TSTP Solution File: SEU144+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 08:46:56 EDT 2022
% Result : Theorem 8.37s 2.92s
% Output : Proof 10.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jun 19 16:50:29 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.59/0.62 ____ _
% 0.59/0.62 ___ / __ \_____(_)___ ________ __________
% 0.59/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.62
% 0.59/0.62 A Theorem Prover for First-Order Logic
% 0.59/0.62 (ePrincess v.1.0)
% 0.59/0.62
% 0.59/0.62 (c) Philipp Rümmer, 2009-2015
% 0.59/0.62 (c) Peter Backeman, 2014-2015
% 0.59/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.62 Bug reports to peter@backeman.se
% 0.59/0.62
% 0.59/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.62
% 0.59/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.48/1.02 Prover 0: Preprocessing ...
% 3.07/1.50 Prover 0: Warning: ignoring some quantifiers
% 3.22/1.55 Prover 0: Constructing countermodel ...
% 4.67/2.05 Prover 0: gave up
% 4.67/2.06 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.25/2.14 Prover 1: Preprocessing ...
% 5.92/2.36 Prover 1: Warning: ignoring some quantifiers
% 5.92/2.38 Prover 1: Constructing countermodel ...
% 6.80/2.56 Prover 1: gave up
% 6.80/2.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.12/2.60 Prover 2: Preprocessing ...
% 7.71/2.77 Prover 2: Warning: ignoring some quantifiers
% 7.71/2.78 Prover 2: Constructing countermodel ...
% 8.37/2.92 Prover 2: proved (356ms)
% 8.37/2.92
% 8.37/2.92 No countermodel exists, formula is valid
% 8.37/2.92 % SZS status Theorem for theBenchmark
% 8.37/2.92
% 8.37/2.92 Generating proof ... Warning: ignoring some quantifiers
% 9.57/3.26 found it (size 31)
% 9.57/3.26
% 9.57/3.26 % SZS output start Proof for theBenchmark
% 9.57/3.26 Assumed formulas after preprocessing and simplification:
% 9.57/3.26 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & singleton(v0) = v2 & subset(v2, v1) = v3 & in(v0, v1) = v4 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v12) | ~ (set_difference(v8, v10) = v11) | ~ (subset(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ~ (set_intersection2(v9, v10) = v12) | ~ (set_intersection2(v8, v10) = v11) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : ((v13 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v9) = v12) | ~ (set_union2(v8, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & subset(v10, v9) = v13) | ( ~ (v13 = 0) & subset(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v8, v11) = v12) | ~ (set_intersection2(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & subset(v8, v10) = v13) | ( ~ (v13 = 0) & subset(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : (( ~ (v13 = 0) & in(v11, v9) = v13) | ( ~ (v13 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & in(v11, v9) = v14 & in(v11, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & ~ (v12 = 0) & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v12 = 0 & ~ (v13 = 0) & in(v11, v9) = v13) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v11 = v8 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v11, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = 0) | ~ (disjoint(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & disjoint(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = 0) | ~ (subset(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v9) = 0) | ~ (in(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (proper_subset(v11, v10) = v9) | ~ (proper_subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v12 = 0 & in(v11, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & disjoint(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v9) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | ( ~ (v12 = 0) & in(v11, v8) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | ( ~ (v12 = 0) & in(v11, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ((v12 = 0 & in(v11, v9) = 0) | (v12 = 0 & in(v11, v8) = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)) & ((v14 = 0 & ~ (v15 = 0) & in(v12, v10) = v15 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & v14 = 0 & in(v12, v10) = 0 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v15 = 0) & in(v12, v10) = v15) | ( ~ (v14 = 0) & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & in(v12, v10) = 0) | (v14 = 0 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v15 = 0) & ~ (v14 = 0) & in(v12, v10) = v15 & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : ((v12 = v10 | v12 = v9 | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v13 = 0) & in(v12, v8) = v13) | ( ~ (v12 = v10) & ~ (v12 = v9))))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ (in(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (proper_subset(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ? [v12] : (set_intersection2(v8, v9) = v11 & in(v12, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = v8) & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = empty_set) & set_intersection2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ( ~ (v11 = empty_set) & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & proper_subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | ~ (subset(v8, v9) = 0) | disjoint(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ? [v11] : (set_union2(v8, v10) = v11 & set_union2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ? [v11] : ((v11 = v9 & set_union2(v8, v10) = v9) | ( ~ (v11 = 0) & subset(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | subset(v10, v8) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | ? [v11] : (set_difference(v11, v9) = v10 & set_union2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | ? [v11] : (set_difference(v8, v10) = v11 & set_intersection2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | ~ (subset(v8, v9) = 0) | subset(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v9, v8) = v10) | set_intersection2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | subset(v10, v8) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v11 = 0 & disjoint(v8, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ? [v11] : (set_difference(v8, v11) = v10 & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | subset(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : (set_difference(v10, v9) = v11 & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : (set_difference(v9, v8) = v11 & set_union2(v8, v11) = v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : ? [v12] : (( ~ (v11 = v9) | ( ~ (v12 = 0) & in(v9, v8) = v12)) & (v11 = v9 | (v12 = 0 & in(v11, v8) = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_difference(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v8, v9) = 0) | proper_subset(v8, v9) = 0) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v9, v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(empty_set, v8) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(empty_set, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_difference(v8, v9) = v8) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_intersection2(v8, v9) = empty_set) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | ? [v10] : (set_intersection2(v8, v9) = v10 & ! [v11] : ~ (in(v11, v10) = 0))) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = v8) | disjoint(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = empty_set) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | unordered_pair(v8, v8) = v9) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | set_difference(v8, v9) = empty_set) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | set_intersection2(v8, v9) = v8) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | set_union2(v8, v9) = v9) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v9, v8) = v10)) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ? [v10] : (set_difference(v9, v8) = v10 & set_union2(v8, v10) = v9)) & ! [v8] : ! [v9] : ( ~ (subset(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v8, v8) = v10)) & ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v9) = empty_set) | disjoint(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ! [v9] : ( ~ (proper_subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (proper_subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v9, v8) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v8] : (v8 = empty_set | ~ (empty(v8) = 0)) & ! [v8] : (v8 = empty_set | ~ (subset(v8, empty_set) = 0)) & ! [v8] : ~ (singleton(v8) = empty_set) & ! [v8] : ~ (proper_subset(v8, v8) = 0) & ! [v8] : ~ (in(v8, empty_set) = 0) & ? [v8] : ? [v9] : ? [v10] : disjoint(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_difference(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : subset(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_intersection2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_union2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : unordered_pair(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : proper_subset(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : in(v9, v8) = v10 & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : ? [v11] : ? [v12] : (((v12 = 0 & in(v10, v9) = 0) | (v11 = 0 & in(v10, v8) = 0)) & (( ~ (v12 = 0) & in(v10, v9) = v12) | ( ~ (v11 = 0) & in(v10, v8) = v11)))) & ? [v8] : ? [v9] : empty(v8) = v9 & ? [v8] : ? [v9] : singleton(v8) = v9 & ? [v8] : (v8 = empty_set | ? [v9] : in(v9, v8) = 0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 10.25/3.38 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 10.25/3.38 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & singleton(all_0_7_7) = all_0_5_5 & subset(all_0_5_5, all_0_6_6) = all_0_4_4 & in(all_0_7_7, all_0_6_6) = all_0_3_3 & ! [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 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v0, v2) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [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, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [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] : (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 | ~ (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(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (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 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [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 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(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(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(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(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] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ((v3 = v1 & set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) & ! [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) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [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] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0)))) & ! [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(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(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(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_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(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = 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] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3)))) & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) & ((all_0_3_3 = 0 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = 0)))
