TSTP Solution File: SEU160+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:08 EDT 2022
% Result : Theorem 23.42s 6.23s
% Output : Proof 25.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 02:16:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.60/0.61 ____ _
% 0.60/0.61 ___ / __ \_____(_)___ ________ __________
% 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.61
% 0.60/0.61 A Theorem Prover for First-Order Logic
% 0.60/0.61 (ePrincess v.1.0)
% 0.60/0.61
% 0.60/0.61 (c) Philipp Rümmer, 2009-2015
% 0.60/0.61 (c) Peter Backeman, 2014-2015
% 0.60/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.61 Bug reports to peter@backeman.se
% 0.60/0.61
% 0.60/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.61
% 0.60/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.94/1.03 Prover 0: Preprocessing ...
% 3.85/1.50 Prover 0: Warning: ignoring some quantifiers
% 4.01/1.54 Prover 0: Constructing countermodel ...
% 22.09/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.41/6.03 Prover 1: Preprocessing ...
% 23.14/6.18 Prover 1: Warning: ignoring some quantifiers
% 23.14/6.19 Prover 1: Constructing countermodel ...
% 23.42/6.23 Prover 1: proved (250ms)
% 23.42/6.23 Prover 0: stopped
% 23.42/6.23
% 23.42/6.23 No countermodel exists, formula is valid
% 23.42/6.23 % SZS status Theorem for theBenchmark
% 23.42/6.23
% 23.42/6.23 Generating proof ... Warning: ignoring some quantifiers
% 24.72/6.52 found it (size 30)
% 24.72/6.52
% 24.72/6.52 % SZS output start Proof for theBenchmark
% 24.72/6.52 Assumed formulas after preprocessing and simplification:
% 24.72/6.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & powerset(empty_set) = v0 & singleton(v2) = v3 & singleton(empty_set) = v0 & subset(v1, v3) = v4 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (in(v12, v13) = v14) | ? [v15] : ? [v16] : (in(v9, v11) = v16 & in(v8, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = 0 | ~ (cartesian_product2(v8, v9) = v10) | ~ (ordered_pair(v13, v14) = v11) | ~ (in(v11, v10) = v12) | ? [v15] : ? [v16] : (in(v14, v9) = v16 & in(v13, v8) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v11) = v12) | ~ (singleton(v10) = v11) | ~ (subset(v8, v12) = v13) | ? [v14] : ? [v15] : (subset(v8, v9) = v14 & in(v10, v8) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v12) | ~ (set_difference(v8, v10) = v11) | ~ (subset(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ~ (set_intersection2(v9, v10) = v12) | ~ (set_intersection2(v8, v10) = v11) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (in(v12, v13) = 0) | (in(v9, v11) = 0 & in(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ? [v13] : ? [v14] : (in(v9, v10) = v14 & in(v8, v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v9) = v12) | ~ (set_union2(v8, v10) = v11) | ? [v13] : ? [v14] : (subset(v10, v9) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v8, v11) = v12) | ~ (set_intersection2(v9, v10) = v11) | ? [v13] : ? [v14] : (subset(v8, v10) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v8 | v10 = v8 | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (union(v8) = v9) | ~ (in(v10, v12) = 0) | ~ (in(v10, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & in(v12, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v12 = 0 & ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v14 & in(v11, v9) = v13 & (v14 = 0 | ( ~ (v13 = 0) & ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v11 = v8 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v11, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v8) = v10) | ~ (set_union2(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v10, v9) = v11) | ~ (singleton(v8) = v10) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = 0) | ~ (disjoint(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_difference(v8, v9) = v10) | ~ (subset(v10, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v9) = v10) | ~ (subset(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (powerset(v8) = v9) | ~ (subset(v10, v8) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v8) = v10) | ~ (subset(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_intersection2(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (set_union2(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v9) = v11) | ~ (singleton(v8) = v10) | ~ (subset(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (proper_subset(v11, v10) = v9) | ~ (proper_subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v8, v9) = v10) | set_difference(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | set_union2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v10) = v11) | ~ (set_difference(v8, v9) = v10) | set_intersection2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ? [v13] : (ordered_pair(v12, v13) = v11 & in(v13, v9) = 0 & in(v12, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v11, v10) = 0) | ~ (unordered_pair(v8, v9) = v11) | (in(v9, v10) = 0 & in(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v15 = 0) & (v13 = 0 | (v14 = 0 & ~ (v15 = 0))))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (cartesian_product2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v20) = v12) | ? [v21] : ? [v22] : (in(v20, v10) = v22 & in(v19, v9) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & (v13 = 0 | (v18 = v12 & v17 = 0 & v16 = 0 & ordered_pair(v14, v15) = v12 & in(v15, v10) = 0 & in(v14, v9) = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)) & (v13 = 0 | (v15 = 0 & v14 = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))) & (v15 = 0 | v14 = 0 | v13 = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v12 = v10) & ~ (v12 = v9))) & (v13 = 0 | v12 = v10 | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v8 = empty_set | ~ (singleton(v9) = v10) | ~ (subset(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ (in(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (proper_subset(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ? [v12] : (set_intersection2(v8, v9) = v11 & in(v12, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = v8) & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = empty_set) & set_intersection2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v9) = v8) | ~ (subset(v8, v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (subset(empty_set, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (union(v10) = v9) | ~ (union(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v10, v9) = 0) | ~ (singleton(v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : (in(v11, v8) = 0 & in(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ (subset(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ (subset(v10, v9) = 0) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (union(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ! [v16] : ( ~ (in(v11, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v9) = v17))) & (v12 = 0 | (v15 = 0 & v14 = 0 & in(v13, v9) = 0 & in(v11, v13) = 0)))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (powerset(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (subset(v11, v9) = v13 & in(v11, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : ? [v12] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = v9)) & (v12 = 0 | v11 = v9))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_difference(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v9, v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(empty_set, v8) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(empty_set, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_difference(v8, v9) = v8) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_intersection2(v8, v9) = empty_set) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | ? [v10] : (set_intersection2(v8, v9) = v10 & ! [v11] : ~ (in(v11, v10) = 0))) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = empty_set) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ! [v9] : ( ~ (proper_subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v9, v8) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v8] : (v8 = empty_set | ~ (empty(v8) = 0)) & ! [v8] : (v8 = empty_set | ~ (subset(v8, empty_set) = 0)) & ! [v8] : ~ (singleton(v8) = empty_set) & ! [v8] : ~ (proper_subset(v8, v8) = 0) & ! [v8] : ~ (in(v8, empty_set) = 0) & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)) & (v12 = 0 | v11 = 0))) & ? [v8] : (v8 = empty_set | ? [v9] : in(v9, v8) = 0) & ((v4 = 0 & ~ (v3 = v1) & ~ (v1 = empty_set)) | ( ~ (v4 = 0) & (v3 = v1 | v1 = empty_set))))
% 24.72/6.57 | 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 yields:
% 24.72/6.57 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & powerset(empty_set) = all_0_7_7 & singleton(all_0_5_5) = all_0_4_4 & singleton(empty_set) = all_0_7_7 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [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] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [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] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [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] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [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 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [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 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [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] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, 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 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [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] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 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 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 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 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [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(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [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 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [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 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [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) & ((all_0_3_3 = 0 & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_6_6 = empty_set)) | ( ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set)))
% 24.72/6.60 |
% 24.72/6.60 | Applying alpha-rule on (1) yields:
% 24.72/6.60 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 24.72/6.60 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 24.72/6.60 | (4) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 24.72/6.60 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 24.72/6.60 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 24.72/6.60 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 24.72/6.60 | (8) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 24.72/6.60 | (9) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 24.72/6.60 | (10) ! [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))
% 24.72/6.60 | (11) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 24.72/6.60 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 24.72/6.60 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 24.72/6.60 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 24.72/6.60 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 24.72/6.60 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 24.72/6.60 | (17) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 24.72/6.60 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 24.72/6.60 | (19) ? [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)))))
