TSTP Solution File: SEU169+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:16 EDT 2022
% Result : Theorem 23.70s 6.32s
% Output : Proof 26.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 04:22:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.01/1.01 Prover 0: Preprocessing ...
% 3.75/1.51 Prover 0: Warning: ignoring some quantifiers
% 3.89/1.54 Prover 0: Constructing countermodel ...
% 21.92/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.33/6.03 Prover 1: Preprocessing ...
% 23.23/6.23 Prover 1: Warning: ignoring some quantifiers
% 23.23/6.24 Prover 1: Constructing countermodel ...
% 23.70/6.32 Prover 1: proved (382ms)
% 23.70/6.32 Prover 0: stopped
% 23.70/6.32
% 23.70/6.32 No countermodel exists, formula is valid
% 23.70/6.32 % SZS status Theorem for theBenchmark
% 23.70/6.32
% 23.70/6.32 Generating proof ... Warning: ignoring some quantifiers
% 25.54/6.80 found it (size 30)
% 25.54/6.80
% 25.54/6.80 % SZS output start Proof for theBenchmark
% 25.54/6.80 Assumed formulas after preprocessing and simplification:
% 25.54/6.80 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & element(v2, v3) = 0 & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & powerset(v1) = v3 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & in(v4, v2) = 0 & in(v4, v1) = v5 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (cartesian_product2(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (in(v13, v14) = v15) | ? [v16] : ? [v17] : (in(v10, v12) = v17 & in(v9, v11) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (cartesian_product2(v10, v12) = v14) | ~ (cartesian_product2(v9, v11) = v13) | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : (subset(v11, v12) = v17 & subset(v9, v10) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (cartesian_product2(v9, v10) = v11) | ~ (ordered_pair(v14, v15) = v12) | ~ (in(v12, v11) = v13) | ? [v16] : ? [v17] : (in(v15, v10) = v17 & in(v14, v9) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_difference(v10, v12) = v13) | ~ (singleton(v11) = v12) | ~ (subset(v9, v13) = v14) | ? [v15] : ? [v16] : (subset(v9, v10) = v15 & in(v11, v9) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_difference(v10, v11) = v13) | ~ (set_difference(v9, v11) = v12) | ~ (subset(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ~ (set_intersection2(v10, v11) = v13) | ~ (set_intersection2(v9, v11) = v12) | ? [v15] : ( ~ (v15 = 0) & subset(v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (in(v13, v14) = 0) | (in(v10, v12) = 0 & in(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (cartesian_product2(v9, v11) = v12) | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (cartesian_product2(v11, v10) = v17 & cartesian_product2(v11, v9) = v16 & subset(v16, v17) = v18 & subset(v9, v10) = v15 & ( ~ (v15 = 0) | (v18 = 0 & v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | ? [v14] : ? [v15] : (in(v10, v11) = v15 & in(v9, v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v10) = v13) | ~ (set_union2(v9, v11) = v12) | ? [v14] : ? [v15] : (subset(v11, v10) = v15 & subset(v9, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v9, v12) = v13) | ~ (set_intersection2(v10, v11) = v12) | ? [v14] : ? [v15] : (subset(v9, v11) = v15 & subset(v9, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ? [v15] : (in(v12, v11) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v10 | ~ (ordered_pair(v11, v12) = v13) | ~ (ordered_pair(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v9 | v11 = v9 | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (union(v9) = v10) | ~ (in(v11, v13) = 0) | ~ (in(v11, v10) = v12) | ? [v14] : ( ~ (v14 = 0) & in(v13, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v9 | ~ (ordered_pair(v11, v12) = v13) | ~ (ordered_pair(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ? [v15] : (in(v12, v11) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | (v13 = 0 & ~ (v15 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v12) | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v11) | ordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ? [v15] : (in(v12, v11) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | (v15 = 0 & v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ? [v15] : (in(v12, v11) = v15 & in(v12, v10) = v14 & (v15 = 0 | ( ~ (v14 = 0) & ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v12 = v9 | ~ (unordered_pair(v9, v10) = v11) | ~ (in(v12, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v9) = v11) | ~ (set_union2(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_difference(v9, v11) = v12) | ~ (singleton(v10) = v11) | in(v10, v9) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v11, v10) = v12) | ~ (singleton(v9) = v11) | in(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = 0) | ~ (disjoint(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v9, v10) = v11) | ~ (subset(v11, v9) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v10) = v11) | ~ (subset(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (powerset(v9) = v10) | ~ (subset(v11, v9) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v11, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (singleton(v9) = v11) | ~ (subset(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v9) = v12) | ~ (set_intersection2(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v11) = v12) | ~ (subset(v9, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v11) = v12) | ~ (set_union2(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v9, v10) = v11) | ~ (in(v10, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v9, v10) = v11) | ~ (in(v9, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v9) = v12) | ~ (unordered_pair(v10, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (are_equipotent(v12, v11) = v10) | ~ (are_equipotent(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (disjoint(v12, v11) = v10) | ~ (disjoint(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cartesian_product2(v12, v11) = v10) | ~ (cartesian_product2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (element(v12, v11) = v10) | ~ (element(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ~ (subset(v11, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (singleton(v9) = v12) | ~ (unordered_pair(v10, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_intersection2(v12, v11) = v10) | ~ (set_intersection2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_union2(v12, v11) = v10) | ~ (set_union2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (proper_subset(v12, v11) = v10) | ~ (proper_subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v9, v10) = v11) | set_difference(v9, v10) = v12) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v9, v11) = v12) | set_union2(v9, v10) = v12) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v11) = v12) | ~ (set_difference(v9, v10) = v11) | set_intersection2(v9, v10) = v12) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ? [v14] : (in(v12, v11) = v14 & in(v12, v10) = v13 & (v14 = 0 | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v9, v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : (ordered_pair(v13, v14) = v12 & in(v14, v10) = 0 & in(v13, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v12, v11) = 0) | ~ (unordered_pair(v9, v10) = v12) | (in(v10, v11) = 0 & in(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ? [v14] : (in(v12, v11) = v14 & in(v12, v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (in(v13, v11) = v16 & in(v13, v10) = v15 & in(v13, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v16 = 0) & (v14 = 0 | (v15 = 0 & ~ (v16 = 0))))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (cartesian_product2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v13, v9) = v14 & ( ~ (v14 = 0) | ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v21) = v13) | ? [v22] : ? [v23] : (in(v21, v11) = v23 & in(v20, v10) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & (v14 = 0 | (v19 = v13 & v18 = 0 & v17 = 0 & ordered_pair(v15, v16) = v13 & in(v16, v11) = 0 & in(v15, v10) = 0)))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (in(v13, v11) = v16 & in(v13, v10) = v15 & in(v13, v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 = 0 | (v16 = 0 & v15 = 0)))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (in(v13, v11) = v16 & in(v13, v10) = v15 & in(v13, v9) = v14 & ( ~ (v14 = 0) | ( ~ (v16 = 0) & ~ (v15 = 0))) & (v16 = 0 | v15 = 0 | v14 = 0))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (in(v13, v9) = v14 & ( ~ (v14 = 0) | ( ~ (v13 = v11) & ~ (v13 = v10))) & (v14 = 0 | v13 = v11 | v13 = v10))) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v9 = empty_set | ~ (singleton(v10) = v11) | ~ (subset(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v9) = v10) | ~ (in(v11, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (proper_subset(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ? [v13] : (set_intersection2(v9, v10) = v12 & in(v13, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ( ~ (v12 = v9) & set_difference(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ( ~ (v12 = empty_set) & set_intersection2(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : (in(v12, v10) = 0 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v10) = v9) | ~ (subset(v9, v9) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v9) = v10) | ~ (subset(empty_set, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v9) = v10) | ~ (in(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (union(v11) = v10) | ~ (union(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v11, v10) = 0) | ~ (singleton(v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v9, v10) = 0) | ~ (in(v11, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v11) = v9) | ~ (singleton(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v9) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : (in(v12, v9) = 0 & in(v11, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v10, v9) = v11) | ? [v12] : ? [v13] : (empty(v10) = v13 & empty(v9) = v12 & ( ~ (v12 = 0) | (( ~ (v13 = 0) | v11 = 0) & ( ~ (v11 = 0) | v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v10, v9) = v11) | ? [v12] : ? [v13] : (empty(v9) = v12 & in(v10, v9) = v13 & (v12 = 0 | (( ~ (v13 = 0) | v11 = 0) & ( ~ (v11 = 0) | v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ (subset(v11, v9) = 0) | in(v11, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v9) = v11) | ~ (subset(v11, v10) = 0) | in(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (in(v11, v9) = 0) | in(v11, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | ? [v12] : ? [v13] : (empty(v11) = v13 & empty(v9) = v12 & ( ~ (v13 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | set_union2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : (empty(v11) = v13 & empty(v9) = v12 & ( ~ (v13 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (union(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (in(v12, v9) = v13 & ( ~ (v13 = 0) | ! [v17] : ( ~ (in(v12, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v17, v10) = v18))) & (v13 = 0 | (v16 = 0 & v15 = 0 & in(v14, v10) = 0 & in(v12, v14) = 0)))) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (powerset(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (subset(v12, v10) = v14 & in(v12, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)) & (v14 = 0 | v13 = 