% 10.25/3.41 |
% 10.25/3.41 | Applying alpha-rule on (1) yields:
% 10.25/3.41 | (2) empty(all_0_0_0) = 0
% 10.25/3.41 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.38/3.41 | (4) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 10.38/3.41 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.38/3.41 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 10.38/3.41 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 10.38/3.41 | (8) ? [v0] : ? [v1] : singleton(v0) = v1
% 10.38/3.41 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3))
% 10.38/3.41 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 10.38/3.41 | (11) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 10.38/3.41 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 10.38/3.41 | (13) ! [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))
% 10.38/3.41 | (14) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3))))
% 10.38/3.41 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 10.38/3.41 | (16) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1)
% 10.38/3.41 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.38/3.41 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 10.38/3.41 | (19) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 10.38/3.41 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3))
% 10.38/3.41 | (21) ~ (all_0_1_1 = 0)
% 10.38/3.41 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 10.38/3.41 | (23) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 10.38/3.41 | (24) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 10.38/3.41 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.38/3.41 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 10.38/3.41 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ((v3 = v1 & set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 10.38/3.41 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 10.38/3.41 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 10.38/3.41 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 10.38/3.41 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 10.38/3.41 | (32) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 10.38/3.41 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 10.38/3.41 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3))
% 10.38/3.41 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 10.38/3.41 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 10.38/3.41 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 10.38/3.41 | (38) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 10.38/3.41 | (39) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 10.38/3.41 | (40) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 10.38/3.41 | (41) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 10.38/3.41 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 10.38/3.41 | (43) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 10.38/3.42 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 10.38/3.42 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 10.38/3.42 | (46) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0))))
% 10.38/3.42 | (47) ? [v0] : ? [v1] : empty(v0) = v1
% 10.38/3.42 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4)))
% 10.38/3.42 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 10.38/3.42 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.38/3.42 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 10.38/3.42 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 10.38/3.42 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 10.38/3.42 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.38/3.42 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 10.38/3.42 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.38/3.42 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 10.38/3.42 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 10.38/3.42 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.38/3.42 | (60) ! [v0] : ~ (in(v0, empty_set) = 0)
% 10.38/3.42 | (61) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set)
% 10.38/3.42 | (62) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 10.38/3.42 | (63) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = v2 | v4 = v1 | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 10.38/3.42 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.38/3.42 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 10.38/3.42 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.38/3.42 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 10.38/3.42 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 10.38/3.42 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4)))
% 10.38/3.42 | (70) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0)
% 10.38/3.42 | (71) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 10.38/3.42 | (72) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 10.38/3.42 | (73) (all_0_3_3 = 0 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = 0))
% 10.38/3.42 | (74) ! [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))
% 10.38/3.42 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 10.38/3.42 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 10.38/3.42 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 10.38/3.42 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4))
% 10.38/3.42 | (79) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0)
% 10.38/3.42 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3))
% 10.38/3.43 | (81) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 10.38/3.43 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 10.38/3.43 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 10.38/3.43 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 10.38/3.43 | (85) ! [v0] : ~ (singleton(v0) = empty_set)
