TSTP Solution File: SEU232+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU232+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:57 EDT 2022
% Result : Theorem 29.40s 7.68s
% Output : Proof 68.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEU232+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 20:33:15 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.62 (c) Peter Backeman, 2014-2015
% 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62 Bug reports to peter@backeman.se
% 0.49/0.62
% 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.62
% 0.49/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.79/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/1.00 Prover 0: Preprocessing ...
% 2.18/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.18/1.23 Prover 0: Constructing countermodel ...
% 11.93/3.54 Prover 0: gave up
% 11.93/3.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.04/3.57 Prover 1: Preprocessing ...
% 12.41/3.67 Prover 1: Warning: ignoring some quantifiers
% 12.41/3.67 Prover 1: Constructing countermodel ...
% 23.88/6.45 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 24.48/6.52 Prover 2: Preprocessing ...
% 24.79/6.62 Prover 2: Warning: ignoring some quantifiers
% 25.05/6.62 Prover 2: Constructing countermodel ...
% 29.22/7.67 Prover 2: proved (1228ms)
% 29.40/7.68 Prover 1: stopped
% 29.40/7.68
% 29.40/7.68 No countermodel exists, formula is valid
% 29.40/7.68 % SZS status Theorem for theBenchmark
% 29.40/7.68
% 29.40/7.68 Generating proof ... Warning: ignoring some quantifiers
% 67.61/27.41 found it (size 161)
% 67.61/27.41
% 67.61/27.41 % SZS output start Proof for theBenchmark
% 67.61/27.41 Assumed formulas after preprocessing and simplification:
% 67.61/27.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v2 = 0) & relation_empty_yielding(v4) = 0 & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(v5) = 0 & relation(v14) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v8) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & epsilon_transitive(v13) = 0 & ordinal(v13) = 0 & ordinal(v1) = 0 & ordinal(v0) = v2 & epsilon_connected(v13) = 0 & function(v14) = 0 & function(v10) = 0 & function(v5) = 0 & function(v3) = 0 & empty(v12) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & in(v0, v1) = 0 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (element(v15, v17) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v15, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v17) = v19) | ? [v20] : ((v20 = 0 & in(v18, v16) = 0) | ( ~ (v20 = 0) & in(v18, v15) = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v16) = v19) | ? [v20] : ((v20 = 0 & in(v18, v17) = 0) | ( ~ (v20 = 0) & in(v18, v15) = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v16) = v19) | ? [v20] : ((v20 = 0 & ~ (v19 = 0) & in(v18, v15) = 0) | ( ~ (v20 = 0) & in(v18, v17) = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v15) = v19) | ? [v20] : ((v19 = 0 & ~ (v20 = 0) & in(v18, v16) = v20) | ( ~ (v20 = 0) & in(v18, v17) = v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | v17 = v16 | ~ (epsilon_connected(v15) = 0) | ~ (in(v17, v16) = v18) | ? [v19] : ((v19 = 0 & in(v16, v17) = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | v17 = v16 | ~ (epsilon_connected(v15) = 0) | ~ (in(v16, v17) = v18) | ? [v19] : ((v19 = 0 & in(v17, v16) = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & subset(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (element(v15, v17) = v18) | ~ (in(v15, v16) = 0) | ? [v19] : ? [v20] : ( ~ (v20 = 0) & powerset(v17) = v19 & element(v16, v19) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(v15, v16) = 0) | ~ (in(v17, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v17, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (element(v18, v17) = v16) | ~ (element(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_difference(v18, v17) = v16) | ~ (set_difference(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset(v18, v17) = v16) | ~ (subset(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (in(v18, v17) = v16) | ~ (in(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (in(v15, v16) = 0) | element(v15, v17) = 0) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (in(v15, v16) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v16) = v19 & in(v18, v15) = 0)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ (in(v18, v15) = 0) | ? [v19] : ((v19 = 0 & in(v18, v17) = 0) | (v19 = 0 & in(v18, v16) = 0))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (((v22 = 0 & in(v19, v17) = 0) | ( ~ (v21 = 0) & in(v19, v16) = v21) | ( ~ (v20 = 0) & in(v19, v15) = v20)) & ((v21 = 0 & ~ (v22 = 0) & in(v19, v17) = v22 & in(v19, v16) = 0) | (v20 = 0 & in(v19, v15) = 0)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v16, v15) = v17) | ~ (epsilon_transitive(v15) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v16, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & in(v18, v16) = v19 & in(v18, v15) = 0)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (in(v15, v16) = v17) | ? [v18] : ((v18 = 0 & empty(v16) = 0) | ( ~ (v18 = 0) & element(v15, v16) = v18))) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_empty_yielding(v17) = v16) | ~ (relation_empty_yielding(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (one_to_one(v17) = v16) | ~ (one_to_one(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation(v17) = v16) | ~ (relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (epsilon_transitive(v17) = v16) | ~ (epsilon_transitive(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (ordinal(v17) = v16) | ~ (ordinal(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (epsilon_connected(v17) = v16) | ~ (epsilon_connected(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (function(v17) = v16) | ~ (function(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (empty(v17) = v16) | ~ (empty(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | subset(v15, v16) = 0) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : ((v18 = 0 & relation(v17) = 0) | ( ~ (v18 = 0) & relation(v16) = v18) | ( ~ (v18 = 0) & relation(v15) = v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset(v15, v16) = 0) | ~ (in(v17, v15) = 0) | in(v17, v16) = 0) & ! [v15] : ! [v16] : ! [v17] : ( ~ (empty(v17) = 0) | ~ (in(v15, v16) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v17) = v18 & element(v16, v18) = v19)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (in(v17, v15) = 0) | ~ (in(v16, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (in(v17, v15) = 0) | ~ (in(v15, v16) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | ~ (in(v15, v16) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v17, v15) = v18)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_difference(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (empty(v16) = 0) | ~ (empty(v15) = 0)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_difference(empty_set, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (relation(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (epsilon_transitive(v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & subset(v17, v15) = v18 & in(v17, v15) = 0)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (ordinal(v15) = v16) | ? [v17] : (( ~ (v17 = 0) & epsilon_transitive(v15) = v17) | ( ~ (v17 = 0) & epsilon_connected(v15) = v17))) & ! [v15] : ! [v16] : (v16 = 0 | ~ (epsilon_connected(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v20 = 0) & ~ (v19 = 0) & ~ (v18 = v17) & in(v18, v17) = v20 & in(v18, v15) = 0 & in(v17, v18) = v19 & in(v17, v15) = 0)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (function(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : ( ~ (element(v15, v16) = 