TSTP Solution File: SEU141+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:46:55 EDT 2022
% Result : Theorem 26.37s 7.47s
% Output : Proof 34.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jun 19 01:51:38 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.50/0.63 ____ _
% 0.50/0.63 ___ / __ \_____(_)___ ________ __________
% 0.50/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.63
% 0.50/0.63 A Theorem Prover for First-Order Logic
% 0.50/0.63 (ePrincess v.1.0)
% 0.50/0.63
% 0.50/0.63 (c) Philipp Rümmer, 2009-2015
% 0.50/0.63 (c) Peter Backeman, 2014-2015
% 0.50/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.63 Bug reports to peter@backeman.se
% 0.50/0.63
% 0.50/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.63
% 0.50/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/1.04 Prover 0: Preprocessing ...
% 2.97/1.37 Prover 0: Warning: ignoring some quantifiers
% 2.97/1.40 Prover 0: Constructing countermodel ...
% 19.72/5.97 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.95/6.04 Prover 1: Preprocessing ...
% 20.65/6.22 Prover 1: Warning: ignoring some quantifiers
% 20.65/6.23 Prover 1: Constructing countermodel ...
% 22.04/6.51 Prover 1: gave up
% 22.04/6.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.04/6.53 Prover 2: Preprocessing ...
% 22.73/6.64 Prover 2: Warning: ignoring some quantifiers
% 22.73/6.65 Prover 2: Constructing countermodel ...
% 26.37/7.46 Prover 2: proved (958ms)
% 26.37/7.47 Prover 0: stopped
% 26.37/7.47
% 26.37/7.47 No countermodel exists, formula is valid
% 26.37/7.47 % SZS status Theorem for theBenchmark
% 26.37/7.47
% 26.37/7.47 Generating proof ... Warning: ignoring some quantifiers
% 34.05/9.30 found it (size 208)
% 34.05/9.30
% 34.05/9.30 % SZS output start Proof for theBenchmark
% 34.05/9.30 Assumed formulas after preprocessing and simplification:
% 34.05/9.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & disjoint(v0, v1) = v2 & set_difference(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v8, v9) = v11) | ~ (set_difference(v7, v9) = v10) | ~ (subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ~ (set_intersection2(v8, v9) = v11) | ~ (set_intersection2(v7, v9) = v10) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v9) = v11) | ? [v12] : ((v12 = 0 & in(v10, v8) = 0) | ( ~ (v12 = 0) & in(v10, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & in(v10, v9) = 0) | ( ~ (v12 = 0) & in(v10, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_union2(v7, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & subset(v9, v8) = v12) | ( ~ (v12 = 0) & subset(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v7, v10) = v11) | ~ (set_intersection2(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & subset(v7, v9) = v12) | ( ~ (v12 = 0) & subset(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = v11) | ? [v12] : (( ~ (v12 = 0) & in(v10, v8) = v12) | ( ~ (v12 = 0) & in(v10, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v9) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & in(v10, v8) = v13 & in(v10, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & in(v10, v7) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ((v12 = 0 & in(v10, v8) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & ~ (v11 = 0) & in(v10, v7) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ((v11 = 0 & ~ (v12 = 0) & in(v10, v8) = v12) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & in(v10, v7) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & in(v10, v8) = 0) | ( ~ (v12 = 0) & in(v10, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v8) = v11) | ? [v12] : ((v12 = 0 & in(v10, v9) = 0) | ( ~ (v12 = 0) & ~ (v11 = 0) & in(v10, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ((v12 = 0 & in(v10, v9) = 0) | ( ~ (v12 = 0) & ~ (v11 = 0) & in(v10, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = 0) | ~ (disjoint(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v7, v9) = v10) | ~ (subset(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = 0) | ~ (subset(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (subset(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (disjoint(v10, v9) = v8) | ~ (disjoint(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_intersection2(v10, v9) = v8) | ~ (set_intersection2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (proper_subset(v10, v9) = v8) | ~ (proper_subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | (v11 = 0 & in(v10, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & disjoint(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v9) = 0) | (in(v10, v8) = 0 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v8) = 0) | ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | ( ~ (v11 = 0) & in(v10, v7) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | ( ~ (v11 = 0) & in(v10, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : ((v11 = 0 & in(v10, v8) = 0) | (v11 = 0 & in(v10, v7) = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v8) = v13) | ( ~ (v12 = 0) & in(v11, v7) = v12)) & ((v13 = 0 & ~ (v14 = 0) & in(v11, v9) = v14 & in(v11, v8) = 0) | (v12 = 0 & in(v11, v7) = 0)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & v13 = 0 & in(v11, v9) = 0 & in(v11, v8) = 0) | (v12 = 0 & in(v11, v7) = 0)) & (( ~ (v14 = 0) & in(v11, v9) = v14) | ( ~ (v13 = 0) & in(v11, v8) = v13) | ( ~ (v12 = 0) & in(v11, v7) = v12)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (((v14 = 0 & in(v11, v9) = 0) | (v13 = 0 & in(v11, v8) = 0) | (v12 = 0 & in(v11, v7) = 0)) & (( ~ (v14 = 0) & ~ (v13 = 0) & in(v11, v9) = v14 & in(v11, v8) = v13) | ( ~ (v12 = 0) & in(v11, v7) = v12)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & disjoint(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (proper_subset(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & disjoint(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ? [v11] : (set_intersection2(v7, v8) = v10 & in(v11, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : ( ~ (v10 = empty_set) & set_intersection2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : (in(v10, v8) = 0 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ( ~ (v10 = empty_set) & set_difference(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | ~ (subset(v7, v8) = 0) | disjoint(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (in(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (in(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v8, v7) = v9) | ? [v10] : (set_union2(v7, v9) = v10 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v8, v7) = v9) | ? [v10] : ((v10 = v8 & set_union2(v7, v9) = v8) | ( ~ (v10 = 0) & subset(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | subset(v9, v7) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v7, v9) = v10 & set_intersection2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ~ (subset(v7, v8) = 0) | subset(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v7) = v9) | set_intersection2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | subset(v9, v7) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & in(v10, v9) = 0) | (v10 = 0 & disjoint(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | ? [v10] : (set_difference(v7, v10) = v9 & set_difference(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | ( ~ (v10 = 0) & empty(v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | subset(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : (set_difference(v9, v8) = v10 & set_difference(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : (set_difference(v8, v7) = v10 & set_union2(v7, v10) = v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | ( ~ (v10 = 0) & empty(v9) = v10))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_difference(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v7, v8) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v7, v8) = 0) | proper_subset(v7, v8) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_intersection2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_difference(empty_set, v7) = v8)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (set_intersection2(v7, empty_set) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(empty_set, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | set_intersection2(v7, v8) = empty_set) & ! [v7] : ! [v8] : ( ~ (disjoint(v7, v8) = 0) | ? [v9] : (set_intersection2(v7, v8) = v9 & ! [v10] : ~ (in(v10, v9) = 0))) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | set_difference(v7, v8) = empty_set) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | set_intersection2(v7, v8) = v7) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | set_union2(v7, v8) = v8) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & proper_subset(v8, v7) = v9)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (set_difference(v8, v7) = v9 & set_union2(v7, v9) = v8)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & proper_subset(v7, v7) = v9)) & ! [v7] : ! [v8] : ( ~ (set_intersection2(v7, v8) = empty_set) | disjoint(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (proper_subset(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (proper_subset(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & proper_subset(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (proper_subset(v7, v8) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (proper_subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & proper_subset(v8, v7) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : (v7 = empty_set | ~ (subset(v7, empty_set) = 0)) & ! [v7] : ~ (proper_subset(v7, v7) = 0) & ! [v7] : ~ (in(v7, empty_set) = 0) & ? [v7] : ? [v8] : ? [v9] : disjoint(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : set_difference(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : set_intersection2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : set_union2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : proper_subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (((v11 = 0 & in(v9, v8) = 0) | (v10 = 0 & in(v9, v7) = 0)) & (( ~ (v11 = 0) & in(v9, v8) = v11) | ( ~ (v10 = 0) & in(v9, v7) = v10)))) & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7) = 0) & ((v3 = v0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = v0))))
