TSTP Solution File: SEU154+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 08:47:03 EDT 2022
% Result : Theorem 7.30s 2.33s
% Output : Proof 9.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n015.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 : Mon Jun 20 03:39:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.64 ____ _
% 0.19/0.64 ___ / __ \_____(_)___ ________ __________
% 0.19/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.64
% 0.19/0.64 A Theorem Prover for First-Order Logic
% 0.19/0.64 (ePrincess v.1.0)
% 0.19/0.64
% 0.19/0.64 (c) Philipp Rümmer, 2009-2015
% 0.19/0.64 (c) Peter Backeman, 2014-2015
% 0.19/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.64 Bug reports to peter@backeman.se
% 0.19/0.64
% 0.19/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.64
% 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/1.05 Prover 0: Preprocessing ...
% 3.33/1.46 Prover 0: Warning: ignoring some quantifiers
% 3.33/1.48 Prover 0: Constructing countermodel ...
% 5.59/1.93 Prover 0: gave up
% 5.59/1.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.85/2.03 Prover 1: Preprocessing ...
% 6.92/2.27 Prover 1: Warning: ignoring some quantifiers
% 6.92/2.27 Prover 1: Constructing countermodel ...
% 7.30/2.33 Prover 1: proved (398ms)
% 7.30/2.33
% 7.30/2.33 No countermodel exists, formula is valid
% 7.30/2.33 % SZS status Theorem for theBenchmark
% 7.30/2.34
% 7.30/2.34 Generating proof ... Warning: ignoring some quantifiers
% 8.61/2.69 found it (size 24)
% 8.61/2.69
% 8.61/2.69 % SZS output start Proof for theBenchmark
% 8.61/2.69 Assumed formulas after preprocessing and simplification:
% 8.61/2.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & ~ (v3 = 0) & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & disjoint(v4, v2) = v5 & powerset(empty_set) = v0 & singleton(v1) = v4 & singleton(empty_set) = v0 & in(v1, v2) = v3 & ! [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] : (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 = v9 | v11 = v9 | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_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] : ( ~ (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 = 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 | ~ (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 | ~ (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 | ~ (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] : ( ~ (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 | ~ (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 | ~ (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] : ( ~ (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 | ~ (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 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [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] : ( ~ (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] : (v9 = empty_set | ? [v10] : in(v10, v9) = 0))
% 8.98/2.75 | 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:
% 8.98/2.75 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & ~ (all_0_5_5 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & disjoint(all_0_4_4, all_0_6_6) = all_0_3_3 & powerset(empty_set) = all_0_8_8 & singleton(all_0_7_7) = all_0_4_4 & singleton(empty_set) = all_0_8_8 & in(all_0_7_7, all_0_6_6) = all_0_5_5 & ! [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] : (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 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_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] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(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 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (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] : ( ~ (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 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 8.98/2.77 |
% 8.98/2.77 | Applying alpha-rule on (1) yields:
% 8.98/2.77 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 8.98/2.77 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 8.98/2.77 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 8.98/2.77 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 8.98/2.77 | (6) ! [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)))))
% 8.98/2.77 | (7) ~ (all_0_5_5 = 0)
% 8.98/2.77 | (8) powerset(empty_set) = all_0_8_8
% 8.98/2.77 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 8.98/2.77 | (10) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 8.98/2.77 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 8.98/2.77 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 8.98/2.77 | (13) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.98/2.77 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 8.98/2.77 | (15) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 8.98/2.77 | (16) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 8.98/2.77 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 8.98/2.77 | (18) singleton(all_0_7_7) = all_0_4_4
% 8.98/2.77 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 8.98/2.78 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.98/2.78 | (21) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 8.98/2.78 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 8.98/2.78 | (23) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 8.98/2.78 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 8.98/2.78 | (25) ? [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)))))
% 8.98/2.78 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 8.98/2.78 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 8.98/2.78 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 9.38/2.78 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 9.38/2.78 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.38/2.78 | (31) ? [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))))