0))) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v10) = v11) | ? [v12] : ? [v13] : (in(v12, v9) = v13 & ( ~ (v13 = 0) | ~ (v12 = v10)) & (v13 = 0 | v12 = v10))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (subset(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v10, v9) = v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_intersection2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(empty_set, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | disjoint(v10, v9) = 0) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | set_difference(v9, v10) = v9) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | set_intersection2(v9, v10) = empty_set) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | ? [v11] : (set_intersection2(v9, v10) = v11 & ! [v12] : ~ (in(v12, v11) = 0))) & ! [v9] : ! [v10] : ( ~ (set_difference(v9, v10) = empty_set) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | union(v10) = v9) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v12 = 0 & ~ (v13 = 0) & element(v11, v10) = 0 & empty(v11) = v13) | (v11 = 0 & empty(v9) = 0))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v9) = v10) | singleton(v9) = v10) & ! [v9] : ! [v10] : ( ~ (proper_subset(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v9, v10) = v11)) & ! [v9] : ! [v10] : ( ~ (proper_subset(v9, v10) = 0) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ( ~ (proper_subset(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & proper_subset(v10, v9) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v9] : (v9 = empty_set | ~ (empty(v9) = 0)) & ! [v9] : (v9 = empty_set | ~ (subset(v9, empty_set) = 0)) & ! [v9] : ~ (singleton(v9) = empty_set) & ! [v9] : ~ (proper_subset(v9, v9) = 0) & ! [v9] : ~ (in(v9, empty_set) = 0) & ? [v9] : ? [v10] : (v10 = v9 | ? [v11] : ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) & ? [v9] : ? [v10] : element(v10, v9) = 0 & ? [v9] : ? [v10] : (in(v9, v10) = 0 & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (in(v12, v10) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v10) = v14)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (are_equipotent(v11, v10) = v12) | ? [v13] : ? [v14] : (subset(v11, v10) = v13 & in(v11, v10) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (subset(v12, v11) = 0) | ? [v13] : ? [v14] : (in(v12, v10) = v14 & in(v11, v10) = v13 & ( ~ (v13 = 0) | v14 = 0)))) & ? [v9] : ? [v10] : (in(v9, v10) = 0 & ! [v11] : ! [v12] : (v12 = 0 | ~ (are_equipotent(v11, v10) = v12) | ? [v13] : ? [v14] : (subset(v11, v10) = v13 & in(v11, v10) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (subset(v12, v11) = 0) | ? [v13] : ? [v14] : (in(v12, v10) = v14 & in(v11, v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : (in(v12, v10) = 0 & ! [v13] : ( ~ (subset(v13, v11) = 0) | in(v13, v12) = 0)))) & ? [v9] : (v9 = empty_set | ? [v10] : in(v10, v9) = 0))
% 25.98/6.87 | 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 yields:
% 25.98/6.87 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & element(all_0_6_6, all_0_5_5) = 0 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & powerset(all_0_7_7) = all_0_5_5 & powerset(empty_set) = all_0_8_8 & singleton(empty_set) = all_0_8_8 & in(all_0_4_4, all_0_6_6) = 0 & in(all_0_4_4, all_0_7_7) = 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] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = 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] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 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 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [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 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [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 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(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] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = 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] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [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 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [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] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (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] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0)))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 25.98/6.89 |
% 25.98/6.89 | Applying alpha-rule on (1) yields:
% 25.98/6.89 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 25.98/6.89 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 25.98/6.89 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 25.98/6.89 | (5) ! [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))))
% 25.98/6.89 | (6) ~ (all_0_1_1 = 0)
% 25.98/6.89 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 25.98/6.89 | (8) ! [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))
% 25.98/6.89 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 25.98/6.89 | (10) ! [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)))
% 25.98/6.89 | (11) ! [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))))
% 25.98/6.89 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 25.98/6.89 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 25.98/6.89 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 25.98/6.89 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 25.98/6.89 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 25.98/6.89 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 25.98/6.89 | (18) ? [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)))
% 25.98/6.89 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 25.98/6.89 | (20) empty(all_0_2_2) = all_0_1_1