% 34.36/9.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 34.36/9.37 | (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 & disjoint(all_0_6_6, all_0_5_5) = all_0_4_4 & set_difference(all_0_6_6, all_0_5_5) = 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 = 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] : (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 | ~ (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] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [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 = 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 | ~ (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] : ( ~ (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] : (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_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] : ( ~ (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] : ( ~ (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] : ~ (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] : 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] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) & ((all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6)))
% 34.36/9.40 |
% 34.36/9.40 | Applying alpha-rule on (1) yields:
% 34.36/9.40 | (2) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 34.36/9.40 | (3) ! [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)))
% 34.36/9.40 | (4) ! [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))
% 34.36/9.40 | (5) ! [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)))
% 34.36/9.40 | (6) ! [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)))
% 34.36/9.40 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3))
% 34.36/9.40 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 34.36/9.40 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 34.36/9.40 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 34.36/9.41 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 34.36/9.41 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 34.36/9.41 | (13) ! [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)))
% 34.36/9.41 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 34.36/9.41 | (15) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 34.36/9.41 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 34.36/9.41 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 34.36/9.41 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 34.36/9.41 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 34.36/9.41 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 34.36/9.41 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 34.36/9.41 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 34.36/9.41 | (23) ! [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)))
% 34.36/9.41 | (24) ! [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)))
% 34.36/9.41 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 34.36/9.41 | (26) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0)
% 34.36/9.41 | (27) ! [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)))
% 34.36/9.41 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3))
% 34.36/9.41 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 34.36/9.41 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 34.36/9.41 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 34.36/9.41 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 34.36/9.41 | (33) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 34.36/9.41 | (34) ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2
% 34.36/9.41 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 34.36/9.41 | (36) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 34.36/9.41 | (37) ! [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)))
% 34.36/9.41 | (38) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 34.36/9.41 | (39) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 34.36/9.41 | (40) set_difference(all_0_6_6, all_0_5_5) = all_0_3_3
% 34.36/9.41 | (41) ! [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))
% 34.36/9.41 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 34.36/9.41 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 34.36/9.42 | (44) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2))
% 34.36/9.42 | (45) ! [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)))
% 34.36/9.42 | (46) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1)
% 34.36/9.42 | (47) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 34.36/9.42 | (48) ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2))
% 34.36/9.42 | (49) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 34.36/9.42 | (50) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 34.36/9.42 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 34.36/9.42 | (52) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 34.36/9.42 | (53) empty(empty_set) = 0
% 34.36/9.42 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 34.36/9.42 | (55) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0)
% 34.36/9.42 | (56) ~ (all_0_1_1 = 0)
% 34.36/9.42 | (57) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 34.36/9.42 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 34.36/9.42 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 34.36/9.42 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3))
% 34.36/9.42 | (61) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set)
% 34.36/9.42 | (62) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 34.36/9.42 | (63) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 34.36/9.42 | (64) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 34.36/9.42 | (65) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 34.36/9.42 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 34.36/9.42 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 34.36/9.42 | (68) ! [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)))
% 34.36/9.42 | (69) ? [v0] : ? [v1] : empty(v0) = v1
% 34.36/9.42 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 34.36/9.42 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 34.36/9.42 | (72) disjoint(all_0_6_6, all_0_5_5) = all_0_4_4
% 34.36/9.42 | (73) ! [v0] : ~ (in(v0, empty_set) = 0)
% 34.36/9.42 | (74) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2
% 34.36/9.42 | (75) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 34.36/9.42 | (76) ! [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)))
% 34.36/9.42 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4))
% 34.36/9.42 | (78) ? [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))))
% 34.36/9.42 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0)
% 34.36/9.43 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 34.36/9.43 | (81) ? [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))))
% 34.36/9.43 | (82) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 34.36/9.43 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 34.36/9.43 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 34.36/9.43 | (85) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 34.36/9.43 | (86) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 34.36/9.43 | (87) ! [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)))
% 34.36/9.43 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 34.36/9.43 | (89) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3))
% 34.36/9.43 | (90) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 34.36/9.43 | (91) empty(all_0_2_2) = all_0_1_1
% 34.36/9.43 | (92) ! [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)))