0) | ? [v17] : ((v17 = 0 & empty(v16) = 0) | (v17 = 0 & in(v15, v16) = 0))) & ! [v15] : ! [v16] : ( ~ (subset(v15, v16) = 0) | ? [v17] : (powerset(v16) = v17 & element(v15, v17) = 0)) & ! [v15] : ! [v16] : ( ~ (one_to_one(v15) = v16) | ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & relation(v15) = 0 & function(v15) = 0) | ( ~ (v17 = 0) & relation(v15) = v17) | ( ~ (v17 = 0) & function(v15) = v17) | ( ~ (v17 = 0) & empty(v15) = v17))) & ! [v15] : ! [v16] : ( ~ (epsilon_transitive(v15) = v16) | ? [v17] : ((v17 = 0 & v16 = 0 & epsilon_connected(v15) = 0) | ( ~ (v17 = 0) & ordinal(v15) = v17))) & ! [v15] : ! [v16] : ( ~ (epsilon_transitive(v15) = 0) | ~ (in(v16, v15) = 0) | subset(v16, v15) = 0) & ! [v15] : ! [v16] : ( ~ (epsilon_connected(v15) = v16) | ? [v17] : ((v17 = 0 & v16 = 0 & epsilon_transitive(v15) = 0) | ( ~ (v17 = 0) & ordinal(v15) = v17))) & ! [v15] : ! [v16] : ( ~ (in(v16, v15) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v15, v16) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | element(v15, v16) = 0) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v15) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : (in(v17, v16) = 0 & ! [v18] : ( ~ (in(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v16) = v19)) & ! [v18] : ( ~ (in(v18, v16) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v17) = v19)))) & ! [v15] : (v15 = empty_set | ~ (empty(v15) = 0)) & ! [v15] : ( ~ (relation(v15) = 0) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & one_to_one(v15) = 0 & function(v15) = 0) | ( ~ (v16 = 0) & function(v15) = v16) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v15] : ( ~ (epsilon_transitive(v15) = 0) | ? [v16] : ((v16 = 0 & ordinal(v15) = 0) | ( ~ (v16 = 0) & epsilon_connected(v15) = v16))) & ! [v15] : ( ~ (ordinal(v15) = 0) | (epsilon_transitive(v15) = 0 & epsilon_connected(v15) = 0)) & ! [v15] : ( ~ (epsilon_connected(v15) = 0) | ? [v16] : ((v16 = 0 & ordinal(v15) = 0) | ( ~ (v16 = 0) & epsilon_transitive(v15) = v16))) & ! [v15] : ( ~ (function(v15) = 0) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & one_to_one(v15) = 0 & relation(v15) = 0) | ( ~ (v16 = 0) & relation(v15) = v16) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v15] : ( ~ (empty(v15) = 0) | relation(v15) = 0) & ! [v15] : ( ~ (empty(v15) = 0) | function(v15) = 0) & ! [v15] : ( ~ (empty(v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & one_to_one(v15) = 0 & relation(v15) = 0 & function(v15) = 0) | ( ~ (v16 = 0) & relation(v15) = v16) | ( ~ (v16 = 0) & function(v15) = v16))) & ? [v15] : ? [v16] : ? [v17] : element(v16, v15) = v17 & ? [v15] : ? [v16] : ? [v17] : set_difference(v16, v15) = v17 & ? [v15] : ? [v16] : ? [v17] : subset(v16, v15) = v17 & ? [v15] : ? [v16] : ? [v17] : in(v16, v15) = v17 & ? [v15] : ? [v16] : powerset(v15) = v16 & ? [v15] : ? [v16] : relation_empty_yielding(v15) = v16 & ? [v15] : ? [v16] : element(v16, v15) = 0 & ? [v15] : ? [v16] : one_to_one(v15) = v16 & ? [v15] : ? [v16] : relation(v15) = v16 & ? [v15] : ? [v16] : epsilon_transitive(v15) = v16 & ? [v15] : ? [v16] : ordinal(v15) = v16 & ? [v15] : ? [v16] : epsilon_connected(v15) = v16 & ? [v15] : ? [v16] : function(v15) = v16 & ? [v15] : ? [v16] : empty(v15) = v16)
% 67.88/27.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 yields:
% 67.88/27.47 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_12_12 = 0) & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(all_0_11_11) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(all_0_9_9) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_6_6) = 0 & relation(all_0_9_9) = 0 & relation(all_0_10_10) = 0 & relation(all_0_11_11) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_13_13) = 0 & ordinal(all_0_14_14) = all_0_12_12 & epsilon_connected(all_0_1_1) = 0 & function(all_0_0_0) = 0 & function(all_0_4_4) = 0 & function(all_0_9_9) = 0 & function(all_0_11_11) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(all_0_8_8) = all_0_7_7 & empty(empty_set) = 0 & in(all_0_14_14, all_0_13_13) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [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] : ( ~ (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] : (v3 = 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ((v4 = 0 & in(v1, v2) = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v4 = 0) & in(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v4 = 0) & in(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [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] : (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] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [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 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v2, v0) = 0) | ~ (in(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v2, v0) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [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] : (in(v2, v1) = 0 & ! [v3] : ( ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4)) & ! [v3] : ( ~ (in(v3, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v2) = v4)))) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 & ? [v0] : ? [v1] : ordinal(v0) = v1 & ? [v0] : ? [v1] : epsilon_connected(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 67.88/27.49 |
% 67.88/27.49 | Applying alpha-rule on (1) yields:
% 67.88/27.49 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 67.88/27.49 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (in(v2, v1) = 0 & ! [v3] : ( ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4)) & ! [v3] : ( ~ (in(v3, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v2) = v4))))
% 67.88/27.49 | (4) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 67.88/27.49 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 67.88/27.49 | (6) empty(all_0_3_3) = 0
% 67.88/27.49 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 67.88/27.49 | (8) empty(all_0_2_2) = 0
% 67.88/27.49 | (9) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 67.88/27.49 | (10) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 67.88/27.49 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 67.88/27.49 | (12) relation(all_0_0_0) = 0
% 67.88/27.49 | (13) relation_empty_yielding(empty_set) = 0
% 67.88/27.49 | (14) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 67.88/27.49 | (15) ~ (all_0_5_5 = 0)
% 67.88/27.49 | (16) relation(all_0_2_2) = 0
% 67.88/27.50 | (17) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 67.88/27.50 | (18) in(all_0_14_14, all_0_13_13) = 0
% 67.88/27.50 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 67.88/27.50 | (20) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 67.88/27.50 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 67.88/27.50 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 67.88/27.50 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 67.88/27.50 | (24) ! [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)))
% 67.88/27.50 | (25) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 67.88/27.50 | (26) relation_empty_yielding(all_0_11_11) = 0
% 67.88/27.50 | (27) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 67.88/27.50 | (28) ? [v0] : ? [v1] : relation(v0) = v1
% 67.88/27.50 | (29) relation(all_0_4_4) = 0
% 67.88/27.50 | (30) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 67.88/27.50 | (31) empty(empty_set) = 0
% 67.88/27.50 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 67.88/27.50 | (33) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 67.88/27.50 | (34) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 67.88/27.50 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 67.88/27.50 | (36) ? [v0] : ? [v1] : element(v1, v0) = 0
