%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 08:47:45 EDT 2022 % Result : Theorem 3.95s 1.54s % Output : Proof 5.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.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 20:42:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.56 ____ _ % 0.18/0.56 ___ / __ \_____(_)___ ________ __________ % 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.56 % 0.18/0.56 A Theorem Prover for First-Order Logic % 0.18/0.56 (ePrincess v.1.0) % 0.18/0.56 % 0.18/0.56 (c) Philipp Rümmer, 2009-2015 % 0.18/0.56 (c) Peter Backeman, 2014-2015 % 0.18/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.56 Bug reports to peter@backeman.se % 0.18/0.56 % 0.18/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.56 % 0.18/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.89 Prover 0: Preprocessing ... % 1.93/1.07 Prover 0: Warning: ignoring some quantifiers % 2.10/1.09 Prover 0: Constructing countermodel ... % 2.63/1.27 Prover 0: gave up % 2.63/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.63/1.30 Prover 1: Preprocessing ... % 3.25/1.40 Prover 1: Warning: ignoring some quantifiers % 3.25/1.41 Prover 1: Constructing countermodel ... % 3.95/1.54 Prover 1: proved (268ms) % 3.95/1.54 % 3.95/1.54 No countermodel exists, formula is valid % 3.95/1.54 % SZS status Theorem for theBenchmark % 3.95/1.54 % 3.95/1.54 Generating proof ... Warning: ignoring some quantifiers % 5.06/1.90 found it (size 21) % 5.06/1.90 % 5.06/1.90 % SZS output start Proof for theBenchmark % 5.06/1.90 Assumed formulas after preprocessing and simplification: % 5.06/1.90 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v5 = 0) & ~ (v3 = v1) & apply(v2, v1) = v3 & relation_empty_yielding(v7) = 0 & relation_empty_yielding(empty_set) = 0 & identity_relation(v0) = v2 & in(v1, v0) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(v8) = 0 & relation(v7) = 0 & relation(empty_set) = 0 & function(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (apply(v15, v14) = v13) | ~ (apply(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (in(v12, v13) = 0) | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | element(v12, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (in(v12, v13) = 0) | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (in(v12, v13) = v14) | ? [v15] : ? [v16] : (empty(v13) = v16 & element(v12, v13) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_empty_yielding(v14) = v13) | ~ (relation_empty_yielding(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (identity_relation(v14) = v13) | ~ (identity_relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (function(v14) = v13) | ~ (function(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (identity_relation(v12) = v14) | ~ (function(v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_dom(v13) = v16 & relation(v13) = v15 & ( ~ (v15 = 0) | (( ~ (v16 = v12) | v14 = v13 | (v18 = 0 & ~ (v19 = v17) & apply(v13, v17) = v19 & in(v17, v12) = 0)) & ( ~ (v14 = v13) | (v16 = v12 & ! [v20] : ! [v21] : (v21 = v20 | ~ (apply(v13, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v20, v12) = v22)))))))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (relation(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (function(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation(v13) = 0) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | function(v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | element(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (relation(v13) = v16 & empty(v13) = v15 & empty(v12) = v14 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (relation(v12) = v15 & empty(v13) = v16 & empty(v12) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & ~ (v16 = 0) & empty(v14) = v16 & element(v14, v13) = 0) | (v14 = 0 & empty(v12) = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (empty(v14) = 