% 34.36/9.43 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 34.36/9.43 | (94) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 34.36/9.43 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ((v3 = v1 & set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 34.36/9.43 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 34.36/9.43 | (97) ? [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))))
% 34.36/9.43 | (98) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 34.36/9.43 | (99) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 34.36/9.43 | (100) ! [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)))
% 34.36/9.43 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 34.36/9.43 | (102) ? [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))))
% 34.36/9.43 | (103) empty(all_0_0_0) = 0
% 34.36/9.43 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 34.36/9.43 | (105) ! [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))
% 34.36/9.44 | (106) (all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6))
% 34.36/9.44 | (107) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 34.36/9.44 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3))
% 34.36/9.44 | (109) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1))
% 34.36/9.44 | (110) ! [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)))
% 34.36/9.44 | (111) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 34.36/9.44 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 34.36/9.44 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0)
% 34.36/9.44 | (114) ! [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)))
% 34.36/9.44 | (115) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 34.36/9.44 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 34.36/9.44 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 34.36/9.44 | (118) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 34.36/9.44 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 34.36/9.44 | (120) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 34.36/9.44 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 34.36/9.44 | (122) ! [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)))
% 34.36/9.44 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 34.36/9.44 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 34.36/9.44 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (98) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 34.36/9.44 | (126) all_0_4_4 = 0 | ? [v0] : ? [v1] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & in(v1, v0) = 0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (112) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 34.36/9.44 | (127) all_0_4_4 = 0 | ? [v0] : (in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = 0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (7) with all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 34.36/9.44 | (128) ? [v0] : (set_union2(all_0_5_5, all_0_3_3) = v0 & set_union2(all_0_5_5, all_0_6_6) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (125) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 34.36/9.44 | (129) subset(all_0_3_3, all_0_6_6) = 0
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (123) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 34.36/9.44 | (130) ? [v0] : (set_difference(v0, all_0_5_5) = all_0_3_3 & set_union2(all_0_6_6, all_0_5_5) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (60) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 34.36/9.44 | (131) ? [v0] : (set_difference(all_0_6_6, all_0_3_3) = v0 & set_intersection2(all_0_6_6, all_0_5_5) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating (131) with all_37_0_36 yields:
% 34.36/9.44 | (132) set_difference(all_0_6_6, all_0_3_3) = all_37_0_36 & set_intersection2(all_0_6_6, all_0_5_5) = all_37_0_36
% 34.36/9.44 |
% 34.36/9.44 | Applying alpha-rule on (132) yields:
% 34.36/9.44 | (133) set_difference(all_0_6_6, all_0_3_3) = all_37_0_36
% 34.36/9.44 | (134) set_intersection2(all_0_6_6, all_0_5_5) = all_37_0_36
% 34.36/9.44 |
% 34.36/9.44 | Instantiating (130) with all_39_0_37 yields:
% 34.36/9.44 | (135) set_difference(all_39_0_37, all_0_5_5) = all_0_3_3 & set_union2(all_0_6_6, all_0_5_5) = all_39_0_37
% 34.36/9.44 |
% 34.36/9.44 | Applying alpha-rule on (135) yields:
% 34.36/9.44 | (136) set_difference(all_39_0_37, all_0_5_5) = all_0_3_3
% 34.36/9.44 | (137) set_union2(all_0_6_6, all_0_5_5) = all_39_0_37
% 34.36/9.44 |
% 34.36/9.44 | Instantiating (128) with all_42_0_39 yields:
% 34.36/9.44 | (138) set_union2(all_0_5_5, all_0_3_3) = all_42_0_39 & set_union2(all_0_5_5, all_0_6_6) = all_42_0_39
% 34.36/9.44 |
% 34.36/9.44 | Applying alpha-rule on (138) yields:
% 34.36/9.44 | (139) set_union2(all_0_5_5, all_0_3_3) = all_42_0_39
% 34.36/9.44 | (140) set_union2(all_0_5_5, all_0_6_6) = all_42_0_39
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (7) with all_37_0_36, all_0_6_6, all_0_3_3 and discharging atoms set_difference(all_0_6_6, all_0_3_3) = all_37_0_36, yields:
% 34.36/9.44 | (141) ? [v0] : (set_union2(all_0_3_3, all_37_0_36) = v0 & set_union2(all_0_3_3, all_0_6_6) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (123) with all_37_0_36, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_3_3) = all_37_0_36, yields:
% 34.36/9.44 | (142) ? [v0] : (set_difference(v0, all_0_3_3) = all_37_0_36 & set_union2(all_0_6_6, all_0_3_3) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (60) with all_37_0_36, all_0_3_3, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_3_3) = all_37_0_36, yields:
% 34.36/9.44 | (143) ? [v0] : (set_difference(all_0_6_6, all_37_0_36) = v0 & set_intersection2(all_0_6_6, all_0_3_3) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (59) with all_0_3_3, all_0_6_6 and discharging atoms subset(all_0_3_3, all_0_6_6) = 0, yields:
% 34.36/9.44 | (144) all_0_3_3 = all_0_6_6 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_3_3) = v0)
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (61) with all_0_6_6, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_6_6) = 0, yields:
% 34.36/9.44 | (145) set_difference(all_0_3_3, all_0_6_6) = empty_set
% 34.36/9.44 |
% 34.36/9.44 | Instantiating formula (26) with all_0_6_6, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_6_6) = 0, yields:
% 34.36/9.44 | (146) set_intersection2(all_0_3_3, all_0_6_6) = all_0_3_3
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (46) with all_0_6_6, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_6_6) = 0, yields:
% 34.36/9.45 | (147) set_union2(all_0_3_3, all_0_6_6) = all_0_6_6
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (20) with all_37_0_36, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_37_0_36, yields:
% 34.36/9.45 | (148) all_37_0_36 = empty_set | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_5_5) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (79) with all_37_0_36, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_37_0_36, yields:
% 34.36/9.45 | (149) subset(all_37_0_36, all_0_6_6) = 0
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (84) with all_42_0_39, all_0_5_5, all_0_3_3 and discharging atoms set_union2(all_0_5_5, all_0_3_3) = all_42_0_39, yields:
% 34.36/9.45 | (150) set_union2(all_0_3_3, all_0_5_5) = all_42_0_39
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (32) with all_42_0_39, all_0_3_3, all_0_5_5 and discharging atoms set_union2(all_0_5_5, all_0_3_3) = all_42_0_39, yields:
% 34.36/9.45 | (151) ? [v0] : (set_difference(all_0_3_3, all_0_5_5) = v0 & set_union2(all_0_5_5, v0) = all_42_0_39)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (84) with all_42_0_39, all_0_5_5, all_0_6_6 and discharging atoms set_union2(all_0_5_5, all_0_6_6) = all_42_0_39, yields:
% 34.36/9.45 | (152) set_union2(all_0_6_6, all_0_5_5) = all_42_0_39
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (116) with all_39_0_37, all_0_5_5, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_0_5_5) = all_39_0_37, yields:
% 34.36/9.45 | (153) subset(all_0_6_6, all_39_0_37) = 0
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (143) with all_53_0_42 yields:
% 34.36/9.45 | (154) set_difference(all_0_6_6, all_37_0_36) = all_53_0_42 & set_intersection2(all_0_6_6, all_0_3_3) = all_53_0_42
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (154) yields:
% 34.36/9.45 | (155) set_difference(all_0_6_6, all_37_0_36) = all_53_0_42
% 34.36/9.45 | (156) set_intersection2(all_0_6_6, all_0_3_3) = all_53_0_42
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (142) with all_55_0_43 yields:
% 34.36/9.45 | (157) set_difference(all_55_0_43, all_0_3_3) = all_37_0_36 & set_union2(all_0_6_6, all_0_3_3) = all_55_0_43
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (157) yields:
% 34.36/9.45 | (158) set_difference(all_55_0_43, all_0_3_3) = all_37_0_36
% 34.36/9.45 | (159) set_union2(all_0_6_6, all_0_3_3) = all_55_0_43
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (141) with all_67_0_52 yields:
% 34.36/9.45 | (160) set_union2(all_0_3_3, all_37_0_36) = all_67_0_52 & set_union2(all_0_3_3, all_0_6_6) = all_67_0_52