% 67.88/27.50 | (37) ordinal(all_0_14_14) = all_0_12_12
% 67.88/27.50 | (38) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 67.88/27.50 | (39) ? [v0] : ? [v1] : function(v0) = v1
% 67.88/27.50 | (40) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 67.88/27.50 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v2, v0) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v2) = v3))
% 67.88/27.50 | (42) relation(all_0_6_6) = 0
% 67.88/27.50 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 67.88/27.50 | (44) ! [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)))
% 67.88/27.50 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 67.88/27.50 | (46) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 67.88/27.50 | (47) relation_empty_yielding(all_0_10_10) = 0
% 67.88/27.50 | (48) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 67.88/27.50 | (49) ? [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))))
% 67.88/27.50 | (50) ? [v0] : ? [v1] : ordinal(v0) = v1
% 67.88/27.50 | (51) ~ (all_0_7_7 = 0)
% 67.88/27.50 | (52) ! [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)))
% 67.88/27.50 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ((v4 = 0 & in(v1, v2) = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 67.88/27.51 | (54) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 67.88/27.51 | (55) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 67.88/27.51 | (56) empty(all_0_6_6) = all_0_5_5
% 67.88/27.51 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 67.88/27.51 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 67.88/27.51 | (59) function(all_0_0_0) = 0
% 67.88/27.51 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 67.88/27.51 | (61) relation(all_0_9_9) = 0
% 67.88/27.51 | (62) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 67.88/27.51 | (63) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 67.88/27.51 | (64) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 67.88/27.51 | (65) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0)
% 67.88/27.51 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 67.88/27.51 | (67) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2
% 67.88/27.51 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 67.88/27.51 | (69) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 67.88/27.51 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 67.88/27.51 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 67.88/27.51 | (72) epsilon_transitive(all_0_1_1) = 0
% 67.88/27.51 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 67.88/27.51 | (74) ordinal(all_0_13_13) = 0
% 67.88/27.51 | (75) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 67.88/27.51 | (76) ordinal(all_0_1_1) = 0
% 67.88/27.51 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 67.88/27.51 | (78) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 67.88/27.51 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 67.88/27.51 | (80) ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0))
% 67.88/27.51 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v2, v0) = 0) | ~ (in(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 67.88/27.51 | (82) ? [v0] : ? [v1] : powerset(v0) = v1
% 67.88/27.51 | (83) relation(all_0_10_10) = 0
% 67.88/27.51 | (84) one_to_one(all_0_9_9) = 0
% 67.88/27.51 | (85) function(all_0_9_9) = 0
% 67.88/27.51 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 67.88/27.51 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 67.88/27.51 | (88) ! [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)))
% 67.88/27.51 | (89) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 67.88/27.51 | (90) ! [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)))
% 67.88/27.51 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 67.88/27.51 | (92) ~ (all_0_12_12 = 0)
% 67.88/27.52 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 67.88/27.52 | (94) empty(all_0_8_8) = all_0_7_7
% 67.88/27.52 | (95) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 67.88/27.52 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 67.88/27.52 | (97) empty(all_0_4_4) = 0
% 67.88/27.52 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 67.88/27.52 | (99) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 67.88/27.52 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 67.88/27.52 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 67.88/27.52 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 67.88/27.52 | (103) epsilon_connected(all_0_1_1) = 0
% 67.88/27.52 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 67.88/27.52 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 67.88/27.52 | (106) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 67.88/27.52 | (107) relation(all_0_11_11) = 0
% 67.88/27.52 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 67.88/27.52 | (109) function(all_0_4_4) = 0
% 67.88/27.52 | (110) function(all_0_11_11) = 0
% 67.88/27.52 | (111) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 67.88/27.52 | (112) relation(empty_set) = 0
% 67.88/27.52 | (113) ? [v0] : ? [v1] : empty(v0) = v1
% 67.88/27.52 | (114) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 67.88/27.52 | (115) ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0))
% 67.88/27.52 |
% 67.88/27.52 | Instantiating formula (34) with all_0_13_13 and discharging atoms ordinal(all_0_13_13) = 0, yields:
% 67.88/27.52 | (116) epsilon_transitive(all_0_13_13) = 0 & epsilon_connected(all_0_13_13) = 0
% 67.88/27.52 |
% 67.88/27.52 | Applying alpha-rule on (116) yields:
% 67.88/27.52 | (117) epsilon_transitive(all_0_13_13) = 0
% 67.88/27.52 | (118) epsilon_connected(all_0_13_13) = 0
% 67.88/27.52 |
% 67.88/27.52 | Instantiating formula (23) with all_0_12_12, all_0_14_14 and discharging atoms ordinal(all_0_14_14) = all_0_12_12, yields:
% 67.88/27.52 | (119) all_0_12_12 = 0 | ? [v0] : (( ~ (v0 = 0) & epsilon_transitive(all_0_14_14) = v0) | ( ~ (v0 = 0) & epsilon_connected(all_0_14_14) = v0))
% 67.88/27.52 |
% 67.88/27.52 +-Applying beta-rule and splitting (119), into two cases.
% 67.88/27.52 |-Branch one:
% 67.88/27.52 | (120) all_0_12_12 = 0
% 67.88/27.52 |
% 67.88/27.52 | Equations (120) can reduce 92 to:
% 67.88/27.52 | (121) $false
% 67.88/27.52 |
% 67.88/27.52 |-The branch is then unsatisfiable
% 67.88/27.52 |-Branch two:
% 67.88/27.52 | (92) ~ (all_0_12_12 = 0)
% 67.88/27.52 | (123) ? [v0] : (( ~ (v0 = 0) & epsilon_transitive(all_0_14_14) = v0) | ( ~ (v0 = 0) & epsilon_connected(all_0_14_14) = v0))
% 67.88/27.52 |
% 67.88/27.52 | Instantiating (123) with all_74_0_80 yields:
% 67.88/27.52 | (124) ( ~ (all_74_0_80 = 0) & epsilon_transitive(all_0_14_14) = all_74_0_80) | ( ~ (all_74_0_80 = 0) & epsilon_connected(all_0_14_14) = all_74_0_80)
% 67.88/27.52 |
% 67.88/27.52 | Instantiating formula (65) with all_0_14_14, all_0_13_13 and discharging atoms epsilon_transitive(all_0_13_13) = 0, in(all_0_14_14, all_0_13_13) = 0, yields:
% 67.88/27.52 | (125) subset(all_0_14_14, all_0_13_13) = 0
% 67.88/27.52 |
% 67.88/27.52 +-Applying beta-rule and splitting (124), into two cases.
% 67.88/27.52 |-Branch one:
% 67.88/27.52 | (126) ~ (all_74_0_80 = 0) & epsilon_transitive(all_0_14_14) = all_74_0_80
% 67.88/27.52 |
% 67.88/27.52 | Applying alpha-rule on (126) yields:
% 67.88/27.52 | (127) ~ (all_74_0_80 = 0)
% 67.88/27.52 | (128) epsilon_transitive(all_0_14_14) = all_74_0_80
% 67.88/27.52 |
% 67.88/27.52 | Instantiating formula (115) with all_74_0_80, all_0_14_14 and discharging atoms epsilon_transitive(all_0_14_14) = all_74_0_80, yields:
% 68.19/27.52 | (129) all_74_0_80 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(v0, all_0_14_14) = v1 & in(v0, all_0_14_14) = 0)
% 68.19/27.52 |
% 68.19/27.52 +-Applying beta-rule and splitting (129), into two cases.
