%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 08:46:24 EDT 2022 % Result : Theorem 4.48s 1.64s % Output : Proof 6.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n024.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 20:27:02 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.56 ____ _ % 0.19/0.57 ___ / __ \_____(_)___ ________ __________ % 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic % 0.19/0.57 (ePrincess v.1.0) % 0.19/0.57 % 0.19/0.57 (c) Philipp Rümmer, 2009-2015 % 0.19/0.57 (c) Peter Backeman, 2014-2015 % 0.19/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.57 Bug reports to peter@backeman.se % 0.19/0.57 % 0.58/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.57 % 0.58/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.63/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.57/0.90 Prover 0: Preprocessing ... % 2.12/1.10 Prover 0: Warning: ignoring some quantifiers % 2.12/1.12 Prover 0: Constructing countermodel ... % 3.10/1.34 Prover 0: gave up % 3.10/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.10/1.38 Prover 1: Preprocessing ... % 3.73/1.48 Prover 1: Warning: ignoring some quantifiers % 3.73/1.49 Prover 1: Constructing countermodel ... % 4.48/1.64 Prover 1: proved (294ms) % 4.48/1.64 % 4.48/1.64 No countermodel exists, formula is valid % 4.48/1.64 % SZS status Theorem for theBenchmark % 4.48/1.64 % 4.48/1.64 Generating proof ... Warning: ignoring some quantifiers % 6.66/2.13 found it (size 44) % 6.66/2.13 % 6.66/2.13 % SZS output start Proof for theBenchmark % 6.66/2.13 Assumed formulas after preprocessing and simplification: % 6.66/2.13 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = 0) & relation_image(v2, v1) = v4 & relation_image(v2, v0) = v3 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & disjoint(v3, v4) = v5 & disjoint(v0, v1) = 0 & one_to_one(v7) = 0 & one_to_one(v2) = 0 & relation(v15) = 0 & relation(v14) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & function(v15) = 0 & function(v12) = 0 & function(v7) = 0 & function(v2) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v12) = 0 & empty(v10) = v11 & empty(v8) = v9 & empty(empty_set) = 0 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_image(v18, v17) = v20) | ~ (relation_image(v18, v16) = v19) | ~ (set_intersection2(v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_image(v18, v25) = v26 & set_intersection2(v16, v17) = v25 & one_to_one(v18) = v24 & relation(v18) = v22 & function(v18) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v26 = v21))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_image(v19, v18) = v17) | ~ (relation_image(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (subset(v19, v18) = v17) | ~ (subset(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (element(v19, v18) = v17) | ~ (element(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (disjoint(v19, v18) = v17) | ~ (disjoint(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_intersection2(v19, v18) = v17) | ~ (set_intersection2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (in(v19, v18) = v17) | ~ (in(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | ~ (in(v16, v17) = 0) | element(v16, v18) = 0) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | ~ (in(v16, v17) = 0) | ? [v20] : ( ~ (v20 = 0) & empty(v18) = v20)) & ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (disjoint(v16, v17) = v18) | ? [v19] : ( ~ (v19 = empty_set) & set_intersection2(v16, v17) = v19)) & ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (in(v16, v17) = v18) | ? [v19] : ? [v20] : (element(v16, v17) = v19 & empty(v17) = v20 & ( ~ (v19 = 0) | v20 = 0))) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_empty_yielding(v18) = v17) | ~ (relation_empty_yielding(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (one_to_one(v18) = v17) | ~ (one_to_one(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation(v18) = v17) | ~ (relation(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (function(v18) = v17) | ~ (function(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (empty(v18) = v17) | ~ (empty(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | subset(v16, v17) = 0) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | set_intersection2(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v18) = v21 & relation(v17) = v20 & relation(v16) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_intersection2(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (empty(v17) = 0) | ~ (empty(v16) = 0)) & ! [v16] : ! [v17] : (v17 = empty_set | ~ (relation_image(v16, empty_set) = v17) | ? [v18] : ( ~ (v18 = 0) & relation(v16) = v18)) & ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_intersection2(v16, empty_set) = v17)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (relation(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (function(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ((v19 = 0 & ~ (v20 = 0) & element(v18, v17) = 0 & empty(v18) = v20) | (v18 = 0 & empty(v16) = 0))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v17) = v18)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (element(v18, v17) = 0 & empty(v18) = 0)) & ! [v16] : ! [v17] : ( ~ (disjoint(v16, v17) = 0) | disjoint(v17, v16) = 0) & ! [v16] : ! [v17] : ( ~ (disjoint(v16, v17) = 0) | set_intersection2(v16, v17) = empty_set) & ! [v16] : ! [v17] : ( ~ (one_to_one(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (relation(v16) = v18 & function(v16) = v20 & empty(v16) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | v17 = 0))) & ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | element(v16, v17) = 0) & ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v17) = v18)) & ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v17, v16) = v18)) & ! [v16] : (v16 = empty_set | ~ (empty(v16) = 0)) & ? [v16] : ? [v17] : element(v17, v16) = 0) % 6.66/2.16 | 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, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields: % 6.66/2.16 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & ~ (all_0_10_10 = 0) & relation_image(all_0_13_13, all_0_14_14) = all_0_11_11 & relation_image(all_0_13_13, all_0_15_15) = all_0_12_12 & relation_empty_yielding(all_0_9_9) = 0 & relation_empty_yielding(empty_set) = 0 & disjoint(all_0_12_12, all_0_11_11) = all_0_10_10 & disjoint(all_0_15_15, all_0_14_14) = 0 & one_to_one(all_0_8_8) = 0 & one_to_one(all_0_13_13) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_9_9) = 0 & relation(all_0_13_13) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_8_8) = 0 & function(all_0_13_13) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_5_5) = all_0_4_4 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v2, v1) = v4) | ~ (relation_image(v2, v0) = v3) | ~ (set_intersection2(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_image(v2, v9) = v10 & set_intersection2(v0, v1) = v9 & one_to_one(v2) = v8 & relation(v2) = v6 & function(v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5))) & ! [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 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(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] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (relation_image(v0, empty_set) = v1) | ? [v2] : ( ~ (v2 = 0) & relation(v0) = v2)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [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] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 6.66/2.17 | % 6.66/2.17 | Applying alpha-rule on (1) yields: % 6.66/2.17 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 6.66/2.17 | (3) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 6.66/2.17 | (4) ~ (all_0_6_6 = 0) % 6.66/2.17 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 6.66/2.17 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 6.66/2.17 | (7) empty(all_0_7_7) = all_0_6_6 % 6.66/2.17 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 6.66/2.17 | (9) relation(all_0_8_8) = 0 % 6.66/2.17 | (10) empty(all_0_1_1) = 0 % 6.66/2.17 | (11) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.66/2.17 | (12) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 6.66/2.17 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 6.66/2.17 | (14) ? [v0] : ? [v1] : element(v1, v0) = 0 % 6.66/2.17 | (15) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 6.66/2.17 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 6.66/2.17 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 6.66/2.18 | (18) relation_empty_yielding(all_0_9_9) = 0 % 6.66/2.18 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 6.66/2.18 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 6.66/2.18 | (21) empty(all_0_3_3) = 0 % 6.66/2.18 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 6.66/2.18 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 6.66/2.18 | (24) relation(all_0_1_1) = 0 % 6.66/2.18 | (25) one_to_one(all_0_13_13) = 0 % 6.66/2.18 | (26) relation_image(all_0_13_13, all_0_15_15) = all_0_12_12 % 6.66/2.18 | (27) empty(all_0_2_2) = 0 % 6.66/2.18 | (28) relation_image(all_0_13_13, all_0_14_14) = all_0_11_11 % 6.66/2.18 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 6.66/2.18 | (30) relation(all_0_9_9) = 0 % 6.66/2.18 | (31) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.66/2.18 | (32) relation(all_0_5_5) = 0 % 6.66/2.18 | (33) ~ (all_0_10_10 = 0) % 6.66/2.18 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 6.66/2.18 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.66/2.18 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 6.66/2.18 | (37) ~ (all_0_4_4 = 0) % 6.66/2.18 | (38) function(all_0_13_13) = 0 % 6.66/2.18 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 6.66/2.18 | (40) empty(empty_set) = 0 % 6.66/2.18 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 6.66/2.18 | (42) relation_empty_yielding(empty_set) = 0 % 6.66/2.18 | (43) relation(all_0_13_13) = 0 % 6.66/2.18 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 6.66/2.18 | (45) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 6.66/2.18 | (46) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 6.66/2.18 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 6.66/2.18 | (48) one_to_one(all_0_8_8) = 0 % 6.66/2.18 | (49) disjoint(all_0_12_12, all_0_11_11) = all_0_10_10 % 6.66/2.18 | (50) relation(empty_set) = 0 % 6.66/2.18 | (51) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 6.66/2.18 | (52) ! [v0] : ! [v1] : (v1 = empty_set | ~ (relation_image(v0, empty_set) = v1) | ? [v2] : ( ~ (v2 = 0) & relation(v0) = v2)) % 6.66/2.18 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 6.66/2.18 | (54) relation(all_0_3_3) = 0 % 6.66/2.18 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 6.66/2.18 | (56) function(all_0_3_3) = 0 % 6.66/2.18 | (57) empty(all_0_5_5) = all_0_4_4 % 6.66/2.18 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 6.66/2.18 | (59) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 6.66/2.18 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 6.66/2.18 | (61) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 6.66/2.18 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v2, v1) = v4) | ~ (relation_image(v2, v0) = v3) | ~ (set_intersection2(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_image(v2, v9) = v10 & set_intersection2(v0, v1) = v9 & one_to_one(v2) = v8 & relation(v2) = v6 & function(v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5))) % 6.66/2.19 | (63) relation(all_0_0_0) = 0 % 6.66/2.19 | (64) function(all_0_8_8) = 0 % 6.66/2.19 | (65) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 6.66/2.19 | (66) function(all_0_0_0) = 0 % 6.66/2.19 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.66/2.19 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.66/2.19 | (69) disjoint(all_0_15_15, all_0_14_14) = 0 % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (60) with all_0_10_10, all_0_11_11, all_0_12_12 and discharging atoms disjoint(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 6.66/2.19 | (70) all_0_10_10 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_12_12, all_0_11_11) = v0) % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (51) with