% 24.72/6.60 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 24.72/6.60 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 25.19/6.61 | (22) ! [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))
% 25.19/6.61 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 25.19/6.61 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 25.19/6.61 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 25.19/6.61 | (26) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 25.19/6.61 | (27) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 25.19/6.61 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 25.19/6.61 | (29) ! [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)))))
% 25.19/6.61 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 25.19/6.61 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 25.19/6.61 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 25.19/6.61 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 25.19/6.61 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 25.19/6.61 | (35) ! [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))))
% 25.19/6.61 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 25.19/6.61 | (37) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 25.19/6.61 | (38) empty(all_0_0_0) = 0
% 25.19/6.61 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 25.19/6.61 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 25.19/6.61 | (41) empty(all_0_2_2) = all_0_1_1
% 25.19/6.61 | (42) ! [v0] : ~ (in(v0, empty_set) = 0)
% 25.19/6.61 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 25.19/6.61 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 25.19/6.61 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 25.19/6.61 | (46) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 25.19/6.61 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 25.19/6.61 | (48) ? [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))))
% 25.19/6.61 | (49) ? [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)))
% 25.19/6.61 | (50) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 25.19/6.61 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 25.19/6.61 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 25.19/6.61 | (53) ! [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)))
% 25.19/6.61 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 25.19/6.61 | (55) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 25.19/6.61 | (56) ! [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))))
% 25.19/6.61 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 25.19/6.62 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 25.19/6.62 | (59) empty(empty_set) = 0
% 25.19/6.62 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 25.19/6.62 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 25.19/6.62 | (62) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 25.19/6.62 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 25.19/6.62 | (64) singleton(all_0_5_5) = all_0_4_4
% 25.19/6.62 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 25.19/6.62 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 25.19/6.62 | (67) ~ (all_0_1_1 = 0)
% 25.19/6.62 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 25.19/6.62 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 25.19/6.62 | (70) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 25.19/6.62 | (71) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 25.19/6.62 | (72) subset(all_0_6_6, all_0_4_4) = all_0_3_3
% 25.19/6.62 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 25.19/6.62 | (74) singleton(empty_set) = all_0_7_7
% 25.19/6.62 | (75) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 25.19/6.62 | (76) ! [v0] : ~ (singleton(v0) = empty_set)
% 25.19/6.62 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 25.19/6.62 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 25.19/6.62 | (79) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 25.19/6.62 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 25.19/6.62 | (81) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 25.19/6.62 | (82) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 25.19/6.62 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 25.19/6.62 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 25.19/6.62 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 25.19/6.62 | (86) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 25.19/6.62 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 25.19/6.62 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 25.19/6.62 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 25.19/6.62 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 25.19/6.62 | (91) ! [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)))))
% 25.19/6.62 | (92) ! [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)))
% 25.19/6.62 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 25.19/6.62 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 25.19/6.62 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 25.19/6.62 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 25.19/6.62 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 25.19/6.62 | (98) ? [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)))
% 25.19/6.62 | (99) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 25.19/6.62 | (100) ! [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))))