% 68.19/27.52 |-Branch one:
% 68.19/27.52 | (130) all_74_0_80 = 0
% 68.19/27.52 |
% 68.19/27.52 | Equations (130) can reduce 127 to:
% 68.19/27.52 | (121) $false
% 68.19/27.52 |
% 68.19/27.52 |-The branch is then unsatisfiable
% 68.19/27.52 |-Branch two:
% 68.19/27.52 | (127) ~ (all_74_0_80 = 0)
% 68.19/27.52 | (133) ? [v0] : ? [v1] : ( ~ (v1 = 0) & subset(v0, all_0_14_14) = v1 & in(v0, all_0_14_14) = 0)
% 68.19/27.53 |
% 68.19/27.53 | Instantiating (133) with all_352_0_147, all_352_1_148 yields:
% 68.19/27.53 | (134) ~ (all_352_0_147 = 0) & subset(all_352_1_148, all_0_14_14) = all_352_0_147 & in(all_352_1_148, all_0_14_14) = 0
% 68.19/27.53 |
% 68.19/27.53 | Applying alpha-rule on (134) yields:
% 68.19/27.53 | (135) ~ (all_352_0_147 = 0)
% 68.19/27.53 | (136) subset(all_352_1_148, all_0_14_14) = all_352_0_147
% 68.19/27.53 | (137) in(all_352_1_148, all_0_14_14) = 0
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (73) with all_352_0_147, all_0_14_14, all_352_1_148 and discharging atoms subset(all_352_1_148, all_0_14_14) = all_352_0_147, yields:
% 68.19/27.53 | (138) all_352_0_147 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_352_1_148) = 0 & in(v0, all_0_14_14) = v1)
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (22) with all_352_1_148, all_0_13_13, all_0_14_14 and discharging atoms subset(all_0_14_14, all_0_13_13) = 0, in(all_352_1_148, all_0_14_14) = 0, yields:
% 68.19/27.53 | (139) in(all_352_1_148, all_0_13_13) = 0
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (20) with all_352_1_148, all_0_14_14 and discharging atoms in(all_352_1_148, all_0_14_14) = 0, yields:
% 68.19/27.53 | (140) ? [v0] : ( ~ (v0 = 0) & in(all_0_14_14, all_352_1_148) = v0)
% 68.19/27.53 |
% 68.19/27.53 | Instantiating (140) with all_576_0_2361 yields:
% 68.19/27.53 | (141) ~ (all_576_0_2361 = 0) & in(all_0_14_14, all_352_1_148) = all_576_0_2361
% 68.19/27.53 |
% 68.19/27.53 | Applying alpha-rule on (141) yields:
% 68.19/27.53 | (142) ~ (all_576_0_2361 = 0)
% 68.19/27.53 | (143) in(all_0_14_14, all_352_1_148) = all_576_0_2361
% 68.19/27.53 |
% 68.19/27.53 +-Applying beta-rule and splitting (138), into two cases.
% 68.19/27.53 |-Branch one:
% 68.19/27.53 | (144) all_352_0_147 = 0
% 68.19/27.53 |
% 68.19/27.53 | Equations (144) can reduce 135 to:
% 68.19/27.53 | (121) $false
% 68.19/27.53 |
% 68.19/27.53 |-The branch is then unsatisfiable
% 68.19/27.53 |-Branch two:
% 68.19/27.53 | (135) ~ (all_352_0_147 = 0)
% 68.19/27.53 | (147) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_352_1_148) = 0 & in(v0, all_0_14_14) = v1)
% 68.19/27.53 |
% 68.19/27.53 | Instantiating (147) with all_609_0_2371, all_609_1_2372 yields:
% 68.19/27.53 | (148) ~ (all_609_0_2371 = 0) & in(all_609_1_2372, all_352_1_148) = 0 & in(all_609_1_2372, all_0_14_14) = all_609_0_2371
% 68.19/27.53 |
% 68.19/27.53 | Applying alpha-rule on (148) yields:
% 68.19/27.53 | (149) ~ (all_609_0_2371 = 0)
% 68.19/27.53 | (150) in(all_609_1_2372, all_352_1_148) = 0
% 68.19/27.53 | (151) in(all_609_1_2372, all_0_14_14) = all_609_0_2371
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (81) with all_352_1_148, all_609_1_2372, all_0_14_14 and discharging atoms in(all_609_1_2372, all_352_1_148) = 0, in(all_352_1_148, all_0_14_14) = 0, yields:
% 68.19/27.53 | (152) ? [v0] : ( ~ (v0 = 0) & in(all_0_14_14, all_609_1_2372) = v0)
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (53) with all_609_0_2371, all_609_1_2372, all_0_14_14, all_0_1_1 and discharging atoms epsilon_connected(all_0_1_1) = 0, in(all_609_1_2372, all_0_14_14) = all_609_0_2371, yields:
% 68.19/27.53 | (153) all_609_0_2371 = 0 | all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_1_1) = v0))
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (53) with all_609_0_2371, all_609_1_2372, all_0_14_14, all_0_13_13 and discharging atoms epsilon_connected(all_0_13_13) = 0, in(all_609_1_2372, all_0_14_14) = all_609_0_2371, yields:
% 68.19/27.53 | (154) all_609_0_2371 = 0 | all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (100) with all_609_0_2371, all_0_14_14, all_609_1_2372 and discharging atoms in(all_609_1_2372, all_0_14_14) = all_609_0_2371, yields:
% 68.19/27.53 | (155) all_609_0_2371 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_14_14) = 0) | ( ~ (v0 = 0) & element(all_609_1_2372, all_0_14_14) = v0))
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (65) with all_352_1_148, all_0_13_13 and discharging atoms epsilon_transitive(all_0_13_13) = 0, in(all_352_1_148, all_0_13_13) = 0, yields:
% 68.19/27.53 | (156) subset(all_352_1_148, all_0_13_13) = 0
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (100) with all_576_0_2361, all_352_1_148, all_0_14_14 and discharging atoms in(all_0_14_14, all_352_1_148) = all_576_0_2361, yields:
% 68.19/27.53 | (157) all_576_0_2361 = 0 | ? [v0] : ((v0 = 0 & empty(all_352_1_148) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_352_1_148) = v0))
% 68.19/27.53 |
% 68.19/27.53 | Instantiating (152) with all_849_0_2412 yields:
% 68.19/27.53 | (158) ~ (all_849_0_2412 = 0) & in(all_0_14_14, all_609_1_2372) = all_849_0_2412
% 68.19/27.53 |
% 68.19/27.53 | Applying alpha-rule on (158) yields:
% 68.19/27.53 | (159) ~ (all_849_0_2412 = 0)
% 68.19/27.53 | (160) in(all_0_14_14, all_609_1_2372) = all_849_0_2412
% 68.19/27.53 |
% 68.19/27.53 +-Applying beta-rule and splitting (157), into two cases.
