0.54/0.56 ___ / __ \_____(_)___ ________ __________ % 0.54/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.56 % 0.54/0.56 A Theorem Prover for First-Order Logic % 0.59/0.56 (ePrincess v.1.0) % 0.59/0.56 % 0.59/0.56 (c) Philipp Rümmer, 2009-2015 % 0.59/0.56 (c) Peter Backeman, 2014-2015 % 0.59/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.56 Bug reports to peter@backeman.se % 0.59/0.56 % 0.59/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.56 % 0.59/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.90 Prover 0: Preprocessing ... % 2.01/1.10 Prover 0: Warning: ignoring some quantifiers % 2.01/1.12 Prover 0: Constructing countermodel ... % 2.52/1.25 Prover 0: proved (635ms) % 2.58/1.25 % 2.58/1.25 No countermodel exists, formula is valid % 2.58/1.25 % SZS status Theorem for theBenchmark % 2.58/1.25 % 2.58/1.25 Generating proof ... Warning: ignoring some quantifiers % 3.55/1.49 found it (size 9) % 3.55/1.49 % 3.55/1.49 % SZS output start Proof for theBenchmark % 3.55/1.49 Assumed formulas after preprocessing and simplification: % 3.55/1.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v5 & relation_dom(v2) = v4 & ordered_pair(v0, v1) = v3 & in(v3, v2) & relation(v8) & relation(v2) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v9) = v10) | ~ (ordered_pair(v12, v11) = v13) | ~ in(v13, v9) | ~ relation(v9) | in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v9) = v10) | ~ (ordered_pair(v11, v12) = v13) | ~ in(v13, v9) | ~ relation(v9) | in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v12) | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v11) | ordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (relation_rng(v11) = v10) | ~ (relation_rng(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (relation_dom(v11) = v10) | ~ (relation_dom(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_rng(v9) = v10) | ~ in(v11, v10) | ~ relation(v9) | ? [v12] : ? [v13] : (ordered_pair(v12, v11) = v13 & in(v13, v9))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_dom(v9) = v10) | ~ in(v11, v10) | ~ relation(v9) | ? [v12] : ? [v13] : (ordered_pair(v11, v12) = v13 & in(v13, v9))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (singleton(v9) = v13 & unordered_pair(v12, v13) = v11 & unordered_pair(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : ? [v14] : (( ~ in(v12, v9) | ! [v15] : ! [v16] : ( ~ (ordered_pair(v15, v12) = v16) | ~ in(v16, v10))) & (in(v12, v9) | (ordered_pair(v13, v12) = v14 & in(v14, v10))))) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : ? [v14] : (( ~ in(v12, v9) | ! [v15] : ! [v16] : ( ~ (ordered_pair(v12, v15) = v16) | ~ in(v16, v10))) & (in(v12, v9) | (ordered_pair(v12, v13) = v14 & in(v14, v10))))) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) & ! [v9] : ! [v10] : ( ~ element(v9, v10) | in(v9, v10) | empty(v10)) & ! [v9] : (v9 = empty_set | ~ empty(v9)) & ? [v9] : ? [v10] : element(v10, v9) & ( ~ in(v1, v5) | ~ in(v0, v4))) % 3.72/1.53 | 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 yields: % 3.72/1.53 | (1) relation_rng(all_0_6_6) = all_0_3_3 & relation_dom(all_0_6_6) = all_0_4_4 & ordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5 & in(all_0_5_5, all_0_6_6) & relation(all_0_0_0) & relation(all_0_6_6) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ empty(all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ in(v4, v0) | ~ relation(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v0) | ~ relation(v0) | in(v2, v1)) & ! [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 | ~ (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 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ in(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ in(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, 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) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [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) & ( ~ in(all_0_7_7, all_0_3_3) | ~ in(all_0_8_8, all_0_4_4)) % 3.72/1.54 | % 3.72/1.54 | Applying alpha-rule on (1) yields: % 3.72/1.54 | (2) relation_dom(all_0_6_6) = all_0_4_4 % 3.72/1.54 | (3) relation_rng(all_0_6_6) = all_0_3_3 % 3.72/1.54 | (4) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.72/1.54 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.72/1.54 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.72/1.54 | (7) empty(empty_set) % 3.72/1.54 | (8) empty(all_0_1_1) % 3.72/1.54 | (9) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.72/1.54 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 3.72/1.54 | (11) ? [v0] : ? [v1] : element(v1, v0) % 3.72/1.54 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 3.72/1.54 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.72/1.54 | (14) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 3.72/1.54 | (15) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) % 3.72/1.54 | (16) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 3.72/1.54 | (17) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 3.72/1.54 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ in(v4, v0) | ~ relation(v0) | in(v2, v1)) % 3.72/1.54 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 3.72/1.54 | (20) relation(all_0_0_0) % 3.72/1.54 | (21) in(all_0_5_5, all_0_6_6) % 3.72/1.54 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.72/1.54 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.72/1.54 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.72/1.54 | (25) relation(all_0_6_6) % 3.72/1.54 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.72/1.55 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.72/1.55 | (28) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.78/1.55 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v0) | ~ relation(v0) | in(v2, v1)) % 3.78/1.55 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ in(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 3.78/1.55 | (31) ordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5 % 3.78/1.55 | (32) empty(all_0_0_0) % 3.78/1.55 | (33) ~ empty(all_0_2_2) % 3.78/1.55 | (34) ~ in(all_0_7_7, all_0_3_3) | ~ in(all_0_8_8, all_0_4_4) % 3.78/1.55 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.78/1.55 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ in(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 3.78/1.55 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.78/1.55 | % 3.78/1.55 | Instantiating formula (18) with all_0_5_5, all_0_8_8, all_0_7_7, all_0_3_3, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_3_3, ordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_5_5, all_0_6_6), relation(all_0_6_6), yields: % 3.78/1.55 | (38) in(all_0_7_7, all_0_3_3) % 3.78/1.55 | % 3.78/1.55 | Instantiating formula (29) with all_0_5_5, all_0_7_7, all_0_8_8, all_0_4_4, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_4_4, ordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_5_5, all_0_6_6), relation(all_0_6_6), yields: % 3.78/1.55 | (39) in(all_0_8_8, all_0_4_4) % 3.78/1.55 | % 3.78/1.55 +-Applying beta-rule and splitting (34), into two cases. % 3.78/1.55 |-Branch one: % 3.78/1.55 | (40) ~ in(all_0_7_7, all_0_3_3) % 3.78/1.55 | % 3.78/1.55 | Using (38) and (40) yields: % 3.78/1.55 | (41) $false % 3.78/1.55 | % 3.78/1.55 |-The branch is then unsatisfiable % 3.78/1.55 |-Branch two: % 3.78/1.55 | (38) in(all_0_7_7, all_0_3_3) % 3.78/1.55 | (43) ~ in(all_0_8_8, all_0_4_4) % 3.78/1.55 | % 3.78/1.55 | Using (39) and (43) yields: % 3.78/1.55 | (41) $false % 3.78/1.55 | % 3.78/1.55 |-The branch is then unsatisfiable % 3.78/1.55 % SZS output end Proof for theBenchmark % 3.78/1.55 % 3.78/1.55 979ms %------------------------------------------------------------------------------