TSTP Solution File: SEU146+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU146+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 08:46:57 EDT 2022
% Result : Theorem 46.54s 22.76s
% Output : Proof 65.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU146+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 01:01:08 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.63/0.61 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/1.00 Prover 0: Preprocessing ...
% 3.18/1.37 Prover 0: Warning: ignoring some quantifiers
% 3.18/1.40 Prover 0: Constructing countermodel ...
% 5.22/1.83 Prover 0: gave up
% 5.22/1.83 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.22/1.88 Prover 1: Preprocessing ...
% 5.95/2.03 Prover 1: Warning: ignoring some quantifiers
% 5.95/2.04 Prover 1: Constructing countermodel ...
% 6.61/2.15 Prover 1: gave up
% 6.61/2.15 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.61/2.19 Prover 2: Preprocessing ...
% 7.36/2.34 Prover 2: Warning: ignoring some quantifiers
% 7.36/2.35 Prover 2: Constructing countermodel ...
% 15.76/4.32 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.76/4.37 Prover 3: Preprocessing ...
% 16.08/4.45 Prover 3: Warning: ignoring some quantifiers
% 16.08/4.45 Prover 3: Constructing countermodel ...
% 16.64/4.59 Prover 3: gave up
% 16.64/4.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 17.07/4.62 Prover 4: Preprocessing ...
% 17.42/4.73 Prover 4: Warning: ignoring some quantifiers
% 17.42/4.74 Prover 4: Constructing countermodel ...
% 21.09/5.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.09/5.64 Prover 5: Preprocessing ...
% 21.66/5.73 Prover 5: Warning: ignoring some quantifiers
% 21.66/5.73 Prover 5: Constructing countermodel ...
% 43.10/20.97 Prover 5: stopped
% 43.32/21.17 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 43.48/21.21 Prover 6: Preprocessing ...
% 43.93/21.30 Prover 6: Warning: ignoring some quantifiers
% 43.93/21.30 Prover 6: Constructing countermodel ...
% 46.54/22.76 Prover 6: proved (1592ms)
% 46.54/22.76 Prover 4: stopped
% 46.54/22.76 Prover 2: stopped
% 46.54/22.76
% 46.54/22.76 No countermodel exists, formula is valid
% 46.54/22.76 % SZS status Theorem for theBenchmark
% 46.54/22.76
% 46.54/22.76 Generating proof ... Warning: ignoring some quantifiers
% 64.99/32.20 found it (size 266)
% 64.99/32.20
% 64.99/32.20 % SZS output start Proof for theBenchmark
% 64.99/32.20 Assumed formulas after preprocessing and simplification:
% 64.99/32.20 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & singleton(v1) = v2 & subset(v0, v2) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_difference(v8, v10) = v11) | ~ (singleton(v9) = v10) | ~ (subset(v7, v11) = v12) | ? [v13] : ((v13 = 0 & in(v9, v7) = 0) | ( ~ (v13 = 0) & subset(v7, v8) = v13))) & ! [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 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v10, v9) = 0)) & ! [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 | ~ (singleton(v7) = v9) | ~ (subset(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v7, v8) = 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] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (in(v7, v9) = v10)) & ! [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 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(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] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ((v11 = v9 | v11 = v8 | (v12 = 0 & in(v11, v7) = 0)) & (( ~ (v12 = 0) & in(v11, v7) = v12) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (set_difference(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & disjoint(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ (in(v9, v8) = 0)) & ! [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 = v7) & set_difference(v7, v8) = v10)) & ! [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 | ~ (singleton(v7) = v8) | ~ (in(v7, v8) = v9)) & ! [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] : (v9 = 0 | ~ (in(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & singleton(v7) = v10 & subset(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(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] : ( ~ (singleton(v7) = v9) | ~ (subset(v9, v8) = 0) | in(v7, v8) = 0) & ! [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] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : ? [v11] : (( ~ (v10 = v8) | ( ~ (v11 = 0) & in(v8, v7) = v11)) & (v10 = v8 | (v11 = 0 & in(v10, v7) = 0)))) & ! [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_difference(v7, v8) = v7) & ! [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) = v7) | disjoint(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [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] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ! [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] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : (singleton(v7) = v9 & subset(v9, v8) = 0)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : (v7 = empty_set | ~ (subset(v7, empty_set) = 0)) & ! [v7] : ~ (singleton(v7) = empty_set) & ! [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] : unordered_pair(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] : ? [v8] : singleton(v7) = v8 & ? [v7] : (v7 = empty_set | ? [v8] : in(v8, v7) = 0) & ((v3 = 0 & ~ (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 = empty_set))))
% 65.27/32.28 | 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:
% 65.27/32.28 | (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_5_5) = all_0_4_4 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v2, v0) = 0) | ( ~ (v6 = 0) & subset(v0, v1) = v6))) & ! [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 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = 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] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4)) & ! [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] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [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] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0)) & ! [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 = all_0_6_6) & ~ (all_0_6_6 = empty_set)) | ( ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set)))
% 65.27/32.31 |
% 65.27/32.31 | Applying alpha-rule on (1) yields:
% 65.27/32.32 | (2) ? [v0] : ? [v1] : empty(v0) = v1
% 65.27/32.32 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 65.27/32.32 | (4) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 65.27/32.32 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 65.27/32.32 | (6) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 65.27/32.32 | (7) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 65.27/32.32 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 65.27/32.32 | (9) ! [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))
% 65.27/32.32 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0))
% 65.27/32.32 | (11) empty(all_0_0_0) = 0
% 65.27/32.32 | (12) ! [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))
% 65.27/32.32 | (13) ! [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)))
% 65.27/32.32 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 65.27/32.32 | (15) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 65.27/32.32 | (16) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 65.27/32.32 | (17) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 65.27/32.32 | (18) ! [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)))
% 65.27/32.32 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 65.27/32.32 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 65.27/32.32 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 65.27/32.32 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 65.27/32.32 | (23) ! [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))
% 65.27/32.32 | (24) ! [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)))
% 65.27/32.32 | (25) ! [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)))
% 65.27/32.32 | (26) ! [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)))
% 65.27/32.32 | (27) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1))
% 65.27/32.32 | (28) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 65.27/32.32 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 65.27/32.32 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 65.27/32.32 | (31) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 65.27/32.32 | (32) ! [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)))
% 65.27/32.32 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 65.27/32.33 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 65.27/32.33 | (35) ? [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))))
% 65.27/32.33 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 65.27/32.33 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 65.27/32.33 | (38) ! [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)))
% 65.27/32.33 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 65.27/32.33 | (40) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 65.27/32.33 | (41) ? [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))))
% 65.27/32.33 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ((v3 = v1 & set_union2(v0, v2) = v1) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 65.27/32.33 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 65.27/32.33 | (44) ? [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))))
% 65.27/32.33 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 65.27/32.33 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 65.27/32.33 | (47) ~ (all_0_1_1 = 0)
% 65.27/32.33 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3))
% 65.27/32.33 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 65.27/32.33 | (50) empty(empty_set) = 0
% 65.27/32.33 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 65.27/32.33 | (52) (all_0_3_3 = 0 & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_6_6 = empty_set)) | ( ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set))
% 65.27/32.33 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0)
% 65.27/32.33 | (54) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 65.27/32.33 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 65.27/32.33 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0)
% 65.27/32.33 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 65.27/32.33 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 65.27/32.33 | (59) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 65.27/32.33 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 65.27/32.33 | (61) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 65.27/32.33 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 65.27/32.33 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0)
% 65.27/32.33 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 65.27/32.33 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 65.27/32.34 | (66) ! [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)))
% 65.27/32.34 | (67) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0)
% 65.27/32.34 | (68) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 65.27/32.34 | (69) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 65.27/32.34 | (70) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 65.27/32.34 | (71) ! [v0] : ~ (in(v0, empty_set) = 0)
% 65.27/32.34 | (72) subset(all_0_6_6, all_0_4_4) = all_0_3_3
% 65.27/32.34 | (73) ? [v0] : ? [v1] : singleton(v0) = v1
% 65.27/32.34 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 65.27/32.34 | (75) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 65.27/32.34 | (76) ! [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)))
% 65.27/32.34 | (77) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 65.27/32.34 | (78) ! [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)))