0 & element(v14, v13) = 0)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ? [v12] : ? [v13] : element(v13, v12) = 0) % 5.47/1.94 | 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, all_0_10_10, all_0_11_11 yields: % 5.47/1.94 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = all_0_10_10) & apply(all_0_9_9, all_0_10_10) = all_0_8_8 & relation_empty_yielding(all_0_4_4) = 0 & relation_empty_yielding(empty_set) = 0 & identity_relation(all_0_11_11) = all_0_9_9 & in(all_0_10_10, all_0_11_11) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10)))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.47/1.95 | % 5.47/1.95 | Applying alpha-rule on (1) yields: % 5.47/1.95 | (2) ~ (all_0_6_6 = 0) % 5.47/1.95 | (3) empty(all_0_7_7) = all_0_6_6 % 5.47/1.95 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.47/1.95 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 5.47/1.95 | (6) empty(all_0_1_1) = 0 % 5.47/1.95 | (7) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) % 5.47/1.95 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.47/1.95 | (9) empty(all_0_3_3) = all_0_2_2 % 5.47/1.95 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.47/1.96 | (11) ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.47/1.96 | (12) relation(empty_set) = 0 % 5.47/1.96 | (13) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.47/1.96 | (14) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) % 5.47/1.96 | (15) function(all_0_0_0) = 0 % 5.47/1.96 | (16) ~ (all_0_8_8 = all_0_10_10) % 5.47/1.96 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 5.47/1.96 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.47/1.96 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 5.47/1.96 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 5.47/1.96 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.47/1.96 | (22) empty(empty_set) = 0 % 5.47/1.96 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 5.47/1.96 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10)))))))) % 5.47/1.96 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 5.47/1.96 | (26) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 5.47/1.96 | (27) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.47/1.96 | (28) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) % 5.47/1.96 | (29) relation_empty_yielding(empty_set) = 0 % 5.47/1.96 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.47/1.96 | (31) relation(all_0_4_4) = 0 % 5.47/1.96 | (32) relation_empty_yielding(all_0_4_4) = 0 % 5.47/1.96 | (33) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) % 5.47/1.96 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.47/1.96 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 5.47/1.96 | (36) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 5.47/1.97 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (in(v0, v1) = 0) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | element(v0, v2) = 0) % 5.47/1.97 | (38) relation(all_0_1_1) = 0 % 5.47/1.97 | (39) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.47/1.97 | (40) ~ (all_0_2_2 = 0) % 5.47/1.97 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 5.47/1.97 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 5.47/1.97 | (43) relation(all_0_3_3) = 0 % 5.47/1.97 | (44) in(all_0_10_10, all_0_11_11) = 0 % 5.47/1.97 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 5.47/1.97 | (46) relation(all_0_0_0) = 0 % 5.47/1.97 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 5.47/1.97 | (48) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 5.47/1.97 | (49) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 5.47/1.97 | (50) apply(all_0_9_9, all_0_10_10) = all_0_8_8 % 5.47/1.97 | (51) identity_relation(all_0_11_11) = all_0_9_9 % 5.47/1.97 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.47/1.97 | (53) empty(all_0_5_5) = 