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (160) yields:
% 34.36/9.45 | (161) set_union2(all_0_3_3, all_37_0_36) = all_67_0_52
% 34.36/9.45 | (162) set_union2(all_0_3_3, all_0_6_6) = all_67_0_52
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (151) with all_80_0_60 yields:
% 34.36/9.45 | (163) set_difference(all_0_3_3, all_0_5_5) = all_80_0_60 & set_union2(all_0_5_5, all_80_0_60) = all_42_0_39
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (163) yields:
% 34.36/9.45 | (164) set_difference(all_0_3_3, all_0_5_5) = all_80_0_60
% 34.36/9.45 | (165) set_union2(all_0_5_5, all_80_0_60) = all_42_0_39
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (70) with all_0_3_3, all_0_6_6, all_0_6_6, all_67_0_52 and discharging atoms set_union2(all_0_3_3, all_0_6_6) = all_67_0_52, set_union2(all_0_3_3, all_0_6_6) = all_0_6_6, yields:
% 34.36/9.45 | (166) all_67_0_52 = all_0_6_6
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (70) with all_0_6_6, all_0_5_5, all_42_0_39, all_39_0_37 and discharging atoms set_union2(all_0_6_6, all_0_5_5) = all_42_0_39, set_union2(all_0_6_6, all_0_5_5) = all_39_0_37, yields:
% 34.36/9.45 | (167) all_42_0_39 = all_39_0_37
% 34.36/9.45 |
% 34.36/9.45 | From (166) and (161) follows:
% 34.36/9.45 | (168) set_union2(all_0_3_3, all_37_0_36) = all_0_6_6
% 34.36/9.45 |
% 34.36/9.45 | From (167) and (150) follows:
% 34.36/9.45 | (169) set_union2(all_0_3_3, all_0_5_5) = all_39_0_37
% 34.36/9.45 |
% 34.36/9.45 | From (166) and (162) follows:
% 34.36/9.45 | (147) set_union2(all_0_3_3, all_0_6_6) = all_0_6_6
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (125) with all_37_0_36, all_0_3_3, all_55_0_43 and discharging atoms set_difference(all_55_0_43, all_0_3_3) = all_37_0_36, yields:
% 34.36/9.45 | (171) subset(all_37_0_36, all_55_0_43) = 0
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (125) with all_80_0_60, all_0_5_5, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_5_5) = all_80_0_60, yields:
% 34.36/9.45 | (172) subset(all_80_0_60, all_0_3_3) = 0
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (60) with all_80_0_60, all_0_5_5, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_5_5) = all_80_0_60, yields:
% 34.36/9.45 | (173) ? [v0] : (set_difference(all_0_3_3, all_80_0_60) = v0 & set_intersection2(all_0_3_3, all_0_5_5) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (123) with empty_set, all_0_6_6, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_6_6) = empty_set, yields:
% 34.36/9.45 | (174) ? [v0] : (set_difference(v0, all_0_6_6) = empty_set & set_union2(all_0_3_3, all_0_6_6) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (60) with empty_set, all_0_6_6, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_6_6) = empty_set, yields:
% 34.36/9.45 | (175) ? [v0] : (set_difference(all_0_3_3, empty_set) = v0 & set_intersection2(all_0_3_3, all_0_6_6) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (95) with all_53_0_42, all_0_6_6, all_37_0_36 and discharging atoms set_difference(all_0_6_6, all_37_0_36) = all_53_0_42, yields:
% 34.36/9.45 | (176) ? [v0] : ((v0 = all_0_6_6 & set_union2(all_37_0_36, all_53_0_42) = all_0_6_6) | ( ~ (v0 = 0) & subset(all_37_0_36, all_0_6_6) = v0))
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (123) with all_53_0_42, all_37_0_36, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_37_0_36) = all_53_0_42, yields:
% 34.36/9.45 | (177) ? [v0] : (set_difference(v0, all_37_0_36) = all_53_0_42 & set_union2(all_0_6_6, all_37_0_36) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (61) with all_0_6_6, all_37_0_36 and discharging atoms subset(all_37_0_36, all_0_6_6) = 0, yields:
% 34.36/9.45 | (178) set_difference(all_37_0_36, all_0_6_6) = empty_set
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (77) with all_0_4_4, all_0_5_5, all_39_0_37, all_0_6_6 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, subset(all_0_6_6, all_39_0_37) = 0, yields:
% 34.36/9.45 | (179) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & disjoint(all_39_0_37, all_0_5_5) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (11) with all_53_0_42, all_0_6_6, all_0_3_3 and discharging atoms set_intersection2(all_0_6_6, all_0_3_3) = all_53_0_42, yields:
% 34.36/9.45 | (180) set_intersection2(all_0_3_3, all_0_6_6) = all_53_0_42
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (108) with all_0_6_6, all_37_0_36, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_37_0_36) = all_0_6_6, yields:
% 34.36/9.45 | (181) ? [v0] : (set_difference(all_0_3_3, all_37_0_36) = v0 & set_difference(all_0_6_6, all_37_0_36) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (108) with all_39_0_37, all_0_5_5, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_5_5) = all_39_0_37, yields:
% 34.36/9.45 | (182) ? [v0] : (set_difference(all_39_0_37, all_0_5_5) = v0 & set_difference(all_0_3_3, all_0_5_5) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (108) with all_0_6_6, all_0_6_6, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_6_6) = all_0_6_6, yields:
% 34.36/9.45 | (183) ? [v0] : (set_difference(all_0_3_3, all_0_6_6) = v0 & set_difference(all_0_6_6, all_0_6_6) = v0)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (84) with all_55_0_43, all_0_6_6, all_0_3_3 and discharging atoms set_union2(all_0_6_6, all_0_3_3) = all_55_0_43, yields:
% 34.36/9.45 | (184) set_union2(all_0_3_3, all_0_6_6) = all_55_0_43
% 34.36/9.45 |
% 34.36/9.45 | Instantiating formula (116) with all_55_0_43, all_0_3_3, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_0_3_3) = all_55_0_43, yields:
% 34.36/9.45 | (185) subset(all_0_6_6, all_55_0_43) = 0
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (174) with all_104_0_61 yields:
% 34.36/9.45 | (186) set_difference(all_104_0_61, all_0_6_6) = empty_set & set_union2(all_0_3_3, all_0_6_6) = all_104_0_61
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (186) yields:
% 34.36/9.45 | (187) set_difference(all_104_0_61, all_0_6_6) = empty_set
% 34.36/9.45 | (188) set_union2(all_0_3_3, all_0_6_6) = all_104_0_61
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (173) with all_145_0_85 yields:
% 34.36/9.45 | (189) set_difference(all_0_3_3, all_80_0_60) = all_145_0_85 & set_intersection2(all_0_3_3, all_0_5_5) = all_145_0_85
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (189) yields:
% 34.36/9.45 | (190) set_difference(all_0_3_3, all_80_0_60) = all_145_0_85
% 34.36/9.45 | (191) set_intersection2(all_0_3_3, all_0_5_5) = all_145_0_85
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (176) with all_150_0_89 yields:
% 34.36/9.45 | (192) (all_150_0_89 = all_0_6_6 & set_union2(all_37_0_36, all_53_0_42) = all_0_6_6) | ( ~ (all_150_0_89 = 0) & subset(all_37_0_36, all_0_6_6) = all_150_0_89)
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (182) with all_161_0_97 yields:
% 34.36/9.45 | (193) set_difference(all_39_0_37, all_0_5_5) = all_161_0_97 & set_difference(all_0_3_3, all_0_5_5) = all_161_0_97
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (193) yields:
% 34.36/9.45 | (194) set_difference(all_39_0_37, all_0_5_5) = all_161_0_97
% 34.36/9.45 | (195) set_difference(all_0_3_3, all_0_5_5) = all_161_0_97
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (177) with all_163_0_98 yields:
% 34.36/9.45 | (196) set_difference(all_163_0_98, all_37_0_36) = all_53_0_42 & set_union2(all_0_6_6, all_37_0_36) = all_163_0_98
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (196) yields:
% 34.36/9.45 | (197) set_difference(all_163_0_98, all_37_0_36) = all_53_0_42
% 34.36/9.45 | (198) set_union2(all_0_6_6, all_37_0_36) = all_163_0_98
% 34.36/9.45 |
% 34.36/9.45 | Instantiating (181) with all_172_0_103 yields:
% 34.36/9.45 | (199) set_difference(all_0_3_3, all_37_0_36) = all_172_0_103 & set_difference(all_0_6_6, all_37_0_36) = all_172_0_103
% 34.36/9.45 |
% 34.36/9.45 | Applying alpha-rule on (199) yields:
% 34.36/9.46 | (200) set_difference(all_0_3_3, all_37_0_36) = all_172_0_103
% 34.36/9.46 | (201) set_difference(all_0_6_6, all_37_0_36) = all_172_0_103
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (183) with all_175_0_105 yields:
% 34.36/9.46 | (202) set_difference(all_0_3_3, all_0_6_6) = all_175_0_105 & set_difference(all_0_6_6, all_0_6_6) = all_175_0_105
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (202) yields:
% 34.36/9.46 | (203) set_difference(all_0_3_3, all_0_6_6) = all_175_0_105
% 34.36/9.46 | (204) set_difference(all_0_6_6, all_0_6_6) = all_175_0_105
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (175) with all_202_0_125 yields:
% 34.36/9.46 | (205) set_difference(all_0_3_3, empty_set) = all_202_0_125 & set_intersection2(all_0_3_3, all_0_6_6) = all_202_0_125
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (205) yields:
% 34.36/9.46 | (206) set_difference(all_0_3_3, empty_set) = all_202_0_125
% 34.36/9.46 | (207) set_intersection2(all_0_3_3, all_0_6_6) = all_202_0_125
% 34.36/9.46 |
% 34.36/9.46 +-Applying beta-rule and splitting (192), into two cases.