% 25.98/6.89 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 25.98/6.89 | (22) ! [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))
% 25.98/6.89 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 25.98/6.89 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 25.98/6.89 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 25.98/6.89 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 25.98/6.89 | (27) empty(all_0_0_0) = 0
% 25.98/6.89 | (28) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 25.98/6.89 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 25.98/6.89 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 25.98/6.89 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 25.98/6.89 | (32) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 25.98/6.89 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 25.98/6.89 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 25.98/6.90 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 25.98/6.90 | (36) ! [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))
% 25.98/6.90 | (37) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 25.98/6.90 | (38) empty(empty_set) = 0
% 25.98/6.90 | (39) ? [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)))
% 26.43/6.90 | (40) element(all_0_6_6, all_0_5_5) = 0
% 26.43/6.90 | (41) singleton(empty_set) = all_0_8_8
% 26.43/6.90 | (42) ! [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))))
% 26.43/6.90 | (43) ? [v0] : ? [v1] : element(v1, v0) = 0
% 26.43/6.90 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 26.43/6.90 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 26.43/6.90 | (46) ! [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))))
% 26.43/6.90 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 26.43/6.90 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 26.43/6.90 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 26.43/6.90 | (50) ! [v0] : ~ (singleton(v0) = empty_set)
% 26.43/6.90 | (51) ! [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))
% 26.43/6.90 | (52) ? [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)))))
% 26.43/6.90 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 26.43/6.90 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 26.43/6.90 | (55) in(all_0_4_4, all_0_6_6) = 0
% 26.43/6.90 | (56) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 26.43/6.90 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 26.43/6.90 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 26.43/6.90 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 26.43/6.90 | (60) powerset(all_0_7_7) = all_0_5_5
% 26.43/6.90 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 26.43/6.90 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 26.43/6.90 | (63) ? [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))))
% 26.43/6.90 | (64) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 26.43/6.90 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 26.43/6.90 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 26.43/6.90 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 26.43/6.90 | (68) ! [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)))))
% 26.43/6.90 | (69) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 26.43/6.90 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 26.43/6.90 | (71) ! [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)))
% 26.43/6.90 | (72) ! [v0] : ~ (in(v0, empty_set) = 0)
% 26.43/6.90 | (73) ! [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))))
% 26.43/6.90 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 26.43/6.90 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 26.43/6.90 | (76) ! [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))
% 26.43/6.90 | (77) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 26.43/6.90 | (78) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 26.43/6.90 | (79) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 26.43/6.90 | (80) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 26.43/6.90 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 26.43/6.90 | (82) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 26.43/6.90 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 26.43/6.90 | (84) in(all_0_4_4, all_0_7_7) = all_0_3_3
% 26.43/6.90 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 26.43/6.90 | (86) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 26.43/6.91 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 26.43/6.91 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 26.43/6.91 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 26.43/6.91 | (90) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 26.43/6.91 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 26.43/6.91 | (92) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 26.43/6.91 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 26.43/6.91 | (94) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0))))
% 26.43/6.91 | (95) ? [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)))
% 26.43/6.91 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 26.43/6.91 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 26.43/6.91 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 26.43/6.91 | (99) ! [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)))
% 26.43/6.91 | (100) ! [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))))
% 26.43/6.91 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 26.43/6.91 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 26.43/6.91 | (103) powerset(empty_set) = all_0_8_8