% 10.38/3.43 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 10.38/3.43 | (87) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 10.38/3.43 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0)
% 10.38/3.43 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 10.38/3.43 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.38/3.43 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 10.38/3.43 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 10.38/3.43 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 10.38/3.43 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 10.38/3.43 | (95) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 10.38/3.43 | (96) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = v1) | ( ~ (v4 = 0) & in(v1, v0) = v4)) & (v3 = v1 | (v4 = 0 & in(v3, v0) = 0))))
% 10.38/3.43 | (97) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2))
% 10.38/3.43 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.38/3.43 | (99) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1))
% 10.38/3.43 | (100) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2
% 10.38/3.43 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v0, v2) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5)))
% 10.38/3.43 | (102) ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2
% 10.38/3.43 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5)))
% 10.38/3.43 | (104) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 10.38/3.43 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 10.38/3.43 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.38/3.43 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 10.38/3.43 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 10.38/3.43 | (109) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 10.38/3.43 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 10.38/3.43 | (111) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 10.38/3.43 | (112) empty(empty_set) = 0
% 10.38/3.43 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 10.38/3.43 | (114) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 10.38/3.43 | (115) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 10.38/3.43 | (116) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 10.38/3.43 | (117) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 10.38/3.43 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 10.49/3.43 | (119) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 10.49/3.43 | (120) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0)
% 10.49/3.43 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0)))
% 10.49/3.43 | (122) singleton(all_0_7_7) = all_0_5_5
% 10.49/3.43 | (123) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 10.49/3.43 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 10.49/3.43 | (125) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 10.49/3.43 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0)
% 10.49/3.43 | (127) subset(all_0_5_5, all_0_6_6) = all_0_4_4
% 10.49/3.43 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5)))
% 10.49/3.44 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3))
% 10.49/3.44 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0)
% 10.49/3.44 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 10.49/3.44 | (132) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 10.49/3.44 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 10.49/3.44 | (134) empty(all_0_2_2) = all_0_1_1
% 10.49/3.44 | (135) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 10.49/3.44 | (136) ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2))
% 10.49/3.44 | (137) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 10.49/3.44 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 10.50/3.44 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 10.50/3.44 | (140) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 10.50/3.44 | (141) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 10.50/3.44 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 10.50/3.44 | (143) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 10.50/3.44 | (144) in(all_0_7_7, all_0_6_6) = all_0_3_3
% 10.50/3.44 | (145) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 10.50/3.44 | (146) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 10.50/3.44 |
% 10.50/3.44 | Instantiating formula (67) with all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = all_0_4_4, yields:
% 10.50/3.44 | (147) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = v1)
% 10.50/3.44 |
% 10.50/3.44 | Instantiating formula (9) with all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = all_0_4_4, yields:
% 10.50/3.44 | (148) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_5_5, all_0_6_6) = v0)
% 10.50/3.44 |
% 10.50/3.44 +-Applying beta-rule and splitting (73), into two cases.
% 10.50/3.44 |-Branch one:
% 10.50/3.44 | (149) all_0_3_3 = 0 & ~ (all_0_4_4 = 0)
% 10.50/3.44 |
% 10.50/3.44 | Applying alpha-rule on (149) yields:
% 10.50/3.44 | (150) all_0_3_3 = 0
% 10.50/3.44 | (151) ~ (all_0_4_4 = 0)
% 10.50/3.44 |
% 10.50/3.44 | From (150) and (144) follows:
% 10.50/3.44 | (152) in(all_0_7_7, all_0_6_6) = 0
% 10.50/3.44 |
% 10.50/3.44 +-Applying beta-rule and splitting (148), into two cases.
% 10.50/3.44 |-Branch one:
% 10.50/3.44 | (153) all_0_4_4 = 0
% 10.50/3.44 |
% 10.50/3.44 | Equations (153) can reduce 151 to:
% 10.50/3.44 | (154) $false
% 10.50/3.44 |
% 10.50/3.44 |-The branch is then unsatisfiable
% 10.50/3.44 |-Branch two:
% 10.50/3.44 | (151) ~ (all_0_4_4 = 0)
% 10.50/3.44 | (156) ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_5_5, all_0_6_6) = v0)
% 10.50/3.44 |
% 10.50/3.44 +-Applying beta-rule and splitting (147), into two cases.
