%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU271+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:48:21 EDT 2022

% Result   : Theorem 7.24s 2.42s
% Output   : Proof 15.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : SEU271+1 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jun 19 14:09:14 EDT 2022
% 0.21/0.36  % CPUTime  : 
% 0.62/0.66          ____       _                          
% 0.62/0.66    ___  / __ \_____(_)___  ________  __________
% 0.62/0.66   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.66  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.62/0.66  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.62/0.66  
% 0.62/0.66  A Theorem Prover for First-Order Logic
% 0.62/0.66  (ePrincess v.1.0)
% 0.62/0.66  
% 0.62/0.66  (c) Philipp Rümmer, 2009-2015
% 0.62/0.66  (c) Peter Backeman, 2014-2015
% 0.62/0.66  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.66  Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.66  Bug reports to peter@backeman.se
% 0.62/0.66  
% 0.62/0.66  For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.66  
% 0.72/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.71  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/1.03  Prover 0: Preprocessing ...
% 2.79/1.33  Prover 0: Warning: ignoring some quantifiers
% 2.79/1.35  Prover 0: Constructing countermodel ...
% 3.71/1.61  Prover 0: gave up
% 3.71/1.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.02/1.65  Prover 1: Preprocessing ...
% 4.66/1.79  Prover 1: Warning: ignoring some quantifiers
% 4.66/1.80  Prover 1: Constructing countermodel ...
% 5.28/1.96  Prover 1: gave up
% 5.28/1.96  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.56/1.99  Prover 2: Preprocessing ...
% 6.13/2.13  Prover 2: Warning: ignoring some quantifiers
% 6.13/2.14  Prover 2: Constructing countermodel ...
% 7.24/2.42  Prover 2: proved (454ms)
% 7.24/2.42  
% 7.24/2.42  No countermodel exists, formula is valid
% 7.24/2.42  % SZS status Theorem for theBenchmark
% 7.24/2.42  
% 7.24/2.42  Generating proof ... Warning: ignoring some quantifiers
% 14.94/4.17  found it (size 176)
% 14.94/4.17  
% 14.94/4.17  % SZS output start Proof for theBenchmark
% 14.94/4.18  Assumed formulas after preprocessing and simplification: 
% 14.94/4.18  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : ( ~ (v8 = 0) &  ~ (v5 = 0) &  ~ (v2 = 0) & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & inclusion_relation(v0) = v1 & antisymmetric(v1) = v2 & one_to_one(v9) = 0 & one_to_one(v6) = 0 & one_to_one(empty_set) = 0 & relation(v13) = 0 & relation(v10) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & epsilon_transitive(v12) = 0 & epsilon_transitive(v9) = 0 & epsilon_transitive(v4) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v12) = 0 & ordinal(v9) = 0 & ordinal(v4) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v12) = 0 & epsilon_connected(v9) = 0 & epsilon_connected(v4) = 0 & epsilon_connected(empty_set) = 0 & function(v13) = 0 & function(v10) = 0 & function(v9) = 0 & function(v6) = 0 & function(v3) = 0 & function(empty_set) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v4) = v5 & empty(empty_set) = 0 &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (inclusion_relation(v14) = v15) |  ~ (ordered_pair(v17, v18) = v19) |  ~ (relation_field(v15) = v16) |  ? [v20] :  ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (((v21 = 0 & subset(v17, v18) = 0) | ( ~ (v20 = 0) & in(v19, v15) = v20)) & ((v20 = 0 & in(v19, v15) = 0) | ( ~ (v21 = 0) & subset(v17, v18) = v21))))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (inclusion_relation(v14) = v15) |  ~ (relation_field(v15) = v16) |  ~ (subset(v17, v18) = v19) |  ? [v20] :  ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v15) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v15) = v21))))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v18 = 0 |  ~ (powerset(v16) = v17) |  ~ (element(v15, v17) = 0) |  ~ (element(v14, v16) = v18) |  ? [v19] : ( ~ (v19 = 0) & in(v14, v15) = v19)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v17 = v16 |  ~ (ordered_pair(v17, v16) = v18) |  ~ (is_antisymmetric_in(v14, v15) = 0) |  ~ (relation(v14) = 0) |  ? [v19] :  ? [v20] : (( ~ (v20 = 0) & ordered_pair(v16, v17) = v19 & in(v19, v14) = v20) | ( ~ (v19 = 0) & in(v18, v14) = v19) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v17 = v16 |  ~ (ordered_pair(v16, v17) = v18) |  ~ (is_antisymmetric_in(v14, v15) = 0) |  ~ (relation(v14) = 0) |  ? [v19] :  ? [v20] : (( ~ (v20 = 0) & ordered_pair(v17, v16) = v19 & in(v19, v14) = v20) | ( ~ (v19 = 0) & in(v18, v14) = v19) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v17 = 0 |  ~ (powerset(v15) = v16) |  ~ (element(v14, v16) = v17) |  ? [v18] : ( ~ (v18 = 0) & subset(v14, v15) = v18)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v17 = 0 |  ~ (element(v14, v16) = v17) |  ~ (in(v14, v15) = 0) |  ? [v18] :  ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (element(v17, v16) = v15) |  ~ (element(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (ordered_pair(v17, v16) = v15) |  ~ (ordered_pair(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (is_antisymmetric_in(v17, v16) = v15) |  ~ (is_antisymmetric_in(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (subset(v17, v16) = v15) |  ~ (subset(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (set_union2(v17, v16) = v15) |  ~ (set_union2(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (unordered_pair(v17, v16) = v15) |  ~ (unordered_pair(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (in(v17, v16) = v15) |  ~ (in(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ (element(v15, v17) = 0) |  ~ (in(v14, v15) = 0) | element(v14, v16) = 0) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ (element(v15, v17) = 0) |  ~ (in(v14, v15) = 0) |  ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = v15 |  ~ (inclusion_relation(v14) = v16) |  ~ (relation_field(v15) = v14) |  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : ((v20 = 0 & v19 = 0 & in(v18, v14) = 0 & in(v17, v14) = 0 & ((v23 = 0 & subset(v17, v18) = 0) | (v22 = 0 & ordered_pair(v17, v18) = v21 & in(v21, v15) = 0)) & (( ~ (v23 = 0) & subset(v17, v18) = v23) | ( ~ (v22 = 0) & ordered_pair(v17, v18) = v21 & in(v21, v15) = v22))) | ( ~ (v17 = 0) & relation(v15) = v17))) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = v14 |  ~ (inclusion_relation(v14) = v15) |  ~ (relation_field(v15) = v16) |  ? [v17] : ( ~ (v17 = 0) & relation(v15) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (element(v14, v15) = v16) |  ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (is_antisymmetric_in(v14, v15) = v16) |  ~ (relation(v14) = 0) |  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] : ( ~ (v18 = v17) & ordered_pair(v18, v17) = v20 & ordered_pair(v17, v18) = v19 & in(v20, v14) = 0 & in(v19, v14) = 0 & in(v18, v15) = 0 & in(v17, v15) = 0)) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (subset(v14, v15) = v16) |  ? [v17] :  ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) &  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (in(v14, v15) = v16) |  ? [v17] : ((v17 = 0 & empty(v15) = 0) | ( ~ (v17 = 0) & element(v14, v15) = v17))) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (powerset(v16) = v15) |  ~ (powerset(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_empty_yielding(v16) = v15) |  ~ (relation_empty_yielding(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_dom(v16) = v15) |  ~ (relation_dom(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_rng(v16) = v15) |  ~ (relation_rng(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (singleton(v16) = v15) |  ~ (singleton(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (inclusion_relation(v16) = v15) |  ~ (inclusion_relation(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_field(v16) = v15) |  ~ (relation_field(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (antisymmetric(v16) = v15) |  ~ (antisymmetric(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (one_to_one(v16) = v15) |  ~ (one_to_one(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation(v16) = v15) |  ~ (relation(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (epsilon_transitive(v16) = v15) |  ~ (epsilon_transitive(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (ordinal(v16) = v15) |  ~ (ordinal(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (epsilon_connected(v16) = v15) |  ~ (epsilon_connected(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (function(v16) = v15) |  ~ (function(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (empty(v16) = v15) |  ~ (empty(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ (element(v14, v16) = 0) | subset(v14, v15) = 0) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (inclusion_relation(v14) = v16) |  ~ (relation(v15) = 0) |  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : (( ~ (v16 = v15) | (v17 = v14 & relation_field(v15) = v14 &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (ordered_pair(v25, v26) = v27) |  ? [v28] :  ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (((v29 = 0 & subset(v25, v26) = 0) | ( ~ (v28 = 0) & in(v27, v15) = v28)) & ((v28 = 0 & in(v27, v15) = 0) | ( ~ (v29 = 0) & subset(v25, v26) = v29))))) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (subset(v25, v26) = v27) |  ? [v28] :  ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (( ~ (v27 = 0) | (v29 = 0 & ordered_pair(v25, v26) = v28 & in(v28, v15) = 0)) & (v27 = 0 | ( ~ (v29 = 0) & ordered_pair(v25, v26) = v28 & in(v28, v15) = v29))))))) & (v16 = v15 | (v21 = 0 & v20 = 0 & in(v19, v14) = 0 & in(v18, v14) = 0 & ((v24 = 0 & subset(v18, v19) = 0) | (v23 = 0 & ordered_pair(v18, v19) = v22 & in(v22, v15) = 0)) & (( ~ (v24 = 0) & subset(v18, v19) = v24) | ( ~ (v23 = 0) & ordered_pair(v18, v19) = v22 & in(v22, v15) = v23))) | ( ~ (v17 = v14) & relation_field(v15) = v17)))) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) |  ? [v17] :  ? [v18] : (singleton(v14) = v18 & unordered_pair(v17, v18) = v16 & unordered_pair(v14, v15) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) |  ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (set_union2(v15, v14) = v16) | set_union2(v14, v15) = v16) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (set_union2(v15, v14) = v16) |  ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (set_union2(v14, v15) = v16) | set_union2(v15, v14) = v16) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (set_union2(v14, v15) = v16) |  ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v15, v14) = v16) | unordered_pair(v14, v15) = v16) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | unordered_pair(v15, v14) = v16) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) |  ? [v17] :  ? [v18] : (singleton(v14) = v18 & ordered_pair(v14, v15) = v17 & unordered_pair(v16, v18) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (empty(v16) = 0) |  ~ (in(v14, v15) = 0) |  ? [v17] :  ? [v18] : ( ~ (v18 = 0) & powerset(v16) = v17 & element(v15, v17) = v18)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (subset(v15, v14) = 0) |  ? [v16] : ( ~ (v16 = 0) & subset(v14, v15) = v16)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (subset(v14, v15) = 0) |  ? [v16] : ( ~ (v16 = 0) & subset(v15, v14) = v16)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (set_union2(v14, v14) = v15)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (set_union2(v14, empty_set) = v15)) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (empty(v15) = 0) |  ~ (empty(v14) = 0)) &  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (subset(v14, v14) = v15)) &  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (ordinal(v14) = v15) |  ? [v16] : (( ~ (v16 = 