% 68.19/27.53 |-Branch one:
% 68.19/27.53 | (161) all_576_0_2361 = 0
% 68.19/27.53 |
% 68.19/27.53 | Equations (161) can reduce 142 to:
% 68.19/27.53 | (121) $false
% 68.19/27.53 |
% 68.19/27.53 |-The branch is then unsatisfiable
% 68.19/27.53 |-Branch two:
% 68.19/27.53 | (142) ~ (all_576_0_2361 = 0)
% 68.19/27.53 | (164) ? [v0] : ((v0 = 0 & empty(all_352_1_148) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_352_1_148) = v0))
% 68.19/27.53 |
% 68.19/27.53 +-Applying beta-rule and splitting (155), into two cases.
% 68.19/27.53 |-Branch one:
% 68.19/27.53 | (165) all_609_0_2371 = 0
% 68.19/27.53 |
% 68.19/27.53 | Equations (165) can reduce 149 to:
% 68.19/27.53 | (121) $false
% 68.19/27.53 |
% 68.19/27.53 |-The branch is then unsatisfiable
% 68.19/27.53 |-Branch two:
% 68.19/27.53 | (149) ~ (all_609_0_2371 = 0)
% 68.19/27.53 | (168) ? [v0] : ((v0 = 0 & empty(all_0_14_14) = 0) | ( ~ (v0 = 0) & element(all_609_1_2372, all_0_14_14) = v0))
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (22) with all_609_1_2372, all_0_13_13, all_352_1_148 and discharging atoms subset(all_352_1_148, all_0_13_13) = 0, in(all_609_1_2372, all_352_1_148) = 0, yields:
% 68.19/27.53 | (169) in(all_609_1_2372, all_0_13_13) = 0
% 68.19/27.53 |
% 68.19/27.53 | Instantiating formula (53) with all_849_0_2412, all_0_14_14, all_609_1_2372, all_0_1_1 and discharging atoms epsilon_connected(all_0_1_1) = 0, in(all_0_14_14, all_609_1_2372) = all_849_0_2412, yields:
% 68.19/27.53 | (170) all_849_0_2412 = 0 | all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_1_1) = v0))
% 68.19/27.54 |
% 68.19/27.54 | Instantiating formula (53) with all_849_0_2412, all_0_14_14, all_609_1_2372, all_0_13_13 and discharging atoms epsilon_connected(all_0_13_13) = 0, in(all_0_14_14, all_609_1_2372) = all_849_0_2412, yields:
% 68.19/27.54 | (171) all_849_0_2412 = 0 | all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.54 |
% 68.19/27.54 | Instantiating formula (100) with all_849_0_2412, all_609_1_2372, all_0_14_14 and discharging atoms in(all_0_14_14, all_609_1_2372) = all_849_0_2412, yields:
% 68.19/27.54 | (172) all_849_0_2412 = 0 | ? [v0] : ((v0 = 0 & empty(all_609_1_2372) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_609_1_2372) = v0))
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (154), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (165) all_609_0_2371 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (165) can reduce 149 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (149) ~ (all_609_0_2371 = 0)
% 68.19/27.54 | (176) all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (171), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (177) all_849_0_2412 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (177) can reduce 159 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (159) ~ (all_849_0_2412 = 0)
% 68.19/27.54 | (180) all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (172), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (177) all_849_0_2412 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (177) can reduce 159 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (159) ~ (all_849_0_2412 = 0)
% 68.19/27.54 | (184) ? [v0] : ((v0 = 0 & empty(all_609_1_2372) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_609_1_2372) = v0))
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (180), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (185) all_609_1_2372 = all_0_14_14
% 68.19/27.54 |
% 68.19/27.54 | From (185) and (150) follows:
% 68.19/27.54 | (186) in(all_0_14_14, all_352_1_148) = 0
% 68.19/27.54 |
% 68.19/27.54 | Instantiating formula (96) with all_0_14_14, all_352_1_148, 0, all_576_0_2361 and discharging atoms in(all_0_14_14, all_352_1_148) = all_576_0_2361, in(all_0_14_14, all_352_1_148) = 0, yields:
% 68.19/27.54 | (161) all_576_0_2361 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (161) can reduce 142 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (189) ~ (all_609_1_2372 = all_0_14_14)
% 68.19/27.54 | (190) ? [v0] : ((v0 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.54 |
% 68.19/27.54 | Instantiating (190) with all_1264_0_2647 yields:
% 68.19/27.54 | (191) (all_1264_0_2647 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (all_1264_0_2647 = 0) & in(all_609_1_2372, all_0_13_13) = all_1264_0_2647) | ( ~ (all_1264_0_2647 = 0) & in(all_0_14_14, all_0_13_13) = all_1264_0_2647)
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (176), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (185) all_609_1_2372 = all_0_14_14
% 68.19/27.54 |
% 68.19/27.54 | Equations (185) can reduce 189 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (189) ~ (all_609_1_2372 = all_0_14_14)
% 68.19/27.54 | (195) ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_13_13) = v0))
% 68.19/27.54 |
% 68.19/27.54 | Instantiating (195) with all_1269_0_2648 yields:
% 68.19/27.54 | (196) (all_1269_0_2648 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (all_1269_0_2648 = 0) & in(all_609_1_2372, all_0_13_13) = all_1269_0_2648) | ( ~ (all_1269_0_2648 = 0) & in(all_0_14_14, all_0_13_13) = all_1269_0_2648)
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (196), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (197) (all_1269_0_2648 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (all_1269_0_2648 = 0) & in(all_609_1_2372, all_0_13_13) = all_1269_0_2648)
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (197), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (198) all_1269_0_2648 = 0 & in(all_0_14_14, all_609_1_2372) = 0
% 68.19/27.54 |
% 68.19/27.54 | Applying alpha-rule on (198) yields:
% 68.19/27.54 | (199) all_1269_0_2648 = 0
% 68.19/27.54 | (200) in(all_0_14_14, all_609_1_2372) = 0
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (170), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (177) all_849_0_2412 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (177) can reduce 159 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (159) ~ (all_849_0_2412 = 0)
% 68.19/27.54 | (204) all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_1_1) = v0))
% 68.19/27.54 |
% 68.19/27.54 | Instantiating formula (96) with all_0_14_14, all_609_1_2372, 0, all_849_0_2412 and discharging atoms in(all_0_14_14, all_609_1_2372) = all_849_0_2412, in(all_0_14_14, all_609_1_2372) = 0, yields:
% 68.19/27.54 | (177) all_849_0_2412 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (177) can reduce 159 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (207) ~ (all_1269_0_2648 = 0) & in(all_609_1_2372, all_0_13_13) = all_1269_0_2648
% 68.19/27.54 |
% 68.19/27.54 | Applying alpha-rule on (207) yields:
% 68.19/27.54 | (208) ~ (all_1269_0_2648 = 0)
% 68.19/27.54 | (209) in(all_609_1_2372, all_0_13_13) = all_1269_0_2648
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (153), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.54 | (165) all_609_0_2371 = 0
% 68.19/27.54 |
% 68.19/27.54 | Equations (165) can reduce 149 to:
% 68.19/27.54 | (121) $false
% 68.19/27.54 |
% 68.19/27.54 |-The branch is then unsatisfiable
% 68.19/27.54 |-Branch two:
% 68.19/27.54 | (149) ~ (all_609_0_2371 = 0)
% 68.19/27.54 | (213) all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_1_1) = v0))
% 68.19/27.54 |
% 68.19/27.54 +-Applying beta-rule and splitting (191), into two cases.
