TSTP Solution File: SEU157+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU157+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:47:05 EDT 2022
% Result : Theorem 4.91s 1.83s
% Output : Proof 7.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU157+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 02:54:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.59 ____ _
% 0.54/0.59 ___ / __ \_____(_)___ ________ __________
% 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.59
% 0.54/0.59 A Theorem Prover for First-Order Logic
% 0.61/0.59 (ePrincess v.1.0)
% 0.61/0.59
% 0.61/0.59 (c) Philipp Rümmer, 2009-2015
% 0.61/0.59 (c) Peter Backeman, 2014-2015
% 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.59 Bug reports to peter@backeman.se
% 0.61/0.59
% 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.59
% 0.61/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.85/1.02 Prover 0: Preprocessing ...
% 3.72/1.56 Prover 0: Warning: ignoring some quantifiers
% 3.72/1.59 Prover 0: Constructing countermodel ...
% 4.91/1.83 Prover 0: proved (1186ms)
% 4.91/1.83
% 4.91/1.83 No countermodel exists, formula is valid
% 4.91/1.83 % SZS status Theorem for theBenchmark
% 4.91/1.83
% 4.91/1.83 Generating proof ... Warning: ignoring some quantifiers
% 7.08/2.34 found it (size 19)
% 7.08/2.34
% 7.08/2.34 % SZS output start Proof for theBenchmark
% 7.08/2.34 Assumed formulas after preprocessing and simplification:
% 7.08/2.34 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v3, v4) = v6 & ordered_pair(v1, v2) = v5 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & empty(v8) & empty(empty_set) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v9, v10) = v11) | ~ (ordered_pair(v13, v14) = v12) | ~ in(v14, v10) | ~ in(v13, v9) | in(v12, v11)) & ! [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] : (v11 = v9 | ~ (ordered_pair(v11, v12) = v13) | ~ (ordered_pair(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v12) = v13) | ~ (singleton(v11) = v12) | ~ subset(v9, v10) | subset(v9, v13) | in(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v13) | ~ (set_difference(v9, v11) = v12) | ~ subset(v9, v10) | subset(v12, v13)) & ! [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(v10, v11) = v13) | ~ (set_intersection2(v9, v11) = v12) | ~ subset(v9, v10) | subset(v12, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v12 = v9 | ~ (unordered_pair(v9, v10) = v11) | ~ in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v9, v11) = v12) | ~ subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v9) = v11) | ~ (set_union2(v11, v10) = v12) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v9) = v12) | ~ (unordered_pair(v10, v11) = v12)) & ! [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 | ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ~ subset(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (singleton(v9) = v12) | ~ (unordered_pair(v10, v11) = v12)) & ! [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] : ( ~ (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, v11) | ~ in(v12, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ in(v12, v11) | in(v12, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ in(v12, v9) | in(v12, v11) | in(v12, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v9) = v10) | ~ in(v12, v9) | ~ in(v11, v12) | in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v9, v10) = v11) | ~ in(v12, v11) | ? [v13] : ? [v14] : (ordered_pair(v13, v14) = v12 & in(v14, v10) & in(v13, v9))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | ~ subset(v9, v11) | ~ subset(v9, v10) | subset(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ disjoint(v9, v10) | ~ in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ in(v12, v11) | in(v12, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ in(v12, v11) | in(v12, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ in(v12, v10) | ~ in(v12, v9) | in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v9, v11) = v12) | ~ subset(v11, v10) | ~ subset(v9, v10) | subset(v12, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v9, v10) = v11) | ~ in(v12, v11) | in(v12, v10) | in(v12, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v9, v10) = v11) | ~ in(v12, v10) | in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v9, v10) = v11) | ~ in(v12, v9) | in(v12, v11)) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_difference(v10, v11) = v12) | ? [v13] : (( ~ in(v13, v10) | ~ in(v13, v9) | in(v13, v11)) & (in(v13, v9) | (in(v13, v10) & ~ in(v13, v11))))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (cartesian_product2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (( ~ in(v13, v9) | ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v18) = v13) | ~ in(v18, v11) | ~ in(v17, v10))) & (in(v13, v9) | (v16 = v13 & ordered_pair(v14, v15) = v13 & in(v15, v11) & in(v14, v10))))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : (( ~ in(v13, v11) | ~ in(v13, v10) | ~ in(v13, v9)) & (in(v13, v9) | (in(v13, v11) & in(v13, v10))))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_union2(v10, v11) = v12) | ? [v13] : (( ~ in(v13, v9) | ( ~ in(v13, v11) & ~ in(v13, v10))) & (in(v13, v11) | in(v13, v10) | in(v13, v9)))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ((v13 = v11 | v13 = v10 | in(v13, v9)) & ( ~ in(v13, v9) | ( ~ (v13 = v11) & ~ (v13 = v10))))) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v9, v10) = v11) | ~ subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v9 = empty_set | ~ (singleton(v10) = v11) | ~ subset(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_difference(v9, v10) = v11) | ~ disjoint(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v9) = v10) | ~ in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_intersection2(v9, v10) = v11) | ~ subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(v9, v10) = v11) | ~ subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v9, v10) = v11) | ~ disjoint(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (union(v11) = v10) | ~ (union(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] : ( ~ (set_difference(v9, v10) = v11) | subset(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ? [v12] : (set_difference(v12, v10) = v11 & set_union2(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v10) = v11) | ~ in(v9, v10) | subset(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9) = v10) | ~ in(v11, v10) | ? [v12] : (in(v12, v9) & in(v11, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (singleton(v9) = v13 & unordered_pair(v12, v13) = v11 & unordered_pair(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ subset(v11, v9) | in(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ in(v11, v10) | subset(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v9) = v11) | ~ disjoint(v11, v10) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v9) = v11) | ~ subset(v11, v10) | in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v9) = v11) | ~ in(v9, v10) | subset(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | set_intersection2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | disjoint(v9, v10) | ? [v12] : in(v12, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | subset(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ? [v12] : (set_difference(v9, v12) = v11 & set_difference(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | ~ empty(v11) | empty(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | set_union2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ~ empty(v11) | empty(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | set_union2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | subset(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ? [v12] : (set_difference(v10, v9) = v12 & set_union2(v9, v12) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | in(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ disjoint(v10, v11) | ~ subset(v9, v10) | disjoint(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ disjoint(v9, v10) | ~ in(v11, v10) | ~ in(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ subset(v10, v11) | ~ subset(v9, v10) | subset(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ subset(v9, v10) | ~ in(v11, v9) | in(v11, v10)) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (union(v10) = v11) | ? [v12] : ? [v13] : (( ~ in(v12, v9) | ! [v14] : ( ~ in(v14, v10) | ~ in(v12, v14))) & (in(v12, v9) | (in(v13, v10) & in(v12, v13))))) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (powerset(v10) = v11) | ? [v12] : (( ~ subset(v12, v10) | ~ in(v12, v9)) & (subset(v12, v10) | in(v12, v9)))) & ? [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v10) = v11) | ? [v12] : (( ~ (v12 = v10) | ~ in(v10, v9)) & (v12 = v10 | in(v12, v9)))) & ? [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | disjoint(v11, v9) | in(v10, v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [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 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : (v10 = v9 | ~ subset(v10, v9) | ~ subset(v9, v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ subset(v9, v10) | proper_subset(v9, 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] : ( ~ (set_difference(v9, v10) = v9) | disjoint(v9, v10)) & ! [v9] : ! [v10] : ( ~ (set_difference(v9, v10) = empty_set) | subset(v9, v10)) & ! [v9] : ! [v10] : ( ~ (singleton(v10) = v9) | subset(v9, v9)) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | unordered_pair(v9, v9) = v10) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | subset(empty_set, v10)) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | in(v9, v10)) & ! [v9] : ! [v10] : ( ~ (set_intersection2(v9, v10) = empty_set) | disjoint(v9, v10)) & ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v9) = v10) | singleton(v9) = v10) & ! [v9] : ! [v10] : ( ~ empty(v10) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ disjoint(v9, v10) | disjoint(v10, v9)) & ! [v9] : ! [v10] : ( ~ subset(v9, v10) | ~ proper_subset(v10, v9)) & ! [v9] : ! [v10] : ( ~ proper_subset(v10, v9) | ~ proper_subset(v9, v10)) & ! [v9] : ! [v10] : ( ~ proper_subset(v9, v10) | subset(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : (v9 = empty_set | ~ empty(v9)) & ! [v9] : (v9 = empty_set | ~ subset(v9, empty_set)) & ! [v9] : ~ (singleton(v9) = empty_set) & ! [v9] : ~ proper_subset(v9, v9) & ! [v9] : ~ in(v9, empty_set) & ? [v9] : ? [v10] : (v10 = v9 | ? [v11] : (( ~ in(v11, v10) | ~ in(v11, v9)) & (in(v11, v10) | in(v11, v9)))) & ? [v9] : ? [v10] : (disjoint(v9, v10) | ? [v11] : (in(v11, v10) & in(v11, v9))) & ? [v9] : ? [v10] : (subset(v9, v10) | ? [v11] : (in(v11, v9) & ~ in(v11, v10))) & ? [v9] : (v9 = empty_set | ? [v10] : in(v10, v9)) & ? [v9] : subset(v9, v9) & ? [v9] : subset(empty_set, v9) & ((in(v5, v6) & ( ~ in(v2, v4) | ~ in(v1, v3))) | (in(v2, v4) & in(v1, v3) & ~ in(v5, v6))))
% 7.46/2.40 | 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:
% 7.46/2.40 | (1) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 & powerset(empty_set) = all_0_8_8 & singleton(empty_set) = all_0_8_8 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [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] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [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(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [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)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [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] : ( ~ (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, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [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] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [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 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, 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] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : subset(v0, v0) & ? [v0] : subset(empty_set, v0) & ((in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)))
% 7.46/2.42 |
% 7.46/2.42 | Applying alpha-rule on (1) yields:
% 7.46/2.42 | (2) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 7.46/2.42 | (3) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 7.46/2.42 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 7.46/2.42 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 7.46/2.42 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 7.46/2.42 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 7.46/2.42 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 7.46/2.42 | (9) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 7.46/2.42 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 7.46/2.43 | (11) singleton(empty_set) = all_0_8_8
% 7.46/2.43 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 7.46/2.43 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 7.46/2.43 | (14) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 7.46/2.43 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 7.46/2.43 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 7.46/2.43 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 7.46/2.43 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 7.46/2.43 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 7.46/2.43 | (20) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 7.46/2.43 | (21) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 7.46/2.43 | (22) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 7.46/2.43 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 7.46/2.43 | (24) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 7.46/2.43 | (25) empty(empty_set)