all_0_14_14, all_0_15_15 and discharging atoms disjoint(all_0_15_15, all_0_14_14) = 0, yields: % 6.66/2.19 | (71) set_intersection2(all_0_15_15, all_0_14_14) = empty_set % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (45) with 0, all_0_13_13 and discharging atoms one_to_one(all_0_13_13) = 0, yields: % 6.66/2.19 | (72) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_13_13) = v0 & function(all_0_13_13) = v2 & empty(all_0_13_13) = v1) % 6.66/2.19 | % 6.66/2.19 | Instantiating (72) with all_15_0_18, all_15_1_19, all_15_2_20 yields: % 6.66/2.19 | (73) relation(all_0_13_13) = all_15_2_20 & function(all_0_13_13) = all_15_0_18 & empty(all_0_13_13) = all_15_1_19 % 6.66/2.19 | % 6.66/2.19 | Applying alpha-rule on (73) yields: % 6.66/2.19 | (74) relation(all_0_13_13) = all_15_2_20 % 6.66/2.19 | (75) function(all_0_13_13) = all_15_0_18 % 6.66/2.19 | (76) empty(all_0_13_13) = all_15_1_19 % 6.66/2.19 | % 6.66/2.19 +-Applying beta-rule and splitting (70), into two cases. % 6.66/2.19 |-Branch one: % 6.66/2.19 | (77) all_0_10_10 = 0 % 6.66/2.19 | % 6.66/2.19 | Equations (77) can reduce 33 to: % 6.66/2.19 | (78) $false % 6.66/2.19 | % 6.66/2.19 |-The branch is then unsatisfiable % 6.66/2.19 |-Branch two: % 6.66/2.19 | (33) ~ (all_0_10_10 = 0) % 6.66/2.19 | (80) ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_12_12, all_0_11_11) = v0) % 6.66/2.19 | % 6.66/2.19 | Instantiating (80) with all_23_0_24 yields: % 6.66/2.19 | (81) ~ (all_23_0_24 = empty_set) & set_intersection2(all_0_12_12, all_0_11_11) = all_23_0_24 % 6.66/2.19 | % 6.66/2.19 | Applying alpha-rule on (81) yields: % 6.66/2.19 | (82) ~ (all_23_0_24 = empty_set) % 6.66/2.19 | (83) set_intersection2(all_0_12_12, all_0_11_11) = all_23_0_24 % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (41) with all_0_13_13, all_15_2_20, 0 and discharging atoms relation(all_0_13_13) = all_15_2_20, relation(all_0_13_13) = 0, yields: % 6.66/2.19 | (84) all_15_2_20 = 0 % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (29) with all_0_13_13, all_15_0_18, 0 and discharging atoms function(all_0_13_13) = all_15_0_18, function(all_0_13_13) = 0, yields: % 6.66/2.19 | (85) all_15_0_18 = 0 % 6.66/2.19 | % 6.66/2.19 | From (84) and (74) follows: % 6.66/2.19 | (43) relation(all_0_13_13) = 0 % 6.66/2.19 | % 6.66/2.19 | From (85) and (75) follows: % 6.66/2.19 | (38) function(all_0_13_13) = 0 % 6.66/2.19 | % 6.66/2.19 | Instantiating formula (62) with all_23_0_24, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms relation_image(all_0_13_13, all_0_14_14) = all_0_11_11, relation_image(all_0_13_13, all_0_15_15) = all_0_12_12, set_intersection2(all_0_12_12, all_0_11_11) = all_23_0_24, yields: % 6.66/2.19 | (88) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_image(all_0_13_13, v3) = v4 & set_intersection2(all_0_15_15, all_0_14_14) = v3 & one_to_one(all_0_13_13) = v2 & relation(all_0_13_13) = v0 & function(all_0_13_13) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = all_23_0_24)) % 6.66/2.19 | % 6.66/2.19 | Instantiating (88) with all_51_0_25, all_51_1_26, all_51_2_27, all_51_3_28, all_51_4_29 yields: % 6.66/2.19 | (89) relation_image(all_0_13_13, all_51_1_26) = all_51_0_25 & set_intersection2(all_0_15_15, all_0_14_14) = all_51_1_26 & one_to_one(all_0_13_13) = all_51_2_27 & relation(all_0_13_13) = all_51_4_29 & function(all_0_13_13) = all_51_3_28 & ( ~ (all_51_2_27 = 0) | ~ (all_51_3_28 = 0) | ~ (all_51_4_29 = 0) | all_51_0_25 = all_23_0_24) % 6.66/2.19 | % 6.66/2.19 | Applying alpha-rule on (89) yields: % 6.66/2.19 | (90) relation(all_0_13_13) = all_51_4_29 % 6.66/2.19 | (91) relation_image(all_0_13_13, all_51_1_26) = all_51_0_25 % 6.66/2.20 | (92) ~ (all_51_2_27 = 0) | ~ (all_51_3_28 = 0) | ~ (all_51_4_29 = 0) | all_51_0_25 = all_23_0_24 % 6.66/2.20 | (93) function(all_0_13_13) = all_51_3_28 % 6.66/2.20 | (94) set_intersection2(all_0_15_15, all_0_14_14) = all_51_1_26 % 6.66/2.20 | (95) one_to_one(all_0_13_13) = all_51_2_27 % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (13) with all_0_15_15, all_0_14_14, all_51_1_26, empty_set and