%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU145+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:46:57 EDT 2022 % Result : Theorem 22.69s 6.18s % Output : Proof 24.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU145+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 19:19:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.72/1.01 Prover 0: Preprocessing ... % 2.94/1.39 Prover 0: Warning: ignoring some quantifiers % 3.15/1.42 Prover 0: Constructing countermodel ... % 21.66/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 21.66/5.97 Prover 1: Preprocessing ... % 22.40/6.11 Prover 1: Warning: ignoring some quantifiers % 22.59/6.12 Prover 1: Constructing countermodel ... % 22.69/6.18 Prover 1: proved (239ms) % 22.69/6.18 Prover 0: stopped % 22.69/6.18 % 22.69/6.18 No countermodel exists, formula is valid % 22.69/6.18 % SZS status Theorem for theBenchmark % 22.69/6.18 % 22.69/6.18 Generating proof ... Warning: ignoring some quantifiers % 24.03/6.50 found it (size 37) % 24.03/6.50 % 24.03/6.50 % SZS output start Proof for theBenchmark % 24.03/6.50 Assumed formulas after preprocessing and simplification: % 24.03/6.50 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v3 = 0) & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & set_difference(v1, v4) = v5 & singleton(v2) = v4 & subset(v0, v5) = v6 & subset(v0, v1) = 0 & in(v2, v0) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_difference(v11, v12) = v14) | ~ (set_difference(v10, v12) = v13) | ~ (subset(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ~ (set_intersection2(v11, v12) = v14) | ~ (set_intersection2(v10, v12) = v13) | ? [v16] : ( ~ (v16 = 0) & subset(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v11) = v14) | ~ (set_union2(v10, v12) = v13) | ? [v15] : ? [v16] : (subset(v12, v11) = v16 & subset(v10, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v10, v13) = v14) | ~ (set_intersection2(v11, v12) = v13) | ? [v15] : ? [v16] : (subset(v10, v12) = v16 & subset(v10, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | (v14 = 0 & ~ (v16 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v16 & in(v13, v11) = v15 & (v16 = 0 | ( ~ (v15 = 0) & ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = 0) | ~ (disjoint(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v10, v11) = v12) | ~ (subset(v12, v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v10) = v13) | ~ (set_intersection2(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v12) = v13) | ~ (subset(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v12) = v13) | ~ (set_union2(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (disjoint(v13, v12) = v11) | ~ (disjoint(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (proper_subset(v13, v12) = v11) | ~ (proper_subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v10, v11) = v12) | set_difference(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | set_union2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v12) = v13) | ~ (set_difference(v10, v11) = v12) | set_intersection2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v12) | ~ (in(v13, v10) = 0) | ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & (v15 = 0 | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = 0) | ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_difference(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0) & (v15 = 0 | (v16 = 0 & ~ (v17 = 0))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v17 = 0 & v16 = 0)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v15 = 0) | ( ~ (v17 = 0) & ~ (v16 = 0))) & (v17 = 0 | v16 = 0 | v15 = 0))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (in(v14, v10) = v15 & ( ~ (v15 = 0) | ( ~ (v14 = v12) & ~ (v14 = v11))) & (v15 = 0 | v14 = v12 | v14 = v11))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v10) = v11) | ~ (in(v12, v11) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (proper_subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : ? [v14] : (set_intersection2(v10, v11) = v13 & in(v14, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : ( ~ (v13 = v10) & set_difference(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : ( ~ (v13 = empty_set) & set_intersection2(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : (in(v13, v11) = 0 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (singleton(v10) = v11) | ~ (in(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (disjoint(v10, v11) = 0) | ~ (in(v12, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = 0) | in(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v11) = v12) | ? [v13] : ? [v14] : (in(v13, v10) = v14 & ( ~ (v14 = 0) | ~ (v13 = v11)) & (v14 = 0 | v13 = v11))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_difference(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (subset(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v11, v10) = v12)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(empty_set, v10) = v11)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(empty_set, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | disjoint(v11, v10) = 0) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | set_difference(v10, v11) = v10) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | set_intersection2(v10, v11) = empty_set) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | ? [v12] : (set_intersection2(v10, v11) = v12 & ! [v13] : ~ (in(v13, v12) = 0))) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = empty_set) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v10) = v11) | singleton(v10) = v11) & ! [v10] : ! [v11] : ( ~ (proper_subset(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (proper_subset(v10, v11) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (proper_subset(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & proper_subset(v11, v10) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : (v10 = empty_set | ~ (subset(v10, empty_set) = 0)) & ! [v10] : ~ (singleton(v10) = empty_set) & ! [v10] : ~ (proper_subset(v10, v10) = 0) & ! [v10] : ~ (in(v10, empty_set) = 0) & ? [v10] : ? [v11] : (v11 = v10 | ? [v12] : ? [v13] : ? [v14] : (in(v12, v11) = v14 & in(v12, v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)) & (v14 = 0 | v13 = 0))) & ? [v10] : (v10 = empty_set | ? [v11] : in(v11, v10) = 0)) % 24.45/6.57 | 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 yields: % 24.45/6.57 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & set_difference(all_0_8_8, all_0_5_5) = all_0_4_4 & singleton(all_0_7_7) = all_0_5_5 & subset(all_0_9_9, all_0_4_4) = all_0_3_3 & subset(all_0_9_9, all_0_8_8) = 0 & in(all_0_7_7, all_0_9_9) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(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 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [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] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 24.77/6.59 | % 24.77/6.59 | Applying alpha-rule on (1) yields: % 24.77/6.59 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 24.77/6.59 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 24.77/6.59 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 24.77/6.59 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) % 24.77/6.59 | (6) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 24.77/6.59 | (7) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) % 24.77/6.59 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 24.77/6.59 | (9) empty(empty_set) = 0 % 24.77/6.59 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 24.77/6.59 | (11) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 24.77/6.59 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 24.77/6.59 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 24.77/6.59 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 24.77/6.59 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) % 24.77/6.59 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 24.77/6.59 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 24.77/6.60 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 24.77/6.60 | (19) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 24.77/6.60 | (20) in(all_0_7_7, all_0_9_9) = all_0_6_6 % 24.77/6.60 | (21) ! [v0] : ~ (singleton(v0) = empty_set) % 24.77/6.60 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 24.77/6.60 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 24.77/6.60 | (24) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) % 24.77/6.60 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 24.77/6.60 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 24.77/6.60 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 24.77/6.60 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 24.77/6.60 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 24.77/6.60 | (30) singleton(all_0_7_7) = all_0_5_5 % 24.77/6.60 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 24.77/6.60 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 24.77/6.60 | (33) set_difference(all_0_8_8, all_0_5_5) = all_0_4_4 % 24.77/6.60 | (34) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 24.77/6.60 | (35) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 24.77/6.60 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) % 24.77/6.60 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 24.77/6.60 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) % 24.77/6.60 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) % 24.77/6.60 | (40) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 24.77/6.60 | (41) ! [v0] : ~ (in(v0, empty_set) = 0) % 24.77/6.60 | (42) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 24.77/6.60 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 24.77/6.60 | (44) empty(all_0_0_0) = 0 % 24.77/6.60 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) % 24.77/6.60 