0) & epsilon_transitive(v14) = v16) | ( ~ (v16 = 0) & epsilon_connected(v14) = v16))) &  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (function(v14) = v15) |  ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) &  ! [v14] :  ! [v15] : ( ~ (element(v14, v15) = 0) |  ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 0))) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = v16 & relation_rng(v14) = v17 & relation_field(v14) = v16 & set_union2(v15, v17) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (relation_rng(v14) = v15) |  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = v16 & relation_dom(v14) = v17 & relation_field(v14) = v16 & set_union2(v17, v15) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (inclusion_relation(v14) = v15) | relation(v15) = 0) &  ! [v14] :  ! [v15] : ( ~ (relation_field(v14) = v15) |  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = v15 & relation_dom(v14) = v16 & relation_rng(v14) = v17 & set_union2(v16, v17) = v15) | ( ~ (v16 = 0) & relation(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (relation_field(v14) = v15) |  ? [v16] :  ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (((v17 = 0 & is_antisymmetric_in(v14, v15) = 0) | ( ~ (v16 = 0) & antisymmetric(v14) = v16)) & ((v16 = 0 & antisymmetric(v14) = 0) | ( ~ (v17 = 0) & is_antisymmetric_in(v14, v15) = v17))))) &  ! [v14] :  ! [v15] : ( ~ (antisymmetric(v14) = v15) |  ? [v16] :  ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (( ~ (v15 = 0) | (v17 = 0 & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = 0)) & (v15 = 0 | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = v17))))) &  ! [v14] :  ! [v15] : ( ~ (subset(v14, v15) = 0) |  ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) &  ! [v14] :  ! [v15] : ( ~ (one_to_one(v14) = v15) |  ? [v16] :  ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v16 = 0) & relation(v14) = v16) | ( ~ (v16 = 0) & function(v14) = v16) | ( ~ (v16 = 0) & empty(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (epsilon_transitive(v14) = v15) |  ? [v16] :  ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (epsilon_transitive(v14) = v15) |  ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (ordinal(v14) = v15) |  ? [v16] :  ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (epsilon_connected(v14) = v15) |  ? [v16] :  ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & ordinal(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (epsilon_connected(v14) = v15) |  ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) &  ! [v14] :  ! [v15] : ( ~ (in(v15, v14) = 0) |  ? [v16] : ( ~ (v16 = 0) & in(v14, v15) = v16)) &  ! [v14] :  ! [v15] : ( ~ (in(v14, v15) = 0) | element(v14, v15) = 0) &  ! [v14] :  ! [v15] : ( ~ (in(v14, v15) = 0) |  ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) &  ! [v14] :  ! [v15] : ( ~ (in(v14, v15) = 0) |  ? [v16] : ( ~ (v16 = 0) & in(v15, v14) = v16)) &  ! [v14] : (v14 = empty_set |  ~ (empty(v14) = 0)) &  ! [v14] : ( ~ (relation(v14) = 0) |  ? [v15] :  ? [v16] :  ? [v17] : (relation_dom(v14) = v16 & relation_rng(v14) = v17 & relation_field(v14) = v15 & set_union2(v16, v17) = v15)) &  ! [v14] : ( ~ (relation(v14) = 0) |  ? [v15] :  ? [v16] :  ? [v17] : (((v17 = 0 & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = 0) | ( ~ (v15 = 0) & antisymmetric(v14) = v15)) & ((v15 = 0 & antisymmetric(v14) = 0) | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_antisymmetric_in(v14, v16) = v17)))) &  ! [v14] : ( ~ (relation(v14) = 0) |  ? [v15] :  ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & function(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) &  ! [v14] : ( ~ (epsilon_transitive(v14) = 0) |  ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_connected(v14) = v15))) &  ! [v14] : ( ~ (ordinal(v14) = 0) | (epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0)) &  ! [v14] : ( ~ (epsilon_connected(v14) = 0) |  ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_transitive(v14) = v15))) &  ! [v14] : ( ~ (function(v14) = 0) |  ? [v15] :  ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) &  ! [v14] : ( ~ (empty(v14) = 0) | function(v14) = 0) &  ! [v14] : ( ~ (empty(v14) = 0) |  ? [v15] :  ? [v16] :  ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & function(v14) = v15))) &  ! [v14] : ( ~ (empty(v14) = 0) | (epsilon_transitive(v14) = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0)) &  ? [v14] :  ? [v15] :  ? [v16] : element(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : ordered_pair(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : is_antisymmetric_in(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : subset(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : set_union2(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : unordered_pair(v15, v14) = v16 &  ? [v14] :  ? [v15] :  ? [v16] : in(v15, v14) = v16 &  ? [v14] :  ? [v15] : powerset(v14) = v15 &  ? [v14] :  ? [v15] : relation_empty_yielding(v14) = v15 &  ? [v14] :  ? [v15] : element(v15, v14) = 0 &  ? [v14] :  ? [v15] : relation_dom(v14) = v15 &  ? [v14] :  ? [v15] : relation_rng(v14) = v15 &  ? [v14] :  ? [v15] : singleton(v14) = v15 &  ? [v14] :  ? [v15] : inclusion_relation(v14) = v15 &  ? [v14] :  ? [v15] : relation_field(v14) = v15 &  ? [v14] :  ? [v15] : antisymmetric(v14) = v15 &  ? [v14] :  ? [v15] : one_to_one(v14) = v15 &  ? [v14] :  ? [v15] : relation(v14) = v15 &  ? [v14] :  ? [v15] : epsilon_transitive(v14) = v15 &  ? [v14] :  ? [v15] : ordinal(v14) = v15 &  ? [v14] :  ? [v15] : epsilon_connected(v14) = v15 &  ? [v14] :  ? [v15] : function(v14) = v15 &  ? [v14] :  ? [v15] : empty(v14) = v15)
% 15.23/4.24  | 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 yields:
% 15.23/4.24  | (1)  ~ (all_0_5_5 = 0) &  ~ (all_0_8_8 = 0) &  ~ (all_0_11_11 = 0) & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(empty_set) = 0 & inclusion_relation(all_0_13_13) = all_0_12_12 & antisymmetric(all_0_12_12) = all_0_11_11 & one_to_one(all_0_4_4) = 0 & one_to_one(all_0_7_7) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_4_4) = 0 & epsilon_transitive(all_0_9_9) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_4_4) = 0 & ordinal(all_0_9_9) = 0 & ordinal(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_4_4) = 0 & epsilon_connected(all_0_9_9) = 0 & epsilon_connected(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_4_4) = 0 & function(all_0_7_7) = 0 & function(all_0_10_10) = 0 & function(empty_set) = 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_9_9) = all_0_8_8 & empty(empty_set) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (inclusion_relation(v0) = v1) |  ~ (ordered_pair(v3, v4) = v5) |  ~ (relation_field(v1) = v2) |  ? [v6] :  ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (inclusion_relation(v0) = v1) |  ~ (relation_field(v1) = v2) |  ~ (subset(v3, v4) = v5) |  ? [v6] :  ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) &  ! [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] : (v3 = v2 |  ~ (ordered_pair(v3, v2) = v4) |  ~ (is_antisymmetric_in(v0, v1) = 0) |  ~ (relation(v0) = 0) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (is_antisymmetric_in(v0, v1) = 0) |  ~ (relation(v0) = 0) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) & ordered_pair(v3, v2) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) &  ! [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] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (is_antisymmetric_in(v3, v2) = v1) |  ~ (is_antisymmetric_in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(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 |  ~ (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] : (v2 = v1 |  ~ (inclusion_relation(v0) = v2) |  ~ (relation_field(v1) = v0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (inclusion_relation(v0) = v1) |  ~ (relation_field(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (is_antisymmetric_in(v0, v1) = v2) |  ~ (relation(v0) = 0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0)) &  ! [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 |  ~ (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 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inclusion_relation(v2) = v1) |  ~ (inclusion_relation(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_field(v2) = v1) |  ~ (relation_field(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antisymmetric(v2) = v1) |  ~ (antisymmetric(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] : ( ~ (inclusion_relation(v0) = v2) |  ~ (relation(v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (subset(v11, v12) = v13) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = 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) | set_union2(v1, v0) = 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] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) &  ! [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] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_antisymmetric_in(v0, v1) = 0) | ( ~ (v2 = 0) & antisymmetric(v0) = v2)) & ((v2 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & is_antisymmetric_in(v0, v1) = v3))))) &  ! [v0] :  ! [v1] : ( ~ (antisymmetric(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3))))) &  ! [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] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (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] : ( ~ (ordinal(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) &  ! [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] : (v0 = empty_set |  ~ (empty(v0) = 0)) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0) | ( ~ (v1 = 0) & antisymmetric(v0) = v1)) & ((v1 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3)))) &  ! [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) | 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] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) &  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : is_antisymmetric_in(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : set_union2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(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] : relation_dom(v0) = v1 &  ? [v0] :  ? [v1] : relation_rng(v0) = v1 &  ? [v0] :  ? [v1] : singleton(v0) = v1 &  ? [v0] :  ? [v1] : inclusion_relation(v0) = v1 &  ? [v0] :  ? [v1] : relation_field(v0) = v1 &  ? [v0] :  ? [v1] : antisymmetric(v0) = v1 &  ? [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
% 15.37/4.27  |
% 15.37/4.27  | Applying alpha-rule on (1) yields:
% 15.37/4.27  | (2)  ! [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)))
% 15.37/4.27  | (3)  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 15.37/4.27  | (4)  ? [v0] :  ? [v1] : function(v0) = v1
% 15.37/4.27  | (5)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 15.37/4.27  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 15.37/4.27  | (7)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 15.37/4.27  | (8) empty(all_0_3_3) = 0
% 15.37/4.27  | (9)  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 15.37/4.27  | (10)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 15.37/4.27  | (11)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 15.37/4.27  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 15.37/4.27  | (13) relation_empty_yielding(all_0_10_10) = 0
% 15.37/4.27  | (14) ordinal(empty_set) = 0
% 15.37/4.27  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (is_antisymmetric_in(v3, v2) = v1) |  ~ (is_antisymmetric_in(v3, v2) = v0))
% 15.37/4.28  | (16)  ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 15.37/4.28  | (17)  ? [v0] :  ? [v1] : relation_rng(v0) = v1
% 15.37/4.28  | (18)  ! [v0] : ( ~ (epsilon_connected(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 15.37/4.28  | (19)  ! [v0] : ( ~ (epsilon_transitive(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 15.37/4.28  | (20)  ? [v0] :  ? [v1] : relation(v0) = v1