% 68.19/27.54 |-Branch one:
% 68.19/27.55 | (214) (all_1264_0_2647 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (all_1264_0_2647 = 0) & in(all_609_1_2372, all_0_13_13) = all_1264_0_2647)
% 68.19/27.55 |
% 68.19/27.55 +-Applying beta-rule and splitting (214), into two cases.
% 68.19/27.55 |-Branch one:
% 68.19/27.55 | (215) all_1264_0_2647 = 0 & in(all_609_1_2372, all_0_14_14) = 0
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (215) yields:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 | (217) in(all_609_1_2372, all_0_14_14) = 0
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_609_1_2372, all_0_14_14, 0, all_609_0_2371 and discharging atoms in(all_609_1_2372, all_0_14_14) = all_609_0_2371, in(all_609_1_2372, all_0_14_14) = 0, yields:
% 68.19/27.55 | (165) all_609_0_2371 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (165) can reduce 149 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (220) ~ (all_1264_0_2647 = 0) & in(all_609_1_2372, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (220) yields:
% 68.19/27.55 | (221) ~ (all_1264_0_2647 = 0)
% 68.19/27.55 | (222) in(all_609_1_2372, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_609_1_2372, all_0_13_13, all_1264_0_2647, all_1269_0_2648 and discharging atoms in(all_609_1_2372, all_0_13_13) = all_1269_0_2648, in(all_609_1_2372, all_0_13_13) = all_1264_0_2647, yields:
% 68.19/27.55 | (223) all_1269_0_2648 = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_609_1_2372, all_0_13_13, 0, all_1269_0_2648 and discharging atoms in(all_609_1_2372, all_0_13_13) = all_1269_0_2648, in(all_609_1_2372, all_0_13_13) = 0, yields:
% 68.19/27.55 | (199) all_1269_0_2648 = 0
% 68.19/27.55 |
% 68.19/27.55 | Combining equations (199,223) yields a new equation:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (216) can reduce 221 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (227) ~ (all_1264_0_2647 = 0) & in(all_0_14_14, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (227) yields:
% 68.19/27.55 | (221) ~ (all_1264_0_2647 = 0)
% 68.19/27.55 | (229) in(all_0_14_14, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_0_14_14, all_0_13_13, all_1264_0_2647, 0 and discharging atoms in(all_0_14_14, all_0_13_13) = all_1264_0_2647, in(all_0_14_14, all_0_13_13) = 0, yields:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (216) can reduce 221 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (232) ~ (all_1269_0_2648 = 0) & in(all_0_14_14, all_0_13_13) = all_1269_0_2648
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (232) yields:
% 68.19/27.55 | (208) ~ (all_1269_0_2648 = 0)
% 68.19/27.55 | (234) in(all_0_14_14, all_0_13_13) = all_1269_0_2648
% 68.19/27.55 |
% 68.19/27.55 +-Applying beta-rule and splitting (153), into two cases.
% 68.19/27.55 |-Branch one:
% 68.19/27.55 | (165) all_609_0_2371 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (165) can reduce 149 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (149) ~ (all_609_0_2371 = 0)
% 68.19/27.55 | (213) all_609_1_2372 = all_0_14_14 | ? [v0] : ((v0 = 0 & in(all_0_14_14, all_609_1_2372) = 0) | ( ~ (v0 = 0) & in(all_609_1_2372, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_0_1_1) = v0))
% 68.19/27.55 |
% 68.19/27.55 +-Applying beta-rule and splitting (191), into two cases.
% 68.19/27.55 |-Branch one:
% 68.19/27.55 | (214) (all_1264_0_2647 = 0 & in(all_609_1_2372, all_0_14_14) = 0) | ( ~ (all_1264_0_2647 = 0) & in(all_609_1_2372, all_0_13_13) = all_1264_0_2647)
% 68.19/27.55 |
% 68.19/27.55 +-Applying beta-rule and splitting (214), into two cases.
% 68.19/27.55 |-Branch one:
% 68.19/27.55 | (215) all_1264_0_2647 = 0 & in(all_609_1_2372, all_0_14_14) = 0
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (215) yields:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 | (217) in(all_609_1_2372, all_0_14_14) = 0
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_609_1_2372, all_0_14_14, 0, all_609_0_2371 and discharging atoms in(all_609_1_2372, all_0_14_14) = all_609_0_2371, in(all_609_1_2372, all_0_14_14) = 0, yields:
% 68.19/27.55 | (165) all_609_0_2371 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (165) can reduce 149 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (220) ~ (all_1264_0_2647 = 0) & in(all_609_1_2372, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (220) yields:
% 68.19/27.55 | (221) ~ (all_1264_0_2647 = 0)
% 68.19/27.55 | (222) in(all_609_1_2372, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_609_1_2372, all_0_13_13, 0, all_1264_0_2647 and discharging atoms in(all_609_1_2372, all_0_13_13) = all_1264_0_2647, in(all_609_1_2372, all_0_13_13) = 0, yields:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (216) can reduce 221 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.55 |-Branch two:
% 68.19/27.55 | (227) ~ (all_1264_0_2647 = 0) & in(all_0_14_14, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Applying alpha-rule on (227) yields:
% 68.19/27.55 | (221) ~ (all_1264_0_2647 = 0)
% 68.19/27.55 | (229) in(all_0_14_14, all_0_13_13) = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_0_14_14, all_0_13_13, all_1269_0_2648, 0 and discharging atoms in(all_0_14_14, all_0_13_13) = all_1269_0_2648, in(all_0_14_14, all_0_13_13) = 0, yields:
% 68.19/27.55 | (199) all_1269_0_2648 = 0
% 68.19/27.55 |
% 68.19/27.55 | Instantiating formula (96) with all_0_14_14, all_0_13_13, all_1264_0_2647, all_1269_0_2648 and discharging atoms in(all_0_14_14, all_0_13_13) = all_1269_0_2648, in(all_0_14_14, all_0_13_13) = all_1264_0_2647, yields:
% 68.19/27.55 | (223) all_1269_0_2648 = all_1264_0_2647
% 68.19/27.55 |
% 68.19/27.55 | Combining equations (223,199) yields a new equation:
% 68.19/27.55 | (255) all_1264_0_2647 = 0
% 68.19/27.55 |
% 68.19/27.55 | Simplifying 255 yields:
% 68.19/27.55 | (216) all_1264_0_2647 = 0
% 68.19/27.55 |
% 68.19/27.55 | Equations (216) can reduce 221 to:
% 68.19/27.55 | (121) $false
% 68.19/27.55 |
% 68.19/27.55 |-The branch is then unsatisfiable
% 68.19/27.56 |-Branch two:
% 68.19/27.56 | (258) ~ (all_74_0_80 = 0) & epsilon_connected(all_0_14_14) = all_74_0_80
% 68.19/27.56 |
% 68.19/27.56 | Applying alpha-rule on (258) yields:
% 68.19/27.56 | (127) ~ (all_74_0_80 = 0)
% 68.19/27.56 | (260) epsilon_connected(all_0_14_14) = all_74_0_80
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (80) with all_74_0_80, all_0_14_14 and discharging atoms epsilon_connected(all_0_14_14) = all_74_0_80, yields:
% 68.19/27.56 | (261) all_74_0_80 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1, all_0_14_14) = 0 & in(v0, v1) = v2 & in(v0, all_0_14_14) = 0)
% 68.19/27.56 |
% 68.19/27.56 +-Applying beta-rule and splitting (261), into two cases.
