TSTP Solution File: SEU149+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU149+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 08:47:00 EDT 2022
% Result : Theorem 3.84s 1.56s
% Output : Proof 6.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU149+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n025.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 07:24:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.59 ____ _
% 0.49/0.59 ___ / __ \_____(_)___ ________ __________
% 0.49/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.60
% 0.49/0.60 A Theorem Prover for First-Order Logic
% 0.49/0.60 (ePrincess v.1.0)
% 0.49/0.60
% 0.49/0.60 (c) Philipp Rümmer, 2009-2015
% 0.49/0.60 (c) Peter Backeman, 2014-2015
% 0.49/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.60 Bug reports to peter@backeman.se
% 0.49/0.60
% 0.49/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.60
% 0.49/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/1.00 Prover 0: Preprocessing ...
% 3.18/1.39 Prover 0: Warning: ignoring some quantifiers
% 3.18/1.42 Prover 0: Constructing countermodel ...
% 3.84/1.56 Prover 0: proved (915ms)
% 3.84/1.56
% 3.84/1.56 No countermodel exists, formula is valid
% 3.84/1.56 % SZS status Theorem for theBenchmark
% 3.84/1.56
% 3.84/1.56 Generating proof ... Warning: ignoring some quantifiers
% 5.25/1.93 found it (size 6)
% 5.25/1.93
% 5.25/1.93 % SZS output start Proof for theBenchmark
% 5.25/1.93 Assumed formulas after preprocessing and simplification:
% 5.25/1.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v2 = v1) & powerset(empty_set) = v0 & singleton(v1) = v4 & singleton(empty_set) = v0 & unordered_pair(v2, v3) = v4 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v10) = v11) | ~ (singleton(v9) = v10) | ~ subset(v7, v8) | subset(v7, v11) | in(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v11) | ~ (set_difference(v7, v9) = v10) | ~ subset(v7, v8) | subset(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v11) | ~ (set_intersection2(v7, v9) = v10) | ~ subset(v7, v8) | subset(v10, v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v8) = v10) | ~ (singleton(v7) = v9) | ~ subset(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_intersection2(v10, v9) = v8) | ~ (set_intersection2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v7) = v9) | ~ (set_union2(v7, v9) = v10) | set_union2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v9) = v10) | ~ (set_difference(v7, v8) = v9) | set_intersection2(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ~ subset(v7, v9) | ~ subset(v7, v8) | subset(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ disjoint(v7, v8) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ in(v10, v8) | ~ in(v10, v7) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v9) = v10) | ~ subset(v9, v8) | ~ subset(v7, v8) | subset(v10, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v8) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v8) | ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) & ~ in(v11, v9))))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v9) | ~ in(v11, v8) | ~ in(v11, v7)) & (in(v11, v7) | (in(v11, v9) & in(v11, v8))))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v7) | ( ~ in(v11, v9) & ~ in(v11, v8))) & (in(v11, v9) | in(v11, v8) | in(v11, v7)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v7 = empty_set | ~ (singleton(v8) = v9) | ~ subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_difference(v7, v8) = v9) | ~ disjoint(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_intersection2(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v7, v8) = v9) | ~ disjoint(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ subset(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ in(v9, v8) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ subset(v9, v8) | in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ in(v7, v8) | subset(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v7) = v9) | set_intersection2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | disjoint(v7, v8) | ? [v10] : in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | subset(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | ? [v10] : (set_difference(v7, v10) = v9 & set_difference(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : (set_difference(v8, v7) = v10 & set_union2(v7, v10) = v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ disjoint(v8, v9) | ~ subset(v7, v8) | disjoint(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ disjoint(v7, v8) | ~ in(v9, v8) | ~ in(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v8, v9) | ~ subset(v7, v8) | subset(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (powerset(v8) = v9) | ? [v10] : (( ~ subset(v10, v8) | ~ in(v10, v7)) & (subset(v10, v8) | in(v10, v7)))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : (( ~ (v10 = v8) | ~ in(v8, v7)) & (v10 = v8 | in(v10, v7)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subset(v8, v7) | ~ subset(v7, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subset(v7, v8) | proper_subset(v7, v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = v7) | disjoint(v7, v8)) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ (singleton(v8) = v7) | subset(v7, v7)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | subset(empty_set, v8)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ (set_intersection2(v7, v8) = empty_set) | disjoint(v7, v8)) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ disjoint(v7, v8) | disjoint(v8, v7)) & ! [v7] : ! [v8] : ( ~ subset(v7, v8) | ~ proper_subset(v8, v7)) & ! [v7] : ! [v8] : ( ~ proper_subset(v8, v7) | ~ proper_subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ proper_subset(v7, v8) | subset(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : (v7 = empty_set | ~ subset(v7, empty_set)) & ! [v7] : ~ (singleton(v7) = empty_set) & ! [v7] : ~ proper_subset(v7, v7) & ! [v7] : ~ in(v7, empty_set) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : (( ~ in(v9, v8) | ~ in(v9, v7)) & (in(v9, v8) | in(v9, v7)))) & ? [v7] : ? [v8] : (disjoint(v7, v8) | ? [v9] : (in(v9, v8) & in(v9, v7))) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7)) & ? [v7] : subset(v7, v7) & ? [v7] : subset(empty_set, v7))
% 5.87/1.99 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 5.87/1.99 | (1) ~ (all_0_4_4 = all_0_5_5) & powerset(empty_set) = all_0_6_6 & singleton(all_0_5_5) = all_0_2_2 & singleton(empty_set) = all_0_6_6 & unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [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] : ( ~ (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] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(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] : ( ~ (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 | ~ (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 | ~ (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] : ( ~ (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) | ~ 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 | ~ (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] : (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)
% 5.87/2.02 |
% 5.87/2.02 | Applying alpha-rule on (1) yields:
% 5.87/2.02 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 5.87/2.02 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 5.87/2.02 | (4) singleton(all_0_5_5) = all_0_2_2