% 15.37/4.28  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_transitive(v2) = v1) |  ~ (epsilon_transitive(v2) = v0))
% 15.37/4.28  | (22)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 15.37/4.28  | (23) function(all_0_7_7) = 0
% 15.37/4.28  | (24)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 15.37/4.28  | (25)  ? [v0] :  ? [v1] : relation_field(v0) = v1
% 15.37/4.28  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 15.37/4.28  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (one_to_one(v2) = v1) |  ~ (one_to_one(v2) = v0))
% 15.37/4.28  | (28)  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 15.37/4.28  | (29) relation(all_0_3_3) = 0
% 15.37/4.28  | (30)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 15.37/4.28  | (31)  ~ (all_0_11_11 = 0)
% 15.37/4.28  | (32)  ~ (all_0_8_8 = 0)
% 15.37/4.28  | (33) ordinal(all_0_4_4) = 0
% 15.37/4.28  | (34)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 15.37/4.28  | (35) relation_empty_yielding(empty_set) = 0
% 15.37/4.28  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (inclusion_relation(v0) = v2) |  ~ (relation_field(v1) = v0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3)))
% 15.37/4.28  | (37)  ? [v0] :  ? [v1] : relation_dom(v0) = v1
% 15.37/4.28  | (38) function(all_0_3_3) = 0
% 15.37/4.28  | (39)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 15.37/4.28  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 15.37/4.28  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 15.37/4.28  | (42)  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_antisymmetric_in(v0, v1) = 0) | ( ~ (v2 = 0) & antisymmetric(v0) = v2)) & ((v2 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & is_antisymmetric_in(v0, v1) = v3)))))
% 15.37/4.28  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 15.37/4.28  | (44)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1))
% 15.37/4.28  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 15.37/4.28  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 15.37/4.28  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 15.37/4.28  | (48)  ! [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))
% 15.37/4.28  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 15.37/4.28  | (50)  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2
% 15.37/4.28  | (51) empty(all_0_9_9) = all_0_8_8
% 15.37/4.28  | (52) epsilon_transitive(all_0_1_1) = 0
% 15.37/4.28  | (53) empty(empty_set) = 0
% 15.37/4.28  | (54)  ? [v0] :  ? [v1] : antisymmetric(v0) = v1
% 15.37/4.28  | (55) one_to_one(empty_set) = 0
% 15.37/4.28  | (56) epsilon_connected(all_0_9_9) = 0
% 15.37/4.28  | (57) epsilon_connected(empty_set) = 0
% 15.37/4.28  | (58)  ? [v0] :  ? [v1] :  ? [v2] : is_antisymmetric_in(v1, v0) = v2
% 15.37/4.28  | (59)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antisymmetric(v2) = v1) |  ~ (antisymmetric(v2) = v0))
% 15.37/4.29  | (60)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 15.37/4.29  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inclusion_relation(v2) = v1) |  ~ (inclusion_relation(v2) = v0))
% 15.37/4.29  | (62)  ? [v0] :  ? [v1] : empty(v0) = v1
% 15.37/4.29  | (63)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (in(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 15.37/4.29  | (64)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 15.37/4.29  | (65)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 15.37/4.29  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 15.37/4.29  | (67) epsilon_transitive(empty_set) = 0
% 15.37/4.29  | (68)  ? [v0] :  ? [v1] : epsilon_transitive(v0) = v1
% 15.37/4.29  | (69)  ~ (all_0_5_5 = 0)
% 15.37/4.29  | (70) empty(all_0_2_2) = 0
% 15.37/4.29  | (71)  ! [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)))
% 15.37/4.29  | (72) one_to_one(all_0_7_7) = 0
% 15.37/4.29  | (73)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_empty_yielding(v2) = v1) |  ~ (relation_empty_yielding(v2) = v0))
% 15.37/4.29  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (ordered_pair(v3, v2) = v4) |  ~ (is_antisymmetric_in(v0, v1) = 0) |  ~ (relation(v0) = 0) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 15.37/4.29  | (75)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_field(v2) = v1) |  ~ (relation_field(v2) = v0))
% 15.37/4.29  | (76)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 15.37/4.29  | (77)  ? [v0] :  ? [v1] : ordinal(v0) = v1
% 15.37/4.29  | (78) function(empty_set) = 0
% 15.37/4.29  | (79) empty(all_0_4_4) = 0
% 15.37/4.29  | (80) epsilon_transitive(all_0_4_4) = 0
% 15.37/4.29  | (81)  ! [v0] :  ! [v1] : ( ~ (ordinal(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 15.37/4.29  | (82)  ! [v0] :  ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0)
% 15.37/4.29  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 15.37/4.29  | (84) epsilon_connected(all_0_4_4) = 0
% 15.37/4.29  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (is_antisymmetric_in(v0, v1) = 0) |  ~ (relation(v0) = 0) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) & ordered_pair(v3, v2) = v5 & in(v5, v0) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 15.37/4.29  | (86)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 15.37/4.29  | (87)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 15.37/4.29  | (88) empty(all_0_6_6) = all_0_5_5
% 15.37/4.29  | (89)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (inclusion_relation(v0) = v1) |  ~ (relation_field(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3))
% 15.37/4.29  | (90)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_connected(v2) = v1) |  ~ (epsilon_connected(v2) = v0))
% 15.37/4.29  | (91)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 15.37/4.29  | (92)  ! [v0] :  ! [v1] : ( ~ (antisymmetric(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3)))))
% 15.37/4.29  | (93)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 15.37/4.29  | (94)  ? [v0] :  ? [v1] : inclusion_relation(v0) = v1
% 15.37/4.29  | (95) relation(all_0_0_0) = 0
% 15.37/4.29  | (96)  ! [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))
% 15.37/4.29  | (97) inclusion_relation(all_0_13_13) = all_0_12_12
% 15.37/4.29  | (98)  ? [v0] :  ? [v1] : singleton(v0) = v1
% 15.37/4.29  | (99)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 15.37/4.29  | (100)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 15.37/4.29  | (101) relation(all_0_10_10) = 0
% 15.37/4.29  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (inclusion_relation(v0) = v1) |  ~ (relation_field(v1) = v2) |  ~ (subset(v3, v4) = v5) |  ? [v6] :  ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7)))))
% 15.37/4.29  | (103)  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 15.37/4.29  | (104)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 15.37/4.29  | (105)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 15.37/4.29  | (106)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 15.37/4.29  | (107) relation(empty_set) = 0
% 15.37/4.29  | (108) function(all_0_10_10) = 0
% 15.37/4.29  | (109)  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(v1, v0) = v2
% 15.37/4.29  | (110)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 15.37/4.29  | (111)  ? [v0] :  ? [v1] :  ? [v2] : set_union2(v1, v0) = v2
% 15.37/4.29  | (112)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 15.37/4.29  | (113) function(all_0_0_0) = 0
% 15.37/4.29  | (114) relation(all_0_7_7) = 0
% 15.37/4.29  | (115)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 15.37/4.29  | (116)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 15.37/4.29  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (inclusion_relation(v0) = v1) |  ~ (ordered_pair(v3, v4) = v5) |  ~ (relation_field(v1) = v2) |  ? [v6] :  ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7)))))
% 15.37/4.30  | (118)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 15.37/4.30  | (119)  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2
% 15.37/4.30  | (120)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal(v2) = v1) |  ~ (ordinal(v2) = v0))
% 15.37/4.30  | (121)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 15.37/4.30  | (122)  ! [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)))
% 15.37/4.30  | (123) ordinal(all_0_1_1) = 0
% 15.37/4.30  | (124)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 15.37/4.30  | (125)  ? [v0] :  ? [v1] : relation_empty_yielding(v0) = v1
% 15.37/4.30  | (126) one_to_one(all_0_4_4) = 0
% 15.37/4.30  | (127)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 15.37/4.30  | (128) relation(all_0_4_4) = 0
% 15.37/4.30  | (129)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 15.37/4.30  | (130)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (is_antisymmetric_in(v0, v1) = v2) |  ~ (relation(v0) = 0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0))
% 15.37/4.30  | (131)  ? [v0] :  ? [v1] : one_to_one(v0) = v1
% 15.37/4.30  | (132)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 15.37/4.30  | (133)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (inclusion_relation(v0) = v2) |  ~ (relation(v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (subset(v11, v12) = v13) |  ? [v14] :  ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3))))
% 15.37/4.30  | (134) epsilon_connected(all_0_1_1) = 0
% 15.37/4.30  | (135)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 15.37/4.30  | (136)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 15.37/4.30  | (137)  ? [v0] :  ? [v1] : powerset(v0) = v1
% 15.37/4.30  | (138)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 15.37/4.30  | (139)  ! [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)))
% 15.37/4.30  | (140)  ? [v0] :  ? [v1] : epsilon_connected(v0) = v1
% 15.37/4.30  | (141)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 15.37/4.30  | (142)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0) | ( ~ (v1 = 0) & antisymmetric(v0) = v1)) & ((v1 = 0 & antisymmetric(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = v3))))
% 15.37/4.30  | (143) antisymmetric(all_0_12_12) = all_0_11_11
% 15.37/4.30  | (144)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 15.37/4.30  | (145)  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2
% 15.37/4.30  | (146)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 15.37/4.30  | (147) ordinal(all_0_9_9) = 0
% 15.37/4.30  | (148)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 15.37/4.30  | (149) epsilon_transitive(all_0_9_9) = 0
% 15.37/4.30  | (150) function(all_0_4_4) = 0
% 15.37/4.30  |
% 15.37/4.30  | Instantiating formula (82) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields:
% 15.37/4.30  | (151) relation(all_0_12_12) = 0
% 15.37/4.30  |
% 15.37/4.30  | Instantiating formula (92) with all_0_11_11, all_0_12_12 and discharging atoms antisymmetric(all_0_12_12) = all_0_11_11, yields:
% 15.37/4.30  | (152)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (( ~ (all_0_11_11 = 0) | (v1 = 0 & relation_field(all_0_12_12) = v0 & is_antisymmetric_in(all_0_12_12, v0) = 0)) & (all_0_11_11 = 0 | ( ~ (v1 = 0) & relation_field(all_0_12_12) = v0 & is_antisymmetric_in(all_0_12_12, v0) = v1))))
% 15.37/4.30  |
% 15.37/4.30  | Instantiating (152) with all_73_0_101, all_73_1_102 yields:
% 15.37/4.30  | (153) ( ~ (all_73_1_102 = 0) & relation(all_0_12_12) = all_73_1_102) | (( ~ (all_0_11_11 = 0) | (all_73_0_101 = 0 & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = 0)) & (all_0_11_11 = 0 | ( ~ (all_73_0_101 = 0) & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101)))
% 15.37/4.30  |
% 15.37/4.30  +-Applying beta-rule and splitting (153), into two cases.