% 26.43/6.91 | (104) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 26.43/6.91 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 26.43/6.91 | (106) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 26.43/6.91 | (107) ! [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)))
% 26.43/6.91 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 26.43/6.91 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 26.43/6.91 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 26.43/6.91 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 26.43/6.91 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 26.43/6.91 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 26.43/6.91 | (114) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 26.43/6.91 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 26.43/6.91 | (116) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 26.43/6.91 | (117) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 26.43/6.91 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 26.43/6.91 | (119) ~ (all_0_3_3 = 0)
% 26.43/6.91 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 26.43/6.91 | (121) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 26.43/6.91 | (122) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 26.43/6.91 | (123) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 26.43/6.91 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 26.43/6.91 | (125) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 26.43/6.91 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 26.43/6.91 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 26.43/6.91 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 26.43/6.91 | (129) ! [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)))))
% 26.43/6.91 | (130) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 26.43/6.91 | (131) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 26.43/6.91 | (132) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 26.43/6.91 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 26.43/6.91 | (134) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 26.43/6.91 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 26.43/6.91 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 26.43/6.91 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 26.43/6.91 | (138) ? [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))))
% 26.43/6.91 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 26.43/6.91 | (140) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 26.43/6.91 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 26.43/6.91 | (142) ? [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))))
% 26.43/6.92 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 26.43/6.92 | (144) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (110) with 0, all_0_6_6, all_0_5_5 and discharging atoms element(all_0_6_6, all_0_5_5) = 0, yields:
% 26.43/6.92 | (145) ? [v0] : ? [v1] : (empty(all_0_5_5) = v0 & empty(all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (140) with 0, all_0_6_6, all_0_5_5 and discharging atoms element(all_0_6_6, all_0_5_5) = 0, yields:
% 26.43/6.92 | (146) ? [v0] : ? [v1] : (empty(all_0_5_5) = v0 & in(all_0_6_6, all_0_5_5) = v1 & (v1 = 0 | v0 = 0))
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (30) with all_0_5_5, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_5_5, yields:
% 26.43/6.92 | (147) union(all_0_5_5) = all_0_7_7
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (49) with all_0_5_5, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_5_5, yields:
% 26.43/6.92 | (148) ? [v0] : ( ~ (v0 = 0) & empty(all_0_5_5) = v0)
% 26.43/6.92 |
% 26.43/6.92 | Instantiating (146) with all_43_0_26, all_43_1_27 yields:
% 26.43/6.92 | (149) empty(all_0_5_5) = all_43_1_27 & in(all_0_6_6, all_0_5_5) = all_43_0_26 & (all_43_0_26 = 0 | all_43_1_27 = 0)
% 26.43/6.92 |
% 26.43/6.92 | Applying alpha-rule on (149) yields:
% 26.43/6.92 | (150) empty(all_0_5_5) = all_43_1_27
% 26.43/6.92 | (151) in(all_0_6_6, all_0_5_5) = all_43_0_26
% 26.43/6.92 | (152) all_43_0_26 = 0 | all_43_1_27 = 0
% 26.43/6.92 |
% 26.43/6.92 | Instantiating (145) with all_55_0_35, all_55_1_36 yields:
% 26.43/6.92 | (153) empty(all_0_5_5) = all_55_1_36 & empty(all_0_6_6) = all_55_0_35 & ( ~ (all_55_1_36 = 0) | all_55_0_35 = 0)
% 26.43/6.92 |
% 26.43/6.92 | Applying alpha-rule on (153) yields:
% 26.43/6.92 | (154) empty(all_0_5_5) = all_55_1_36
% 26.43/6.92 | (155) empty(all_0_6_6) = all_55_0_35
% 26.43/6.92 | (156) ~ (all_55_1_36 = 0) | all_55_0_35 = 0
% 26.43/6.92 |
% 26.43/6.92 | Instantiating (148) with all_64_0_40 yields:
% 26.43/6.92 | (157) ~ (all_64_0_40 = 0) & empty(all_0_5_5) = all_64_0_40
% 26.43/6.92 |
% 26.43/6.92 | Applying alpha-rule on (157) yields:
% 26.43/6.92 | (158) ~ (all_64_0_40 = 0)
% 26.43/6.92 | (159) empty(all_0_5_5) = all_64_0_40
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (57) with all_0_5_5, all_55_1_36, all_64_0_40 and discharging atoms empty(all_0_5_5) = all_64_0_40, empty(all_0_5_5) = all_55_1_36, yields:
% 26.43/6.92 | (160) all_64_0_40 = all_55_1_36
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (57) with all_0_5_5, all_43_1_27, all_64_0_40 and discharging atoms empty(all_0_5_5) = all_64_0_40, empty(all_0_5_5) = all_43_1_27, yields:
% 26.43/6.92 | (161) all_64_0_40 = all_43_1_27
% 26.43/6.92 |
% 26.43/6.92 | Combining equations (161,160) yields a new equation:
% 26.43/6.92 | (162) all_55_1_36 = all_43_1_27
% 26.43/6.92 |
% 26.43/6.92 | Combining equations (162,160) yields a new equation:
% 26.43/6.92 | (161) all_64_0_40 = all_43_1_27
% 26.43/6.92 |
% 26.43/6.92 | Equations (161) can reduce 158 to:
% 26.43/6.92 | (164) ~ (all_43_1_27 = 0)
% 26.43/6.92 |
% 26.43/6.92 +-Applying beta-rule and splitting (152), into two cases.