% 68.19/27.56 |-Branch one:
% 68.19/27.56 | (130) all_74_0_80 = 0
% 68.19/27.56 |
% 68.19/27.56 | Equations (130) can reduce 127 to:
% 68.19/27.56 | (121) $false
% 68.19/27.56 |
% 68.19/27.56 |-The branch is then unsatisfiable
% 68.19/27.56 |-Branch two:
% 68.19/27.56 | (127) ~ (all_74_0_80 = 0)
% 68.19/27.56 | (265) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1, all_0_14_14) = 0 & in(v0, v1) = v2 & in(v0, all_0_14_14) = 0)
% 68.19/27.56 |
% 68.19/27.56 | Instantiating (265) with all_352_0_2800, all_352_1_2801, all_352_2_2802, all_352_3_2803 yields:
% 68.19/27.56 | (266) ~ (all_352_0_2800 = 0) & ~ (all_352_1_2801 = 0) & ~ (all_352_2_2802 = all_352_3_2803) & in(all_352_2_2802, all_352_3_2803) = all_352_0_2800 & in(all_352_2_2802, all_0_14_14) = 0 & in(all_352_3_2803, all_352_2_2802) = all_352_1_2801 & in(all_352_3_2803, all_0_14_14) = 0
% 68.19/27.56 |
% 68.19/27.56 | Applying alpha-rule on (266) yields:
% 68.19/27.56 | (267) ~ (all_352_2_2802 = all_352_3_2803)
% 68.19/27.56 | (268) in(all_352_3_2803, all_352_2_2802) = all_352_1_2801
% 68.19/27.56 | (269) ~ (all_352_1_2801 = 0)
% 68.19/27.56 | (270) ~ (all_352_0_2800 = 0)
% 68.19/27.56 | (271) in(all_352_2_2802, all_0_14_14) = 0
% 68.19/27.56 | (272) in(all_352_2_2802, all_352_3_2803) = all_352_0_2800
% 68.19/27.56 | (273) in(all_352_3_2803, all_0_14_14) = 0
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (53) with all_352_0_2800, all_352_2_2802, all_352_3_2803, all_0_13_13 and discharging atoms epsilon_connected(all_0_13_13) = 0, in(all_352_2_2802, all_352_3_2803) = all_352_0_2800, yields:
% 68.19/27.56 | (274) all_352_0_2800 = 0 | all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_3_2803, all_352_2_2802) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_13_13) = v0))
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (22) with all_352_2_2802, all_0_13_13, all_0_14_14 and discharging atoms subset(all_0_14_14, all_0_13_13) = 0, in(all_352_2_2802, all_0_14_14) = 0, yields:
% 68.19/27.56 | (275) in(all_352_2_2802, all_0_13_13) = 0
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (53) with all_352_1_2801, all_352_3_2803, all_352_2_2802, all_0_1_1 and discharging atoms epsilon_connected(all_0_1_1) = 0, in(all_352_3_2803, all_352_2_2802) = all_352_1_2801, yields:
% 68.19/27.56 | (276) all_352_1_2801 = 0 | all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_2_2802, all_352_3_2803) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_1_1) = v0))
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (53) with all_352_1_2801, all_352_3_2803, all_352_2_2802, all_0_13_13 and discharging atoms epsilon_connected(all_0_13_13) = 0, in(all_352_3_2803, all_352_2_2802) = all_352_1_2801, yields:
% 68.19/27.56 | (277) all_352_1_2801 = 0 | all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_2_2802, all_352_3_2803) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_13_13) = v0))
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (100) with all_352_1_2801, all_352_2_2802, all_352_3_2803 and discharging atoms in(all_352_3_2803, all_352_2_2802) = all_352_1_2801, yields:
% 68.19/27.56 | (278) all_352_1_2801 = 0 | ? [v0] : ((v0 = 0 & empty(all_352_2_2802) = 0) | ( ~ (v0 = 0) & element(all_352_3_2803, all_352_2_2802) = v0))
% 68.19/27.56 |
% 68.19/27.56 | Instantiating formula (22) with all_352_3_2803, all_0_13_13, all_0_14_14 and discharging atoms subset(all_0_14_14, all_0_13_13) = 0, in(all_352_3_2803, all_0_14_14) = 0, yields:
% 68.19/27.56 | (279) in(all_352_3_2803, all_0_13_13) = 0
% 68.19/27.56 |
% 68.19/27.56 +-Applying beta-rule and splitting (274), into two cases.
% 68.19/27.56 |-Branch one:
% 68.19/27.56 | (280) all_352_0_2800 = 0
% 68.19/27.56 |
% 68.19/27.56 | Equations (280) can reduce 270 to:
% 68.19/27.56 | (121) $false
% 68.19/27.56 |
% 68.19/27.56 |-The branch is then unsatisfiable
% 68.19/27.56 |-Branch two:
% 68.19/27.56 | (270) ~ (all_352_0_2800 = 0)
% 68.19/27.56 | (283) all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_3_2803, all_352_2_2802) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_13_13) = v0))
% 68.19/27.56 |
% 68.19/27.56 +-Applying beta-rule and splitting (277), into two cases.
% 68.19/27.56 |-Branch one:
% 68.19/27.56 | (284) all_352_1_2801 = 0
% 68.19/27.56 |
% 68.19/27.56 | Equations (284) can reduce 269 to:
% 68.19/27.56 | (121) $false
% 68.19/27.56 |
% 68.19/27.56 |-The branch is then unsatisfiable
% 68.19/27.56 |-Branch two:
% 68.19/27.56 | (269) ~ (all_352_1_2801 = 0)
% 68.19/27.56 | (287) all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_2_2802, all_352_3_2803) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_13_13) = v0))
% 68.19/27.56 |
% 68.19/27.56 +-Applying beta-rule and splitting (278), into two cases.