% 15.37/4.30  |-Branch one:
% 15.37/4.30  | (154)  ~ (all_73_1_102 = 0) & relation(all_0_12_12) = all_73_1_102
% 15.37/4.30  |
% 15.37/4.30  	| Applying alpha-rule on (154) yields:
% 15.37/4.30  	| (155)  ~ (all_73_1_102 = 0)
% 15.37/4.30  	| (156) relation(all_0_12_12) = all_73_1_102
% 15.37/4.30  	|
% 15.37/4.30  	| Instantiating formula (144) with all_0_12_12, 0, all_73_1_102 and discharging atoms relation(all_0_12_12) = all_73_1_102, relation(all_0_12_12) = 0, yields:
% 15.37/4.30  	| (157) all_73_1_102 = 0
% 15.37/4.30  	|
% 15.37/4.30  	| Equations (157) can reduce 155 to:
% 15.37/4.30  	| (158) $false
% 15.37/4.30  	|
% 15.37/4.30  	|-The branch is then unsatisfiable
% 15.37/4.30  |-Branch two:
% 15.37/4.30  | (159) ( ~ (all_0_11_11 = 0) | (all_73_0_101 = 0 & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = 0)) & (all_0_11_11 = 0 | ( ~ (all_73_0_101 = 0) & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101))
% 15.37/4.30  |
% 15.37/4.30  	| Applying alpha-rule on (159) yields:
% 15.37/4.30  	| (160)  ~ (all_0_11_11 = 0) | (all_73_0_101 = 0 & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = 0)
% 15.37/4.31  	| (161) all_0_11_11 = 0 | ( ~ (all_73_0_101 = 0) & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101)
% 15.37/4.31  	|
% 15.37/4.31  	+-Applying beta-rule and splitting (161), into two cases.
% 15.37/4.31  	|-Branch one:
% 15.37/4.31  	| (162) all_0_11_11 = 0
% 15.37/4.31  	|
% 15.37/4.31  		| Equations (162) can reduce 31 to:
% 15.37/4.31  		| (158) $false
% 15.37/4.31  		|
% 15.37/4.31  		|-The branch is then unsatisfiable
% 15.37/4.31  	|-Branch two:
% 15.37/4.31  	| (31)  ~ (all_0_11_11 = 0)
% 15.37/4.31  	| (165)  ~ (all_73_0_101 = 0) & relation_field(all_0_12_12) = all_73_1_102 & is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101
% 15.37/4.31  	|
% 15.37/4.31  		| Applying alpha-rule on (165) yields:
% 15.37/4.31  		| (166)  ~ (all_73_0_101 = 0)
% 15.37/4.31  		| (167) relation_field(all_0_12_12) = all_73_1_102
% 15.37/4.31  		| (168) is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101
% 15.37/4.31  		|
% 15.37/4.31  		| Instantiating formula (89) with all_73_1_102, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation_field(all_0_12_12) = all_73_1_102, yields:
% 15.37/4.31  		| (169) all_73_1_102 = all_0_13_13 |  ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0)
% 15.37/4.31  		|
% 15.37/4.31  		| Instantiating formula (130) with all_73_0_101, all_73_1_102, all_0_12_12 and discharging atoms is_antisymmetric_in(all_0_12_12, all_73_1_102) = all_73_0_101, relation(all_0_12_12) = 0, yields:
% 15.37/4.31  		| (170) all_73_0_101 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = v2 & in(v3, all_0_12_12) = 0 & in(v2, all_0_12_12) = 0 & in(v1, all_73_1_102) = 0 & in(v0, all_73_1_102) = 0)
% 15.37/4.31  		|
% 15.37/4.31  		| Instantiating formula (133) with all_0_12_12, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation(all_0_12_12) = 0, yields:
% 15.37/4.31  		| (171) relation_field(all_0_12_12) = all_0_13_13 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4)))))
% 15.37/4.31  		|
% 15.37/4.31  		| Applying alpha-rule on (171) yields:
% 15.37/4.31  		| (172) relation_field(all_0_12_12) = all_0_13_13
% 15.37/4.31  		| (173)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4)))))
% 15.37/4.31  		| (174)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4)))))
% 15.37/4.31  		|
% 15.37/4.31  		| Instantiating formula (44) with all_0_12_12 and discharging atoms relation(all_0_12_12) = 0, yields:
% 15.37/4.31  		| (175)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_0_12_12) = v1 & relation_rng(all_0_12_12) = v2 & relation_field(all_0_12_12) = v0 & set_union2(v1, v2) = v0)
% 15.37/4.31  		|
% 15.37/4.31  		| Instantiating (175) with all_108_0_158, all_108_1_159, all_108_2_160 yields:
% 15.37/4.31  		| (176) relation_dom(all_0_12_12) = all_108_1_159 & relation_rng(all_0_12_12) = all_108_0_158 & relation_field(all_0_12_12) = all_108_2_160 & set_union2(all_108_1_159, all_108_0_158) = all_108_2_160
% 15.37/4.31  		|
% 15.37/4.31  		| Applying alpha-rule on (176) yields:
% 15.37/4.31  		| (177) relation_dom(all_0_12_12) = all_108_1_159
% 15.37/4.31  		| (178) relation_rng(all_0_12_12) = all_108_0_158
% 15.37/4.31  		| (179) relation_field(all_0_12_12) = all_108_2_160
% 15.37/4.31  		| (180) set_union2(all_108_1_159, all_108_0_158) = all_108_2_160
% 15.37/4.31  		|
% 15.37/4.31  		+-Applying beta-rule and splitting (169), into two cases.
% 15.37/4.31  		|-Branch one:
% 15.37/4.31  		| (181) all_73_1_102 = all_0_13_13
% 15.37/4.31  		|
% 15.37/4.31  			| From (181) and (167) follows:
% 15.37/4.31  			| (172) relation_field(all_0_12_12) = all_0_13_13
% 15.37/4.31  			|
% 15.37/4.31  			+-Applying beta-rule and splitting (170), into two cases.
% 15.37/4.31  			|-Branch one:
% 15.37/4.31  			| (183) all_73_0_101 = 0
% 15.37/4.31  			|
% 15.37/4.31  				| Equations (183) can reduce 166 to:
% 15.37/4.31  				| (158) $false
% 15.37/4.31  				|
% 15.37/4.31  				|-The branch is then unsatisfiable
% 15.37/4.31  			|-Branch two:
% 15.37/4.31  			| (166)  ~ (all_73_0_101 = 0)
% 15.37/4.31  			| (186)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = v2 & in(v3, all_0_12_12) = 0 & in(v2, all_0_12_12) = 0 & in(v1, all_73_1_102) = 0 & in(v0, all_73_1_102) = 0)
% 15.37/4.31  			|
% 15.37/4.31  				| Instantiating (186) with all_126_0_176, all_126_1_177, all_126_2_178, all_126_3_179 yields:
% 15.37/4.31  				| (187)  ~ (all_126_2_178 = all_126_3_179) & ordered_pair(all_126_2_178, all_126_3_179) = all_126_0_176 & ordered_pair(all_126_3_179, all_126_2_178) = all_126_1_177 & in(all_126_0_176, all_0_12_12) = 0 & in(all_126_1_177, all_0_12_12) = 0 & in(all_126_2_178, all_73_1_102) = 0 & in(all_126_3_179, all_73_1_102) = 0
% 15.37/4.31  				|
% 15.37/4.31  				| Applying alpha-rule on (187) yields:
% 15.37/4.31  				| (188) in(all_126_3_179, all_73_1_102) = 0
% 15.37/4.31  				| (189) in(all_126_0_176, all_0_12_12) = 0
% 15.37/4.31  				| (190) in(all_126_2_178, all_73_1_102) = 0
% 15.37/4.31  				| (191) in(all_126_1_177, all_0_12_12) = 0
% 15.37/4.31  				| (192) ordered_pair(all_126_2_178, all_126_3_179) = all_126_0_176
% 15.37/4.31  				| (193)  ~ (all_126_2_178 = all_126_3_179)
% 15.37/4.31  				| (194) ordered_pair(all_126_3_179, all_126_2_178) = all_126_1_177
% 15.37/4.31  				|
% 15.37/4.31  				| From (181) and (190) follows:
% 15.37/4.31  				| (195) in(all_126_2_178, all_0_13_13) = 0
% 15.37/4.31  				|
% 15.37/4.31  				| From (181) and (188) follows:
% 15.37/4.31  				| (196) in(all_126_3_179, all_0_13_13) = 0
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating formula (75) with all_0_12_12, all_0_13_13, all_108_2_160 and discharging atoms relation_field(all_0_12_12) = all_108_2_160, relation_field(all_0_12_12) = all_0_13_13, yields:
% 15.37/4.31  				| (197) all_108_2_160 = all_0_13_13
% 15.37/4.31  				|
% 15.37/4.31  				| From (197) and (179) follows:
% 15.37/4.31  				| (172) relation_field(all_0_12_12) = all_0_13_13
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating formula (173) with all_126_0_176, all_126_3_179, all_126_2_178 and discharging atoms ordered_pair(all_126_2_178, all_126_3_179) = all_126_0_176, yields:
% 15.37/4.31  				| (199)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & in(all_126_2_178, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_126_3_179, all_0_13_13) = v0) | (((v1 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (v0 = 0) & in(all_126_0_176, all_0_12_12) = v0)) & ((v0 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_126_2_178, all_126_3_179) = v1))))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating formula (173) with all_126_1_177, all_126_2_178, all_126_3_179 and discharging atoms ordered_pair(all_126_3_179, all_126_2_178) = all_126_1_177, yields:
% 15.37/4.31  				| (200)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & in(all_126_2_178, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_126_3_179, all_0_13_13) = v0) | (((v1 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (v0 = 0) & in(all_126_1_177, all_0_12_12) = v0)) & ((v0 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_126_3_179, all_126_2_178) = v1))))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating formula (117) with all_126_0_176, all_126_3_179, all_126_2_178, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordered_pair(all_126_2_178, all_126_3_179) = all_126_0_176, relation_field(all_0_12_12) = all_0_13_13, yields:
% 15.37/4.31  				| (201)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | ( ~ (v0 = 0) & in(all_126_2_178, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_126_3_179, all_0_13_13) = v0) | (((v1 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (v0 = 0) & in(all_126_0_176, all_0_12_12) = v0)) & ((v0 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_126_2_178, all_126_3_179) = v1))))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating formula (117) with all_126_1_177, all_126_2_178, all_126_3_179, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordered_pair(all_126_3_179, all_126_2_178) = all_126_1_177, relation_field(all_0_12_12) = all_0_13_13, yields:
% 15.37/4.31  				| (202)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | ( ~ (v0 = 0) & in(all_126_2_178, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_126_3_179, all_0_13_13) = v0) | (((v1 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (v0 = 0) & in(all_126_1_177, all_0_12_12) = v0)) & ((v0 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_126_3_179, all_126_2_178) = v1))))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating (202) with all_152_0_188, all_152_1_189 yields:
% 15.37/4.31  				| (203) ( ~ (all_152_1_189 = 0) & relation(all_0_12_12) = all_152_1_189) | ( ~ (all_152_1_189 = 0) & in(all_126_2_178, all_0_13_13) = all_152_1_189) | ( ~ (all_152_1_189 = 0) & in(all_126_3_179, all_0_13_13) = all_152_1_189) | (((all_152_0_188 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_152_1_189 = 0) & in(all_126_1_177, all_0_12_12) = all_152_1_189)) & ((all_152_1_189 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_152_0_188 = 0) & subset(all_126_3_179, all_126_2_178) = all_152_0_188)))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating (201) with all_153_0_190, all_153_1_191 yields:
% 15.37/4.31  				| (204) ( ~ (all_153_1_191 = 0) & relation(all_0_12_12) = all_153_1_191) | ( ~ (all_153_1_191 = 0) & in(all_126_2_178, all_0_13_13) = all_153_1_191) | ( ~ (all_153_1_191 = 0) & in(all_126_3_179, all_0_13_13) = all_153_1_191) | (((all_153_0_190 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_153_1_191 = 0) & in(all_126_0_176, all_0_12_12) = all_153_1_191)) & ((all_153_1_191 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_153_0_190 = 0) & subset(all_126_2_178, all_126_3_179) = all_153_0_190)))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating (200) with all_176_0_208, all_176_1_209 yields:
% 15.37/4.31  				| (205) ( ~ (all_176_1_209 = 0) & in(all_126_2_178, all_0_13_13) = all_176_1_209) | ( ~ (all_176_1_209 = 0) & in(all_126_3_179, all_0_13_13) = all_176_1_209) | (((all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209)) & ((all_176_1_209 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_176_0_208 = 0) & subset(all_126_3_179, all_126_2_178) = all_176_0_208)))
% 15.37/4.31  				|
% 15.37/4.31  				| Instantiating (199) with all_177_0_210, all_177_1_211 yields:
% 15.37/4.31  				| (206) ( ~ (all_177_1_211 = 0) & in(all_126_2_178, all_0_13_13) = all_177_1_211) | ( ~ (all_177_1_211 = 0) & in(all_126_3_179, all_0_13_13) = all_177_1_211) | (((all_177_0_210 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_177_1_211 = 0) & in(all_126_0_176, all_0_12_12) = all_177_1_211)) & ((all_177_1_211 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_177_0_210 = 0) & subset(all_126_2_178, all_126_3_179) = all_177_0_210)))
% 15.37/4.31  				|
% 15.37/4.31  				+-Applying beta-rule and splitting (205), into two cases.
% 15.37/4.31  				|-Branch one:
% 15.37/4.31  				| (207) ( ~ (all_176_1_209 = 0) & in(all_126_2_178, all_0_13_13) = all_176_1_209) | ( ~ (all_176_1_209 = 0) & in(all_126_3_179, all_0_13_13) = all_176_1_209)
% 15.37/4.31  				|
% 15.37/4.31  					+-Applying beta-rule and splitting (207), into two cases.
% 15.37/4.31  					|-Branch one:
% 15.37/4.31  					| (208)  ~ (all_176_1_209 = 0) & in(all_126_2_178, all_0_13_13) = all_176_1_209
% 15.37/4.31  					|
% 15.37/4.31  						| Applying alpha-rule on (208) yields:
% 15.37/4.31  						| (209)  ~ (all_176_1_209 = 0)
% 15.37/4.31  						| (210) in(all_126_2_178, all_0_13_13) = all_176_1_209
% 15.37/4.31  						|
% 15.37/4.31  						| Instantiating formula (93) with all_126_2_178, all_0_13_13, all_176_1_209, 0 and discharging atoms in(all_126_2_178, all_0_13_13) = all_176_1_209, in(all_126_2_178, all_0_13_13) = 0, yields:
% 15.37/4.31  						| (211) all_176_1_209 = 0
% 15.37/4.31  						|
% 15.37/4.31  						| Equations (211) can reduce 209 to:
% 15.37/4.31  						| (158) $false
% 15.37/4.31  						|
% 15.37/4.31  						|-The branch is then unsatisfiable
% 15.37/4.31  					|-Branch two:
% 15.37/4.31  					| (213)  ~ (all_176_1_209 = 0) & in(all_126_3_179, all_0_13_13) = all_176_1_209
% 15.37/4.31  					|
% 15.37/4.31  						| Applying alpha-rule on (213) yields:
% 15.37/4.31  						| (209)  ~ (all_176_1_209 = 0)
% 15.37/4.31  						| (215) in(all_126_3_179, all_0_13_13) = all_176_1_209
% 15.37/4.31  						|
% 15.37/4.31  						| Instantiating formula (93) with all_126_3_179, all_0_13_13, all_176_1_209, 0 and discharging atoms in(all_126_3_179, all_0_13_13) = all_176_1_209, in(all_126_3_179, all_0_13_13) = 0, yields:
% 15.37/4.31  						| (211) all_176_1_209 = 0
% 15.37/4.31  						|
% 15.37/4.31  						| Equations (211) can reduce 209 to:
% 15.37/4.32  						| (158) $false
% 15.37/4.32  						|
% 15.37/4.32  						|-The branch is then unsatisfiable
% 15.37/4.32  				|-Branch two:
% 15.37/4.32  				| (218) ((all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209)) & ((all_176_1_209 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_176_0_208 = 0) & subset(all_126_3_179, all_126_2_178) = all_176_0_208))
% 15.37/4.32  				|
% 15.37/4.32  					| Applying alpha-rule on (218) yields:
% 15.37/4.32  					| (219) (all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209)
% 15.37/4.32  					| (220) (all_176_1_209 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_176_0_208 = 0) & subset(all_126_3_179, all_126_2_178) = all_176_0_208)
% 15.37/4.32  					|
% 15.37/4.32  					+-Applying beta-rule and splitting (203), into two cases.
% 15.37/4.32  					|-Branch one:
% 15.37/4.32  					| (221) ( ~ (all_152_1_189 = 0) & relation(all_0_12_12) = all_152_1_189) | ( ~ (all_152_1_189 = 0) & in(all_126_2_178, all_0_13_13) = all_152_1_189) | ( ~ (all_152_1_189 = 0) & in(all_126_3_179, all_0_13_13) = all_152_1_189)
% 15.37/4.32  					|
% 15.37/4.32  						+-Applying beta-rule and splitting (221), into two cases.
% 15.37/4.32  						|-Branch one:
% 15.37/4.32  						| (222) ( ~ (all_152_1_189 = 0) & relation(all_0_12_12) = all_152_1_189) | ( ~ (all_152_1_189 = 0) & in(all_126_2_178, all_0_13_13) = all_152_1_189)
% 15.37/4.32  						|
% 15.37/4.32  							+-Applying beta-rule and splitting (222), into two cases.
% 15.37/4.32  							|-Branch one:
% 15.37/4.32  							| (223)  ~ (all_152_1_189 = 0) & relation(all_0_12_12) = all_152_1_189
% 15.37/4.32  							|
% 15.37/4.32  								| Applying alpha-rule on (223) yields:
% 15.37/4.32  								| (224)  ~ (all_152_1_189 = 0)
% 15.37/4.32  								| (225) relation(all_0_12_12) = all_152_1_189
% 15.37/4.32  								|
% 15.37/4.32  								| Instantiating formula (144) with all_0_12_12, all_152_1_189, 0 and discharging atoms relation(all_0_12_12) = all_152_1_189, relation(all_0_12_12) = 0, yields:
% 15.37/4.32  								| (226) all_152_1_189 = 0
% 15.37/4.32  								|
% 15.37/4.32  								| Equations (226) can reduce 224 to:
% 15.37/4.32  								| (158) $false
% 15.37/4.32  								|
% 15.37/4.32  								|-The branch is then unsatisfiable
% 15.37/4.32  							|-Branch two:
% 15.37/4.32  							| (228)  ~ (all_152_1_189 = 0) & in(all_126_2_178, all_0_13_13) = all_152_1_189
% 15.37/4.32  							|
% 15.37/4.32  								| Applying alpha-rule on (228) yields:
% 15.37/4.32  								| (224)  ~ (all_152_1_189 = 0)
% 15.37/4.32  								| (230) in(all_126_2_178, all_0_13_13) = all_152_1_189
% 15.37/4.32  								|
% 15.37/4.32  								| Instantiating formula (93) with all_126_2_178, all_0_13_13, all_152_1_189, 0 and discharging atoms in(all_126_2_178, all_0_13_13) = all_152_1_189, in(all_126_2_178, all_0_13_13) = 0, yields:
% 15.37/4.32  								| (226) all_152_1_189 = 0
% 15.37/4.32  								|
% 15.37/4.32  								| Equations (226) can reduce 224 to:
% 15.37/4.32  								| (158) $false
% 15.37/4.32  								|
% 15.37/4.32  								|-The branch is then unsatisfiable
% 15.37/4.32  						|-Branch two:
% 15.37/4.32  						| (233)  ~ (all_152_1_189 = 0) & in(all_126_3_179, all_0_13_13) = all_152_1_189
% 15.37/4.32  						|
% 15.37/4.32  							| Applying alpha-rule on (233) yields:
% 15.37/4.32  							| (224)  ~ (all_152_1_189 = 0)
% 15.37/4.32  							| (235) in(all_126_3_179, all_0_13_13) = all_152_1_189
% 15.37/4.32  							|
% 15.37/4.32  							| Instantiating formula (93) with all_126_3_179, all_0_13_13, all_152_1_189, 0 and discharging atoms in(all_126_3_179, all_0_13_13) = all_152_1_189, in(all_126_3_179, all_0_13_13) = 0, yields:
% 15.37/4.32  							| (226) all_152_1_189 = 0
% 15.37/4.32  							|
% 15.37/4.32  							| Equations (226) can reduce 224 to:
% 15.37/4.32  							| (158) $false
% 15.37/4.32  							|
% 15.37/4.32  							|-The branch is then unsatisfiable
% 15.37/4.32  					|-Branch two:
% 15.37/4.32  					| (238) ((all_152_0_188 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_152_1_189 = 0) & in(all_126_1_177, all_0_12_12) = all_152_1_189)) & ((all_152_1_189 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_152_0_188 = 0) & subset(all_126_3_179, all_126_2_178) = all_152_0_188))
% 15.37/4.32  					|
% 15.37/4.32  						| Applying alpha-rule on (238) yields:
% 15.37/4.32  						| (239) (all_152_0_188 = 0 & subset(all_126_3_179, all_126_2_178) = 0) | ( ~ (all_152_1_189 = 0) & in(all_126_1_177, all_0_12_12) = all_152_1_189)
% 15.37/4.32  						| (240) (all_152_1_189 = 0 & in(all_126_1_177, all_0_12_12) = 0) | ( ~ (all_152_0_188 = 0) & subset(all_126_3_179, all_126_2_178) = all_152_0_188)
% 15.37/4.32  						|
% 15.37/4.32  						+-Applying beta-rule and splitting (239), into two cases.