% 10.50/3.44 |-Branch one:
% 10.50/3.44 | (153) all_0_4_4 = 0
% 10.50/3.44 |
% 10.50/3.44 | Equations (153) can reduce 151 to:
% 10.50/3.44 | (154) $false
% 10.50/3.44 |
% 10.50/3.44 |-The branch is then unsatisfiable
% 10.50/3.44 |-Branch two:
% 10.50/3.44 | (151) ~ (all_0_4_4 = 0)
% 10.50/3.44 | (160) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = v1)
% 10.50/3.44 |
% 10.50/3.44 | Instantiating (160) with all_68_0_45, all_68_1_46 yields:
% 10.50/3.44 | (161) ~ (all_68_0_45 = 0) & in(all_68_1_46, all_0_5_5) = 0 & in(all_68_1_46, all_0_6_6) = all_68_0_45
% 10.50/3.44 |
% 10.50/3.44 | Applying alpha-rule on (161) yields:
% 10.50/3.44 | (162) ~ (all_68_0_45 = 0)
% 10.50/3.44 | (163) in(all_68_1_46, all_0_5_5) = 0
% 10.50/3.44 | (164) in(all_68_1_46, all_0_6_6) = all_68_0_45
% 10.50/3.44 |
% 10.50/3.44 | Instantiating formula (138) with all_68_1_46, all_0_5_5, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, in(all_68_1_46, all_0_5_5) = 0, yields:
% 10.50/3.45 | (165) all_68_1_46 = all_0_7_7
% 10.50/3.45 |
% 10.50/3.45 | From (165) and (164) follows:
% 10.50/3.45 | (166) in(all_0_7_7, all_0_6_6) = all_68_0_45
% 10.50/3.45 |
% 10.50/3.45 | Instantiating formula (3) with all_0_7_7, all_0_6_6, all_68_0_45, 0 and discharging atoms in(all_0_7_7, all_0_6_6) = all_68_0_45, in(all_0_7_7, all_0_6_6) = 0, yields:
% 10.50/3.45 | (167) all_68_0_45 = 0
% 10.50/3.45 |
% 10.50/3.45 | Equations (167) can reduce 162 to:
% 10.50/3.45 | (154) $false
% 10.50/3.45 |
% 10.50/3.45 |-The branch is then unsatisfiable
% 10.50/3.45 |-Branch two:
% 10.50/3.45 | (169) all_0_4_4 = 0 & ~ (all_0_3_3 = 0)
% 10.50/3.45 |
% 10.50/3.45 | Applying alpha-rule on (169) yields:
% 10.50/3.45 | (153) all_0_4_4 = 0
% 10.50/3.45 | (171) ~ (all_0_3_3 = 0)
% 10.50/3.45 |
% 10.50/3.45 | From (153) and (127) follows:
% 10.50/3.45 | (172) subset(all_0_5_5, all_0_6_6) = 0
% 10.50/3.45 |
% 10.50/3.45 | Instantiating formula (139) with all_0_3_3, all_0_7_7, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = 0, in(all_0_7_7, all_0_6_6) = all_0_3_3, yields:
% 10.50/3.45 | (173) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_7_7, all_0_5_5) = v0)
% 10.50/3.45 |
% 10.50/3.45 +-Applying beta-rule and splitting (173), into two cases.
% 10.50/3.45 |-Branch one:
% 10.50/3.45 | (150) all_0_3_3 = 0
% 10.50/3.45 |
% 10.50/3.45 | Equations (150) can reduce 171 to:
% 10.50/3.45 | (154) $false
% 10.50/3.45 |
% 10.50/3.45 |-The branch is then unsatisfiable
% 10.50/3.45 |-Branch two:
% 10.50/3.45 | (171) ~ (all_0_3_3 = 0)
% 10.50/3.45 | (177) ? [v0] : ( ~ (v0 = 0) & in(all_0_7_7, all_0_5_5) = v0)
% 10.50/3.45 |
% 10.50/3.45 | Instantiating (177) with all_73_0_50 yields:
% 10.50/3.45 | (178) ~ (all_73_0_50 = 0) & in(all_0_7_7, all_0_5_5) = all_73_0_50
% 10.50/3.45 |
% 10.50/3.45 | Applying alpha-rule on (178) yields:
% 10.50/3.45 | (179) ~ (all_73_0_50 = 0)
% 10.50/3.45 | (180) in(all_0_7_7, all_0_5_5) = all_73_0_50
% 10.50/3.45 |
% 10.50/3.45 | Instantiating formula (12) with all_73_0_50, all_0_5_5, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, in(all_0_7_7, all_0_5_5) = all_73_0_50, yields:
% 10.50/3.45 | (181) all_73_0_50 = 0
% 10.50/3.45 |
% 10.50/3.45 | Equations (181) can reduce 179 to:
% 10.50/3.45 | (154) $false
% 10.50/3.45 |
% 10.50/3.45 |-The branch is then unsatisfiable
% 10.50/3.45 % SZS output end Proof for theBenchmark
% 10.50/3.45
% 10.50/3.45 2818ms
%------------------------------------------------------------------------------