%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 08:48:51 EDT 2022 % Result : Theorem 2.53s 1.25s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.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 12:43:25 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.57 ____ _ % 0.49/0.57 ___ / __ \_____(_)___ ________ __________ % 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.57 % 0.49/0.57 A Theorem Prover for First-Order Logic % 0.49/0.57 (ePrincess v.1.0) % 0.49/0.57 % 0.49/0.57 (c) Philipp Rümmer, 2009-2015 % 0.49/0.57 (c) Peter Backeman, 2014-2015 % 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.57 Bug reports to peter@backeman.se % 0.49/0.57 % 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.57 % 0.49/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.41/0.89 Prover 0: Preprocessing ... % 1.96/1.07 Prover 0: Warning: ignoring some quantifiers % 2.03/1.09 Prover 0: Constructing countermodel ... % 2.53/1.25 Prover 0: proved (625ms) % 2.53/1.25 % 2.53/1.25 No countermodel exists, formula is valid % 2.53/1.25 % SZS status Theorem for theBenchmark % 2.53/1.25 % 2.53/1.25 Generating proof ... Warning: ignoring some quantifiers % 3.95/1.57 found it (size 81) % 3.95/1.57 % 3.95/1.57 % SZS output start Proof for theBenchmark % 3.95/1.58 Assumed formulas after preprocessing and simplification: % 3.95/1.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (interior(v0, v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & one_sorted_str(v6) & element(v3, v2) & top_str(v5) & top_str(v0) & topological_space(v0) & ~ open_subset(v4, v0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (subset_complement(v7, v9) = v10) | ~ (subset_complement(v7, v8) = v9) | ? [v11] : (powerset(v7) = v11 & ~ element(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (interior(v10, v9) = v8) | ~ (interior(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (topstr_closure(v10, v9) = v8) | ~ (topstr_closure(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset_complement(v10, v9) = v8) | ~ (subset_complement(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (the_carrier(v7) = v9) | ~ (subset_complement(v9, v8) = v10) | ~ open_subset(v8, v7) | ~ top_str(v7) | ~ topological_space(v7) | closed_subset(v10, v7) | ? [v11] : (powerset(v9) = v11 & ~ element(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (the_carrier(v7) = v9) | ~ (subset_complement(v9, v8) = v10) | ~ closed_subset(v8, v7) | ~ top_str(v7) | ~ topological_space(v7) | open_subset(v10, v7) | ? [v11] : (powerset(v9) = v11 & ~ element(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (the_carrier(v9) = v8) | ~ (the_carrier(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (interior(v7, v8) = v9) | ~ top_str(v7) | ? [v10] : ? [v11] : (the_carrier(v7) = v10 & powerset(v10) = v11 & ( ~ element(v8, v11) | element(v9, v11)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (topstr_closure(v7, v8) = v9) | ~ top_str(v7) | ~ topological_space(v7) | closed_subset(v9, v7) | ? [v10] : ? [v11] : (the_carrier(v7) = v10 & powerset(v10) = v11 & ~ element(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (topstr_closure(v7, v8) = v9) | ~ top_str(v7) | ? [v10] : ? [v11] : (the_carrier(v7) = v10 & powerset(v10) = v11 & ( ~ element(v8, v11) | element(v9, v11)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset_complement(v7, v8) = v9) | ? [v10] : (powerset(v7) = v10 & ( ~ element(v8, v10) | element(v9, v10)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ subset(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ top_str(v7) | ~ topological_space(v7) | ? [v9] : ? [v10] : (powerset(v8) = v9 & open_subset(v10, v7) & element(v10, v9))) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ top_str(v7) | ~ topological_space(v7) | ? [v9] : ? [v10] : (powerset(v8) = v9 & element(v10, v9) & closed_subset(v10, v7))) & ! [v7] : ! [v8] : ( ~ (the_carrier(v7) = v8) | ~ top_str(v7) | ? [v9] : (powerset(v8) = v9 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (topstr_closure(v7, v11) = v12) | ~ (subset_complement(v8, v12) = v13) | ~ (subset_complement(v8, v10) = v11) | ~ element(v10, v9) | interior(v7, v10) = v13) & ! [v10] : ! [v11] : ( ~ (interior(v7, v10) = v11) | ~ element(v10, v9) | ? [v12] : ? [v13] : (topstr_closure(v7, v12) = v13 & subset_complement(v8, v13) = v11 & subset_complement(v8, v10) = v12)))) & ! [v7] : ( ~ top_str(v7) | one_sorted_str(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ? [v7] : subset(v7, v7)) % 3.95/1.62 | 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 yields: % 3.95/1.62 | (1) interior(all_0_6_6, all_0_3_3) = all_0_2_2 & the_carrier(all_0_6_6) = all_0_5_5 & powerset(all_0_5_5) = all_0_4_4 & one_sorted_str(all_0_0_0) & element(all_0_3_3, all_0_4_4) & top_str(all_0_1_1) & top_str(all_0_6_6) & topological_space(all_0_6_6) & ~ open_subset(all_0_2_2, all_0_6_6) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (subset_complement(v2, v1) = v3) | ~ open_subset(v1, v0) | ~ top_str(v0) | ~ topological_space(v0) | closed_subset(v3, v0) | ? [v4] : (powerset(v2) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (subset_complement(v2, v1) = v3) | ~ closed_subset(v1, v0) | ~ top_str(v0) | ~ topological_space(v0) | open_subset(v3, v0) | ? [v4] : (powerset(v2) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (interior(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ~ topological_space(v0) | closed_subset(v2, v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ~ topological_space(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & open_subset(v3, v0) & element(v3, v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ~ topological_space(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & closed_subset(v3, v0))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v4) = v5) | ~ (subset_complement(v1, v5) = v6) | ~ (subset_complement(v1, v3) = v4) | ~ element(v3, v2) | interior(v0, v3) = v6) & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ~ element(v3, v2) | ? [v5] : ? [v6] : (topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5)))) & ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 3.95/1.63 | % 3.95/1.63 | Applying alpha-rule on (1) yields: % 3.95/1.63 | (2) powerset(all_0_5_5) = all_0_4_4 % 3.95/1.63 