% 15.37/4.32  						|-Branch one:
% 15.37/4.32  						| (241) all_152_0_188 = 0 & subset(all_126_3_179, all_126_2_178) = 0
% 15.37/4.32  						|
% 15.37/4.32  							| Applying alpha-rule on (241) yields:
% 15.37/4.32  							| (242) all_152_0_188 = 0
% 15.37/4.32  							| (243) subset(all_126_3_179, all_126_2_178) = 0
% 15.37/4.32  							|
% 15.37/4.32  							+-Applying beta-rule and splitting (240), into two cases.
% 15.37/4.32  							|-Branch one:
% 15.37/4.32  							| (244) all_152_1_189 = 0 & in(all_126_1_177, all_0_12_12) = 0
% 15.37/4.32  							|
% 15.37/4.32  								| Applying alpha-rule on (244) yields:
% 15.37/4.32  								| (226) all_152_1_189 = 0
% 15.37/4.32  								| (191) in(all_126_1_177, all_0_12_12) = 0
% 15.37/4.32  								|
% 15.37/4.32  								+-Applying beta-rule and splitting (204), into two cases.
% 15.37/4.32  								|-Branch one:
% 15.37/4.32  								| (247) ( ~ (all_153_1_191 = 0) & relation(all_0_12_12) = all_153_1_191) | ( ~ (all_153_1_191 = 0) & in(all_126_2_178, all_0_13_13) = all_153_1_191) | ( ~ (all_153_1_191 = 0) & in(all_126_3_179, all_0_13_13) = all_153_1_191)
% 15.37/4.32  								|
% 15.37/4.32  									+-Applying beta-rule and splitting (247), into two cases.
% 15.37/4.32  									|-Branch one:
% 15.37/4.32  									| (248) ( ~ (all_153_1_191 = 0) & relation(all_0_12_12) = all_153_1_191) | ( ~ (all_153_1_191 = 0) & in(all_126_2_178, all_0_13_13) = all_153_1_191)
% 15.37/4.32  									|
% 15.37/4.32  										+-Applying beta-rule and splitting (248), into two cases.
% 15.37/4.32  										|-Branch one:
% 15.37/4.32  										| (249)  ~ (all_153_1_191 = 0) & relation(all_0_12_12) = all_153_1_191
% 15.37/4.32  										|
% 15.37/4.32  											| Applying alpha-rule on (249) yields:
% 15.37/4.32  											| (250)  ~ (all_153_1_191 = 0)
% 15.37/4.32  											| (251) relation(all_0_12_12) = all_153_1_191
% 15.37/4.32  											|
% 15.37/4.32  											| Instantiating formula (144) with all_0_12_12, all_153_1_191, 0 and discharging atoms relation(all_0_12_12) = all_153_1_191, relation(all_0_12_12) = 0, yields:
% 15.37/4.32  											| (252) all_153_1_191 = 0
% 15.37/4.32  											|
% 15.37/4.32  											| Equations (252) can reduce 250 to:
% 15.37/4.32  											| (158) $false
% 15.37/4.32  											|
% 15.37/4.32  											|-The branch is then unsatisfiable
% 15.37/4.32  										|-Branch two:
% 15.37/4.32  										| (254)  ~ (all_153_1_191 = 0) & in(all_126_2_178, all_0_13_13) = all_153_1_191
% 15.37/4.32  										|
% 15.37/4.32  											| Applying alpha-rule on (254) yields:
% 15.37/4.32  											| (250)  ~ (all_153_1_191 = 0)
% 15.37/4.32  											| (256) in(all_126_2_178, all_0_13_13) = all_153_1_191
% 15.37/4.32  											|
% 15.37/4.32  											| Instantiating formula (93) with all_126_2_178, all_0_13_13, all_153_1_191, 0 and discharging atoms in(all_126_2_178, all_0_13_13) = all_153_1_191, in(all_126_2_178, all_0_13_13) = 0, yields:
% 15.37/4.32  											| (252) all_153_1_191 = 0
% 15.37/4.32  											|
% 15.37/4.32  											| Equations (252) can reduce 250 to:
% 15.37/4.32  											| (158) $false
% 15.37/4.32  											|
% 15.37/4.32  											|-The branch is then unsatisfiable
% 15.37/4.32  									|-Branch two:
% 15.37/4.32  									| (259)  ~ (all_153_1_191 = 0) & in(all_126_3_179, all_0_13_13) = all_153_1_191
% 15.37/4.32  									|
% 15.37/4.32  										| Applying alpha-rule on (259) yields:
% 15.37/4.32  										| (250)  ~ (all_153_1_191 = 0)
% 15.37/4.32  										| (261) in(all_126_3_179, all_0_13_13) = all_153_1_191
% 15.37/4.32  										|
% 15.37/4.32  										| Instantiating formula (93) with all_126_3_179, all_0_13_13, all_153_1_191, 0 and discharging atoms in(all_126_3_179, all_0_13_13) = all_153_1_191, in(all_126_3_179, all_0_13_13) = 0, yields:
% 15.37/4.32  										| (252) all_153_1_191 = 0
% 15.37/4.32  										|
% 15.37/4.32  										| Equations (252) can reduce 250 to:
% 15.37/4.32  										| (158) $false
% 15.37/4.32  										|
% 15.37/4.32  										|-The branch is then unsatisfiable
% 15.37/4.32  								|-Branch two:
% 15.37/4.32  								| (264) ((all_153_0_190 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_153_1_191 = 0) & in(all_126_0_176, all_0_12_12) = all_153_1_191)) & ((all_153_1_191 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_153_0_190 = 0) & subset(all_126_2_178, all_126_3_179) = all_153_0_190))
% 15.37/4.32  								|
% 15.37/4.32  									| Applying alpha-rule on (264) yields:
% 15.37/4.32  									| (265) (all_153_0_190 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_153_1_191 = 0) & in(all_126_0_176, all_0_12_12) = all_153_1_191)
% 15.37/4.32  									| (266) (all_153_1_191 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_153_0_190 = 0) & subset(all_126_2_178, all_126_3_179) = all_153_0_190)
% 15.37/4.32  									|
% 15.37/4.32  									+-Applying beta-rule and splitting (265), into two cases.
% 15.37/4.32  									|-Branch one:
% 15.37/4.32  									| (267) all_153_0_190 = 0 & subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.32  									|
% 15.37/4.32  										| Applying alpha-rule on (267) yields:
% 15.37/4.32  										| (268) all_153_0_190 = 0
% 15.37/4.32  										| (269) subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.32  										|
% 15.37/4.32  										+-Applying beta-rule and splitting (266), into two cases.
% 15.37/4.32  										|-Branch one:
% 15.37/4.32  										| (270) all_153_1_191 = 0 & in(all_126_0_176, all_0_12_12) = 0
% 15.37/4.32  										|
% 15.37/4.32  											| Applying alpha-rule on (270) yields:
% 15.37/4.32  											| (252) all_153_1_191 = 0
% 15.37/4.32  											| (189) in(all_126_0_176, all_0_12_12) = 0
% 15.37/4.32  											|
% 15.37/4.32  											+-Applying beta-rule and splitting (206), into two cases.
% 15.37/4.32  											|-Branch one:
% 15.37/4.32  											| (273) ( ~ (all_177_1_211 = 0) & in(all_126_2_178, all_0_13_13) = all_177_1_211) | ( ~ (all_177_1_211 = 0) & in(all_126_3_179, all_0_13_13) = all_177_1_211)
% 15.37/4.32  											|
% 15.37/4.32  												+-Applying beta-rule and splitting (273), into two cases.