discharging atoms set_intersection2(all_0_15_15, all_0_14_14) = all_51_1_26, set_intersection2(all_0_15_15, all_0_14_14) = empty_set, yields: % 6.66/2.20 | (96) all_51_1_26 = empty_set % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (44) with all_0_13_13, all_51_2_27, 0 and discharging atoms one_to_one(all_0_13_13) = all_51_2_27, one_to_one(all_0_13_13) = 0, yields: % 6.66/2.20 | (97) all_51_2_27 = 0 % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (41) with all_0_13_13, all_51_4_29, 0 and discharging atoms relation(all_0_13_13) = all_51_4_29, relation(all_0_13_13) = 0, yields: % 6.66/2.20 | (98) all_51_4_29 = 0 % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (29) with all_0_13_13, all_51_3_28, 0 and discharging atoms function(all_0_13_13) = all_51_3_28, function(all_0_13_13) = 0, yields: % 6.66/2.20 | (99) all_51_3_28 = 0 % 6.66/2.20 | % 6.66/2.20 | From (96) and (91) follows: % 6.66/2.20 | (100) relation_image(all_0_13_13, empty_set) = all_51_0_25 % 6.66/2.20 | % 6.66/2.20 | From (98) and (90) follows: % 6.66/2.20 | (43) relation(all_0_13_13) = 0 % 6.66/2.20 | % 6.66/2.20 +-Applying beta-rule and splitting (92), into two cases. % 6.66/2.20 |-Branch one: % 6.66/2.20 | (102) ~ (all_51_2_27 = 0) % 6.66/2.20 | % 6.66/2.20 | Equations (97) can reduce 102 to: % 6.66/2.20 | (78) $false % 6.66/2.20 | % 6.66/2.20 |-The branch is then unsatisfiable % 6.66/2.20 |-Branch two: % 6.66/2.20 | (97) all_51_2_27 = 0 % 6.66/2.20 | (105) ~ (all_51_3_28 = 0) | ~ (all_51_4_29 = 0) | all_51_0_25 = all_23_0_24 % 6.66/2.20 | % 6.66/2.20 +-Applying beta-rule and splitting (105), into two cases. % 6.66/2.20 |-Branch one: % 6.66/2.20 | (106) ~ (all_51_3_28 = 0) % 6.66/2.20 | % 6.66/2.20 | Equations (99) can reduce 106 to: % 6.66/2.20 | (78) $false % 6.66/2.20 | % 6.66/2.20 |-The branch is then unsatisfiable % 6.66/2.20 |-Branch two: % 6.66/2.20 | (99) all_51_3_28 = 0 % 6.66/2.20 | (109) ~ (all_51_4_29 = 0) | all_51_0_25 = all_23_0_24 % 6.66/2.20 | % 6.66/2.20 +-Applying beta-rule and splitting (109), into two cases. % 6.66/2.20 |-Branch one: % 6.66/2.20 | (110) ~ (all_51_4_29 = 0) % 6.66/2.20 | % 6.66/2.20 | Equations (98) can reduce 110 to: % 6.66/2.20 | (78) $false % 6.66/2.20 | % 6.66/2.20 |-The branch is then unsatisfiable % 6.66/2.20 |-Branch two: % 6.66/2.20 | (98) all_51_4_29 = 0 % 6.66/2.20 | (113) all_51_0_25 = all_23_0_24 % 6.66/2.20 | % 6.66/2.20 | From (113) and (100) follows: % 6.66/2.20 | (114) relation_image(all_0_13_13, empty_set) = all_23_0_24 % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (52) with all_23_0_24, all_0_13_13 and discharging atoms relation_image(all_0_13_13, empty_set) = all_23_0_24, yields: % 6.66/2.20 | (115) all_23_0_24 = empty_set | ? [v0] : ( ~ (v0 = 0) & relation(all_0_13_13) = v0) % 6.66/2.20 | % 6.66/2.20 +-Applying beta-rule and splitting (115), into two cases. % 6.66/2.20 |-Branch one: % 6.66/2.20 | (116) all_23_0_24 = empty_set % 6.66/2.20 | % 6.66/2.20 | Equations (116) can reduce 82 to: % 6.66/2.20 | (78) $false % 6.66/2.20 | % 6.66/2.20 |-The branch is then unsatisfiable % 6.66/2.20 |-Branch two: % 6.66/2.20 | (82) ~ (all_23_0_24 = empty_set) % 6.66/2.20 | (119) ? [v0] : ( ~ (v0 = 0) & relation(all_0_13_13) = v0) % 6.66/2.20 | % 6.66/2.20 | Instantiating (119) with all_112_0_39 yields: % 6.66/2.20 | (120) ~ (all_112_0_39 = 0) & relation(all_0_13_13) = all_112_0_39 % 6.66/2.20 | % 6.66/2.20 | Applying alpha-rule on (120) yields: % 6.66/2.20 | (121) ~ (all_112_0_39 = 0) % 6.66/2.20 | (122) relation(all_0_13_13) = all_112_0_39 % 6.66/2.20 | % 6.66/2.20 | Instantiating formula (41) with all_0_13_13, all_112_0_39, 0 and discharging atoms relation(all_0_13_13) = all_112_0_39, relation(all_0_13_13) = 0, yields: % 6.66/2.20 | (123) all_112_0_39 = 0 % 6.66/2.20 | % 6.66/2.20 | Equations (123) can reduce 121 to: % 6.66/2.20 | (78) $false % 6.66/2.20 | % 6.66/2.20 |-The branch is then unsatisfiable % 6.66/2.20 % SZS output end Proof for theBenchmark % 6.66/2.20 % 6.66/2.20 1627ms %------------------------------------------------------------------------------