% 68.19/27.56 |-Branch one:
% 68.19/27.56 | (284) all_352_1_2801 = 0
% 68.19/27.56 |
% 68.19/27.56 | Equations (284) can reduce 269 to:
% 68.19/27.56 | (121) $false
% 68.19/27.56 |
% 68.19/27.56 |-The branch is then unsatisfiable
% 68.19/27.56 |-Branch two:
% 68.19/27.56 | (269) ~ (all_352_1_2801 = 0)
% 68.19/27.56 | (291) ? [v0] : ((v0 = 0 & empty(all_352_2_2802) = 0) | ( ~ (v0 = 0) & element(all_352_3_2803, all_352_2_2802) = v0))
% 68.19/27.57 |
% 68.19/27.57 +-Applying beta-rule and splitting (276), into two cases.
% 68.19/27.57 |-Branch one:
% 68.19/27.57 | (284) all_352_1_2801 = 0
% 68.19/27.57 |
% 68.19/27.57 | Equations (284) can reduce 269 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 |-Branch two:
% 68.19/27.57 | (269) ~ (all_352_1_2801 = 0)
% 68.19/27.57 | (295) all_352_2_2802 = all_352_3_2803 | ? [v0] : ((v0 = 0 & in(all_352_2_2802, all_352_3_2803) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_1_1) = v0))
% 68.19/27.57 |
% 68.19/27.57 +-Applying beta-rule and splitting (295), into two cases.
% 68.19/27.57 |-Branch one:
% 68.19/27.57 | (296) all_352_2_2802 = all_352_3_2803
% 68.19/27.57 |
% 68.19/27.57 | Equations (296) can reduce 267 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 |-Branch two:
% 68.19/27.57 | (267) ~ (all_352_2_2802 = all_352_3_2803)
% 68.19/27.57 | (299) ? [v0] : ((v0 = 0 & in(all_352_2_2802, all_352_3_2803) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_1_1) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_1_1) = v0))
% 68.19/27.57 |
% 68.19/27.57 +-Applying beta-rule and splitting (283), into two cases.
% 68.19/27.57 |-Branch one:
% 68.19/27.57 | (296) all_352_2_2802 = all_352_3_2803
% 68.19/27.57 |
% 68.19/27.57 | Equations (296) can reduce 267 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 |-Branch two:
% 68.19/27.57 | (267) ~ (all_352_2_2802 = all_352_3_2803)
% 68.19/27.57 | (303) ? [v0] : ((v0 = 0 & in(all_352_3_2803, all_352_2_2802) = 0) | ( ~ (v0 = 0) & in(all_352_2_2802, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_352_3_2803, all_0_13_13) = v0))
% 68.19/27.57 |
% 68.19/27.57 | Instantiating (303) with all_639_0_5590 yields:
% 68.19/27.57 | (304) (all_639_0_5590 = 0 & in(all_352_3_2803, all_352_2_2802) = 0) | ( ~ (all_639_0_5590 = 0) & in(all_352_2_2802, all_0_13_13) = all_639_0_5590) | ( ~ (all_639_0_5590 = 0) & in(all_352_3_2803, all_0_13_13) = all_639_0_5590)
% 68.19/27.57 |
% 68.19/27.57 +-Applying beta-rule and splitting (304), into two cases.
% 68.19/27.57 |-Branch one:
% 68.19/27.57 | (305) (all_639_0_5590 = 0 & in(all_352_3_2803, all_352_2_2802) = 0) | ( ~ (all_639_0_5590 = 0) & in(all_352_2_2802, all_0_13_13) = all_639_0_5590)
% 68.19/27.57 |
% 68.19/27.57 +-Applying beta-rule and splitting (305), into two cases.
% 68.19/27.57 |-Branch one:
% 68.19/27.57 | (306) all_639_0_5590 = 0 & in(all_352_3_2803, all_352_2_2802) = 0
% 68.19/27.57 |
% 68.19/27.57 | Applying alpha-rule on (306) yields:
% 68.19/27.57 | (307) all_639_0_5590 = 0
% 68.19/27.57 | (308) in(all_352_3_2803, all_352_2_2802) = 0
% 68.19/27.57 |
% 68.19/27.57 | Instantiating formula (96) with all_352_3_2803, all_352_2_2802, 0, all_352_1_2801 and discharging atoms in(all_352_3_2803, all_352_2_2802) = all_352_1_2801, in(all_352_3_2803, all_352_2_2802) = 0, yields:
% 68.19/27.57 | (284) all_352_1_2801 = 0
% 68.19/27.57 |
% 68.19/27.57 | Equations (284) can reduce 269 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 |-Branch two:
% 68.19/27.57 | (311) ~ (all_639_0_5590 = 0) & in(all_352_2_2802, all_0_13_13) = all_639_0_5590
% 68.19/27.57 |
% 68.19/27.57 | Applying alpha-rule on (311) yields:
% 68.19/27.57 | (312) ~ (all_639_0_5590 = 0)
% 68.19/27.57 | (313) in(all_352_2_2802, all_0_13_13) = all_639_0_5590
% 68.19/27.57 |
% 68.19/27.57 | Instantiating formula (96) with all_352_2_2802, all_0_13_13, 0, all_639_0_5590 and discharging atoms in(all_352_2_2802, all_0_13_13) = all_639_0_5590, in(all_352_2_2802, all_0_13_13) = 0, yields:
% 68.19/27.57 | (307) all_639_0_5590 = 0
% 68.19/27.57 |
% 68.19/27.57 | Equations (307) can reduce 312 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 |-Branch two:
% 68.19/27.57 | (316) ~ (all_639_0_5590 = 0) & in(all_352_3_2803, all_0_13_13) = all_639_0_5590
% 68.19/27.57 |
% 68.19/27.57 | Applying alpha-rule on (316) yields:
% 68.19/27.57 | (312) ~ (all_639_0_5590 = 0)
% 68.19/27.57 | (318) in(all_352_3_2803, all_0_13_13) = all_639_0_5590
% 68.19/27.57 |
% 68.19/27.57 | Instantiating formula (96) with all_352_3_2803, all_0_13_13, 0, all_639_0_5590 and discharging atoms in(all_352_3_2803, all_0_13_13) = all_639_0_5590, in(all_352_3_2803, all_0_13_13) = 0, yields:
% 68.19/27.57 | (307) all_639_0_5590 = 0
% 68.19/27.57 |
% 68.19/27.57 | Equations (307) can reduce 312 to:
% 68.19/27.57 | (121) $false
% 68.19/27.57 |
% 68.19/27.57 |-The branch is then unsatisfiable
% 68.19/27.57 % SZS output end Proof for theBenchmark
% 68.19/27.57
% 68.19/27.57 26940ms
%------------------------------------------------------------------------------