% 15.37/4.32  												|-Branch one:
% 15.37/4.32  												| (274)  ~ (all_177_1_211 = 0) & in(all_126_2_178, all_0_13_13) = all_177_1_211
% 15.37/4.32  												|
% 15.37/4.32  													| Applying alpha-rule on (274) yields:
% 15.37/4.32  													| (275)  ~ (all_177_1_211 = 0)
% 15.37/4.32  													| (276) in(all_126_2_178, all_0_13_13) = all_177_1_211
% 15.37/4.32  													|
% 15.37/4.32  													| Instantiating formula (93) with all_126_2_178, all_0_13_13, all_177_1_211, 0 and discharging atoms in(all_126_2_178, all_0_13_13) = all_177_1_211, in(all_126_2_178, all_0_13_13) = 0, yields:
% 15.37/4.32  													| (277) all_177_1_211 = 0
% 15.37/4.32  													|
% 15.37/4.32  													| Equations (277) can reduce 275 to:
% 15.37/4.32  													| (158) $false
% 15.37/4.32  													|
% 15.37/4.32  													|-The branch is then unsatisfiable
% 15.37/4.32  												|-Branch two:
% 15.37/4.32  												| (279)  ~ (all_177_1_211 = 0) & in(all_126_3_179, all_0_13_13) = all_177_1_211
% 15.37/4.32  												|
% 15.37/4.32  													| Applying alpha-rule on (279) yields:
% 15.37/4.32  													| (275)  ~ (all_177_1_211 = 0)
% 15.37/4.32  													| (281) in(all_126_3_179, all_0_13_13) = all_177_1_211
% 15.37/4.32  													|
% 15.37/4.32  													| Instantiating formula (93) with all_126_3_179, all_0_13_13, all_177_1_211, 0 and discharging atoms in(all_126_3_179, all_0_13_13) = all_177_1_211, in(all_126_3_179, all_0_13_13) = 0, yields:
% 15.37/4.32  													| (277) all_177_1_211 = 0
% 15.37/4.32  													|
% 15.37/4.32  													| Equations (277) can reduce 275 to:
% 15.37/4.32  													| (158) $false
% 15.37/4.32  													|
% 15.37/4.32  													|-The branch is then unsatisfiable
% 15.37/4.32  											|-Branch two:
% 15.37/4.32  											| (284) ((all_177_0_210 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_177_1_211 = 0) & in(all_126_0_176, all_0_12_12) = all_177_1_211)) & ((all_177_1_211 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_177_0_210 = 0) & subset(all_126_2_178, all_126_3_179) = all_177_0_210))
% 15.37/4.32  											|
% 15.37/4.32  												| Applying alpha-rule on (284) yields:
% 15.37/4.32  												| (285) (all_177_0_210 = 0 & subset(all_126_2_178, all_126_3_179) = 0) | ( ~ (all_177_1_211 = 0) & in(all_126_0_176, all_0_12_12) = all_177_1_211)
% 15.37/4.32  												| (286) (all_177_1_211 = 0 & in(all_126_0_176, all_0_12_12) = 0) | ( ~ (all_177_0_210 = 0) & subset(all_126_2_178, all_126_3_179) = all_177_0_210)
% 15.37/4.32  												|
% 15.37/4.32  												+-Applying beta-rule and splitting (220), into two cases.
% 15.37/4.32  												|-Branch one:
% 15.37/4.32  												| (287) all_176_1_209 = 0 & in(all_126_1_177, all_0_12_12) = 0
% 15.37/4.32  												|
% 15.37/4.32  													| Applying alpha-rule on (287) yields:
% 15.37/4.32  													| (211) all_176_1_209 = 0
% 15.37/4.32  													| (191) in(all_126_1_177, all_0_12_12) = 0
% 15.37/4.32  													|
% 15.37/4.32  													+-Applying beta-rule and splitting (219), into two cases.
% 15.37/4.32  													|-Branch one:
% 15.37/4.32  													| (290) all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0
% 15.37/4.32  													|
% 15.37/4.32  														| Applying alpha-rule on (290) yields:
% 15.37/4.32  														| (291) all_176_0_208 = 0
% 15.37/4.32  														| (243) subset(all_126_3_179, all_126_2_178) = 0
% 15.37/4.32  														|
% 15.37/4.32  														+-Applying beta-rule and splitting (286), into two cases.
% 15.37/4.32  														|-Branch one:
% 15.37/4.32  														| (293) all_177_1_211 = 0 & in(all_126_0_176, all_0_12_12) = 0
% 15.37/4.32  														|
% 15.37/4.32  															| Applying alpha-rule on (293) yields:
% 15.37/4.32  															| (277) all_177_1_211 = 0
% 15.37/4.32  															| (189) in(all_126_0_176, all_0_12_12) = 0
% 15.37/4.32  															|
% 15.37/4.32  															+-Applying beta-rule and splitting (285), into two cases.
% 15.37/4.32  															|-Branch one:
% 15.37/4.32  															| (296) all_177_0_210 = 0 & subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.32  															|
% 15.37/4.32  																| Applying alpha-rule on (296) yields:
% 15.37/4.32  																| (297) all_177_0_210 = 0
% 15.37/4.32  																| (269) subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.32  																|
% 15.37/4.32  																| Instantiating formula (30) with all_126_2_178, all_126_3_179 and discharging atoms subset(all_126_2_178, all_126_3_179) = 0, yields:
% 15.37/4.32  																| (299) all_126_2_178 = all_126_3_179 |  ? [v0] : ( ~ (v0 = 0) & subset(all_126_3_179, all_126_2_178) = v0)
% 15.37/4.32  																|
% 15.37/4.32  																+-Applying beta-rule and splitting (299), into two cases.
% 15.37/4.32  																|-Branch one:
% 15.37/4.32  																| (300) all_126_2_178 = all_126_3_179
% 15.37/4.32  																|
% 15.37/4.32  																	| Equations (300) can reduce 193 to:
% 15.37/4.32  																	| (158) $false
% 15.37/4.32  																	|
% 15.37/4.32  																	|-The branch is then unsatisfiable
% 15.37/4.32  																|-Branch two:
% 15.37/4.32  																| (193)  ~ (all_126_2_178 = all_126_3_179)
% 15.37/4.32  																| (303)  ? [v0] : ( ~ (v0 = 0) & subset(all_126_3_179, all_126_2_178) = v0)
% 15.37/4.33  																|
% 15.37/4.33  																	| Instantiating (303) with all_279_0_298 yields:
% 15.37/4.33  																	| (304)  ~ (all_279_0_298 = 0) & subset(all_126_3_179, all_126_2_178) = all_279_0_298
% 15.37/4.33  																	|
% 15.37/4.33  																	| Applying alpha-rule on (304) yields:
% 15.37/4.33  																	| (305)  ~ (all_279_0_298 = 0)
% 15.37/4.33  																	| (306) subset(all_126_3_179, all_126_2_178) = all_279_0_298
% 15.37/4.33  																	|
% 15.37/4.33  																	| Instantiating formula (121) with all_126_3_179, all_126_2_178, all_279_0_298, 0 and discharging atoms subset(all_126_3_179, all_126_2_178) = all_279_0_298, subset(all_126_3_179, all_126_2_178) = 0, yields:
% 15.37/4.33  																	| (307) all_279_0_298 = 0
% 15.37/4.33  																	|
% 15.37/4.33  																	| Equations (307) can reduce 305 to:
% 15.37/4.33  																	| (158) $false
% 15.37/4.33  																	|
% 15.37/4.33  																	|-The branch is then unsatisfiable
% 15.37/4.33  															|-Branch two:
% 15.37/4.33  															| (309)  ~ (all_177_1_211 = 0) & in(all_126_0_176, all_0_12_12) = all_177_1_211
% 15.37/4.33  															|
% 15.37/4.33  																| Applying alpha-rule on (309) yields:
% 15.37/4.33  																| (275)  ~ (all_177_1_211 = 0)
% 15.37/4.33  																| (311) in(all_126_0_176, all_0_12_12) = all_177_1_211
% 15.37/4.33  																|
% 15.37/4.33  																| Equations (277) can reduce 275 to:
% 15.37/4.33  																| (158) $false
% 15.37/4.33  																|
% 15.37/4.33  																|-The branch is then unsatisfiable
% 15.37/4.33  														|-Branch two:
% 15.37/4.33  														| (313)  ~ (all_177_0_210 = 0) & subset(all_126_2_178, all_126_3_179) = all_177_0_210
% 15.37/4.33  														|
% 15.37/4.33  															| Applying alpha-rule on (313) yields:
% 15.37/4.33  															| (314)  ~ (all_177_0_210 = 0)
% 15.37/4.33  															| (315) subset(all_126_2_178, all_126_3_179) = all_177_0_210
% 15.37/4.33  															|
% 15.37/4.33  															+-Applying beta-rule and splitting (285), into two cases.
% 15.37/4.33  															|-Branch one:
% 15.37/4.33  															| (296) all_177_0_210 = 0 & subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.33  															|
% 15.37/4.33  																| Applying alpha-rule on (296) yields:
% 15.37/4.33  																| (297) all_177_0_210 = 0
% 15.37/4.33  																| (269) subset(all_126_2_178, all_126_3_179) = 0
% 15.37/4.33  																|
% 15.37/4.33  																| Equations (297) can reduce 314 to:
% 15.37/4.33  																| (158) $false
% 15.37/4.33  																|
% 15.37/4.33  																|-The branch is then unsatisfiable
% 15.37/4.33  															|-Branch two:
% 15.37/4.33  															| (309)  ~ (all_177_1_211 = 0) & in(all_126_0_176, all_0_12_12) = all_177_1_211
% 15.37/4.33  															|
% 15.37/4.33  																| Applying alpha-rule on (309) yields:
% 15.37/4.33  																| (275)  ~ (all_177_1_211 = 0)
% 15.37/4.33  																| (311) in(all_126_0_176, all_0_12_12) = all_177_1_211
% 15.37/4.33  																|
% 15.37/4.33  																| Instantiating formula (93) with all_126_0_176, all_0_12_12, all_177_1_211, 0 and discharging atoms in(all_126_0_176, all_0_12_12) = all_177_1_211, in(all_126_0_176, all_0_12_12) = 0, yields:
% 15.72/4.33  																| (277) all_177_1_211 = 0
% 15.72/4.33  																|
% 15.72/4.33  																| Equations (277) can reduce 275 to:
% 15.72/4.33  																| (158) $false
% 15.72/4.33  																|
% 15.72/4.33  																|-The branch is then unsatisfiable
% 15.72/4.33  													|-Branch two:
% 15.72/4.33  													| (325)  ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  													|
% 15.72/4.33  														| Applying alpha-rule on (325) yields:
% 15.72/4.33  														| (209)  ~ (all_176_1_209 = 0)
% 15.72/4.33  														| (327) in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  														|
% 15.72/4.33  														| Equations (211) can reduce 209 to:
% 15.72/4.33  														| (158) $false
% 15.72/4.33  														|
% 15.72/4.33  														|-The branch is then unsatisfiable
% 15.72/4.33  												|-Branch two:
% 15.72/4.33  												| (329)  ~ (all_176_0_208 = 0) & subset(all_126_3_179, all_126_2_178) = all_176_0_208
% 15.72/4.33  												|
% 15.72/4.33  													| Applying alpha-rule on (329) yields:
% 15.72/4.33  													| (330)  ~ (all_176_0_208 = 0)
% 15.72/4.33  													| (331) subset(all_126_3_179, all_126_2_178) = all_176_0_208
% 15.72/4.33  													|
% 15.72/4.33  													+-Applying beta-rule and splitting (219), into two cases.