% 7.46/2.43 | (26) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2)))))
% 7.46/2.43 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 7.46/2.43 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 7.46/2.43 | (29) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 7.46/2.43 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 7.46/2.43 | (31) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 7.46/2.43 | (32) ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3
% 7.46/2.43 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 7.46/2.43 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 7.46/2.43 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 7.46/2.43 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 7.46/2.43 | (37) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 7.46/2.43 | (38) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 7.46/2.43 | (39) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 7.46/2.43 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 7.46/2.43 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 7.46/2.43 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 7.46/2.43 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 7.46/2.43 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 7.46/2.43 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 7.46/2.44 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 7.46/2.44 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 7.46/2.44 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 7.46/2.44 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 7.46/2.44 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 7.46/2.44 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 7.46/2.44 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 7.46/2.44 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 7.46/2.44 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 7.46/2.44 | (55) ~ empty(all_0_1_1)
% 7.46/2.44 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 7.46/2.44 | (57) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 7.46/2.44 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 7.46/2.44 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 7.46/2.44 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 7.46/2.44 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 7.46/2.44 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 7.46/2.44 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 7.46/2.44 | (64) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 7.46/2.44 | (65) ! [v0] : ~ in(v0, empty_set)
% 7.46/2.44 | (66) ! [v0] : ~ proper_subset(v0, v0)
% 7.46/2.44 | (67) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 7.46/2.44 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 7.46/2.44 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 7.46/2.44 | (70) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 7.46/2.44 | (71) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 7.46/2.44 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 7.46/2.44 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 7.46/2.44 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 7.46/2.44 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 7.46/2.44 | (76) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2
% 7.46/2.44 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 7.46/2.45 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 7.46/2.45 | (79) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 7.46/2.45 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 7.46/2.45 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 7.46/2.45 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 7.46/2.45 | (83) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1)))))
% 7.46/2.45 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 7.46/2.45 | (85) ! [v0] : ~ (singleton(v0) = empty_set)
% 7.46/2.45 | (86) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 7.46/2.45 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 7.46/2.45 | (88) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 7.46/2.45 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 7.46/2.45 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 7.46/2.45 | (91) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 7.46/2.45 | (92) ? [v0] : subset(empty_set, v0)
% 7.46/2.45 | (93) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4)))))
% 7.46/2.45 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 7.46/2.45 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 7.46/2.45 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 7.46/2.45 | (97) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 7.46/2.45 | (98) powerset(empty_set) = all_0_8_8
% 7.46/2.45 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 7.46/2.45 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 7.46/2.45 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 7.46/2.45 | (102) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 7.46/2.45 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 7.46/2.45 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 7.46/2.45 | (105) (in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2))
% 7.46/2.45 | (106) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 7.46/2.45 | (107) ? [v0] : subset(v0, v0)
% 7.46/2.45 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 7.46/2.45 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 7.46/2.45 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2))
% 7.46/2.45 | (111) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 7.46/2.45 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 7.46/2.45 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 7.46/2.45 | (114) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 7.46/2.45 | (115) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 7.46/2.45 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0)))
% 7.46/2.45 | (117) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 7.46/2.46 | (118) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 7.46/2.46 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 7.46/2.46 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 7.46/2.46 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 7.46/2.46 | (122) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 7.46/2.46 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 7.46/2.46 | (124) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 7.46/2.46 | (125) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.46/2.46 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 7.46/2.46 | (127) empty(all_0_0_0)
% 7.46/2.46 | (128) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 7.46/2.46 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 7.46/2.46 |
% 7.46/2.46 +-Applying beta-rule and splitting (105), into two cases.