% 9.38/2.78 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 9.38/2.78 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 9.38/2.78 | (34) ! [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)))))
% 9.38/2.78 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 9.38/2.78 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 9.38/2.78 | (37) ! [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))
% 9.38/2.78 | (38) ! [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))))
% 9.38/2.79 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 9.38/2.79 | (40) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 9.38/2.79 | (41) ~ (all_0_1_1 = 0)
% 9.38/2.79 | (42) ! [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)))
% 9.38/2.79 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 9.38/2.79 | (44) ! [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)))
% 9.38/2.79 | (45) empty(all_0_0_0) = 0
% 9.38/2.79 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 9.38/2.79 | (47) ! [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)))
% 9.38/2.79 | (48) ! [v0] : ~ (in(v0, empty_set) = 0)
% 9.38/2.79 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 9.38/2.79 | (50) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 9.38/2.79 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 9.38/2.79 | (52) ! [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))
% 9.38/2.79 | (53) ? [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)))
% 9.38/2.79 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 9.38/2.79 | (55) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 9.38/2.79 | (56) ~ (all_0_3_3 = 0)
% 9.38/2.79 | (57) ! [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))))
% 9.38/2.79 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 9.38/2.79 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 9.38/2.79 | (60) ? [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)))
% 9.38/2.79 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.45/2.79 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 9.45/2.80 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 9.45/2.80 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 9.45/2.80 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 9.45/2.80 | (66) ! [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)))
% 9.45/2.80 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.45/2.80 | (68) ? [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)))
% 9.45/2.80 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.45/2.80 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 9.45/2.80 | (71) singleton(empty_set) = all_0_8_8
% 9.45/2.80 | (72) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 9.45/2.80 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 9.45/2.80 | (74) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 9.45/2.80 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 9.45/2.80 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 9.45/2.80 | (77) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 9.45/2.80 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 9.45/2.80 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 9.45/2.80 | (80) empty(all_0_2_2) = all_0_1_1
% 9.45/2.80 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 9.45/2.80 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 9.45/2.80 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.45/2.80 | (84) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 9.45/2.80 | (85) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 9.45/2.80 | (86) ! [v0] : ~ (singleton(v0) = empty_set)
% 9.45/2.80 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 9.45/2.80 | (88) empty(empty_set) = 0
% 9.45/2.80 | (89) disjoint(all_0_4_4, all_0_6_6) = all_0_3_3
% 9.45/2.80 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 9.45/2.80 | (91) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 9.45/2.80 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 9.45/2.80 | (93) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 9.45/2.80 | (94) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 9.45/2.80 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 9.45/2.80 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 9.45/2.81 | (97) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 9.45/2.81 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 9.45/2.81 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 9.45/2.81 | (100) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 9.45/2.81 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 9.45/2.81 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 9.45/2.81 | (103) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 9.45/2.81 | (104) in(all_0_7_7, all_0_6_6) = all_0_5_5
% 9.45/2.81 | (105) ! [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))))
% 9.45/2.81 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 9.45/2.81 | (107) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 9.45/2.81 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 9.45/2.81 | (109) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 9.45/2.81 | (110) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 9.45/2.81 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 9.45/2.81 |
% 9.45/2.81 | Instantiating formula (79) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 9.45/2.81 | (112) all_0_3_3 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_6_6) = v0 & in(v1, v0) = 0)
% 9.45/2.81 |
% 9.45/2.81 | Instantiating formula (103) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 9.45/2.81 | (113) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_4_4, all_0_6_6) = v0)
% 9.45/2.81 |
% 9.45/2.81 | Instantiating formula (62) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms disjoint(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 9.45/2.81 | (114) all_0_3_3 = 0 | ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0)
% 9.45/2.81 |
% 9.45/2.81 +-Applying beta-rule and splitting (112), into two cases.