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 24.77/6.60 | (47) ~ (all_0_6_6 = 0) % 24.77/6.60 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) % 24.77/6.60 | (49) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 24.77/6.60 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 24.77/6.60 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 24.77/6.60 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 24.77/6.60 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 24.77/6.60 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) % 24.77/6.60 | (55) subset(all_0_9_9, all_0_4_4) = all_0_3_3 % 24.77/6.60 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) % 24.77/6.60 | (57) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) % 24.77/6.60 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 24.77/6.60 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 24.77/6.60 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 24.77/6.60 | (61) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) % 24.77/6.60 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 24.77/6.61 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 24.77/6.61 | (64) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 24.77/6.61 | (65) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 24.77/6.61 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) % 24.77/6.61 | (67) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) % 24.77/6.61 | (68) ~ (all_0_1_1 = 0) % 24.77/6.61 | (69) subset(all_0_9_9, all_0_8_8) = 0 % 24.77/6.61 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 24.77/6.61 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 24.77/6.61 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) % 24.77/6.61 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 24.77/6.61 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) % 24.77/6.61 | (75) ! [v0] : ~ (proper_subset(v0, v0) = 0) % 24.77/6.61 | (76) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 24.77/6.61 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 24.77/6.61 | (78) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 24.77/6.61 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 24.77/6.61 | (80) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) % 24.77/6.61 | (81) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 24.77/6.61 | (82) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 24.77/6.61 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) % 24.77/6.61 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 24.77/6.61 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) % 24.77/6.61 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 24.77/6.61 | (87) empty(all_0_2_2) = all_0_1_1 % 24.77/6.61 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) % 24.77/6.61 | (89) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) % 24.77/6.61 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 24.77/6.61 | (91) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 24.77/6.61 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 24.77/6.61 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) % 24.77/6.61 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 24.77/6.61 | (95) ~ (all_0_3_3 = 0) % 24.77/6.61 | (96) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) % 24.77/6.61 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 24.77/6.61 | % 24.77/6.61 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_4_4) = all_0_3_3, yields: % 24.77/6.61 | (98) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_9_9) = 0) % 24.77/6.61 | % 24.77/6.61 +-Applying beta-rule and splitting (98), into two cases. % 24.77/6.61 |-Branch one: % 24.77/6.61 | (99) all_0_3_3 = 0 % 24.77/6.61 | % 24.77/6.61 | Equations (99) can reduce 95 to: % 24.77/6.61 | (100) $false % 24.77/6.61 | % 24.77/6.61 |-The branch is then unsatisfiable % 24.77/6.61 |-Branch two: % 24.77/6.61 | (95) ~ (all_0_3_3 = 0) % 24.77/6.61 | (102) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_9_9) = 0) % 24.77/6.61 | % 24.77/6.61 | Instantiating (102) with all_54_0_18, all_54_1_19 yields: % 24.77/6.61 | (103) ~ (all_54_0_18 = 0) & in(all_54_1_19, all_0_4_4) = all_54_0_18 & in(all_54_1_19, all_0_9_9) = 0 % 24.77/6.61 | % 24.77/6.61 | Applying alpha-rule on (103) yields: % 24.77/6.61 | (104) ~ (all_54_0_18 = 0) % 24.77/6.62 | (105) in(all_54_1_19, all_0_4_4) = all_54_0_18 % 24.77/6.62 | (106) in(all_54_1_19, all_0_9_9) = 0 % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (77) with all_0_7_7, all_0_9_9, 0, all_0_6_6 and discharging atoms in(all_0_7_7, all_0_9_9) = all_0_6_6, yields: % 24.77/6.62 | (107) all_0_6_6 = 0 | ~ (in(all_0_7_7, all_0_9_9) = 0) % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (26) with all_54_1_19, all_0_8_8, all_0_9_9 and discharging atoms subset(all_0_9_9, all_0_8_8) = 0, in(all_54_1_19, all_0_9_9) = 0, yields: % 24.77/6.62 | (108) in(all_54_1_19, all_0_8_8) = 