% 7.46/2.46 |-Branch one:
% 7.46/2.46 | (130) in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))
% 7.46/2.46 |
% 7.46/2.46 | Applying alpha-rule on (130) yields:
% 7.46/2.46 | (131) in(all_0_3_3, all_0_2_2)
% 7.46/2.46 | (132) ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5)
% 7.46/2.46 |
% 7.46/2.46 | Instantiating formula (116) with all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, in(all_0_3_3, all_0_2_2), yields:
% 7.46/2.46 | (133) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_0_3_3 & in(v1, all_0_4_4) & in(v0, all_0_5_5))
% 7.46/2.46 |
% 7.46/2.46 | Instantiating (133) with all_71_0_29, all_71_1_30 yields:
% 7.46/2.46 | (134) ordered_pair(all_71_1_30, all_71_0_29) = all_0_3_3 & in(all_71_0_29, all_0_4_4) & in(all_71_1_30, all_0_5_5)
% 7.46/2.46 |
% 7.46/2.46 | Applying alpha-rule on (134) yields:
% 7.46/2.46 | (135) ordered_pair(all_71_1_30, all_71_0_29) = all_0_3_3
% 7.46/2.46 | (136) in(all_71_0_29, all_0_4_4)
% 7.46/2.46 | (137) in(all_71_1_30, all_0_5_5)
% 7.46/2.46 |
% 7.46/2.46 | Instantiating formula (8) with all_0_3_3, all_71_0_29, all_71_1_30, all_0_6_6, all_0_7_7 and discharging atoms ordered_pair(all_71_1_30, all_71_0_29) = all_0_3_3, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields:
% 7.46/2.46 | (138) all_71_0_29 = all_0_6_6
% 7.46/2.46 |
% 7.46/2.46 | Instantiating formula (81) with all_0_3_3, all_71_0_29, all_71_1_30, all_0_6_6, all_0_7_7 and discharging atoms ordered_pair(all_71_1_30, all_71_0_29) = all_0_3_3, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, yields:
% 7.46/2.46 | (139) all_71_1_30 = all_0_7_7
% 7.46/2.46 |
% 7.46/2.46 | From (138) and (136) follows:
% 7.46/2.46 | (140) in(all_0_6_6, all_0_4_4)
% 7.46/2.46 |
% 7.46/2.46 | From (139) and (137) follows:
% 7.46/2.46 | (141) in(all_0_7_7, all_0_5_5)
% 7.46/2.46 |
% 7.46/2.46 +-Applying beta-rule and splitting (132), into two cases.
% 7.46/2.46 |-Branch one:
% 7.46/2.46 | (142) ~ in(all_0_6_6, all_0_4_4)
% 7.46/2.46 |
% 7.46/2.46 | Using (140) and (142) yields:
% 7.46/2.46 | (143) $false
% 7.46/2.46 |
% 7.46/2.46 |-The branch is then unsatisfiable
% 7.46/2.46 |-Branch two:
% 7.46/2.46 | (140) in(all_0_6_6, all_0_4_4)
% 7.46/2.46 | (145) ~ in(all_0_7_7, all_0_5_5)
% 7.46/2.46 |
% 7.46/2.46 | Using (141) and (145) yields:
% 7.46/2.46 | (143) $false
% 7.46/2.46 |
% 7.46/2.46 |-The branch is then unsatisfiable
% 7.46/2.46 |-Branch two:
% 7.46/2.46 | (147) in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)
% 7.46/2.46 |
% 7.46/2.46 | Applying alpha-rule on (147) yields:
% 7.46/2.46 | (140) in(all_0_6_6, all_0_4_4)
% 7.46/2.46 | (141) in(all_0_7_7, all_0_5_5)
% 7.46/2.46 | (150) ~ in(all_0_3_3, all_0_2_2)
% 7.46/2.46 |
% 7.46/2.46 | Instantiating formula (110) with all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_6_6, all_0_4_4), in(all_0_7_7, all_0_5_5), ~ in(all_0_3_3, all_0_2_2), yields:
% 7.46/2.46 | (143) $false
% 7.46/2.46 |
% 7.46/2.46 |-The branch is then unsatisfiable
% 7.46/2.46 % SZS output end Proof for theBenchmark
% 7.46/2.46
% 7.46/2.46 1863ms
%------------------------------------------------------------------------------