% 15.72/4.33  													|-Branch one:
% 15.72/4.33  													| (290) all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0
% 15.72/4.33  													|
% 15.72/4.33  														| Applying alpha-rule on (290) yields:
% 15.72/4.33  														| (291) all_176_0_208 = 0
% 15.72/4.33  														| (243) subset(all_126_3_179, all_126_2_178) = 0
% 15.72/4.33  														|
% 15.72/4.33  														| Equations (291) can reduce 330 to:
% 15.72/4.33  														| (158) $false
% 15.72/4.33  														|
% 15.72/4.33  														|-The branch is then unsatisfiable
% 15.72/4.33  													|-Branch two:
% 15.72/4.33  													| (325)  ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  													|
% 15.72/4.33  														| Applying alpha-rule on (325) yields:
% 15.72/4.33  														| (209)  ~ (all_176_1_209 = 0)
% 15.72/4.33  														| (327) in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  														|
% 15.72/4.33  														| Instantiating formula (93) with all_126_1_177, all_0_12_12, all_176_1_209, 0 and discharging atoms in(all_126_1_177, all_0_12_12) = all_176_1_209, in(all_126_1_177, all_0_12_12) = 0, yields:
% 15.72/4.33  														| (211) all_176_1_209 = 0
% 15.72/4.33  														|
% 15.72/4.33  														| Equations (211) can reduce 209 to:
% 15.72/4.33  														| (158) $false
% 15.72/4.33  														|
% 15.72/4.33  														|-The branch is then unsatisfiable
% 15.72/4.33  										|-Branch two:
% 15.72/4.33  										| (341)  ~ (all_153_0_190 = 0) & subset(all_126_2_178, all_126_3_179) = all_153_0_190
% 15.72/4.33  										|
% 15.72/4.33  											| Applying alpha-rule on (341) yields:
% 15.72/4.33  											| (342)  ~ (all_153_0_190 = 0)
% 15.72/4.33  											| (343) subset(all_126_2_178, all_126_3_179) = all_153_0_190
% 15.72/4.33  											|
% 15.72/4.33  											| Equations (268) can reduce 342 to:
% 15.72/4.33  											| (158) $false
% 15.72/4.33  											|
% 15.72/4.33  											|-The branch is then unsatisfiable
% 15.72/4.33  									|-Branch two:
% 15.72/4.33  									| (345)  ~ (all_153_1_191 = 0) & in(all_126_0_176, all_0_12_12) = all_153_1_191
% 15.72/4.33  									|
% 15.72/4.33  										| Applying alpha-rule on (345) yields:
% 15.72/4.33  										| (250)  ~ (all_153_1_191 = 0)
% 15.72/4.33  										| (347) in(all_126_0_176, all_0_12_12) = all_153_1_191
% 15.72/4.33  										|
% 15.72/4.33  										| Instantiating formula (93) with all_126_0_176, all_0_12_12, all_153_1_191, 0 and discharging atoms in(all_126_0_176, all_0_12_12) = all_153_1_191, in(all_126_0_176, all_0_12_12) = 0, yields:
% 15.72/4.33  										| (252) all_153_1_191 = 0
% 15.72/4.33  										|
% 15.72/4.33  										| Equations (252) can reduce 250 to:
% 15.72/4.33  										| (158) $false
% 15.72/4.33  										|
% 15.72/4.33  										|-The branch is then unsatisfiable
% 15.72/4.33  							|-Branch two:
% 15.72/4.33  							| (350)  ~ (all_152_0_188 = 0) & subset(all_126_3_179, all_126_2_178) = all_152_0_188
% 15.72/4.33  							|
% 15.72/4.33  								| Applying alpha-rule on (350) yields:
% 15.72/4.33  								| (351)  ~ (all_152_0_188 = 0)
% 15.72/4.33  								| (352) subset(all_126_3_179, all_126_2_178) = all_152_0_188
% 15.72/4.33  								|
% 15.72/4.33  								| Equations (242) can reduce 351 to:
% 15.72/4.33  								| (158) $false
% 15.72/4.33  								|
% 15.72/4.33  								|-The branch is then unsatisfiable
% 15.72/4.33  						|-Branch two:
% 15.72/4.33  						| (354)  ~ (all_152_1_189 = 0) & in(all_126_1_177, all_0_12_12) = all_152_1_189
% 15.72/4.33  						|
% 15.72/4.33  							| Applying alpha-rule on (354) yields:
% 15.72/4.33  							| (224)  ~ (all_152_1_189 = 0)
% 15.72/4.33  							| (356) in(all_126_1_177, all_0_12_12) = all_152_1_189
% 15.72/4.33  							|
% 15.72/4.33  							+-Applying beta-rule and splitting (219), into two cases.
% 15.72/4.33  							|-Branch one:
% 15.72/4.33  							| (290) all_176_0_208 = 0 & subset(all_126_3_179, all_126_2_178) = 0
% 15.72/4.33  							|
% 15.72/4.33  								| Applying alpha-rule on (290) yields:
% 15.72/4.33  								| (291) all_176_0_208 = 0
% 15.72/4.33  								| (243) subset(all_126_3_179, all_126_2_178) = 0
% 15.72/4.33  								|
% 15.72/4.33  								+-Applying beta-rule and splitting (220), into two cases.
% 15.72/4.33  								|-Branch one:
% 15.72/4.33  								| (287) all_176_1_209 = 0 & in(all_126_1_177, all_0_12_12) = 0
% 15.72/4.33  								|
% 15.72/4.33  									| Applying alpha-rule on (287) yields:
% 15.72/4.33  									| (211) all_176_1_209 = 0
% 15.72/4.33  									| (191) in(all_126_1_177, all_0_12_12) = 0
% 15.72/4.33  									|
% 15.72/4.33  									| Instantiating formula (93) with all_126_1_177, all_0_12_12, all_152_1_189, 0 and discharging atoms in(all_126_1_177, all_0_12_12) = all_152_1_189, in(all_126_1_177, all_0_12_12) = 0, yields:
% 15.72/4.33  									| (226) all_152_1_189 = 0
% 15.72/4.33  									|
% 15.72/4.33  									| Equations (226) can reduce 224 to:
% 15.72/4.33  									| (158) $false
% 15.72/4.33  									|
% 15.72/4.33  									|-The branch is then unsatisfiable
% 15.72/4.33  								|-Branch two:
% 15.72/4.33  								| (329)  ~ (all_176_0_208 = 0) & subset(all_126_3_179, all_126_2_178) = all_176_0_208
% 15.72/4.33  								|
% 15.72/4.33  									| Applying alpha-rule on (329) yields:
% 15.72/4.33  									| (330)  ~ (all_176_0_208 = 0)
% 15.72/4.33  									| (331) subset(all_126_3_179, all_126_2_178) = all_176_0_208
% 15.72/4.33  									|
% 15.72/4.33  									| Equations (291) can reduce 330 to:
% 15.72/4.33  									| (158) $false
% 15.72/4.33  									|
% 15.72/4.33  									|-The branch is then unsatisfiable
% 15.72/4.33  							|-Branch two:
% 15.72/4.33  							| (325)  ~ (all_176_1_209 = 0) & in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  							|
% 15.72/4.33  								| Applying alpha-rule on (325) yields:
% 15.72/4.33  								| (209)  ~ (all_176_1_209 = 0)
% 15.72/4.33  								| (327) in(all_126_1_177, all_0_12_12) = all_176_1_209
% 15.72/4.33  								|
% 15.72/4.33  								| Instantiating formula (93) with all_126_1_177, all_0_12_12, all_176_1_209, 0 and discharging atoms in(all_126_1_177, all_0_12_12) = all_176_1_209, in(all_126_1_177, all_0_12_12) = 0, yields:
% 15.72/4.33  								| (211) all_176_1_209 = 0
% 15.72/4.33  								|
% 15.72/4.33  								| Instantiating formula (93) with all_126_1_177, all_0_12_12, all_152_1_189, all_176_1_209 and discharging atoms in(all_126_1_177, all_0_12_12) = all_176_1_209, in(all_126_1_177, all_0_12_12) = all_152_1_189, yields:
% 15.72/4.33  								| (373) all_176_1_209 = all_152_1_189
% 15.72/4.33  								|
% 15.72/4.33  								| Combining equations (211,373) yields a new equation:
% 15.72/4.33  								| (226) all_152_1_189 = 0
% 15.72/4.33  								|
% 15.72/4.33  								| Equations (226) can reduce 224 to:
% 15.72/4.33  								| (158) $false
% 15.72/4.33  								|
% 15.72/4.33  								|-The branch is then unsatisfiable
% 15.72/4.33  		|-Branch two:
% 15.72/4.33  		| (376)  ~ (all_73_1_102 = all_0_13_13)
% 15.72/4.33  		| (377)  ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0)
% 15.72/4.33  		|
% 15.72/4.33  			| Instantiating formula (75) with all_0_12_12, all_108_2_160, all_73_1_102 and discharging atoms relation_field(all_0_12_12) = all_108_2_160, relation_field(all_0_12_12) = all_73_1_102, yields:
% 15.72/4.33  			| (378) all_108_2_160 = all_73_1_102
% 15.72/4.33  			|
% 15.72/4.33  			| Instantiating formula (75) with all_0_12_12, all_0_13_13, all_108_2_160 and discharging atoms relation_field(all_0_12_12) = all_108_2_160, relation_field(all_0_12_12) = all_0_13_13, yields:
% 15.72/4.33  			| (197) all_108_2_160 = all_0_13_13
% 15.72/4.33  			|
% 15.72/4.33  			| Combining equations (197,378) yields a new equation:
% 15.72/4.33  			| (181) all_73_1_102 = all_0_13_13
% 15.72/4.33  			|
% 15.72/4.33  			| Equations (181) can reduce 376 to:
% 15.72/4.33  			| (158) $false
% 15.72/4.33  			|
% 15.72/4.33  			|-The branch is then unsatisfiable
% 15.72/4.33  % SZS output end Proof for theBenchmark
% 15.72/4.33  
% 15.72/4.33  3662ms
%------------------------------------------------------------------------------