% 9.45/2.81 |-Branch one:
% 9.45/2.81 | (115) all_0_3_3 = 0
% 9.45/2.81 |
% 9.45/2.81 | Equations (115) can reduce 56 to:
% 9.45/2.81 | (116) $false
% 9.55/2.81 |
% 9.55/2.81 |-The branch is then unsatisfiable
% 9.55/2.81 |-Branch two:
% 9.55/2.81 | (56) ~ (all_0_3_3 = 0)
% 9.55/2.81 | (118) ? [v0] : ? [v1] : (set_intersection2(all_0_4_4, all_0_6_6) = v0 & in(v1, v0) = 0)
% 9.55/2.81 |
% 9.55/2.81 +-Applying beta-rule and splitting (113), into two cases.
% 9.55/2.81 |-Branch one:
% 9.55/2.81 | (115) all_0_3_3 = 0
% 9.55/2.81 |
% 9.55/2.81 | Equations (115) can reduce 56 to:
% 9.55/2.81 | (116) $false
% 9.55/2.81 |
% 9.55/2.81 |-The branch is then unsatisfiable
% 9.55/2.81 |-Branch two:
% 9.55/2.81 | (56) ~ (all_0_3_3 = 0)
% 9.55/2.81 | (122) ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_4_4, all_0_6_6) = v0)
% 9.55/2.81 |
% 9.55/2.81 +-Applying beta-rule and splitting (114), into two cases.
% 9.55/2.81 |-Branch one:
% 9.55/2.81 | (115) all_0_3_3 = 0
% 9.55/2.81 |
% 9.55/2.81 | Equations (115) can reduce 56 to:
% 9.55/2.82 | (116) $false
% 9.55/2.82 |
% 9.55/2.82 |-The branch is then unsatisfiable
% 9.55/2.82 |-Branch two:
% 9.55/2.82 | (56) ~ (all_0_3_3 = 0)
% 9.55/2.82 | (126) ? [v0] : (in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = 0)
% 9.55/2.82 |
% 9.55/2.82 | Instantiating (126) with all_50_0_21 yields:
% 9.55/2.82 | (127) in(all_50_0_21, all_0_4_4) = 0 & in(all_50_0_21, all_0_6_6) = 0
% 9.55/2.82 |
% 9.55/2.82 | Applying alpha-rule on (127) yields:
% 9.55/2.82 | (128) in(all_50_0_21, all_0_4_4) = 0
% 9.57/2.82 | (129) in(all_50_0_21, all_0_6_6) = 0
% 9.57/2.82 |
% 9.57/2.82 | Instantiating formula (97) with all_50_0_21, all_0_4_4, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_4_4, in(all_50_0_21, all_0_4_4) = 0, yields:
% 9.57/2.82 | (130) all_50_0_21 = all_0_7_7
% 9.57/2.82 |
% 9.57/2.82 | Instantiating formula (20) with all_0_7_7, all_0_6_6, 0, all_0_5_5 and discharging atoms in(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 9.57/2.82 | (131) all_0_5_5 = 0 | ~ (in(all_0_7_7, all_0_6_6) = 0)
% 9.57/2.82 |
% 9.57/2.82 | From (130) and (129) follows:
% 9.57/2.82 | (132) in(all_0_7_7, all_0_6_6) = 0
% 9.57/2.82 |
% 9.57/2.82 +-Applying beta-rule and splitting (131), into two cases.
% 9.57/2.82 |-Branch one:
% 9.57/2.82 | (133) ~ (in(all_0_7_7, all_0_6_6) = 0)
% 9.57/2.82 |
% 9.57/2.82 | Using (132) and (133) yields:
% 9.57/2.82 | (134) $false
% 9.57/2.82 |
% 9.57/2.82 |-The branch is then unsatisfiable
% 9.57/2.82 |-Branch two:
% 9.57/2.82 | (132) in(all_0_7_7, all_0_6_6) = 0
% 9.57/2.82 | (136) all_0_5_5 = 0
% 9.57/2.82 |
% 9.57/2.82 | Equations (136) can reduce 7 to:
% 9.57/2.82 | (116) $false
% 9.57/2.82 |
% 9.57/2.82 |-The branch is then unsatisfiable
% 9.57/2.82 % SZS output end Proof for theBenchmark
% 9.57/2.82
% 9.57/2.82 2171ms
%------------------------------------------------------------------------------