% 65.27/32.34 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 65.27/32.34 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 65.27/32.34 | (81) ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2
% 65.27/32.34 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 65.27/32.34 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 65.27/32.34 | (84) ? [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))))
% 65.27/32.34 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4))
% 65.27/32.34 | (86) ! [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)))
% 65.27/32.34 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 65.27/32.34 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 65.27/32.34 | (89) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1)
% 65.27/32.34 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 65.27/32.34 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v2, v0) = 0) | ( ~ (v6 = 0) & subset(v0, v1) = v6)))
% 65.27/32.34 | (92) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 65.27/32.34 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 65.27/32.34 | (94) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 65.27/32.34 | (95) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 65.27/32.34 | (96) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 65.27/32.34 | (97) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 65.27/32.34 | (98) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 65.27/32.35 | (99) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 65.27/32.35 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 65.27/32.35 | (101) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 65.27/32.35 | (102) ! [v0] : ~ (singleton(v0) = empty_set)
% 65.27/32.35 | (103) singleton(all_0_5_5) = all_0_4_4
% 65.27/32.35 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 65.27/32.35 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 65.27/32.35 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 65.27/32.35 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 65.27/32.35 | (108) empty(all_0_2_2) = all_0_1_1
% 65.27/32.35 | (109) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0)
% 65.27/32.35 | (110) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 65.27/32.35 | (111) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 65.27/32.35 | (112) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 65.27/32.35 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 65.27/32.35 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 65.27/32.35 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4))
% 65.27/32.35 | (116) ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2))
% 65.27/32.35 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3))
% 65.27/32.35 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 65.27/32.35 | (119) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 65.27/32.35 | (120) ? [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))))
% 65.27/32.35 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 65.27/32.35 | (122) ! [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)))
% 65.27/32.35 | (123) ! [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)))
% 65.27/32.35 | (124) ? [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)))))
% 65.27/32.35 | (125) ! [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)))
% 65.27/32.35 | (126) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2))
% 65.27/32.35 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 65.27/32.35 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 65.27/32.35 | (129) ! [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)))
% 65.27/32.35 | (130) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 65.27/32.35 | (131) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0)
% 65.27/32.35 | (132) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 65.27/32.36 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 65.27/32.36 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 65.27/32.36 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3))
% 65.27/32.36 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 65.27/32.36 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 65.27/32.36 | (138) ! [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)))
% 65.27/32.36 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3))
% 65.27/32.36 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 65.27/32.36 | (141) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 65.27/32.36 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 65.27/32.36 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 65.27/32.36 | (144) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3))
% 65.27/32.36 | (145) ! [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)))
% 65.27/32.36 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 65.27/32.36 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 65.27/32.36 | (148) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2
% 65.27/32.36 | (149) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set)
% 65.27/32.36 | (150) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (74) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 65.27/32.36 | (151) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (117) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 65.27/32.36 | (152) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_6_6, all_0_4_4) = v0)
% 65.27/32.36 |
% 65.27/32.36 +-Applying beta-rule and splitting (52), into two cases.
% 65.27/32.36 |-Branch one:
% 65.27/32.36 | (153) all_0_3_3 = 0 & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_6_6 = empty_set)
% 65.27/32.36 |
% 65.27/32.36 | Applying alpha-rule on (153) yields:
% 65.27/32.36 | (154) all_0_3_3 = 0
% 65.27/32.36 | (155) ~ (all_0_4_4 = all_0_6_6)
% 65.27/32.36 | (156) ~ (all_0_6_6 = empty_set)
% 65.27/32.36 |
% 65.27/32.36 | From (154) and (72) follows:
% 65.27/32.36 | (157) subset(all_0_6_6, all_0_4_4) = 0
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (5) with all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, yields:
% 65.27/32.36 | (158) all_0_4_4 = all_0_6_6 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_4_4, all_0_6_6) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (67) with all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, yields:
% 65.27/32.36 | (159) set_intersection2(all_0_6_6, all_0_4_4) = all_0_6_6
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (27) with all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, yields:
% 65.27/32.36 | (160) ? [v0] : (set_difference(all_0_4_4, all_0_6_6) = v0 & set_union2(all_0_6_6, v0) = all_0_4_4)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating (160) with all_58_0_43 yields:
% 65.27/32.36 | (161) set_difference(all_0_4_4, all_0_6_6) = all_58_0_43 & set_union2(all_0_6_6, all_58_0_43) = all_0_4_4
% 65.27/32.36 |
% 65.27/32.36 | Applying alpha-rule on (161) yields:
% 65.27/32.36 | (162) set_difference(all_0_4_4, all_0_6_6) = all_58_0_43
% 65.27/32.36 | (163) set_union2(all_0_6_6, all_58_0_43) = all_0_4_4
% 65.27/32.36 |
% 65.27/32.36 +-Applying beta-rule and splitting (158), into two cases.
% 65.27/32.36 |-Branch one:
% 65.27/32.36 | (164) all_0_4_4 = all_0_6_6
% 65.27/32.36 |
% 65.27/32.36 | Equations (164) can reduce 155 to:
% 65.27/32.36 | (165) $false
% 65.27/32.36 |
% 65.27/32.36 |-The branch is then unsatisfiable
% 65.27/32.36 |-Branch two:
% 65.27/32.36 | (155) ~ (all_0_4_4 = all_0_6_6)
% 65.27/32.36 | (167) ? [v0] : ( ~ (v0 = 0) & subset(all_0_4_4, all_0_6_6) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating (167) with all_70_0_45 yields:
% 65.27/32.36 | (168) ~ (all_70_0_45 = 0) & subset(all_0_4_4, all_0_6_6) = all_70_0_45
% 65.27/32.36 |
% 65.27/32.36 | Applying alpha-rule on (168) yields:
% 65.27/32.36 | (169) ~ (all_70_0_45 = 0)
% 65.27/32.36 | (170) subset(all_0_4_4, all_0_6_6) = all_70_0_45
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (48) with all_58_0_43, all_0_6_6, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_0_6_6) = all_58_0_43, yields:
% 65.27/32.36 | (171) ? [v0] : (set_difference(all_0_4_4, all_58_0_43) = v0 & set_intersection2(all_0_4_4, all_0_6_6) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (80) with all_70_0_45, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_4_4, subset(all_0_4_4, all_0_6_6) = all_70_0_45, yields:
% 65.27/32.36 | (172) all_70_0_45 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (74) with all_70_0_45, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_70_0_45, yields:
% 65.27/32.36 | (173) all_70_0_45 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (117) with all_70_0_45, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_70_0_45, yields:
% 65.27/32.36 | (174) all_70_0_45 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_4_4, all_0_6_6) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (88) with all_0_6_6, all_0_4_4, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_4_4) = all_0_6_6, yields:
% 65.27/32.36 | (175) all_0_6_6 = empty_set | ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_4_4) = v0)
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (37) with all_0_6_6, all_0_6_6, all_0_4_4 and discharging atoms set_intersection2(all_0_6_6, all_0_4_4) = all_0_6_6, yields:
% 65.27/32.36 | (176) set_intersection2(all_0_4_4, all_0_6_6) = all_0_6_6
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (55) with all_0_6_6, all_0_4_4, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_4_4) = all_0_6_6, yields:
% 65.27/32.36 | (177) ? [v0] : ? [v1] : ((v1 = 0 & in(v0, all_0_6_6) = 0) | (v0 = 0 & disjoint(all_0_6_6, all_0_4_4) = 0))
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (21) with all_0_4_4, all_0_6_6, all_58_0_43 and discharging atoms set_union2(all_0_6_6, all_58_0_43) = all_0_4_4, yields:
% 65.27/32.36 | (178) set_union2(all_58_0_43, all_0_6_6) = all_0_4_4
% 65.27/32.36 |
% 65.27/32.36 | Instantiating formula (139) with all_0_4_4, all_58_0_43, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_58_0_43) = all_0_4_4, yields:
% 65.27/32.36 | (179) ? [v0] : (set_difference(all_0_4_4, all_58_0_43) = v0 & set_difference(all_0_6_6, all_58_0_43) = v0)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (30) with all_0_4_4, all_58_0_43, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_58_0_43) = all_0_4_4, yields:
% 65.27/32.37 | (180) ? [v0] : (set_difference(all_58_0_43, all_0_6_6) = v0 & set_union2(all_0_6_6, v0) = all_0_4_4)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (171) with all_84_0_50 yields:
% 65.27/32.37 | (181) set_difference(all_0_4_4, all_58_0_43) = all_84_0_50 & set_intersection2(all_0_4_4, all_0_6_6) = all_84_0_50
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (181) yields:
% 65.27/32.37 | (182) set_difference(all_0_4_4, all_58_0_43) = all_84_0_50
% 65.27/32.37 | (183) set_intersection2(all_0_4_4, all_0_6_6) = all_84_0_50
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (177) with all_96_0_57, all_96_1_58 yields:
% 65.27/32.37 | (184) (all_96_0_57 = 0 & in(all_96_1_58, all_0_6_6) = 0) | (all_96_1_58 = 0 & disjoint(all_0_6_6, all_0_4_4) = 0)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (180) with all_97_0_59 yields:
% 65.27/32.37 | (185) set_difference(all_58_0_43, all_0_6_6) = all_97_0_59 & set_union2(all_0_6_6, all_97_0_59) = all_0_4_4
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (185) yields:
% 65.27/32.37 | (186) set_difference(all_58_0_43, all_0_6_6) = all_97_0_59
% 65.27/32.37 | (187) set_union2(all_0_6_6, all_97_0_59) = all_0_4_4
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (179) with all_99_0_60 yields:
% 65.27/32.37 | (188) set_difference(all_0_4_4, all_58_0_43) = all_99_0_60 & set_difference(all_0_6_6, all_58_0_43) = all_99_0_60
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (188) yields:
% 65.27/32.37 | (189) set_difference(all_0_4_4, all_58_0_43) = all_99_0_60
% 65.27/32.37 | (190) set_difference(all_0_6_6, all_58_0_43) = all_99_0_60
% 65.27/32.37 |
% 65.27/32.37 +-Applying beta-rule and splitting (174), into two cases.