% 34.36/9.46 |-Branch one:
% 34.36/9.46 | (208) all_150_0_89 = all_0_6_6 & set_union2(all_37_0_36, all_53_0_42) = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (208) yields:
% 34.36/9.46 | (209) all_150_0_89 = all_0_6_6
% 34.36/9.46 | (210) set_union2(all_37_0_36, all_53_0_42) = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (31) with all_39_0_37, all_0_5_5, all_161_0_97, all_0_3_3 and discharging atoms set_difference(all_39_0_37, all_0_5_5) = all_161_0_97, set_difference(all_39_0_37, all_0_5_5) = all_0_3_3, yields:
% 34.36/9.46 | (211) all_161_0_97 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (31) with all_0_3_3, all_0_5_5, all_161_0_97, all_80_0_60 and discharging atoms set_difference(all_0_3_3, all_0_5_5) = all_161_0_97, set_difference(all_0_3_3, all_0_5_5) = all_80_0_60, yields:
% 34.36/9.46 | (212) all_161_0_97 = all_80_0_60
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (31) with all_0_3_3, all_0_6_6, all_175_0_105, empty_set and discharging atoms set_difference(all_0_3_3, all_0_6_6) = all_175_0_105, set_difference(all_0_3_3, all_0_6_6) = empty_set, yields:
% 34.36/9.46 | (213) all_175_0_105 = empty_set
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (31) with all_0_6_6, all_37_0_36, all_172_0_103, all_53_0_42 and discharging atoms set_difference(all_0_6_6, all_37_0_36) = all_172_0_103, set_difference(all_0_6_6, all_37_0_36) = all_53_0_42, yields:
% 34.36/9.46 | (214) all_172_0_103 = all_53_0_42
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (29) with all_0_3_3, all_0_6_6, all_202_0_125, all_0_3_3 and discharging atoms set_intersection2(all_0_3_3, all_0_6_6) = all_202_0_125, set_intersection2(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 34.36/9.46 | (215) all_202_0_125 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (29) with all_0_3_3, all_0_6_6, all_53_0_42, all_202_0_125 and discharging atoms set_intersection2(all_0_3_3, all_0_6_6) = all_202_0_125, set_intersection2(all_0_3_3, all_0_6_6) = all_53_0_42, yields:
% 34.36/9.46 | (216) all_202_0_125 = all_53_0_42
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (70) with all_0_3_3, all_0_6_6, all_104_0_61, all_0_6_6 and discharging atoms set_union2(all_0_3_3, all_0_6_6) = all_104_0_61, set_union2(all_0_3_3, all_0_6_6) = all_0_6_6, yields:
% 34.36/9.46 | (217) all_104_0_61 = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (70) with all_0_3_3, all_0_6_6, all_55_0_43, all_104_0_61 and discharging atoms set_union2(all_0_3_3, all_0_6_6) = all_104_0_61, set_union2(all_0_3_3, all_0_6_6) = all_55_0_43, yields:
% 34.36/9.46 | (218) all_104_0_61 = all_55_0_43
% 34.36/9.46 |
% 34.36/9.46 | Combining equations (216,215) yields a new equation:
% 34.36/9.46 | (219) all_53_0_42 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Simplifying 219 yields:
% 34.36/9.46 | (220) all_53_0_42 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Combining equations (212,211) yields a new equation:
% 34.36/9.46 | (221) all_80_0_60 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Simplifying 221 yields:
% 34.36/9.46 | (222) all_80_0_60 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | Combining equations (217,218) yields a new equation:
% 34.36/9.46 | (223) all_55_0_43 = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Combining equations (220,214) yields a new equation:
% 34.36/9.46 | (224) all_172_0_103 = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | From (220) and (197) follows:
% 34.36/9.46 | (225) set_difference(all_163_0_98, all_37_0_36) = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | From (222) and (190) follows:
% 34.36/9.46 | (226) set_difference(all_0_3_3, all_0_3_3) = all_145_0_85
% 34.36/9.46 |
% 34.36/9.46 | From (224) and (200) follows:
% 34.36/9.46 | (227) set_difference(all_0_3_3, all_37_0_36) = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | From (215) and (206) follows:
% 34.36/9.46 | (228) set_difference(all_0_3_3, empty_set) = all_0_3_3
% 34.36/9.46 |
% 34.36/9.46 | From (213) and (204) follows:
% 34.36/9.46 | (229) set_difference(all_0_6_6, all_0_6_6) = empty_set
% 34.36/9.46 |
% 34.36/9.46 | From (222) and (172) follows:
% 34.36/9.46 | (230) subset(all_0_3_3, all_0_3_3) = 0
% 34.36/9.46 |
% 34.36/9.46 | From (223) and (171) follows:
% 34.36/9.46 | (149) subset(all_37_0_36, all_0_6_6) = 0
% 34.36/9.46 |
% 34.36/9.46 | From (223) and (185) follows:
% 34.36/9.46 | (232) subset(all_0_6_6, all_0_6_6) = 0
% 34.36/9.46 |
% 34.36/9.46 | From (220) and (210) follows:
% 34.36/9.46 | (233) set_union2(all_37_0_36, all_0_3_3) = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (95) with all_0_3_3, all_163_0_98, all_37_0_36 and discharging atoms set_difference(all_163_0_98, all_37_0_36) = all_0_3_3, yields:
% 34.36/9.46 | (234) ? [v0] : ((v0 = all_163_0_98 & set_union2(all_37_0_36, all_0_3_3) = all_163_0_98) | ( ~ (v0 = 0) & subset(all_37_0_36, all_163_0_98) = v0))
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (7) with empty_set, all_37_0_36, all_0_6_6 and discharging atoms set_difference(all_37_0_36, all_0_6_6) = empty_set, yields:
% 34.36/9.46 | (235) ? [v0] : (set_union2(all_0_6_6, all_37_0_36) = v0 & set_union2(all_0_6_6, empty_set) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (60) with all_0_3_3, all_37_0_36, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_37_0_36) = all_0_3_3, yields:
% 34.36/9.46 | (236) ? [v0] : (set_difference(all_0_3_3, all_0_3_3) = v0 & set_intersection2(all_0_3_3, all_37_0_36) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (90) with all_145_0_85, all_0_3_3, all_0_3_3 and discharging atoms set_difference(all_0_3_3, all_0_3_3) = all_145_0_85, yields:
% 34.36/9.46 | (237) all_145_0_85 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_3_3) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (7) with all_0_3_3, all_0_3_3, empty_set and discharging atoms set_difference(all_0_3_3, empty_set) = all_0_3_3, yields:
% 34.36/9.46 | (238) ? [v0] : set_union2(empty_set, all_0_3_3) = v0
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (95) with all_0_3_3, all_0_3_3, empty_set and discharging atoms set_difference(all_0_3_3, empty_set) = all_0_3_3, yields:
% 34.36/9.46 | (239) ? [v0] : ((v0 = all_0_3_3 & set_union2(empty_set, all_0_3_3) = all_0_3_3) | ( ~ (v0 = 0) & subset(empty_set, all_0_3_3) = v0))
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (60) with all_0_3_3, empty_set, all_0_3_3 and discharging atoms set_difference(all_0_3_3, empty_set) = all_0_3_3, yields:
% 34.36/9.46 | (240) ? [v0] : (set_difference(all_0_3_3, all_0_3_3) = v0 & set_intersection2(all_0_3_3, empty_set) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (7) with empty_set, all_0_6_6, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_6_6) = empty_set, yields:
% 34.36/9.46 | (241) ? [v0] : (set_union2(all_0_6_6, all_0_6_6) = v0 & set_union2(all_0_6_6, empty_set) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (123) with empty_set, all_0_6_6, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_6_6) = empty_set, yields:
% 34.36/9.46 | (242) ? [v0] : (set_difference(v0, all_0_6_6) = empty_set & set_union2(all_0_6_6, all_0_6_6) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (109) with all_0_3_3, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_3_3) = 0, yields:
% 34.36/9.46 | (243) ? [v0] : (set_difference(all_0_3_3, all_0_3_3) = v0 & set_union2(all_0_3_3, v0) = all_0_3_3)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (46) with all_0_6_6, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_6_6) = 0, yields:
% 34.36/9.46 | (244) set_union2(all_0_6_6, all_0_6_6) = all_0_6_6
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (20) with all_145_0_85, all_0_5_5, all_0_3_3 and discharging atoms set_intersection2(all_0_3_3, all_0_5_5) = all_145_0_85, yields:
% 34.36/9.46 | (245) all_145_0_85 = empty_set | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_3_3, all_0_5_5) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (18) with all_145_0_85, all_0_5_5, all_0_3_3 and discharging atoms set_intersection2(all_0_3_3, all_0_5_5) = all_145_0_85, yields:
% 34.36/9.46 | (246) ? [v0] : ? [v1] : ((v1 = 0 & in(v0, all_145_0_85) = 0) | (v0 = 0 & disjoint(all_0_3_3, all_0_5_5) = 0))
% 34.36/9.46 |
% 34.36/9.46 | Instantiating formula (9) with all_0_6_6, all_0_3_3, all_37_0_36 and discharging atoms set_union2(all_37_0_36, all_0_3_3) = all_0_6_6, yields:
% 34.36/9.46 | (247) all_0_3_3 = all_0_6_6 | ? [v0] : ( ~ (v0 = 0) & subset(all_37_0_36, all_0_3_3) = v0)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (240) with all_257_0_140 yields:
% 34.36/9.46 | (248) set_difference(all_0_3_3, all_0_3_3) = all_257_0_140 & set_intersection2(all_0_3_3, empty_set) = all_257_0_140
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (248) yields:
% 34.36/9.46 | (249) set_difference(all_0_3_3, all_0_3_3) = all_257_0_140
% 34.36/9.46 | (250) set_intersection2(all_0_3_3, empty_set) = all_257_0_140
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (234) with all_272_0_154 yields:
% 34.36/9.46 | (251) (all_272_0_154 = all_163_0_98 & set_union2(all_37_0_36, all_0_3_3) = all_163_0_98) | ( ~ (all_272_0_154 = 0) & subset(all_37_0_36, all_163_0_98) = all_272_0_154)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (239) with all_281_0_159 yields:
% 34.36/9.46 | (252) (all_281_0_159 = all_0_3_3 & set_union2(empty_set, all_0_3_3) = all_0_3_3) | ( ~ (all_281_0_159 = 0) & subset(empty_set, all_0_3_3) = all_281_0_159)
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (235) with all_291_0_166 yields:
% 34.36/9.46 | (253) set_union2(all_0_6_6, all_37_0_36) = all_291_0_166 & set_union2(all_0_6_6, empty_set) = all_291_0_166
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (253) yields:
% 34.36/9.46 | (254) set_union2(all_0_6_6, all_37_0_36) = all_291_0_166
% 34.36/9.46 | (255) set_union2(all_0_6_6, empty_set) = all_291_0_166
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (241) with all_308_0_175 yields:
% 34.36/9.46 | (256) set_union2(all_0_6_6, all_0_6_6) = all_308_0_175 & set_union2(all_0_6_6, empty_set) = all_308_0_175
% 34.36/9.46 |
% 34.36/9.46 | Applying alpha-rule on (256) yields:
% 34.36/9.46 | (257) set_union2(all_0_6_6, all_0_6_6) = all_308_0_175
% 34.36/9.46 | (258) set_union2(all_0_6_6, empty_set) = all_308_0_175
% 34.36/9.46 |
% 34.36/9.46 | Instantiating (238) with all_316_0_179 yields:
% 34.36/9.46 | (259) set_union2(empty_set, all_0_3_3) = all_316_0_179
% 34.36/9.47 |
% 34.36/9.47 | Instantiating (243) with all_358_0_207 yields:
% 34.36/9.47 | (260) set_difference(all_0_3_3, all_0_3_3) = all_358_0_207 & set_union2(all_0_3_3, all_358_0_207) = all_0_3_3
% 34.36/9.47 |
% 34.36/9.47 | Applying alpha-rule on (260) yields:
% 34.36/9.47 | (261) set_difference(all_0_3_3, all_0_3_3) = all_358_0_207
% 34.36/9.47 | (262) set_union2(all_0_3_3, all_358_0_207) = all_0_3_3
% 34.36/9.47 |
% 34.36/9.47 | Instantiating (242) with all_373_0_217 yields:
% 34.36/9.47 | (263) set_difference(all_373_0_217, all_0_6_6) = empty_set & set_union2(all_0_6_6, all_0_6_6) = all_373_0_217
% 34.36/9.47 |
% 34.36/9.47 | Applying alpha-rule on (263) yields:
% 34.36/9.47 | (264) set_difference(all_373_0_217, all_0_6_6) = empty_set
% 34.36/9.47 | (265) set_union2(all_0_6_6, all_0_6_6) = all_373_0_217
% 34.36/9.47 |
% 34.36/9.47 | Instantiating (236) with all_417_0_243 yields:
% 34.36/9.47 | (266) set_difference(all_0_3_3, all_0_3_3) = all_417_0_243 & set_intersection2(all_0_3_3, all_37_0_36) = all_417_0_243
% 34.36/9.47 |
% 34.36/9.47 | Applying alpha-rule on (266) yields:
% 34.36/9.47 | (267) set_difference(all_0_3_3, all_0_3_3) = all_417_0_243
% 34.36/9.47 | (268) set_intersection2(all_0_3_3, all_37_0_36) = all_417_0_243
% 34.36/9.47 |
% 34.36/9.47 | Instantiating (246) with all_437_0_256, all_437_1_257 yields:
% 34.36/9.47 | (269) (all_437_0_256 = 0 & in(all_437_1_257, all_145_0_85) = 0) | (all_437_1_257 = 0 & disjoint(all_0_3_3, all_0_5_5) = 0)
% 34.36/9.47 |
% 34.36/9.47 +-Applying beta-rule and splitting (237), into two cases.
% 34.36/9.47 |-Branch one:
% 34.36/9.47 | (270) all_145_0_85 = empty_set
% 34.36/9.47 |
% 34.36/9.47 +-Applying beta-rule and splitting (252), into two cases.