% 5.87/2.02 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 5.87/2.02 | (6) ! [v0] : ~ in(v0, empty_set)
% 5.87/2.02 | (7) ? [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))))
% 5.87/2.02 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 5.87/2.02 | (9) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 5.87/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 5.87/2.02 | (11) powerset(empty_set) = all_0_6_6
% 5.87/2.02 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 5.87/2.02 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 5.87/2.02 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 5.87/2.02 | (15) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 5.87/2.02 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.87/2.02 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 5.87/2.02 | (18) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 5.87/2.02 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 5.87/2.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 5.87/2.02 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 5.87/2.02 | (22) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 5.87/2.02 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 5.87/2.02 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 5.87/2.02 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 5.87/2.02 | (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)))))
% 5.87/2.02 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 5.87/2.02 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 5.87/2.02 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 5.87/2.03 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 5.87/2.03 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 5.87/2.03 | (32) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 5.87/2.03 | (33) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 5.87/2.03 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 5.87/2.03 | (35) ? [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)))))
% 5.87/2.03 | (36) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 5.87/2.03 | (37) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 5.87/2.03 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 5.87/2.03 | (39) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 5.87/2.03 | (40) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 5.87/2.03 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 5.87/2.03 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 5.87/2.03 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 5.87/2.03 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 5.87/2.03 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 5.87/2.03 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 5.87/2.03 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 5.87/2.03 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 5.87/2.03 | (49) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 5.87/2.03 | (50) ? [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)))))
% 5.87/2.03 | (51) ! [v0] : ~ proper_subset(v0, v0)
% 5.87/2.03 | (52) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 5.87/2.03 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 5.87/2.03 | (54) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 5.87/2.03 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 5.87/2.03 | (56) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 5.87/2.03 | (57) ~ (all_0_4_4 = all_0_5_5)
% 5.87/2.03 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 5.87/2.03 | (59) ? [v0] : subset(empty_set, v0)
% 5.87/2.03 | (60) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 5.87/2.03 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 5.87/2.03 | (62) unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2
% 5.87/2.03 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 5.87/2.03 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 5.87/2.03 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 5.87/2.03 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 5.87/2.03 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 5.87/2.03 | (68) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 5.87/2.03 | (69) ~ empty(all_0_1_1)
% 5.87/2.03 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 5.87/2.03 | (71) empty(empty_set)
% 5.87/2.03 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 5.87/2.04 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 5.87/2.04 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 5.87/2.04 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 5.87/2.04 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 5.87/2.04 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 5.87/2.04 | (78) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 5.87/2.04 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 5.87/2.04 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 5.87/2.04 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 5.87/2.04 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 5.87/2.04 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 5.87/2.04 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 5.87/2.04 | (85) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 5.87/2.04 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 5.87/2.04 | (87) ! [v0] : ~ (singleton(v0) = empty_set)
% 5.87/2.04 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.87/2.04 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 5.87/2.04 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 5.87/2.04 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 5.87/2.04 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 5.87/2.04 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 5.87/2.04 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 5.87/2.04 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 5.87/2.04 | (96) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 5.87/2.04 | (97) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 5.87/2.04 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.87/2.04 | (99) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 5.87/2.04 | (100) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 5.87/2.04 | (101) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 5.87/2.04 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 5.87/2.04 | (103) ? [v0] : subset(v0, v0)
% 5.87/2.04 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 5.87/2.04 | (105) singleton(empty_set) = all_0_6_6
% 5.87/2.04 | (106) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 5.87/2.04 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 5.87/2.04 | (108) empty(all_0_0_0)
% 5.87/2.04 |
% 5.87/2.04 | Instantiating formula (84) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 5.87/2.04 | (109) in(all_0_4_4, all_0_2_2)
% 5.87/2.04 |
% 5.87/2.04 | Instantiating formula (21) with all_0_4_4, all_0_2_2, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, in(all_0_4_4, all_0_2_2), yields:
% 5.87/2.04 | (110) all_0_4_4 = all_0_5_5
% 5.87/2.04 |
% 6.15/2.05 | Equations (110) can reduce 57 to:
% 6.15/2.05 | (111) $false
% 6.15/2.05 |
% 6.15/2.05 |-The branch is then unsatisfiable
% 6.15/2.05 % SZS output end Proof for theBenchmark
% 6.15/2.05
% 6.15/2.05 1440ms
%------------------------------------------------------------------------------