% 65.27/32.37 |-Branch one:
% 65.27/32.37 | (191) all_70_0_45 = 0
% 65.27/32.37 |
% 65.27/32.37 | Equations (191) can reduce 169 to:
% 65.27/32.37 | (165) $false
% 65.27/32.37 |
% 65.27/32.37 |-The branch is then unsatisfiable
% 65.27/32.37 |-Branch two:
% 65.27/32.37 | (169) ~ (all_70_0_45 = 0)
% 65.27/32.37 | (194) ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_4_4, all_0_6_6) = v0)
% 65.27/32.37 |
% 65.27/32.37 +-Applying beta-rule and splitting (175), into two cases.
% 65.27/32.37 |-Branch one:
% 65.27/32.37 | (195) all_0_6_6 = empty_set
% 65.27/32.37 |
% 65.27/32.37 | Equations (195) can reduce 156 to:
% 65.27/32.37 | (165) $false
% 65.27/32.37 |
% 65.27/32.37 |-The branch is then unsatisfiable
% 65.27/32.37 |-Branch two:
% 65.27/32.37 | (156) ~ (all_0_6_6 = empty_set)
% 65.27/32.37 | (198) ? [v0] : ( ~ (v0 = 0) & disjoint(all_0_6_6, all_0_4_4) = v0)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (198) with all_111_0_62 yields:
% 65.27/32.37 | (199) ~ (all_111_0_62 = 0) & disjoint(all_0_6_6, all_0_4_4) = all_111_0_62
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (199) yields:
% 65.27/32.37 | (200) ~ (all_111_0_62 = 0)
% 65.27/32.37 | (201) disjoint(all_0_6_6, all_0_4_4) = all_111_0_62
% 65.27/32.37 |
% 65.27/32.37 +-Applying beta-rule and splitting (172), into two cases.
% 65.27/32.37 |-Branch one:
% 65.27/32.37 | (191) all_70_0_45 = 0
% 65.27/32.37 |
% 65.27/32.37 | Equations (191) can reduce 169 to:
% 65.27/32.37 | (165) $false
% 65.27/32.37 |
% 65.27/32.37 |-The branch is then unsatisfiable
% 65.27/32.37 |-Branch two:
% 65.27/32.37 | (169) ~ (all_70_0_45 = 0)
% 65.27/32.37 | (205) ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (205) with all_116_0_63 yields:
% 65.27/32.37 | (206) ~ (all_116_0_63 = 0) & in(all_0_5_5, all_0_6_6) = all_116_0_63
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (206) yields:
% 65.27/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.27/32.37 | (208) in(all_0_5_5, all_0_6_6) = all_116_0_63
% 65.27/32.37 |
% 65.27/32.37 +-Applying beta-rule and splitting (173), into two cases.
% 65.27/32.37 |-Branch one:
% 65.27/32.37 | (191) all_70_0_45 = 0
% 65.27/32.37 |
% 65.27/32.37 | Equations (191) can reduce 169 to:
% 65.27/32.37 | (165) $false
% 65.27/32.37 |
% 65.27/32.37 |-The branch is then unsatisfiable
% 65.27/32.37 |-Branch two:
% 65.27/32.37 | (169) ~ (all_70_0_45 = 0)
% 65.27/32.37 | (212) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (212) with all_121_0_64, all_121_1_65 yields:
% 65.27/32.37 | (213) ~ (all_121_0_64 = 0) & in(all_121_1_65, all_0_4_4) = 0 & in(all_121_1_65, all_0_6_6) = all_121_0_64
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (213) yields:
% 65.27/32.37 | (214) ~ (all_121_0_64 = 0)
% 65.27/32.37 | (215) in(all_121_1_65, all_0_4_4) = 0
% 65.27/32.37 | (216) in(all_121_1_65, all_0_6_6) = all_121_0_64
% 65.27/32.37 |
% 65.27/32.37 +-Applying beta-rule and splitting (184), into two cases.
% 65.27/32.37 |-Branch one:
% 65.27/32.37 | (217) all_96_0_57 = 0 & in(all_96_1_58, all_0_6_6) = 0
% 65.27/32.37 |
% 65.27/32.37 | Applying alpha-rule on (217) yields:
% 65.27/32.37 | (218) all_96_0_57 = 0
% 65.27/32.37 | (219) in(all_96_1_58, all_0_6_6) = 0
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (100) with all_0_4_4, all_58_0_43, all_84_0_50, all_99_0_60 and discharging atoms set_difference(all_0_4_4, all_58_0_43) = all_99_0_60, set_difference(all_0_4_4, all_58_0_43) = all_84_0_50, yields:
% 65.27/32.37 | (220) all_99_0_60 = all_84_0_50
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (65) with all_0_4_4, all_0_6_6, all_0_6_6, all_84_0_50 and discharging atoms set_intersection2(all_0_4_4, all_0_6_6) = all_84_0_50, set_intersection2(all_0_4_4, all_0_6_6) = all_0_6_6, yields:
% 65.27/32.37 | (221) all_84_0_50 = all_0_6_6
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (101) with all_121_1_65, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_4_4, in(all_121_1_65, all_0_4_4) = 0, yields:
% 65.27/32.37 | (222) all_121_1_65 = all_0_5_5
% 65.27/32.37 |
% 65.27/32.37 | Combining equations (221,220) yields a new equation:
% 65.27/32.37 | (223) all_99_0_60 = all_0_6_6
% 65.27/32.37 |
% 65.27/32.37 | From (221) and (182) follows:
% 65.27/32.37 | (224) set_difference(all_0_4_4, all_58_0_43) = all_0_6_6
% 65.27/32.37 |
% 65.27/32.37 | From (223) and (190) follows:
% 65.27/32.37 | (225) set_difference(all_0_6_6, all_58_0_43) = all_0_6_6
% 65.27/32.37 |
% 65.27/32.37 | From (221) and (183) follows:
% 65.27/32.37 | (176) set_intersection2(all_0_4_4, all_0_6_6) = all_0_6_6
% 65.27/32.37 |
% 65.27/32.37 | From (222) and (215) follows:
% 65.27/32.37 | (227) in(all_0_5_5, all_0_4_4) = 0
% 65.27/32.37 |
% 65.27/32.37 | From (222) and (216) follows:
% 65.27/32.37 | (228) in(all_0_5_5, all_0_6_6) = all_121_0_64
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (134) with all_0_5_5, all_0_6_6, all_121_0_64, all_116_0_63 and discharging atoms in(all_0_5_5, all_0_6_6) = all_121_0_64, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.27/32.37 | (229) all_121_0_64 = all_116_0_63
% 65.27/32.37 |
% 65.27/32.37 | Equations (229) can reduce 214 to:
% 65.27/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.27/32.37 |
% 65.27/32.37 | From (229) and (228) follows:
% 65.27/32.37 | (208) in(all_0_5_5, all_0_6_6) = all_116_0_63
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (123) with 0, all_96_1_58, all_0_6_6, all_0_6_6, all_0_4_4 and discharging atoms set_intersection2(all_0_4_4, all_0_6_6) = all_0_6_6, in(all_96_1_58, all_0_6_6) = 0, yields:
% 65.27/32.37 | (232) ? [v0] : ((v0 = 0 & in(all_96_1_58, all_0_4_4) = 0) | ( ~ (v0 = 0) & in(all_96_1_58, all_0_6_6) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (129) with 0, all_0_5_5, all_0_6_6, all_58_0_43, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_58_0_43) = all_0_6_6, in(all_0_5_5, all_0_4_4) = 0, yields:
% 65.27/32.37 | (233) ? [v0] : (( ~ (v0 = 0) & in(all_0_5_5, all_58_0_43) = v0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (32) with all_0_5_5, all_0_4_4, all_0_6_6, all_58_0_43 and discharging atoms set_union2(all_58_0_43, all_0_6_6) = all_0_4_4, in(all_0_5_5, all_0_4_4) = 0, yields:
% 65.27/32.37 | (234) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_58_0_43) = 0) | (v0 = 0 & in(all_0_5_5, all_0_6_6) = 0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (38) with all_116_0_63, all_0_5_5, all_97_0_59, all_0_6_6, all_58_0_43 and discharging atoms set_difference(all_58_0_43, all_0_6_6) = all_97_0_59, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.27/32.37 | (235) all_116_0_63 = 0 | ? [v0] : ((v0 = 0 & in(all_0_5_5, all_97_0_59) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_58_0_43) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (125) with all_116_0_63, all_0_5_5, all_0_6_6, all_58_0_43, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_58_0_43) = all_0_6_6, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.27/32.37 | (236) all_116_0_63 = 0 | ? [v0] : ((v0 = 0 & in(all_0_5_5, all_58_0_43) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (138) with all_116_0_63, all_0_5_5, all_0_4_4, all_0_6_6, all_58_0_43 and discharging atoms set_union2(all_58_0_43, all_0_6_6) = all_0_4_4, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.27/32.37 | (237) all_116_0_63 = 0 | ? [v0] : ((v0 = 0 & in(all_0_5_5, all_58_0_43) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_4_4) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating formula (24) with all_116_0_63, all_0_5_5, all_0_4_4, all_97_0_59, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_97_0_59) = all_0_4_4, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.27/32.37 | (238) all_116_0_63 = 0 | ? [v0] : ((v0 = 0 & in(all_0_5_5, all_97_0_59) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_4_4) = v0))