0 % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (83) with 0, all_54_1_19, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_5_5) = all_0_4_4, in(all_54_1_19, all_0_8_8) = 0, yields: % 24.77/6.62 | (109) ? [v0] : ? [v1] : (in(all_54_1_19, all_0_4_4) = v0 & in(all_54_1_19, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (70) with all_54_1_19, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_5_5) = all_0_4_4, in(all_54_1_19, all_0_8_8) = 0, yields: % 24.77/6.62 | (110) ? [v0] : ? [v1] : (in(all_54_1_19, all_0_4_4) = v1 & in(all_54_1_19, all_0_5_5) = v0 & (v1 = 0 | v0 = 0)) % 24.77/6.62 | % 24.77/6.62 | Instantiating (110) with all_95_0_26, all_95_1_27 yields: % 24.77/6.62 | (111) in(all_54_1_19, all_0_4_4) = all_95_0_26 & in(all_54_1_19, all_0_5_5) = all_95_1_27 & (all_95_0_26 = 0 | all_95_1_27 = 0) % 24.77/6.62 | % 24.77/6.62 | Applying alpha-rule on (111) yields: % 24.77/6.62 | (112) in(all_54_1_19, all_0_4_4) = all_95_0_26 % 24.77/6.62 | (113) in(all_54_1_19, all_0_5_5) = all_95_1_27 % 24.77/6.62 | (114) all_95_0_26 = 0 | all_95_1_27 = 0 % 24.77/6.62 | % 24.77/6.62 | Instantiating (109) with all_97_0_28, all_97_1_29 yields: % 24.77/6.62 | (115) in(all_54_1_19, all_0_4_4) = all_97_1_29 & in(all_54_1_19, all_0_5_5) = all_97_0_28 & ( ~ (all_97_0_28 = 0) | ~ (all_97_1_29 = 0)) % 24.77/6.62 | % 24.77/6.62 | Applying alpha-rule on (115) yields: % 24.77/6.62 | (116) in(all_54_1_19, all_0_4_4) = all_97_1_29 % 24.77/6.62 | (117) in(all_54_1_19, all_0_5_5) = all_97_0_28 % 24.77/6.62 | (118) ~ (all_97_0_28 = 0) | ~ (all_97_1_29 = 0) % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (77) with all_54_1_19, all_0_4_4, all_97_1_29, all_54_0_18 and discharging atoms in(all_54_1_19, all_0_4_4) = all_97_1_29, in(all_54_1_19, all_0_4_4) = all_54_0_18, yields: % 24.77/6.62 | (119) all_97_1_29 = all_54_0_18 % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (77) with all_54_1_19, all_0_4_4, all_95_0_26, all_97_1_29 and discharging atoms in(all_54_1_19, all_0_4_4) = all_97_1_29, in(all_54_1_19, all_0_4_4) = all_95_0_26, yields: % 24.77/6.62 | (120) all_97_1_29 = all_95_0_26 % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (51) with all_54_1_19, all_0_5_5, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, yields: % 24.77/6.62 | (121) all_54_1_19 = all_0_7_7 | ~ (in(all_54_1_19, all_0_5_5) = 0) % 24.77/6.62 | % 24.77/6.62 | Instantiating formula (77) with all_54_1_19, all_0_5_5, all_95_1_27, all_97_0_28 and discharging atoms in(all_54_1_19, all_0_5_5) = all_97_0_28, in(all_54_1_19, all_0_5_5) = all_95_1_27, yields: % 24.77/6.62 | (122) all_97_0_28 = all_95_1_27 % 24.77/6.62 | % 24.77/6.62 | Combining equations (120,119) yields a new equation: % 24.77/6.62 | (123) all_95_0_26 = all_54_0_18 % 24.77/6.62 | % 24.77/6.62 | Simplifying 123 yields: % 24.77/6.62 | (124) all_95_0_26 = all_54_0_18 % 24.77/6.62 | % 24.77/6.62 | From (122) and (117) follows: % 24.77/6.62 | (113) in(all_54_1_19, all_0_5_5) = all_95_1_27 % 24.77/6.62 | % 24.77/6.62 +-Applying beta-rule and splitting (114), into two cases. % 24.77/6.62 |-Branch one: % 24.77/6.62 | (126) all_95_0_26 = 0 % 24.77/6.62 | % 24.77/6.62 | Combining equations (126,124) yields a new equation: % 24.77/6.62 | (127) all_54_0_18 = 0 % 24.77/6.62 | % 24.77/6.62 | Equations (127) can reduce 104 to: % 24.77/6.62 | (100) $false % 24.77/6.62 | % 24.77/6.62 |-The branch is then unsatisfiable % 24.77/6.62 |-Branch two: % 24.77/6.62 | (129) ~ (all_95_0_26 = 0) % 24.77/6.62 | (130) all_95_1_27 = 0 % 24.77/6.62 | % 24.77/6.62 | From (130) and (113) follows: % 24.77/6.62 | (131) in(all_54_1_19, all_0_5_5) = 0 % 24.77/6.62 | % 24.77/6.62 +-Applying beta-rule and splitting (121), into two cases. % 24.77/6.62 |-Branch one: % 24.77/6.62 | (132) ~ (in(all_54_1_19, all_0_5_5) = 0) % 24.77/6.62 | % 24.77/6.62 | Using (131) and (132) yields: % 24.77/6.62 | (133) $false % 24.77/6.62 | % 24.77/6.62 |-The branch is then unsatisfiable % 24.77/6.62 |-Branch two: % 24.77/6.62 | (131) in(all_54_1_19, all_0_5_5) = 0 % 24.77/6.62 | (135) all_54_1_19 = all_0_7_7 % 24.77/6.62 | % 24.77/6.62 | From (135) and (106) follows: % 24.77/6.62 | (136) in(all_0_7_7, all_0_9_9) = 0 % 24.77/6.62 | % 24.77/6.62 +-Applying beta-rule and splitting (107), into two cases. % 24.77/6.62 |-Branch one: % 24.77/6.62 | (137) ~ (in(all_0_7_7, all_0_9_9) = 0) % 24.77/6.62 | % 24.77/6.62 | Using (136) and (137) yields: % 24.77/6.62 | (133) $false % 24.77/6.62 | % 24.77/6.62 |-The branch is then unsatisfiable % 24.77/6.62 |-Branch two: % 24.77/6.62 | (136) in(all_0_7_7, all_0_9_9) = 0 % 24.77/6.62 | (140) all_0_6_6 = 0 % 24.77/6.62 | % 24.77/6.62 | Equations (140) can reduce 47 to: % 24.77/6.62 | (100) $false % 24.77/6.62 | % 24.77/6.62 |-The branch is then unsatisfiable % 24.77/6.62 % SZS output end Proof for theBenchmark % 24.77/6.62 % 24.77/6.62 6019ms %------------------------------------------------------------------------------