% 25.19/6.62 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 25.19/6.62 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 25.19/6.62 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 25.19/6.62 | (104) ! [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)))
% 25.19/6.62 | (105) powerset(empty_set) = all_0_7_7
% 25.19/6.62 | (106) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 25.19/6.63 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 25.19/6.63 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 25.19/6.63 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 25.19/6.63 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 25.19/6.63 | (111) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 25.19/6.63 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 25.19/6.63 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 25.19/6.63 | (114) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 25.19/6.63 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 25.19/6.63 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 25.19/6.63 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 25.19/6.63 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 25.19/6.63 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 25.19/6.63 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 25.19/6.63 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 25.19/6.63 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 25.19/6.63 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 25.19/6.63 | (124) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 25.19/6.63 | (125) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 25.19/6.63 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 25.19/6.63 | (127) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 25.19/6.63 | (128) (all_0_3_3 = 0 & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_6_6 = empty_set)) | ( ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set))
% 25.19/6.63 |
% 25.19/6.63 | Instantiating formula (113) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms singleton(all_0_5_5) = all_0_4_4, yields:
% 25.19/6.63 | (129) all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set | ~ (subset(all_0_6_6, all_0_4_4) = 0)
% 25.19/6.63 |
% 25.19/6.63 | Instantiating formula (99) with all_0_3_3, all_0_6_6 yields:
% 25.19/6.63 | (130) all_0_3_3 = 0 | ~ (subset(all_0_6_6, all_0_6_6) = all_0_3_3)
% 25.19/6.63 |
% 25.19/6.63 | Instantiating formula (13) with all_0_3_3, all_0_4_4 yields:
% 25.19/6.63 | (131) all_0_3_3 = 0 | ~ (subset(empty_set, all_0_4_4) = all_0_3_3)
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (128), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (132) all_0_3_3 = 0 & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_6_6 = empty_set)
% 25.19/6.63 |
% 25.19/6.63 | Applying alpha-rule on (132) yields:
% 25.19/6.63 | (133) all_0_3_3 = 0
% 25.19/6.63 | (134) ~ (all_0_4_4 = all_0_6_6)
% 25.19/6.63 | (135) ~ (all_0_6_6 = empty_set)
% 25.19/6.63 |
% 25.19/6.63 | From (133) and (72) follows:
% 25.19/6.63 | (136) subset(all_0_6_6, all_0_4_4) = 0
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (129), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (137) ~ (subset(all_0_6_6, all_0_4_4) = 0)
% 25.19/6.63 |
% 25.19/6.63 | Using (136) and (137) yields:
% 25.19/6.63 | (138) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (136) subset(all_0_6_6, all_0_4_4) = 0
% 25.19/6.63 | (140) all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (140), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (141) all_0_6_6 = empty_set
% 25.19/6.63 |
% 25.19/6.63 | Equations (141) can reduce 135 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (135) ~ (all_0_6_6 = empty_set)
% 25.19/6.63 | (144) all_0_4_4 = all_0_6_6
% 25.19/6.63 |
% 25.19/6.63 | Equations (144) can reduce 134 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (146) ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set)
% 25.19/6.63 |
% 25.19/6.63 | Applying alpha-rule on (146) yields:
% 25.19/6.63 | (147) ~ (all_0_3_3 = 0)
% 25.19/6.63 | (140) all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (131), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (149) ~ (subset(empty_set, all_0_4_4) = all_0_3_3)
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (130), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (150) ~ (subset(all_0_6_6, all_0_6_6) = all_0_3_3)
% 25.19/6.63 |
% 25.19/6.63 | Using (72) and (150) yields:
% 25.19/6.63 | (134) ~ (all_0_4_4 = all_0_6_6)
% 25.19/6.63 |
% 25.19/6.63 | Using (72) and (149) yields:
% 25.19/6.63 | (135) ~ (all_0_6_6 = empty_set)
% 25.19/6.63 |
% 25.19/6.63 +-Applying beta-rule and splitting (140), into two cases.
% 25.19/6.63 |-Branch one:
% 25.19/6.63 | (141) all_0_6_6 = empty_set
% 25.19/6.63 |
% 25.19/6.63 | Equations (141) can reduce 135 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (135) ~ (all_0_6_6 = empty_set)
% 25.19/6.63 | (144) all_0_4_4 = all_0_6_6
% 25.19/6.63 |
% 25.19/6.63 | Equations (144) can reduce 134 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (158) subset(all_0_6_6, all_0_6_6) = all_0_3_3
% 25.19/6.63 | (133) all_0_3_3 = 0
% 25.19/6.63 |
% 25.19/6.63 | Equations (133) can reduce 147 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 |-Branch two:
% 25.19/6.63 | (161) subset(empty_set, all_0_4_4) = all_0_3_3
% 25.19/6.63 | (133) all_0_3_3 = 0
% 25.19/6.63 |
% 25.19/6.63 | Equations (133) can reduce 147 to:
% 25.19/6.63 | (142) $false
% 25.19/6.63 |
% 25.19/6.63 |-The branch is then unsatisfiable
% 25.19/6.63 % SZS output end Proof for theBenchmark
% 25.19/6.63
% 25.19/6.63 6004ms
%------------------------------------------------------------------------------