0 % 5.47/1.97 | % 5.47/1.97 | Instantiating formula (14) with all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, yields: % 5.47/1.97 | (54) relation(all_0_9_9) = 0 % 5.47/1.97 | % 5.47/1.97 | Instantiating formula (7) with all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, yields: % 5.47/1.97 | (55) function(all_0_9_9) = 0 % 5.47/1.97 | % 5.47/1.97 | Instantiating formula (24) with all_0_9_9, all_0_9_9, all_0_11_11 and discharging atoms identity_relation(all_0_11_11) = all_0_9_9, function(all_0_9_9) = 0, yields: % 5.47/1.97 | (56) ? [v0] : ? [v1] : (relation_dom(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (v1 = all_0_11_11 & ! [v2] : ! [v3] : (v3 = v2 | ~ (apply(all_0_9_9, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, all_0_11_11) = v4))))) % 5.47/1.97 | % 5.47/1.97 | Instantiating (56) with all_30_0_21, all_30_1_22 yields: % 5.47/1.97 | (57) relation_dom(all_0_9_9) = all_30_0_21 & relation(all_0_9_9) = all_30_1_22 & ( ~ (all_30_1_22 = 0) | (all_30_0_21 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2)))) % 5.47/1.97 | % 5.47/1.97 | Applying alpha-rule on (57) yields: % 5.47/1.97 | (58) relation_dom(all_0_9_9) = all_30_0_21 % 5.47/1.97 | (59) relation(all_0_9_9) = all_30_1_22 % 5.47/1.97 | (60) ~ (all_30_1_22 = 0) | (all_30_0_21 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2))) % 5.47/1.97 | % 5.47/1.98 | Instantiating formula (19) with all_0_9_9, all_30_1_22, 0 and discharging atoms relation(all_0_9_9) = all_30_1_22, relation(all_0_9_9) = 0, yields: % 5.47/1.98 | (61) all_30_1_22 = 0 % 5.47/1.98 | % 5.47/1.98 +-Applying beta-rule and splitting (60), into two cases. % 5.47/1.98 |-Branch one: % 5.47/1.98 | (62) ~ (all_30_1_22 = 0) % 5.47/1.98 | % 5.47/1.98 | Equations (61) can reduce 62 to: % 5.47/1.98 | (63) $false % 5.47/1.98 | % 5.47/1.98 |-The branch is then unsatisfiable % 5.47/1.98 |-Branch two: % 5.47/1.98 | (61) all_30_1_22 = 0 % 5.47/1.98 | (65) all_30_0_21 = all_0_11_11 & ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2)) % 5.47/1.98 | % 5.47/1.98 | Applying alpha-rule on (65) yields: % 5.47/1.98 | (66) all_30_0_21 = all_0_11_11 % 5.47/1.98 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (apply(all_0_9_9, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_11_11) = v2)) % 5.47/1.98 | % 5.47/1.98 | Instantiating formula (67) with all_0_8_8, all_0_10_10 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_8_8, yields: % 5.47/1.98 | (68) all_0_8_8 = all_0_10_10 | ? [v0] : ( ~ (v0 = 0) & in(all_0_10_10, all_0_11_11) = v0) % 5.47/1.98 | % 5.47/1.98 +-Applying beta-rule and splitting (68), into two cases. % 5.47/1.98 |-Branch one: % 5.47/1.98 | (69) all_0_8_8 = all_0_10_10 % 5.47/1.98 | % 5.47/1.98 | Equations (69) can reduce 16 to: % 5.47/1.98 | (63) $false % 5.47/1.98 | % 5.47/1.98 |-The branch is then unsatisfiable % 5.47/1.98 |-Branch two: % 5.47/1.98 | (16) ~ (all_0_8_8 = all_0_10_10) % 5.47/1.98 | (72) ? [v0] : ( ~ (v0 = 0) & in(all_0_10_10, all_0_11_11) = v0) % 5.47/1.98 | % 5.47/1.98 | Instantiating (72) with all_55_0_31 yields: % 5.47/1.98 | (73) ~ (all_55_0_31 = 0) & in(all_0_10_10, all_0_11_11) = all_55_0_31 % 5.47/1.98 | % 5.47/1.98 | Applying alpha-rule on (73) yields: % 5.47/1.98 | (74) ~ (all_55_0_31 = 0) % 5.47/1.98 | (75) in(all_0_10_10, all_0_11_11) = all_55_0_31 % 5.47/1.98 | % 5.47/1.98 | Instantiating formula (4) with all_0_10_10, all_0_11_11, all_55_0_31, 0 and discharging atoms in(all_0_10_10, all_0_11_11) = all_55_0_31, in(all_0_10_10, all_0_11_11) = 0, yields: % 5.47/1.98 | (76) all_55_0_31 = 0 % 5.47/1.98 | % 5.47/1.98 | Equations (76) can reduce 74 to: % 5.47/1.98 | (63) $false % 5.47/1.98 | % 5.47/1.98 |-The branch is then unsatisfiable % 5.47/1.98 % SZS output end Proof for theBenchmark % 5.47/1.98 % 5.47/1.98 1408ms %------------------------------------------------------------------------------