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (233) with all_157_0_68 yields:
% 65.27/32.37 | (239) ( ~ (all_157_0_68 = 0) & in(all_0_5_5, all_58_0_43) = all_157_0_68) | ( ~ (all_157_0_68 = 0) & in(all_0_5_5, all_0_6_6) = all_157_0_68)
% 65.27/32.37 |
% 65.27/32.37 | Instantiating (232) with all_187_0_88 yields:
% 65.27/32.37 | (240) (all_187_0_88 = 0 & in(all_96_1_58, all_0_4_4) = 0) | ( ~ (all_187_0_88 = 0) & in(all_96_1_58, all_0_6_6) = all_187_0_88)
% 65.77/32.37 |
% 65.77/32.37 | Instantiating (234) with all_233_0_116 yields:
% 65.77/32.37 | (241) (all_233_0_116 = 0 & in(all_0_5_5, all_58_0_43) = 0) | (all_233_0_116 = 0 & in(all_0_5_5, all_0_6_6) = 0)
% 65.77/32.37 |
% 65.77/32.37 +-Applying beta-rule and splitting (237), into two cases.
% 65.77/32.37 |-Branch one:
% 65.77/32.37 | (242) all_116_0_63 = 0
% 65.77/32.37 |
% 65.77/32.37 | Equations (242) can reduce 207 to:
% 65.77/32.37 | (165) $false
% 65.77/32.37 |
% 65.77/32.37 |-The branch is then unsatisfiable
% 65.77/32.37 |-Branch two:
% 65.77/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.77/32.37 | (245) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_58_0_43) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_4_4) = v0))
% 65.77/32.37 |
% 65.77/32.37 +-Applying beta-rule and splitting (238), into two cases.
% 65.77/32.37 |-Branch one:
% 65.77/32.37 | (242) all_116_0_63 = 0
% 65.77/32.37 |
% 65.77/32.37 | Equations (242) can reduce 207 to:
% 65.77/32.37 | (165) $false
% 65.77/32.37 |
% 65.77/32.37 |-The branch is then unsatisfiable
% 65.77/32.37 |-Branch two:
% 65.77/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.77/32.37 | (249) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_97_0_59) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_4_4) = v0))
% 65.77/32.37 |
% 65.77/32.37 +-Applying beta-rule and splitting (235), into two cases.
% 65.77/32.37 |-Branch one:
% 65.77/32.37 | (242) all_116_0_63 = 0
% 65.77/32.37 |
% 65.77/32.37 | Equations (242) can reduce 207 to:
% 65.77/32.37 | (165) $false
% 65.77/32.37 |
% 65.77/32.37 |-The branch is then unsatisfiable
% 65.77/32.37 |-Branch two:
% 65.77/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.77/32.37 | (253) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_97_0_59) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_58_0_43) = v0))
% 65.77/32.37 |
% 65.77/32.37 +-Applying beta-rule and splitting (236), into two cases.
% 65.77/32.37 |-Branch one:
% 65.77/32.37 | (242) all_116_0_63 = 0
% 65.77/32.37 |
% 65.77/32.37 | Equations (242) can reduce 207 to:
% 65.77/32.37 | (165) $false
% 65.77/32.37 |
% 65.77/32.37 |-The branch is then unsatisfiable
% 65.77/32.37 |-Branch two:
% 65.77/32.37 | (207) ~ (all_116_0_63 = 0)
% 65.77/32.37 | (257) ? [v0] : ((v0 = 0 & in(all_0_5_5, all_58_0_43) = 0) | ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0))
% 65.77/32.37 |
% 65.77/32.38 +-Applying beta-rule and splitting (241), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (258) all_233_0_116 = 0 & in(all_0_5_5, all_58_0_43) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (258) yields:
% 65.77/32.38 | (259) all_233_0_116 = 0
% 65.77/32.38 | (260) in(all_0_5_5, all_58_0_43) = 0
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (239), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (261) ~ (all_157_0_68 = 0) & in(all_0_5_5, all_58_0_43) = all_157_0_68
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (261) yields:
% 65.77/32.38 | (262) ~ (all_157_0_68 = 0)
% 65.77/32.38 | (263) in(all_0_5_5, all_58_0_43) = all_157_0_68
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (134) with all_0_5_5, all_58_0_43, 0, all_157_0_68 and discharging atoms in(all_0_5_5, all_58_0_43) = all_157_0_68, in(all_0_5_5, all_58_0_43) = 0, yields:
% 65.77/32.38 | (264) all_157_0_68 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (264) can reduce 262 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (266) ~ (all_157_0_68 = 0) & in(all_0_5_5, all_0_6_6) = all_157_0_68
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (266) yields:
% 65.77/32.38 | (262) ~ (all_157_0_68 = 0)
% 65.77/32.38 | (268) in(all_0_5_5, all_0_6_6) = all_157_0_68
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (240), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (269) all_187_0_88 = 0 & in(all_96_1_58, all_0_4_4) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (269) yields:
% 65.77/32.38 | (270) all_187_0_88 = 0
% 65.77/32.38 | (271) in(all_96_1_58, all_0_4_4) = 0
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (101) with all_96_1_58, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_4_4, in(all_96_1_58, all_0_4_4) = 0, yields:
% 65.77/32.38 | (272) all_96_1_58 = all_0_5_5
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (134) with all_0_5_5, all_0_6_6, all_157_0_68, all_116_0_63 and discharging atoms in(all_0_5_5, all_0_6_6) = all_157_0_68, in(all_0_5_5, all_0_6_6) = all_116_0_63, yields:
% 65.77/32.38 | (273) all_157_0_68 = all_116_0_63
% 65.77/32.38 |
% 65.77/32.38 | Equations (273) can reduce 262 to:
% 65.77/32.38 | (207) ~ (all_116_0_63 = 0)
% 65.77/32.38 |
% 65.77/32.38 | From (272) and (219) follows:
% 65.77/32.38 | (275) in(all_0_5_5, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | From (273) and (268) follows:
% 65.77/32.38 | (208) in(all_0_5_5, all_0_6_6) = all_116_0_63
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (134) with all_0_5_5, all_0_6_6, 0, all_116_0_63 and discharging atoms in(all_0_5_5, all_0_6_6) = all_116_0_63, in(all_0_5_5, all_0_6_6) = 0, yields:
% 65.77/32.38 | (242) all_116_0_63 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (242) can reduce 207 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (279) ~ (all_187_0_88 = 0) & in(all_96_1_58, all_0_6_6) = all_187_0_88
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (279) yields:
% 65.77/32.38 | (280) ~ (all_187_0_88 = 0)
% 65.77/32.38 | (281) in(all_96_1_58, all_0_6_6) = all_187_0_88
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (134) with all_96_1_58, all_0_6_6, all_187_0_88, 0 and discharging atoms in(all_96_1_58, all_0_6_6) = all_187_0_88, in(all_96_1_58, all_0_6_6) = 0, yields:
% 65.77/32.38 | (270) all_187_0_88 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (270) can reduce 280 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (284) all_233_0_116 = 0 & in(all_0_5_5, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (284) yields:
% 65.77/32.38 | (259) all_233_0_116 = 0
% 65.77/32.38 | (275) in(all_0_5_5, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (134) with all_0_5_5, all_0_6_6, 0, all_116_0_63 and discharging atoms in(all_0_5_5, all_0_6_6) = all_116_0_63, in(all_0_5_5, all_0_6_6) = 0, yields:
% 65.77/32.38 | (242) all_116_0_63 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (242) can reduce 207 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (289) all_96_1_58 = 0 & disjoint(all_0_6_6, all_0_4_4) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (289) yields:
% 65.77/32.38 | (290) all_96_1_58 = 0
% 65.77/32.38 | (291) disjoint(all_0_6_6, all_0_4_4) = 0
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (140) with all_0_6_6, all_0_4_4, 0, all_111_0_62 and discharging atoms disjoint(all_0_6_6, all_0_4_4) = all_111_0_62, disjoint(all_0_6_6, all_0_4_4) = 0, yields:
% 65.77/32.38 | (292) all_111_0_62 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (292) can reduce 200 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (294) ~ (all_0_3_3 = 0) & (all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set)
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (294) yields:
% 65.77/32.38 | (295) ~ (all_0_3_3 = 0)
% 65.77/32.38 | (296) all_0_4_4 = all_0_6_6 | all_0_6_6 = empty_set
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (151), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (154) all_0_3_3 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (154) can reduce 295 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (295) ~ (all_0_3_3 = 0)
% 65.77/32.38 | (300) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (300) with all_56_0_473, all_56_1_474 yields:
% 65.77/32.38 | (301) ~ (all_56_0_473 = 0) & in(all_56_1_474, all_0_4_4) = all_56_0_473 & in(all_56_1_474, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (301) yields:
% 65.77/32.38 | (302) ~ (all_56_0_473 = 0)
% 65.77/32.38 | (303) in(all_56_1_474, all_0_4_4) = all_56_0_473
% 65.77/32.38 | (304) in(all_56_1_474, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (152), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (154) all_0_3_3 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (154) can reduce 295 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (295) ~ (all_0_3_3 = 0)
% 65.77/32.38 | (308) ? [v0] : ( ~ (v0 = empty_set) & set_difference(all_0_6_6, all_0_4_4) = v0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (308) with all_61_0_475 yields:
% 65.77/32.38 | (309) ~ (all_61_0_475 = empty_set) & set_difference(all_0_6_6, all_0_4_4) = all_61_0_475
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (309) yields:
% 65.77/32.38 | (310) ~ (all_61_0_475 = empty_set)
% 65.77/32.38 | (311) set_difference(all_0_6_6, all_0_4_4) = all_61_0_475
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (135) with all_61_0_475, all_0_6_6, all_0_4_4 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.38 | (312) ? [v0] : (set_union2(all_0_4_4, all_61_0_475) = v0 & set_union2(all_0_4_4, all_0_6_6) = v0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (53) with all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.38 | (313) subset(all_61_0_475, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (83) with all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.38 | (314) ? [v0] : (set_difference(v0, all_0_4_4) = all_61_0_475 & set_union2(all_0_6_6, all_0_4_4) = v0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (48) with all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.38 | (315) ? [v0] : (set_difference(all_0_6_6, all_61_0_475) = v0 & set_intersection2(all_0_6_6, all_0_4_4) = v0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (38) with all_56_0_473, all_56_1_474, all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, in(all_56_1_474, all_0_4_4) = all_56_0_473, yields:
% 65.77/32.38 | (316) all_56_0_473 = 0 | ? [v0] : ((v0 = 0 & in(all_56_1_474, all_61_0_475) = 0) | ( ~ (v0 = 0) & in(all_56_1_474, all_0_6_6) = v0))
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (76) with all_56_0_473, all_56_1_474, all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, in(all_56_1_474, all_0_4_4) = all_56_0_473, yields:
% 65.77/32.38 | (317) ? [v0] : ((v0 = 0 & ~ (all_56_0_473 = 0) & in(all_56_1_474, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_56_1_474, all_61_0_475) = v0))
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (85) with all_56_0_473, all_0_4_4, all_56_1_474 and discharging atoms in(all_56_1_474, all_0_4_4) = all_56_0_473, yields:
% 65.77/32.38 | (318) all_56_0_473 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_56_1_474) = v0 & subset(v0, all_0_4_4) = v1)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (122) with all_56_1_474, all_61_0_475, all_0_4_4, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_4_4) = all_61_0_475, in(all_56_1_474, all_0_6_6) = 0, yields:
% 65.77/32.38 | (319) ? [v0] : ((v0 = 0 & in(all_56_1_474, all_61_0_475) = 0) | (v0 = 0 & in(all_56_1_474, all_0_4_4) = 0))
% 65.77/32.38 |
% 65.77/32.38 | Instantiating formula (10) with all_0_6_6, all_56_1_474 and discharging atoms in(all_56_1_474, all_0_6_6) = 0, yields:
% 65.77/32.38 | (320) ? [v0] : (singleton(all_56_1_474) = v0 & subset(v0, all_0_6_6) = 0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (320) with all_74_0_477 yields:
% 65.77/32.38 | (321) singleton(all_56_1_474) = all_74_0_477 & subset(all_74_0_477, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (321) yields:
% 65.77/32.38 | (322) singleton(all_56_1_474) = all_74_0_477
% 65.77/32.38 | (323) subset(all_74_0_477, all_0_6_6) = 0
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (314) with all_78_0_479 yields:
% 65.77/32.38 | (324) set_difference(all_78_0_479, all_0_4_4) = all_61_0_475 & set_union2(all_0_6_6, all_0_4_4) = all_78_0_479
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (324) yields:
% 65.77/32.38 | (325) set_difference(all_78_0_479, all_0_4_4) = all_61_0_475
% 65.77/32.38 | (326) set_union2(all_0_6_6, all_0_4_4) = all_78_0_479
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (319) with all_81_0_481 yields:
% 65.77/32.38 | (327) (all_81_0_481 = 0 & in(all_56_1_474, all_61_0_475) = 0) | (all_81_0_481 = 0 & in(all_56_1_474, all_0_4_4) = 0)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (317) with all_82_0_482 yields:
% 65.77/32.38 | (328) (all_82_0_482 = 0 & ~ (all_56_0_473 = 0) & in(all_56_1_474, all_0_6_6) = 0) | ( ~ (all_82_0_482 = 0) & in(all_56_1_474, all_61_0_475) = all_82_0_482)
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (312) with all_84_0_484 yields:
% 65.77/32.38 | (329) set_union2(all_0_4_4, all_61_0_475) = all_84_0_484 & set_union2(all_0_4_4, all_0_6_6) = all_84_0_484
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (329) yields:
% 65.77/32.38 | (330) set_union2(all_0_4_4, all_61_0_475) = all_84_0_484
% 65.77/32.38 | (331) set_union2(all_0_4_4, all_0_6_6) = all_84_0_484
% 65.77/32.38 |
% 65.77/32.38 | Instantiating (315) with all_86_0_485 yields:
% 65.77/32.38 | (332) set_difference(all_0_6_6, all_61_0_475) = all_86_0_485 & set_intersection2(all_0_6_6, all_0_4_4) = all_86_0_485
% 65.77/32.38 |
% 65.77/32.38 | Applying alpha-rule on (332) yields:
% 65.77/32.38 | (333) set_difference(all_0_6_6, all_61_0_475) = all_86_0_485
% 65.77/32.38 | (334) set_intersection2(all_0_6_6, all_0_4_4) = all_86_0_485
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (316), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (335) all_56_0_473 = 0
% 65.77/32.38 |
% 65.77/32.38 | Equations (335) can reduce 302 to:
% 65.77/32.38 | (165) $false
% 65.77/32.38 |
% 65.77/32.38 |-The branch is then unsatisfiable
% 65.77/32.38 |-Branch two:
% 65.77/32.38 | (302) ~ (all_56_0_473 = 0)
% 65.77/32.38 | (338) ? [v0] : ((v0 = 0 & in(all_56_1_474, all_61_0_475) = 0) | ( ~ (v0 = 0) & in(all_56_1_474, all_0_6_6) = v0))
% 65.77/32.38 |
% 65.77/32.38 +-Applying beta-rule and splitting (327), into two cases.