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) % 3.95/1.63 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (subset_complement(v2, v1) = v3) | ~ closed_subset(v1, v0) | ~ top_str(v0) | ~ topological_space(v0) | open_subset(v3, v0) | ? [v4] : (powerset(v2) = v4 & ~ element(v1, v4))) % 3.95/1.63 | (5) one_sorted_str(all_0_0_0) % 3.95/1.63 | (6) ? [v0] : ? [v1] : element(v1, v0) % 3.95/1.63 | (7) top_str(all_0_1_1) % 3.95/1.63 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 3.95/1.63 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 3.95/1.63 | (10) top_str(all_0_6_6) % 3.95/1.63 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.95/1.63 | (12) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ~ topological_space(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & closed_subset(v3, v0))) % 3.95/1.63 | (13) ~ open_subset(all_0_2_2, all_0_6_6) % 3.95/1.63 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (interior(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) % 3.95/1.63 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 3.95/1.63 | (16) element(all_0_3_3, all_0_4_4) % 3.95/1.63 | (17) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ~ topological_space(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & open_subset(v3, v0) & element(v3, v2))) % 3.95/1.63 | (18) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v4) = v5) | ~ (subset_complement(v1, v5) = v6) | ~ (subset_complement(v1, v3) = v4) | ~ element(v3, v2) | interior(v0, v3) = v6) & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ~ element(v3, v2) | ? [v5] : ? [v6] : (topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5)))) % 3.95/1.64 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) % 3.95/1.64 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ~ topological_space(v0) | closed_subset(v2, v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ~ element(v1, v4))) % 3.95/1.64 | (21) topological_space(all_0_6_6) % 3.95/1.64 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) % 3.95/1.64 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 3.95/1.64 | (24) interior(all_0_6_6, all_0_3_3) = all_0_2_2 % 3.95/1.64 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (subset_complement(v2, v1) = v3) | ~ open_subset(v1, v0) | ~ top_str(v0) | ~ topological_space(v0) | closed_subset(v3, v0) | ? [v4] : (powerset(v2) = v4 & ~ element(v1, v4))) % 3.95/1.64 | (26) ? [v0] : subset(v0, v0) % 3.95/1.64 | (27) the_carrier(all_0_6_6) = all_0_5_5 % 3.95/1.64 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 3.95/1.64 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 3.95/1.64 | (30) ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) % 3.95/1.64 | % 3.95/1.64 | Instantiating formula (18) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, top_str(all_0_6_6), yields: % 3.95/1.64 | (31) ? [v0] : (powerset(all_0_5_5) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (topstr_closure(all_0_6_6, v2) = v3) | ~ (subset_complement(all_0_5_5, v3) = v4) | ~ (subset_complement(all_0_5_5, v1) = v2) | ~ element(v1, v0) | interior(all_0_6_6, v1) = v4) & ! [v1] : ! [v2] : ( ~ (interior(all_0_6_6, v1) = v2) | ~ element(v1, v0) | ? [v3] : ? [v4] : (topstr_closure(all_0_6_6, v3) = v4 & subset_complement(all_0_5_5, v4) = v2 & subset_complement(all_0_5_5, v1) = v3))) % 3.95/1.64 | % 3.95/1.64 | Instantiating formula (14) with all_0_2_2, all_0_3_3, all_0_6_6 and discharging atoms interior(all_0_6_6, all_0_3_3) = all_0_2_2, top_str(all_0_6_6), yields: % 3.95/1.64 | (32) ? [v0] : ? [v1] : (the_carrier(all_0_6_6) = v0 & powerset(v0) = v1 & ( ~ element(all_0_3_3, v1) | element(all_0_2_2, v1))) % 3.95/1.64 | % 3.95/1.64 | Instantiating formula (17) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, top_str(all_0_6_6), topological_space(all_0_6_6), yields: % 3.95/1.64 | (33) ? [v0] : ? [v1] : (powerset(all_0_5_5) = v0 & open_subset(v1, all_0_6_6) & element(v1, v0)) % 3.95/1.64 | % 3.95/1.64 | Instantiating formula (12) with all_0_5_5, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, top_str(all_0_6_6), topological_space(all_0_6_6), yields: % 3.95/1.64 | (34) ? [v0] : ? [v1] : (powerset(all_0_5_5) = v0 & element(v1, v0) & closed_subset(v1, all_0_6_6)) % 3.95/1.64 | % 3.95/1.64 | Instantiating (32) with all_13_0_10, all_13_1_11 yields: % 3.95/1.64 | (35) the_carrier(all_0_6_6) = all_13_1_11 & powerset(all_13_1_11) = all_13_0_10 & ( ~ element(all_0_3_3, all_13_0_10) | element(all_0_2_2, all_13_0_10)) % 3.95/1.64 | % 3.95/1.64 | Applying alpha-rule on (35) yields: % 3.95/1.64 | (36) the_carrier(all_0_6_6) = all_13_1_11 % 3.95/1.64 | (37) powerset(all_13_1_11) = all_13_0_10 % 3.95/1.64 | (38) ~ element(all_0_3_3, all_13_0_10) | element(all_0_2_2, all_13_0_10) % 3.95/1.64 | % 3.95/1.64 | Instantiating (34) with all_15_0_12, all_15_1_13 yields: % 3.95/1.64 | (39) powerset(all_0_5_5) = all_15_1_13 & element(all_15_0_12, all_15_1_13) & closed_subset(all_15_0_12, all_0_6_6) % 3.95/1.64 | % 3.95/1.64 | Applying alpha-rule on (39) yields: % 3.95/1.64 | (40) powerset(all_0_5_5) = all_15_1_13 % 3.95/1.64 | (41) element(all_15_0_12, all_15_1_13) % 3.95/1.64 | (42) closed_subset(all_15_0_12, all_0_6_6) % 3.95/1.64 | % 3.95/1.64 | Instantiating (31) with all_17_0_14 yields: % 3.95/1.64 | (43) powerset(all_0_5_5) = all_17_0_14 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (topstr_closure(all_0_6_6, v1) = v2) | ~ (subset_complement(all_0_5_5, v2) = v3) | ~ (subset_complement(all_0_5_5, v0) = v1) | ~ element(v0, all_17_0_14) | interior(all_0_6_6, v0) = v3) & ! [v0] : ! [v1] : ( ~ (interior(all_0_6_6, v0) = v1) | ~ element(v0, all_17_0_14) | ? [v2] : ? [v3] : (topstr_closure(all_0_6_6, v2) = v3 & subset_complement(all_0_5_5, v3) = v1 & subset_complement(all_0_5_5, v0) = v2)) % 3.95/1.64 | % 3.95/1.64 | Applying alpha-rule on (43) yields: % 3.95/1.64 | (44) powerset(all_0_5_5) = all_17_0_14 % 3.95/1.64 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (topstr_closure(all_0_6_6, v1) = v2) | ~ (subset_complement(all_0_5_5, v2) = v3) | ~ (subset_complement(all_0_5_5, v0) = v1) | ~ element(v0, all_17_0_14) | interior(all_0_6_6, v0) = v3) % 3.95/1.64 | (46) ! [v0] : ! [v1] : ( ~ (interior(all_0_6_6, v0) = v1) | ~ element(v0, all_17_0_14) | ? [v2] : ? [v3] : (topstr_closure(all_0_6_6, v2) = v3 & subset_complement(all_0_5_5, v3) = v1 & subset_complement(all_0_5_5, v0) = v2)) % 3.95/1.65 | % 3.95/1.65 | Instantiating (33) with all_20_0_15, all_20_1_16 yields: % 3.95/1.65 | (47) powerset(all_0_5_5) = all_20_1_16 & open_subset(all_20_0_15, all_0_6_6) & element(all_20_0_15, all_20_1_16) % 3.95/1.65 | % 3.95/1.65 | Applying alpha-rule on (47) yields: % 3.95/1.65 | (48) powerset(all_0_5_5) = all_20_1_16 % 3.95/1.65 | (49) open_subset(all_20_0_15, all_0_6_6) % 3.95/1.65 | (50) element(all_20_0_15, all_20_1_16) % 3.95/1.65 | % 3.95/1.65 | Instantiating formula (29) with all_0_6_6, all_13_1_11, all_0_5_5 and discharging atoms the_carrier(all_0_6_6) = all_13_1_11, the_carrier(all_0_6_6) = all_0_5_5, yields: % 3.95/1.65 | (51) all_13_1_11 = all_0_5_5 % 3.95/1.65 | % 3.95/1.65 | Instantiating formula (11) with all_0_5_5, all_17_0_14, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_17_0_14, powerset(all_0_5_5) = all_0_4_4, yields: % 3.95/1.65 | (52) all_17_0_14 = all_0_4_4 % 3.95/1.65 | % 3.95/1.65 | Instantiating formula (11) with all_0_5_5, all_17_0_14, all_20_1_16 and discharging atoms powerset(all_0_5_5) = all_20_1_16, powerset(all_0_5_5) = all_17_0_14, yields: % 3.95/1.65 | (53) all_20_1_16 = all_17_0_14 % 3.95/1.65 | % 3.95/1.65 | Instantiating formula (11) with all_0_5_5, all_15_1_13, all_20_1_16 and discharging atoms powerset(all_0_5_5) = all_20_1_16, powerset(all_0_5_5) = all_15_1_13, yields: % 3.95/1.65 | (54) all_20_1_16 = all_15_1_13 % 3.95/1.65 | % 3.95/1.65 | Combining equations (53,54) yields a new equation: % 3.95/1.65 | (55) all_17_0_14 = all_15_1_13 % 3.95/1.65 | % 4.27/1.65 | Simplifying 55 yields: % 4.27/1.65 | (56) all_17_0_14 = all_15_1_13 % 4.27/1.65 | % 4.27/1.65 | Combining equations (56,52) yields a new equation: % 4.27/1.65 | (57) all_15_1_13 = all_0_4_4 % 4.27/1.65 | % 4.27/1.65 | Simplifying 57 yields: % 4.27/1.65 | (58) all_15_1_13 = all_0_4_4 % 4.27/1.65 | % 4.27/1.65 | From (51) and (36) follows: % 4.27/1.65 | (27) the_carrier(all_0_6_6) = all_0_5_5 % 4.27/1.65 | % 4.27/1.65 | From (51) and (37) follows: % 4.27/1.65 | (60) powerset(all_0_5_5) = all_13_0_10 % 4.27/1.65 | % 4.27/1.65 | From (58) and (40) follows: % 4.27/1.65 | (2) powerset(all_0_5_5) = all_0_4_4 % 4.27/1.65 | % 4.27/1.65 | Instantiating formula (11) with all_0_5_5, all_13_0_10, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_13_0_10, powerset(all_0_5_5) = all_0_4_4, yields: % 4.27/1.65 | (62) all_13_0_10 = all_0_4_4 % 4.27/1.65 | % 4.27/1.65 | From (62) and (60) follows: % 4.27/1.65 | (2) powerset(all_0_5_5) = all_0_4_4 % 4.27/1.65 | % 4.27/1.65 +-Applying beta-rule and splitting (38), into two cases. % 4.27/1.65 |-Branch one: % 4.27/1.65 | (64) ~ element(all_0_3_3, all_13_0_10) % 4.27/1.65 | % 4.27/1.65 | From (62) and (64) follows: % 4.27/1.65 | (65) ~ element(all_0_3_3, all_0_4_4) % 4.27/1.65 | % 4.27/1.65 | Using (16) and (65) yields: % 4.27/1.65 | (66) $false % 4.27/1.65 | % 4.27/1.65 |-The branch is then unsatisfiable % 4.27/1.65 |-Branch two: % 4.27/1.65 | (67) element(all_0_3_3, all_13_0_10) % 4.27/1.65 | (68) element(all_0_2_2, all_13_0_10) % 4.27/1.65 | % 4.27/1.65 | From (62) and (67) follows: % 4.27/1.65 | (16) element(all_0_3_3, all_0_4_4) % 4.27/1.65 | % 4.27/1.65 | Instantiating formula (46) with all_0_2_2, all_0_3_3 and discharging atoms interior(all_0_6_6, all_0_3_3) = all_0_2_2, yields: % 4.27/1.65 | (70) ~ element(all_0_3_3, all_17_0_14) | ? [v0] : ? [v1] : (topstr_closure(all_0_6_6, v0) = v1 & subset_complement(all_0_5_5, v1) = all_0_2_2 & subset_complement(all_0_5_5, all_0_3_3) = v0) % 4.27/1.65 | % 4.27/1.65 +-Applying beta-rule and splitting (70), into two cases. % 4.27/1.65 |-Branch one: % 4.27/1.65 | (71) ~ element(all_0_3_3, all_17_0_14) % 4.27/1.65 | % 4.27/1.65 | From (52) and (71) follows: % 4.27/1.65 | (65) ~ element(all_0_3_3, all_0_4_4) % 4.27/1.66 | % 4.27/1.66 | Using (16) and (65) yields: % 4.27/1.66 | (66) $false % 4.27/1.66 | % 4.27/1.66 |-The branch is then unsatisfiable % 4.27/1.66 |-Branch two: % 4.27/1.66 | (74) element(all_0_3_3, all_17_0_14) % 4.27/1.66 | (75) ? [v0] : ? [v1] : (topstr_closure(all_0_6_6, v0) = v1 & subset_complement(all_0_5_5, v1) = all_0_2_2 & subset_complement(all_0_5_5, all_0_3_3) = v0) % 4.27/1.66 | % 4.27/1.66 | Instantiating (75) with all_56_0_17, all_56_1_18 yields: % 4.27/1.66 | (76) topstr_closure(all_0_6_6, all_56_1_18) = all_56_0_17 & subset_complement(all_0_5_5, all_56_0_17) = all_0_2_2 & subset_complement(all_0_5_5, all_0_3_3) = all_56_1_18 % 4.27/1.66 | % 4.27/1.66 | Applying alpha-rule on (76) yields: % 4.27/1.66 | (77) topstr_closure(all_0_6_6, all_56_1_18) = all_56_0_17 % 4.27/1.66 | (78) subset_complement(all_0_5_5, all_56_0_17) = all_0_2_2 % 4.27/1.66 | (79) subset_complement(all_0_5_5, all_0_3_3) = all_56_1_18 % 4.27/1.66 | % 4.27/1.66 | From (52) and (74) follows: % 4.27/1.66 | (16) element(all_0_3_3, all_0_4_4) % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (20) with all_56_0_17, all_56_1_18, all_0_6_6 and discharging atoms topstr_closure(all_0_6_6, all_56_1_18) = all_56_0_17, top_str(all_0_6_6), topological_space(all_0_6_6), yields: % 4.27/1.66 | (81) closed_subset(all_56_0_17, all_0_6_6) | ? [v0] : ? [v1] : (the_carrier(all_0_6_6) = v0 & powerset(v0) = v1 & ~ element(all_56_1_18, v1)) % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (19) with all_56_0_17, all_56_1_18, all_0_6_6 and discharging atoms topstr_closure(all_0_6_6, all_56_1_18) = all_56_0_17, top_str(all_0_6_6), yields: % 4.27/1.66 | (82) ? [v0] : ? [v1] : (the_carrier(all_0_6_6) = v0 & powerset(v0) = v1 & ( ~ element(all_56_1_18, v1) | element(all_56_0_17, v1))) % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (23) with all_56_1_18, all_0_3_3, all_0_5_5 and discharging atoms subset_complement(all_0_5_5, all_0_3_3) = all_56_1_18, yields: % 4.27/1.66 | (83) ? [v0] : (powerset(all_0_5_5) = v0 & ( ~ element(all_0_3_3, v0) | element(all_56_1_18, v0))) % 4.27/1.66 | % 4.27/1.66 | Instantiating (83) with all_63_0_19 yields: % 4.27/1.66 | (84) powerset(all_0_5_5) = all_63_0_19 & ( ~ element(all_0_3_3, all_63_0_19) | element(all_56_1_18, all_63_0_19)) % 4.27/1.66 | % 4.27/1.66 | Applying alpha-rule on (84) yields: % 4.27/1.66 | (85) powerset(all_0_5_5) = all_63_0_19 % 4.27/1.66 | (86) ~ element(all_0_3_3, all_63_0_19) | element(all_56_1_18, all_63_0_19) % 4.27/1.66 | % 4.27/1.66 | Instantiating (82) with all_65_0_20, all_65_1_21 yields: % 4.27/1.66 | (87) the_carrier(all_0_6_6) = all_65_1_21 & powerset(all_65_1_21) = all_65_0_20 & ( ~ element(all_56_1_18, all_65_0_20) | element(all_56_0_17, all_65_0_20)) % 4.27/1.66 | % 4.27/1.66 | Applying alpha-rule on (87) yields: % 4.27/1.66 | (88) the_carrier(all_0_6_6) = all_65_1_21 % 4.27/1.66 | (89) powerset(all_65_1_21) = all_65_0_20 % 4.27/1.66 | (90) ~ element(all_56_1_18, all_65_0_20) | element(all_56_0_17, all_65_0_20) % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (29) with all_0_6_6, all_65_1_21, all_0_5_5 and discharging atoms the_carrier(all_0_6_6) = all_65_1_21, the_carrier(all_0_6_6) = all_0_5_5, yields: % 4.27/1.66 | (91) all_65_1_21 = all_0_5_5 % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (11) with all_0_5_5, all_63_0_19, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_63_0_19, powerset(all_0_5_5) = all_0_4_4, yields: % 4.27/1.66 | (92) all_63_0_19 = all_0_4_4 % 4.27/1.66 | % 4.27/1.66 | From (91) and (88) follows: % 4.27/1.66 | (27) the_carrier(all_0_6_6) = all_0_5_5 % 4.27/1.66 | % 4.27/1.66 | From (91) and (89) follows: % 4.27/1.66 | (94) powerset(all_0_5_5) = all_65_0_20 % 4.27/1.66 | % 4.27/1.66 | From (92) and (85) follows: % 4.27/1.66 | (2) powerset(all_0_5_5) = all_0_4_4 % 4.27/1.66 | % 4.27/1.66 +-Applying beta-rule and splitting (86), into two cases. % 4.27/1.66 |-Branch one: % 4.27/1.66 | (96) ~ element(all_0_3_3, all_63_0_19) % 4.27/1.66 | % 4.27/1.66 | From (92) and (96) follows: % 4.27/1.66 | (65) ~ element(all_0_3_3, all_0_4_4) % 4.27/1.66 | % 4.27/1.66 | Using (16) and (65) yields: % 4.27/1.66 | (66) $false % 4.27/1.66 | % 4.27/1.66 |-The branch is then unsatisfiable % 4.27/1.66 |-Branch two: % 4.27/1.66 | (99) element(all_0_3_3, all_63_0_19) % 4.27/1.66 | (100) element(all_56_1_18, all_63_0_19) % 4.27/1.66 | % 4.27/1.66 | From (92) and (100) follows: % 4.27/1.66 | (101) element(all_56_1_18, all_0_4_4) % 4.27/1.66 | % 4.27/1.66 | Instantiating formula (11) with all_0_5_5, all_65_0_20, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_65_0_20, powerset(all_0_5_5) = all_0_4_4, yields: % 4.27/1.66 | (102) all_65_0_20 = all_0_4_4 % 4.27/1.66 | % 4.27/1.66 | From (102) and (94) follows: % 4.27/1.67 | (2) powerset(all_0_5_5) = all_0_4_4 % 4.27/1.67 | % 4.27/1.67 +-Applying beta-rule and splitting (90), into two cases. % 4.27/1.67 |-Branch one: % 4.27/1.67 | (104) ~ element(all_56_1_18, all_65_0_20) % 4.27/1.67 | % 4.27/1.67 | From (102) and (104) follows: % 4.27/1.67 | (105) ~ element(all_56_1_18, all_0_4_4) % 4.27/1.67 | % 4.27/1.67 | Using (101) and (105) yields: % 4.27/1.67 | (66) $false % 4.27/1.67 | % 4.27/1.67 |-The branch is then unsatisfiable % 4.27/1.67 |-Branch two: % 4.27/1.67 | (107) element(all_56_1_18, all_65_0_20) % 4.27/1.67 | (108) element(all_56_0_17, all_65_0_20) % 4.27/1.67 | % 4.27/1.67 | From (102) and (108) follows: % 4.27/1.67 | (109) element(all_56_0_17, all_0_4_4) % 4.27/1.67 | % 4.27/1.67 | From (102) and (107) follows: % 4.27/1.67 | (101) element(all_56_1_18, all_0_4_4) % 4.27/1.67 | % 4.27/1.67 +-Applying beta-rule and splitting (81), into two cases. % 4.27/1.67 |-Branch one: % 4.27/1.67 | (111) closed_subset(all_56_0_17, all_0_6_6) % 4.27/1.67 | % 4.27/1.67 | Instantiating formula (4) with all_0_2_2, all_0_5_5, all_56_0_17, all_0_6_6 and discharging atoms the_carrier(all_0_6_6) = all_0_5_5, subset_complement(all_0_5_5, all_56_0_17) = all_0_2_2, closed_subset(all_56_0_17, all_0_6_6), top_str(all_0_6_6), topological_space(all_0_6_6), ~ open_subset(all_0_2_2, all_0_6_6), yields: % 4.27/1.67 | (112) ? [v0] : (powerset(all_0_5_5) = v0 & ~ element(all_56_0_17, v0)) % 4.27/1.67 | % 4.27/1.67 | Instantiating (112) with all_93_0_22 yields: % 4.27/1.67 | (113) powerset(all_0_5_5) = all_93_0_22 & ~ element(all_56_0_17, all_93_0_22) % 4.27/1.67 | % 4.27/1.67 | Applying alpha-rule on (113) yields: % 4.27/1.67 | (114) powerset(all_0_5_5) = all_93_0_22 % 4.27/1.67 | (115) ~ element(all_56_0_17, all_93_0_22) % 4.27/1.67 | % 4.27/1.67 | Instantiating formula (11) with all_0_5_5, all_93_0_22, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_93_0_22, powerset(all_0_5_5) = all_0_4_4, yields: % 4.27/1.67 | (116) all_93_0_22 = all_0_4_4 % 4.27/1.67 | % 4.27/1.67 | From (116) and (115) follows: % 4.27/1.67 | (117) ~ element(all_56_0_17, all_0_4_4) % 4.27/1.67 | % 4.27/1.67 | Using (109) and (117) yields: % 4.27/1.67 | (66) $false % 4.27/1.67 | % 4.27/1.67 |-The branch is then unsatisfiable % 4.27/1.67 |-Branch two: % 4.27/1.67 | (119) ~ closed_subset(all_56_0_17, all_0_6_6) % 4.27/1.67 | (120) ? [v0] : ? [v1] : (the_carrier(all_0_6_6) = v0 & powerset(v0) = v1 & ~ element(all_56_1_18, v1)) % 4.27/1.67 | % 4.27/1.67 | Instantiating (120) with all_87_0_23, all_87_1_24 yields: % 4.27/1.67 | (121) the_carrier(all_0_6_6) = all_87_1_24 & powerset(all_87_1_24) = all_87_0_23 & ~ element(all_56_1_18, all_87_0_23) % 4.27/1.67 | % 4.27/1.67 | Applying alpha-rule on (121) yields: % 4.27/1.67 | (122) the_carrier(all_0_6_6) = all_87_1_24 % 4.27/1.67 | (123) powerset(all_87_1_24) = all_87_0_23 % 4.27/1.67 | (124) ~ element(all_56_1_18, all_87_0_23) % 4.27/1.67 | % 4.27/1.67 | Instantiating formula (29) with all_0_6_6, all_87_1_24, all_0_5_5 and discharging atoms the_carrier(all_0_6_6) = all_87_1_24, the_carrier(all_0_6_6) = all_0_5_5, yields: % 4.27/1.67 | (125) all_87_1_24 = all_0_5_5 % 4.27/1.67 | % 4.27/1.67 | From (125) and (123) follows: % 4.27/1.67 | (126) powerset(all_0_5_5) = all_87_0_23 % 4.27/1.67 | % 4.27/1.67 | Instantiating formula (11) with all_0_5_5, all_87_0_23, all_0_4_4 and discharging atoms powerset(all_0_5_5) = all_87_0_23, powerset(all_0_5_5) = all_0_4_4, yields: % 4.27/1.67 | (127) all_87_0_23 = all_0_4_4 % 4.27/1.67 | % 4.27/1.67 | From (127) and (124) follows: % 4.27/1.67 | (105) ~ element(all_56_1_18, all_0_4_4) % 4.27/1.67 | % 4.27/1.67 | Using (101) and (105) yields: % 4.27/1.67 | (66) $false % 4.27/1.67 | % 4.27/1.67 |-The branch is then unsatisfiable % 4.27/1.67 % SZS output end Proof for theBenchmark % 4.27/1.68 % 4.27/1.68 1089ms %------------------------------------------------------------------------------