% 34.36/9.47 |-Branch one:
% 34.36/9.47 | (271) all_281_0_159 = all_0_3_3 & set_union2(empty_set, all_0_3_3) = all_0_3_3
% 34.36/9.47 |
% 34.36/9.47 | Applying alpha-rule on (271) yields:
% 34.36/9.47 | (272) all_281_0_159 = all_0_3_3
% 34.85/9.47 | (273) set_union2(empty_set, all_0_3_3) = all_0_3_3
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with all_0_6_6, all_37_0_36, all_291_0_166, all_163_0_98 and discharging atoms set_union2(all_0_6_6, all_37_0_36) = all_291_0_166, set_union2(all_0_6_6, all_37_0_36) = all_163_0_98, yields:
% 34.85/9.47 | (274) all_291_0_166 = all_163_0_98
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with all_0_6_6, all_0_6_6, all_308_0_175, all_373_0_217 and discharging atoms set_union2(all_0_6_6, all_0_6_6) = all_373_0_217, set_union2(all_0_6_6, all_0_6_6) = all_308_0_175, yields:
% 34.85/9.47 | (275) all_373_0_217 = all_308_0_175
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with all_0_6_6, all_0_6_6, all_0_6_6, all_373_0_217 and discharging atoms set_union2(all_0_6_6, all_0_6_6) = all_373_0_217, set_union2(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 34.85/9.47 | (276) all_373_0_217 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with all_0_6_6, empty_set, all_291_0_166, all_308_0_175 and discharging atoms set_union2(all_0_6_6, empty_set) = all_308_0_175, set_union2(all_0_6_6, empty_set) = all_291_0_166, yields:
% 34.85/9.47 | (277) all_308_0_175 = all_291_0_166
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with empty_set, all_0_3_3, all_0_3_3, all_316_0_179 and discharging atoms set_union2(empty_set, all_0_3_3) = all_316_0_179, set_union2(empty_set, all_0_3_3) = all_0_3_3, yields:
% 34.85/9.47 | (278) all_316_0_179 = all_0_3_3
% 34.85/9.47 |
% 34.85/9.47 | Combining equations (276,275) yields a new equation:
% 34.85/9.47 | (279) all_308_0_175 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Combining equations (277,279) yields a new equation:
% 34.85/9.47 | (280) all_291_0_166 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Simplifying 280 yields:
% 34.85/9.47 | (281) all_291_0_166 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Combining equations (274,281) yields a new equation:
% 34.85/9.47 | (282) all_163_0_98 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Simplifying 282 yields:
% 34.85/9.47 | (283) all_163_0_98 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | From (278) and (259) follows:
% 34.85/9.47 | (273) set_union2(empty_set, all_0_3_3) = all_0_3_3
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (251), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (285) all_272_0_154 = all_163_0_98 & set_union2(all_37_0_36, all_0_3_3) = all_163_0_98
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (285) yields:
% 34.85/9.47 | (286) all_272_0_154 = all_163_0_98
% 34.85/9.47 | (287) set_union2(all_37_0_36, all_0_3_3) = all_163_0_98
% 34.85/9.47 |
% 34.85/9.47 | From (283) and (287) follows:
% 34.85/9.47 | (233) set_union2(all_37_0_36, all_0_3_3) = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (106), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (289) all_0_3_3 = all_0_6_6 & ~ (all_0_4_4 = 0)
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (289) yields:
% 34.85/9.47 | (290) all_0_3_3 = all_0_6_6
% 34.85/9.47 | (291) ~ (all_0_4_4 = 0)
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (127), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (292) all_0_4_4 = 0
% 34.85/9.47 |
% 34.85/9.47 | Equations (292) can reduce 291 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (291) ~ (all_0_4_4 = 0)
% 34.85/9.47 | (295) ? [v0] : (in(v0, all_0_5_5) = 0 & in(v0, all_0_6_6) = 0)
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (269), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (296) all_437_0_256 = 0 & in(all_437_1_257, all_145_0_85) = 0
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (296) yields:
% 34.85/9.47 | (297) all_437_0_256 = 0
% 34.85/9.47 | (298) in(all_437_1_257, all_145_0_85) = 0
% 34.85/9.47 |
% 34.85/9.47 | From (270) and (298) follows:
% 34.85/9.47 | (299) in(all_437_1_257, empty_set) = 0
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (73) with all_437_1_257 and discharging atoms in(all_437_1_257, empty_set) = 0, yields:
% 34.85/9.47 | (300) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (301) all_437_1_257 = 0 & disjoint(all_0_3_3, all_0_5_5) = 0
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (301) yields:
% 34.85/9.47 | (302) all_437_1_257 = 0
% 34.85/9.47 | (303) disjoint(all_0_3_3, all_0_5_5) = 0
% 34.85/9.47 |
% 34.85/9.47 | From (290) and (303) follows:
% 34.85/9.47 | (304) disjoint(all_0_6_6, all_0_5_5) = 0
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (126), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (292) all_0_4_4 = 0
% 34.85/9.47 |
% 34.85/9.47 | Equations (292) can reduce 291 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (291) ~ (all_0_4_4 = 0)
% 34.85/9.47 | (308) ? [v0] : ? [v1] : (set_intersection2(all_0_6_6, all_0_5_5) = v0 & in(v1, v0) = 0)
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (179), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (292) all_0_4_4 = 0
% 34.85/9.47 |
% 34.85/9.47 | Equations (292) can reduce 291 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (291) ~ (all_0_4_4 = 0)
% 34.85/9.47 | (312) ? [v0] : ( ~ (v0 = 0) & disjoint(all_39_0_37, all_0_5_5) = v0)
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (17) with all_0_6_6, all_0_5_5, 0, all_0_4_4 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_0_4_4, disjoint(all_0_6_6, all_0_5_5) = 0, yields:
% 34.85/9.47 | (292) all_0_4_4 = 0
% 34.85/9.47 |
% 34.85/9.47 | Equations (292) can reduce 291 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (315) all_0_4_4 = 0 & ~ (all_0_3_3 = all_0_6_6)
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (315) yields:
% 34.85/9.47 | (292) all_0_4_4 = 0
% 34.85/9.47 | (317) ~ (all_0_3_3 = all_0_6_6)
% 34.85/9.47 |
% 34.85/9.47 | From (292) and (72) follows:
% 34.85/9.47 | (304) disjoint(all_0_6_6, all_0_5_5) = 0
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (144), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (290) all_0_3_3 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Equations (290) can reduce 317 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (317) ~ (all_0_3_3 = all_0_6_6)
% 34.85/9.47 | (322) ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_3_3) = v0)
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (247), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (290) all_0_3_3 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Equations (290) can reduce 317 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (317) ~ (all_0_3_3 = all_0_6_6)
% 34.85/9.47 | (326) ? [v0] : ( ~ (v0 = 0) & subset(all_37_0_36, all_0_3_3) = v0)
% 34.85/9.47 |
% 34.85/9.47 +-Applying beta-rule and splitting (148), into two cases.