% 65.77/32.38 |-Branch one:
% 65.77/32.38 | (339) all_81_0_481 = 0 & in(all_56_1_474, all_61_0_475) = 0
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (339) yields:
% 65.77/32.39 | (340) all_81_0_481 = 0
% 65.77/32.39 | (341) in(all_56_1_474, all_61_0_475) = 0
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (328), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (342) all_82_0_482 = 0 & ~ (all_56_0_473 = 0) & in(all_56_1_474, all_0_6_6) = 0
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (342) yields:
% 65.77/32.39 | (343) all_82_0_482 = 0
% 65.77/32.39 | (302) ~ (all_56_0_473 = 0)
% 65.77/32.39 | (304) in(all_56_1_474, all_0_6_6) = 0
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (118) with all_61_0_475, all_0_4_4, all_78_0_479 and discharging atoms set_difference(all_78_0_479, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.39 | (346) all_61_0_475 = empty_set | ? [v0] : ( ~ (v0 = 0) & subset(all_78_0_479, all_0_4_4) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (135) with all_61_0_475, all_78_0_479, all_0_4_4 and discharging atoms set_difference(all_78_0_479, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.39 | (347) ? [v0] : (set_union2(all_0_4_4, all_78_0_479) = v0 & set_union2(all_0_4_4, all_61_0_475) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (42) with all_61_0_475, all_78_0_479, all_0_4_4 and discharging atoms set_difference(all_78_0_479, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.39 | (348) ? [v0] : ((v0 = all_78_0_479 & set_union2(all_0_4_4, all_61_0_475) = all_78_0_479) | ( ~ (v0 = 0) & subset(all_0_4_4, all_78_0_479) = v0))
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (48) with all_61_0_475, all_0_4_4, all_78_0_479 and discharging atoms set_difference(all_78_0_479, all_0_4_4) = all_61_0_475, yields:
% 65.77/32.39 | (349) ? [v0] : (set_difference(all_78_0_479, all_61_0_475) = v0 & set_intersection2(all_78_0_479, all_0_4_4) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (83) with all_86_0_485, all_61_0_475, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_61_0_475) = all_86_0_485, yields:
% 65.77/32.39 | (350) ? [v0] : (set_difference(v0, all_61_0_475) = all_86_0_485 & set_union2(all_0_6_6, all_61_0_475) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (149) with all_0_6_6, all_74_0_477 and discharging atoms subset(all_74_0_477, all_0_6_6) = 0, yields:
% 65.77/32.39 | (351) set_difference(all_74_0_477, all_0_6_6) = empty_set
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (149) with all_0_6_6, all_61_0_475 and discharging atoms subset(all_61_0_475, all_0_6_6) = 0, yields:
% 65.77/32.39 | (352) set_difference(all_61_0_475, all_0_6_6) = empty_set
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (139) with all_84_0_484, all_61_0_475, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_61_0_475) = all_84_0_484, yields:
% 65.77/32.39 | (353) ? [v0] : (set_difference(all_84_0_484, all_61_0_475) = v0 & set_difference(all_0_4_4, all_61_0_475) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (30) with all_84_0_484, all_61_0_475, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_61_0_475) = all_84_0_484, yields:
% 65.77/32.39 | (354) ? [v0] : (set_difference(all_61_0_475, all_0_4_4) = v0 & set_union2(all_0_4_4, v0) = all_84_0_484)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (21) with all_84_0_484, all_0_4_4, all_0_6_6 and discharging atoms set_union2(all_0_4_4, all_0_6_6) = all_84_0_484, yields:
% 65.77/32.39 | (355) set_union2(all_0_6_6, all_0_4_4) = all_84_0_484
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (57) with all_84_0_484, all_0_6_6, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_0_6_6) = all_84_0_484, yields:
% 65.77/32.39 | (356) subset(all_0_4_4, all_84_0_484) = 0
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (350) with all_126_0_490 yields:
% 65.77/32.39 | (357) set_difference(all_126_0_490, all_61_0_475) = all_86_0_485 & set_union2(all_0_6_6, all_61_0_475) = all_126_0_490
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (357) yields:
% 65.77/32.39 | (358) set_difference(all_126_0_490, all_61_0_475) = all_86_0_485
% 65.77/32.39 | (359) set_union2(all_0_6_6, all_61_0_475) = all_126_0_490
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (348) with all_136_0_498 yields:
% 65.77/32.39 | (360) (all_136_0_498 = all_78_0_479 & set_union2(all_0_4_4, all_61_0_475) = all_78_0_479) | ( ~ (all_136_0_498 = 0) & subset(all_0_4_4, all_78_0_479) = all_136_0_498)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (354) with all_143_0_503 yields:
% 65.77/32.39 | (361) set_difference(all_61_0_475, all_0_4_4) = all_143_0_503 & set_union2(all_0_4_4, all_143_0_503) = all_84_0_484
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (361) yields:
% 65.77/32.39 | (362) set_difference(all_61_0_475, all_0_4_4) = all_143_0_503
% 65.77/32.39 | (363) set_union2(all_0_4_4, all_143_0_503) = all_84_0_484
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (353) with all_148_0_506 yields:
% 65.77/32.39 | (364) set_difference(all_84_0_484, all_61_0_475) = all_148_0_506 & set_difference(all_0_4_4, all_61_0_475) = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (364) yields:
% 65.77/32.39 | (365) set_difference(all_84_0_484, all_61_0_475) = all_148_0_506
% 65.77/32.39 | (366) set_difference(all_0_4_4, all_61_0_475) = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (349) with all_158_0_514 yields:
% 65.77/32.39 | (367) set_difference(all_78_0_479, all_61_0_475) = all_158_0_514 & set_intersection2(all_78_0_479, all_0_4_4) = all_158_0_514
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (367) yields:
% 65.77/32.39 | (368) set_difference(all_78_0_479, all_61_0_475) = all_158_0_514
% 65.77/32.39 | (369) set_intersection2(all_78_0_479, all_0_4_4) = all_158_0_514
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (347) with all_174_0_523 yields:
% 65.77/32.39 | (370) set_union2(all_0_4_4, all_78_0_479) = all_174_0_523 & set_union2(all_0_4_4, all_61_0_475) = all_174_0_523
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (370) yields:
% 65.77/32.39 | (371) set_union2(all_0_4_4, all_78_0_479) = all_174_0_523
% 65.77/32.39 | (372) set_union2(all_0_4_4, all_61_0_475) = all_174_0_523
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (346), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (373) all_61_0_475 = empty_set
% 65.77/32.39 |
% 65.77/32.39 | Equations (373) can reduce 310 to:
% 65.77/32.39 | (165) $false
% 65.77/32.39 |
% 65.77/32.39 |-The branch is then unsatisfiable
% 65.77/32.39 |-Branch two:
% 65.77/32.39 | (310) ~ (all_61_0_475 = empty_set)
% 65.77/32.39 | (376) ? [v0] : ( ~ (v0 = 0) & subset(all_78_0_479, all_0_4_4) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (376) with all_205_0_537 yields:
% 65.77/32.39 | (377) ~ (all_205_0_537 = 0) & subset(all_78_0_479, all_0_4_4) = all_205_0_537
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (377) yields:
% 65.77/32.39 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.39 | (379) subset(all_78_0_479, all_0_4_4) = all_205_0_537
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (82) with all_0_4_4, all_61_0_475, all_174_0_523, all_84_0_484 and discharging atoms set_union2(all_0_4_4, all_61_0_475) = all_174_0_523, set_union2(all_0_4_4, all_61_0_475) = all_84_0_484, yields:
% 65.77/32.39 | (380) all_174_0_523 = all_84_0_484
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (82) with all_0_6_6, all_0_4_4, all_84_0_484, all_78_0_479 and discharging atoms set_union2(all_0_6_6, all_0_4_4) = all_84_0_484, set_union2(all_0_6_6, all_0_4_4) = all_78_0_479, yields:
% 65.77/32.39 | (381) all_84_0_484 = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | Combining equations (381,380) yields a new equation:
% 65.77/32.39 | (382) all_174_0_523 = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | From (381) and (365) follows:
% 65.77/32.39 | (383) set_difference(all_78_0_479, all_61_0_475) = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | From (381) and (356) follows:
% 65.77/32.39 | (384) subset(all_0_4_4, all_78_0_479) = 0
% 65.77/32.39 |
% 65.77/32.39 | From (381) and (363) follows:
% 65.77/32.39 | (385) set_union2(all_0_4_4, all_143_0_503) = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | From (382) and (371) follows:
% 65.77/32.39 | (386) set_union2(all_0_4_4, all_78_0_479) = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | From (381) and (331) follows:
% 65.77/32.39 | (387) set_union2(all_0_4_4, all_0_6_6) = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (360), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (388) all_136_0_498 = all_78_0_479 & set_union2(all_0_4_4, all_61_0_475) = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (388) yields:
% 65.77/32.39 | (389) all_136_0_498 = all_78_0_479
% 65.77/32.39 | (390) set_union2(all_0_4_4, all_61_0_475) = all_78_0_479
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (100) with all_78_0_479, all_61_0_475, all_148_0_506, all_158_0_514 and discharging atoms set_difference(all_78_0_479, all_61_0_475) = all_158_0_514, set_difference(all_78_0_479, all_61_0_475) = all_148_0_506, yields:
% 65.77/32.39 | (391) all_158_0_514 = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | From (391) and (369) follows:
% 65.77/32.39 | (392) set_intersection2(all_78_0_479, all_0_4_4) = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (135) with empty_set, all_74_0_477, all_0_6_6 and discharging atoms set_difference(all_74_0_477, all_0_6_6) = empty_set, yields:
% 65.77/32.39 | (393) ? [v0] : (set_union2(all_0_6_6, all_74_0_477) = v0 & set_union2(all_0_6_6, empty_set) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (135) with empty_set, all_61_0_475, all_0_6_6 and discharging atoms set_difference(all_61_0_475, all_0_6_6) = empty_set, yields:
% 65.77/32.39 | (394) ? [v0] : (set_union2(all_0_6_6, all_61_0_475) = v0 & set_union2(all_0_6_6, empty_set) = v0)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (53) with all_148_0_506, all_61_0_475, all_0_4_4 and discharging atoms set_difference(all_0_4_4, all_61_0_475) = all_148_0_506, yields:
% 65.77/32.39 | (395) subset(all_148_0_506, all_0_4_4) = 0
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (74) with all_205_0_537, all_0_4_4, all_78_0_479 and discharging atoms subset(all_78_0_479, all_0_4_4) = all_205_0_537, yields:
% 65.77/32.39 | (396) all_205_0_537 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_78_0_479) = 0 & in(v0, all_0_4_4) = v1)
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (67) with all_78_0_479, all_0_4_4 and discharging atoms subset(all_0_4_4, all_78_0_479) = 0, yields:
% 65.77/32.39 | (397) set_intersection2(all_0_4_4, all_78_0_479) = all_0_4_4
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (37) with all_148_0_506, all_78_0_479, all_0_4_4 and discharging atoms set_intersection2(all_78_0_479, all_0_4_4) = all_148_0_506, yields:
% 65.77/32.39 | (398) set_intersection2(all_0_4_4, all_78_0_479) = all_148_0_506
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (13) with all_205_0_537, all_78_0_479, all_143_0_503, all_0_4_4, all_0_4_4 and discharging atoms subset(all_78_0_479, all_0_4_4) = all_205_0_537, set_union2(all_0_4_4, all_143_0_503) = all_78_0_479, yields:
% 65.77/32.39 | (399) all_205_0_537 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_143_0_503, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (13) with all_205_0_537, all_78_0_479, all_78_0_479, all_0_4_4, all_0_4_4 and discharging atoms subset(all_78_0_479, all_0_4_4) = all_205_0_537, set_union2(all_0_4_4, all_78_0_479) = all_78_0_479, yields:
% 65.77/32.39 | (400) all_205_0_537 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_78_0_479, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (13) with all_205_0_537, all_78_0_479, all_61_0_475, all_0_4_4, all_0_4_4 and discharging atoms subset(all_78_0_479, all_0_4_4) = all_205_0_537, set_union2(all_0_4_4, all_61_0_475) = all_78_0_479, yields:
% 65.77/32.39 | (401) all_205_0_537 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_61_0_475, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (13) with all_205_0_537, all_78_0_479, all_0_6_6, all_0_4_4, all_0_4_4 and discharging atoms subset(all_78_0_479, all_0_4_4) = all_205_0_537, set_union2(all_0_4_4, all_0_6_6) = all_78_0_479, yields:
% 65.77/32.39 | (402) all_205_0_537 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_6_6, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 | Instantiating formula (86) with 0, all_56_1_474, all_126_0_490, all_61_0_475, all_0_6_6 and discharging atoms set_union2(all_0_6_6, all_61_0_475) = all_126_0_490, in(all_56_1_474, all_0_6_6) = 0, yields:
% 65.77/32.39 | (403) in(all_56_1_474, all_126_0_490) = 0
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (394) with all_305_0_559 yields:
% 65.77/32.39 | (404) set_union2(all_0_6_6, all_61_0_475) = all_305_0_559 & set_union2(all_0_6_6, empty_set) = all_305_0_559
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (404) yields:
% 65.77/32.39 | (405) set_union2(all_0_6_6, all_61_0_475) = all_305_0_559
% 65.77/32.39 | (406) set_union2(all_0_6_6, empty_set) = all_305_0_559
% 65.77/32.39 |
% 65.77/32.39 | Instantiating (393) with all_434_0_643 yields:
% 65.77/32.39 | (407) set_union2(all_0_6_6, all_74_0_477) = all_434_0_643 & set_union2(all_0_6_6, empty_set) = all_434_0_643
% 65.77/32.39 |
% 65.77/32.39 | Applying alpha-rule on (407) yields:
% 65.77/32.39 | (408) set_union2(all_0_6_6, all_74_0_477) = all_434_0_643
% 65.77/32.39 | (409) set_union2(all_0_6_6, empty_set) = all_434_0_643
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (399), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (410) all_205_0_537 = 0
% 65.77/32.39 |
% 65.77/32.39 | Equations (410) can reduce 378 to:
% 65.77/32.39 | (165) $false
% 65.77/32.39 |
% 65.77/32.39 |-The branch is then unsatisfiable
% 65.77/32.39 |-Branch two:
% 65.77/32.39 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.39 | (413) ? [v0] : (( ~ (v0 = 0) & subset(all_143_0_503, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (401), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (410) all_205_0_537 = 0
% 65.77/32.39 |
% 65.77/32.39 | Equations (410) can reduce 378 to:
% 65.77/32.39 | (165) $false
% 65.77/32.39 |
% 65.77/32.39 |-The branch is then unsatisfiable
% 65.77/32.39 |-Branch two:
% 65.77/32.39 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.39 | (417) ? [v0] : (( ~ (v0 = 0) & subset(all_61_0_475, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.39 |
% 65.77/32.39 +-Applying beta-rule and splitting (396), into two cases.
% 65.77/32.39 |-Branch one:
% 65.77/32.39 | (410) all_205_0_537 = 0
% 65.77/32.39 |
% 65.77/32.39 | Equations (410) can reduce 378 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.40 | (421) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_78_0_479) = 0 & in(v0, all_0_4_4) = v1)
% 65.77/32.40 |
% 65.77/32.40 +-Applying beta-rule and splitting (400), into two cases.
% 65.77/32.40 |-Branch one:
% 65.77/32.40 | (410) all_205_0_537 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (410) can reduce 378 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.40 | (425) ? [v0] : (( ~ (v0 = 0) & subset(all_78_0_479, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0))
% 65.77/32.40 |
% 65.77/32.40 +-Applying beta-rule and splitting (402), into two cases.