% 26.43/6.92 |-Branch one:
% 26.43/6.92 | (165) all_43_0_26 = 0
% 26.43/6.92 |
% 26.43/6.92 | From (165) and (151) follows:
% 26.43/6.92 | (166) in(all_0_6_6, all_0_5_5) = 0
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (51) with all_0_6_6, all_0_3_3, all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms union(all_0_5_5) = all_0_7_7, in(all_0_4_4, all_0_6_6) = 0, in(all_0_4_4, all_0_7_7) = all_0_3_3, yields:
% 26.43/6.92 | (167) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_5_5) = v0)
% 26.43/6.92 |
% 26.43/6.92 +-Applying beta-rule and splitting (167), into two cases.
% 26.43/6.92 |-Branch one:
% 26.43/6.92 | (168) all_0_3_3 = 0
% 26.43/6.92 |
% 26.43/6.92 | Equations (168) can reduce 119 to:
% 26.43/6.92 | (169) $false
% 26.43/6.92 |
% 26.43/6.92 |-The branch is then unsatisfiable
% 26.43/6.92 |-Branch two:
% 26.43/6.92 | (119) ~ (all_0_3_3 = 0)
% 26.43/6.92 | (171) ? [v0] : ( ~ (v0 = 0) & in(all_0_6_6, all_0_5_5) = v0)
% 26.43/6.92 |
% 26.43/6.92 | Instantiating (171) with all_108_0_52 yields:
% 26.43/6.92 | (172) ~ (all_108_0_52 = 0) & in(all_0_6_6, all_0_5_5) = all_108_0_52
% 26.43/6.92 |
% 26.43/6.92 | Applying alpha-rule on (172) yields:
% 26.43/6.92 | (173) ~ (all_108_0_52 = 0)
% 26.43/6.92 | (174) in(all_0_6_6, all_0_5_5) = all_108_0_52
% 26.43/6.92 |
% 26.43/6.92 | Instantiating formula (133) with all_0_6_6, all_0_5_5, all_108_0_52, 0 and discharging atoms in(all_0_6_6, all_0_5_5) = all_108_0_52, in(all_0_6_6, all_0_5_5) = 0, yields:
% 26.43/6.92 | (175) all_108_0_52 = 0
% 26.43/6.92 |
% 26.43/6.92 | Equations (175) can reduce 173 to:
% 26.43/6.92 | (169) $false
% 26.43/6.92 |
% 26.43/6.92 |-The branch is then unsatisfiable
% 26.43/6.92 |-Branch two:
% 26.43/6.92 | (177) ~ (all_43_0_26 = 0)
% 26.43/6.92 | (178) all_43_1_27 = 0
% 26.43/6.92 |
% 26.43/6.92 | Equations (178) can reduce 164 to:
% 26.43/6.92 | (169) $false
% 26.43/6.92 |
% 26.43/6.92 |-The branch is then unsatisfiable
% 26.43/6.92 % SZS output end Proof for theBenchmark
% 26.43/6.92
% 26.43/6.92 6322ms
%------------------------------------------------------------------------------