% 34.85/9.47 |-Branch one:
% 34.85/9.47 | (327) all_37_0_36 = empty_set
% 34.85/9.47 |
% 34.85/9.47 | From (327) and (233) follows:
% 34.85/9.47 | (328) set_union2(empty_set, all_0_3_3) = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (70) with empty_set, all_0_3_3, all_0_6_6, all_0_3_3 and discharging atoms set_union2(empty_set, all_0_3_3) = all_0_3_3, set_union2(empty_set, all_0_3_3) = all_0_6_6, yields:
% 34.85/9.47 | (290) all_0_3_3 = all_0_6_6
% 34.85/9.47 |
% 34.85/9.47 | Equations (290) can reduce 317 to:
% 34.85/9.47 | (293) $false
% 34.85/9.47 |
% 34.85/9.47 |-The branch is then unsatisfiable
% 34.85/9.47 |-Branch two:
% 34.85/9.47 | (331) ~ (all_37_0_36 = empty_set)
% 34.85/9.47 | (332) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_5_5) = v0)
% 34.85/9.47 |
% 34.85/9.47 | Instantiating (332) with all_515_0_306 yields:
% 34.85/9.47 | (333) ~ (all_515_0_306 = 0) & disjoint(all_0_6_6, all_0_5_5) = all_515_0_306
% 34.85/9.47 |
% 34.85/9.47 | Applying alpha-rule on (333) yields:
% 34.85/9.47 | (334) ~ (all_515_0_306 = 0)
% 34.85/9.47 | (335) disjoint(all_0_6_6, all_0_5_5) = all_515_0_306
% 34.85/9.47 |
% 34.85/9.47 | Instantiating formula (17) with all_0_6_6, all_0_5_5, 0, all_515_0_306 and discharging atoms disjoint(all_0_6_6, all_0_5_5) = all_515_0_306, disjoint(all_0_6_6, all_0_5_5) = 0, yields:
% 34.85/9.47 | (336) all_515_0_306 = 0
% 34.85/9.47 |
% 34.85/9.47 | Equations (336) can reduce 334 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 |-Branch two:
% 34.85/9.48 | (338) ~ (all_272_0_154 = 0) & subset(all_37_0_36, all_163_0_98) = all_272_0_154
% 34.85/9.48 |
% 34.85/9.48 | Applying alpha-rule on (338) yields:
% 34.85/9.48 | (339) ~ (all_272_0_154 = 0)
% 34.85/9.48 | (340) subset(all_37_0_36, all_163_0_98) = all_272_0_154
% 34.85/9.48 |
% 34.85/9.48 | From (283) and (340) follows:
% 34.85/9.48 | (341) subset(all_37_0_36, all_0_6_6) = all_272_0_154
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (121) with all_37_0_36, all_0_6_6, all_272_0_154, 0 and discharging atoms subset(all_37_0_36, all_0_6_6) = all_272_0_154, subset(all_37_0_36, all_0_6_6) = 0, yields:
% 34.85/9.48 | (342) all_272_0_154 = 0
% 34.85/9.48 |
% 34.85/9.48 | Equations (342) can reduce 339 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 |-Branch two:
% 34.85/9.48 | (344) ~ (all_281_0_159 = 0) & subset(empty_set, all_0_3_3) = all_281_0_159
% 34.85/9.48 |
% 34.85/9.48 | Applying alpha-rule on (344) yields:
% 34.85/9.48 | (345) ~ (all_281_0_159 = 0)
% 34.85/9.48 | (346) subset(empty_set, all_0_3_3) = all_281_0_159
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (120) with all_281_0_159, all_0_3_3 and discharging atoms subset(empty_set, all_0_3_3) = all_281_0_159, yields:
% 34.85/9.48 | (347) all_281_0_159 = 0
% 34.85/9.48 |
% 34.85/9.48 | Equations (347) can reduce 345 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 |-Branch two:
% 34.85/9.48 | (349) ~ (all_145_0_85 = empty_set)
% 34.85/9.48 | (350) ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_3_3) = v0)
% 34.85/9.48 |
% 34.85/9.48 +-Applying beta-rule and splitting (245), into two cases.
% 34.85/9.48 |-Branch one:
% 34.85/9.48 | (270) all_145_0_85 = empty_set
% 34.85/9.48 |
% 34.85/9.48 | Equations (270) can reduce 349 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 |-Branch two:
% 34.85/9.48 | (349) ~ (all_145_0_85 = empty_set)
% 34.85/9.48 | (354) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_3_3, all_0_5_5) = v0)
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (31) with all_0_3_3, all_0_3_3, all_417_0_243, all_145_0_85 and discharging atoms set_difference(all_0_3_3, all_0_3_3) = all_417_0_243, set_difference(all_0_3_3, all_0_3_3) = all_145_0_85, yields:
% 34.85/9.48 | (355) all_417_0_243 = all_145_0_85
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (31) with all_0_3_3, all_0_3_3, all_358_0_207, all_417_0_243 and discharging atoms set_difference(all_0_3_3, all_0_3_3) = all_417_0_243, set_difference(all_0_3_3, all_0_3_3) = all_358_0_207, yields:
% 34.85/9.48 | (356) all_417_0_243 = all_358_0_207
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (31) with all_0_3_3, all_0_3_3, all_257_0_140, all_417_0_243 and discharging atoms set_difference(all_0_3_3, all_0_3_3) = all_417_0_243, set_difference(all_0_3_3, all_0_3_3) = all_257_0_140, yields:
% 34.85/9.48 | (357) all_417_0_243 = all_257_0_140
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (52) with all_257_0_140, all_0_3_3 and discharging atoms set_intersection2(all_0_3_3, empty_set) = all_257_0_140, yields:
% 34.85/9.48 | (358) all_257_0_140 = empty_set
% 34.85/9.48 |
% 34.85/9.48 | Combining equations (355,356) yields a new equation:
% 34.85/9.48 | (359) all_358_0_207 = all_145_0_85
% 34.85/9.48 |
% 34.85/9.48 | Combining equations (357,356) yields a new equation:
% 34.85/9.48 | (360) all_358_0_207 = all_257_0_140
% 34.85/9.48 |
% 34.85/9.48 | Combining equations (360,359) yields a new equation:
% 34.85/9.48 | (361) all_257_0_140 = all_145_0_85
% 34.85/9.48 |
% 34.85/9.48 | Simplifying 361 yields:
% 34.85/9.48 | (362) all_257_0_140 = all_145_0_85
% 34.85/9.48 |
% 34.85/9.48 | Combining equations (358,362) yields a new equation:
% 34.85/9.48 | (270) all_145_0_85 = empty_set
% 34.85/9.48 |
% 34.85/9.48 | Equations (270) can reduce 349 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 |-Branch two:
% 34.85/9.48 | (365) ~ (all_150_0_89 = 0) & subset(all_37_0_36, all_0_6_6) = all_150_0_89
% 34.85/9.48 |
% 34.85/9.48 | Applying alpha-rule on (365) yields:
% 34.85/9.48 | (366) ~ (all_150_0_89 = 0)
% 34.85/9.48 | (367) subset(all_37_0_36, all_0_6_6) = all_150_0_89
% 34.85/9.48 |
% 34.85/9.48 | Instantiating formula (121) with all_37_0_36, all_0_6_6, all_150_0_89, 0 and discharging atoms subset(all_37_0_36, all_0_6_6) = all_150_0_89, subset(all_37_0_36, all_0_6_6) = 0, yields:
% 34.85/9.48 | (368) all_150_0_89 = 0
% 34.85/9.48 |
% 34.85/9.48 | Equations (368) can reduce 366 to:
% 34.85/9.48 | (293) $false
% 34.85/9.48 |
% 34.85/9.48 |-The branch is then unsatisfiable
% 34.85/9.48 % SZS output end Proof for theBenchmark
% 34.85/9.48
% 34.85/9.48 8841ms
%------------------------------------------------------------------------------