% 65.77/32.40 |-Branch one:
% 65.77/32.40 | (410) all_205_0_537 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (410) can reduce 378 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (378) ~ (all_205_0_537 = 0)
% 65.77/32.40 | (429) ? [v0] : (( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_6_6, all_0_4_4) = v0))
% 65.77/32.40 |
% 65.77/32.40 | Instantiating (429) with all_632_0_1135 yields:
% 65.77/32.40 | (430) ( ~ (all_632_0_1135 = 0) & subset(all_0_4_4, all_0_4_4) = all_632_0_1135) | ( ~ (all_632_0_1135 = 0) & subset(all_0_6_6, all_0_4_4) = all_632_0_1135)
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (65) with all_0_4_4, all_78_0_479, all_0_4_4, all_148_0_506 and discharging atoms set_intersection2(all_0_4_4, all_78_0_479) = all_148_0_506, set_intersection2(all_0_4_4, all_78_0_479) = all_0_4_4, yields:
% 65.77/32.40 | (431) all_148_0_506 = all_0_4_4
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (82) with all_0_6_6, all_61_0_475, all_305_0_559, all_126_0_490 and discharging atoms set_union2(all_0_6_6, all_61_0_475) = all_305_0_559, set_union2(all_0_6_6, all_61_0_475) = all_126_0_490, yields:
% 65.77/32.40 | (432) all_305_0_559 = all_126_0_490
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (34) with all_434_0_643, all_0_6_6 and discharging atoms set_union2(all_0_6_6, empty_set) = all_434_0_643, yields:
% 65.77/32.40 | (433) all_434_0_643 = all_0_6_6
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (82) with all_0_6_6, empty_set, all_305_0_559, all_434_0_643 and discharging atoms set_union2(all_0_6_6, empty_set) = all_434_0_643, set_union2(all_0_6_6, empty_set) = all_305_0_559, yields:
% 65.77/32.40 | (434) all_434_0_643 = all_305_0_559
% 65.77/32.40 |
% 65.77/32.40 | Combining equations (434,433) yields a new equation:
% 65.77/32.40 | (435) all_305_0_559 = all_0_6_6
% 65.77/32.40 |
% 65.77/32.40 | Simplifying 435 yields:
% 65.77/32.40 | (436) all_305_0_559 = all_0_6_6
% 65.77/32.40 |
% 65.77/32.40 | Combining equations (436,432) yields a new equation:
% 65.77/32.40 | (437) all_126_0_490 = all_0_6_6
% 65.77/32.40 |
% 65.77/32.40 | From (431) and (395) follows:
% 65.77/32.40 | (438) subset(all_0_4_4, all_0_4_4) = 0
% 65.77/32.40 |
% 65.77/32.40 | From (437) and (403) follows:
% 65.77/32.40 | (304) in(all_56_1_474, all_0_6_6) = 0
% 65.77/32.40 |
% 65.77/32.40 +-Applying beta-rule and splitting (430), into two cases.
% 65.77/32.40 |-Branch one:
% 65.77/32.40 | (440) ~ (all_632_0_1135 = 0) & subset(all_0_4_4, all_0_4_4) = all_632_0_1135
% 65.77/32.40 |
% 65.77/32.40 | Applying alpha-rule on (440) yields:
% 65.77/32.40 | (441) ~ (all_632_0_1135 = 0)
% 65.77/32.40 | (442) subset(all_0_4_4, all_0_4_4) = all_632_0_1135
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (136) with all_0_4_4, all_0_4_4, 0, all_632_0_1135 and discharging atoms subset(all_0_4_4, all_0_4_4) = all_632_0_1135, subset(all_0_4_4, all_0_4_4) = 0, yields:
% 65.77/32.40 | (443) all_632_0_1135 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (443) can reduce 441 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (445) ~ (all_632_0_1135 = 0) & subset(all_0_6_6, all_0_4_4) = all_632_0_1135
% 65.77/32.40 |
% 65.77/32.40 | Applying alpha-rule on (445) yields:
% 65.77/32.40 | (441) ~ (all_632_0_1135 = 0)
% 65.77/32.40 | (447) subset(all_0_6_6, all_0_4_4) = all_632_0_1135
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (136) with all_0_6_6, all_0_4_4, all_632_0_1135, all_0_3_3 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_632_0_1135, subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 65.77/32.40 | (448) all_632_0_1135 = all_0_3_3
% 65.77/32.40 |
% 65.77/32.40 | Equations (448) can reduce 441 to:
% 65.77/32.40 | (295) ~ (all_0_3_3 = 0)
% 65.77/32.40 |
% 65.77/32.40 | From (448) and (447) follows:
% 65.77/32.40 | (72) subset(all_0_6_6, all_0_4_4) = all_0_3_3
% 65.77/32.40 |
% 65.77/32.40 +-Applying beta-rule and splitting (296), into two cases.
% 65.77/32.40 |-Branch one:
% 65.77/32.40 | (195) all_0_6_6 = empty_set
% 65.77/32.40 |
% 65.77/32.40 | From (195) and (304) follows:
% 65.77/32.40 | (452) in(all_56_1_474, empty_set) = 0
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (71) with all_56_1_474 and discharging atoms in(all_56_1_474, empty_set) = 0, yields:
% 65.77/32.40 | (453) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (156) ~ (all_0_6_6 = empty_set)
% 65.77/32.40 | (164) all_0_4_4 = all_0_6_6
% 65.77/32.40 |
% 65.77/32.40 | From (164) and (72) follows:
% 65.77/32.40 | (456) subset(all_0_6_6, all_0_6_6) = all_0_3_3
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (3) with all_0_3_3, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_6_6) = all_0_3_3, yields:
% 65.77/32.40 | (154) all_0_3_3 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (154) can reduce 295 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (459) ~ (all_136_0_498 = 0) & subset(all_0_4_4, all_78_0_479) = all_136_0_498
% 65.77/32.40 |
% 65.77/32.40 | Applying alpha-rule on (459) yields:
% 65.77/32.40 | (460) ~ (all_136_0_498 = 0)
% 65.77/32.40 | (461) subset(all_0_4_4, all_78_0_479) = all_136_0_498
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (136) with all_0_4_4, all_78_0_479, 0, all_136_0_498 and discharging atoms subset(all_0_4_4, all_78_0_479) = all_136_0_498, subset(all_0_4_4, all_78_0_479) = 0, yields:
% 65.77/32.40 | (462) all_136_0_498 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (462) can reduce 460 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (464) ~ (all_82_0_482 = 0) & in(all_56_1_474, all_61_0_475) = all_82_0_482
% 65.77/32.40 |
% 65.77/32.40 | Applying alpha-rule on (464) yields:
% 65.77/32.40 | (465) ~ (all_82_0_482 = 0)
% 65.77/32.40 | (466) in(all_56_1_474, all_61_0_475) = all_82_0_482
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (134) with all_56_1_474, all_61_0_475, 0, all_82_0_482 and discharging atoms in(all_56_1_474, all_61_0_475) = all_82_0_482, in(all_56_1_474, all_61_0_475) = 0, yields:
% 65.77/32.40 | (343) all_82_0_482 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (343) can reduce 465 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (469) all_81_0_481 = 0 & in(all_56_1_474, all_0_4_4) = 0
% 65.77/32.40 |
% 65.77/32.40 | Applying alpha-rule on (469) yields:
% 65.77/32.40 | (340) all_81_0_481 = 0
% 65.77/32.40 | (471) in(all_56_1_474, all_0_4_4) = 0
% 65.77/32.40 |
% 65.77/32.40 +-Applying beta-rule and splitting (318), into two cases.
% 65.77/32.40 |-Branch one:
% 65.77/32.40 | (335) all_56_0_473 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (335) can reduce 302 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 |-Branch two:
% 65.77/32.40 | (302) ~ (all_56_0_473 = 0)
% 65.77/32.40 | (475) ? [v0] : ? [v1] : ( ~ (v1 = 0) & singleton(all_56_1_474) = v0 & subset(v0, all_0_4_4) = v1)
% 65.77/32.40 |
% 65.77/32.40 | Instantiating formula (134) with all_56_1_474, all_0_4_4, 0, all_56_0_473 and discharging atoms in(all_56_1_474, all_0_4_4) = all_56_0_473, in(all_56_1_474, all_0_4_4) = 0, yields:
% 65.77/32.40 | (335) all_56_0_473 = 0
% 65.77/32.40 |
% 65.77/32.40 | Equations (335) can reduce 302 to:
% 65.77/32.40 | (165) $false
% 65.77/32.40 |
% 65.77/32.40 |-The branch is then unsatisfiable
% 65.77/32.40 % SZS output end Proof for theBenchmark
% 65.77/32.40
% 65.77/32.40 31775ms
%------------------------------------------------------------------------------