%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU294+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n028.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 08:48:33 EDT 2022

% Result   : Theorem 18.35s 5.14s
% Output   : Proof 21.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU294+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 20 04:41:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.66/0.63          ____       _                          
% 0.66/0.63    ___  / __ \_____(_)___  ________  __________
% 0.66/0.63   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.63  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.66/0.63  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.66/0.63  
% 0.66/0.63  A Theorem Prover for First-Order Logic
% 0.66/0.63  (ePrincess v.1.0)
% 0.66/0.63  
% 0.66/0.63  (c) Philipp Rümmer, 2009-2015
% 0.66/0.63  (c) Peter Backeman, 2014-2015
% 0.66/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63  Bug reports to peter@backeman.se
% 0.66/0.63  
% 0.66/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63  
% 0.66/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/1.04  Prover 0: Preprocessing ...
% 2.34/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.34/1.26  Prover 0: Constructing countermodel ...
% 3.07/1.48  Prover 0: gave up
% 3.07/1.48  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.07/1.52  Prover 1: Preprocessing ...
% 3.65/1.66  Prover 1: Warning: ignoring some quantifiers
% 4.09/1.67  Prover 1: Constructing countermodel ...
% 16.98/4.83  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.38/4.88  Prover 2: Preprocessing ...
% 18.06/5.04  Prover 2: Warning: ignoring some quantifiers
% 18.06/5.05  Prover 2: Constructing countermodel ...
% 18.35/5.14  Prover 2: proved (315ms)
% 18.35/5.14  Prover 1: stopped
% 18.35/5.14  
% 18.35/5.14  No countermodel exists, formula is valid
% 18.35/5.14  % SZS status Theorem for theBenchmark
% 18.35/5.14  
% 18.35/5.14  Generating proof ... Warning: ignoring some quantifiers
% 20.68/5.61  found it (size 23)
% 20.68/5.61  
% 20.68/5.61  % SZS output start Proof for theBenchmark
% 20.68/5.61  Assumed formulas after preprocessing and simplification: 
% 20.68/5.62  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : ( ~ (v21 = 0) &  ~ (v19 = 0) &  ~ (v11 = 0) &  ~ (v9 = 0) &  ~ (v6 = 0) &  ~ (v2 = 0) & subset(v0, v1) = 0 & relation_empty_yielding(v4) = 0 & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(v12) = 0 & one_to_one(v7) = 0 & one_to_one(empty_set) = 0 & natural(v20) = 0 & relation(v17) = 0 & relation(v15) = 0 & relation(v13) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & function(v17) = 0 & function(v13) = 0 & function(v12) = 0 & function(v7) = 0 & function(v3) = 0 & function(empty_set) = 0 & finite(v18) = 0 & finite(v1) = 0 & finite(v0) = v2 & empty(v20) = v21 & empty(v18) = v19 & empty(v15) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v12) = 0 & empty(v10) = v11 & empty(v8) = v9 & empty(v5) = v6 & empty(empty_set) = 0 & epsilon_connected(v20) = 0 & epsilon_connected(v16) = 0 & epsilon_connected(v12) = 0 & epsilon_connected(v5) = 0 & epsilon_connected(empty_set) = 0 & epsilon_transitive(v20) = 0 & epsilon_transitive(v16) = 0 & epsilon_transitive(v12) = 0 & epsilon_transitive(v5) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v20) = 0 & ordinal(v16) = 0 & ordinal(v12) = 0 & ordinal(v5) = 0 & ordinal(empty_set) = 0 &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] :  ! [v26] : (v26 = 0 |  ~ (powerset(v24) = v25) |  ~ (element(v23, v25) = 0) |  ~ (element(v22, v24) = v26) |  ? [v27] : ( ~ (v27 = 0) & in(v22, v23) = v27)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v25 = 0 |  ~ (powerset(v23) = v24) |  ~ (element(v22, v24) = v25) |  ? [v26] : ( ~ (v26 = 0) & subset(v22, v23) = v26)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v25 = 0 |  ~ (powerset(v22) = v23) |  ~ (finite(v24) = v25) |  ? [v26] : (( ~ (v26 = 0) & finite(v22) = v26) | ( ~ (v26 = 0) & element(v24, v23) = v26))) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v25 = 0 |  ~ (element(v22, v24) = v25) |  ~ (in(v22, v23) = 0) |  ? [v26] :  ? [v27] : ( ~ (v27 = 0) & powerset(v24) = v26 & element(v23, v26) = v27)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v23 = v22 |  ~ (subset(v25, v24) = v23) |  ~ (subset(v25, v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v23 = v22 |  ~ (element(v25, v24) = v23) |  ~ (element(v25, v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : (v23 = v22 |  ~ (in(v25, v24) = v23) |  ~ (in(v25, v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ~ (element(v23, v25) = 0) |  ~ (in(v22, v23) = 0) | element(v22, v24) = 0) &  ! [v22] :  ! [v23] :  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ~ (element(v23, v25) = 0) |  ~ (in(v22, v23) = 0) |  ? [v26] : ( ~ (v26 = 0) & empty(v24) = v26)) &  ! [v22] :  ! [v23] :  ! [v24] : (v24 = 0 |  ~ (subset(v22, v23) = v24) |  ? [v25] :  ? [v26] : ( ~ (v26 = 0) & powerset(v23) = v25 & element(v22, v25) = v26)) &  ! [v22] :  ! [v23] :  ! [v24] : (v24 = 0 |  ~ (element(v22, v23) = v24) |  ? [v25] : ( ~ (v25 = 0) & in(v22, v23) = v25)) &  ! [v22] :  ! [v23] :  ! [v24] : (v24 = 0 |  ~ (in(v22, v23) = v24) |  ? [v25] : ((v25 = 0 & empty(v23) = 0) | ( ~ (v25 = 0) & element(v22, v23) = v25))) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (relation_empty_yielding(v24) = v23) |  ~ (relation_empty_yielding(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (one_to_one(v24) = v23) |  ~ (one_to_one(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (powerset(v24) = v23) |  ~ (powerset(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (natural(v24) = v23) |  ~ (natural(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (relation(v24) = v23) |  ~ (relation(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (function(v24) = v23) |  ~ (function(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (finite(v24) = v23) |  ~ (finite(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (empty(v24) = v23) |  ~ (empty(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (epsilon_connected(v24) = v23) |  ~ (epsilon_connected(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (epsilon_transitive(v24) = v23) |  ~ (epsilon_transitive(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : (v23 = v22 |  ~ (ordinal(v24) = v23) |  ~ (ordinal(v24) = v22)) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (powerset(v23) = v24) |  ~ (element(v22, v24) = 0) | subset(v22, v23) = 0) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (powerset(v22) = v23) |  ~ (element(v24, v23) = 0) |  ? [v25] : ((v25 = 0 & finite(v24) = 0) | ( ~ (v25 = 0) & finite(v22) = v25))) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (empty(v24) = 0) |  ~ (in(v22, v23) = 0) |  ? [v25] :  ? [v26] : ( ~ (v26 = 0) & powerset(v24) = v25 & element(v23, v25) = v26)) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (epsilon_connected(v23) = v24) |  ~ (ordinal(v22) = 0) |  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & epsilon_transitive(v23) = 0 & ordinal(v23) = 0) | ( ~ (v25 = 0) & element(v23, v22) = v25))) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (epsilon_transitive(v23) = v24) |  ~ (ordinal(v22) = 0) |  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & epsilon_connected(v23) = 0 & ordinal(v23) = 0) | ( ~ (v25 = 0) & element(v23, v22) = v25))) &  ! [v22] :  ! [v23] :  ! [v24] : ( ~ (ordinal(v23) = v24) |  ~ (ordinal(v22) = 0) |  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & epsilon_connected(v23) = 0 & epsilon_transitive(v23) = 0) | ( ~ (v25 = 0) & element(v23, v22) = v25))) &  ! [v22] :  ! [v23] : (v23 = v22 |  ~ (empty(v23) = 0) |  ~ (empty(v22) = 0)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (subset(v22, v22) = v23)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (relation(v22) = v23) |  ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (function(v22) = v23) |  ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (finite(v22) = v23) |  ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (empty(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ( ~ (v26 = 0) & powerset(v22) = v24 & finite(v25) = 0 & empty(v25) = v26 & element(v25, v24) = 0)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (empty(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ( ~ (v26 = 0) & powerset(v22) = v24 & empty(v25) = v26 & element(v25, v24) = 0)) &  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (ordinal(v22) = v23) |  ? [v24] : (( ~ (v24 = 0) & epsilon_connected(v22) = v24) | ( ~ (v24 = 0) & epsilon_transitive(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (subset(v22, v23) = 0) |  ? [v24] : (powerset(v23) = v24 & element(v22, v24) = 0)) &  ! [v22] :  ! [v23] : ( ~ (one_to_one(v22) = v23) |  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & relation(v22) = 0 & function(v22) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | ( ~ (v24 = 0) & empty(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] :  ? [v27] : ((v27 = 0 & v25 = 0 &  ~ (v26 = 0) & finite(v24) = 0 & empty(v24) = v26 & element(v24, v23) = 0) | (v24 = 0 & empty(v22) = 0))) &  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ((v25 = 0 &  ~ (v26 = 0) & empty(v24) = v26 & element(v24, v23) = 0) | (v24 = 0 & empty(v22) = 0))) &  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ? [v24] : ( ~ (v24 = 0) & empty(v23) = v24)) &  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ? [v24] : (one_to_one(v24) = 0 & natural(v24) = 0 & relation(v24) = 0 & function(v24) = 0 & finite(v24) = 0 & empty(v24) = 0 & epsilon_connected(v24) = 0 & element(v24, v23) = 0 & epsilon_transitive(v24) = 0 & ordinal(v24) = 0)) &  ! [v22] :  ! [v23] : ( ~ (powerset(v22) = v23) |  ? [v24] : (empty(v24) = 0 & element(v24, v23) = 0)) &  ! [v22] :  ! [v23] : ( ~ (natural(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0 & ordinal(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24) | ( ~ (v24 = 0) & ordinal(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_connected(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & natural(v22) = 0 & epsilon_transitive(v22) = 0 & ordinal(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24) | ( ~ (v24 = 0) & ordinal(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_connected(v22) = v23) |  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & epsilon_transitive(v22) = 0 & ordinal(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_connected(v22) = v23) |  ? [v24] : ((v24 = 0 & v23 = 0 & epsilon_transitive(v22) = 0) | ( ~ (v24 = 0) & ordinal(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (element(v23, v22) = 0) |  ~ (ordinal(v22) = 0) | (epsilon_connected(v23) = 0 & epsilon_transitive(v23) = 0 & ordinal(v23) = 0)) &  ! [v22] :  ! [v23] : ( ~ (element(v22, v23) = 0) |  ? [v24] : ((v24 = 0 & empty(v23) = 0) | (v24 = 0 & in(v22, v23) = 0))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_transitive(v22) = v23) |  ? [v24] :  ? [v25] :  ? [v26] : ((v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & natural(v22) = 0 & epsilon_connected(v22) = 0 & ordinal(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24) | ( ~ (v24 = 0) & ordinal(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_transitive(v22) = v23) |  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & epsilon_connected(v22) = 0 & ordinal(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (epsilon_transitive(v22) = v23) |  ? [v24] : ((v24 = 0 & v23 = 0 & epsilon_connected(v22) = 0) | ( ~ (v24 = 0) & ordinal(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (ordinal(v22) = v23) |  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0) | ( ~ (v24 = 0) & empty(v22) = v24))) &  ! [v22] :  ! [v23] : ( ~ (in(v23, v22) = 0) |  ? [v24] : ( ~ (v24 = 0) & in(v22, v23) = v24)) &  ! [v22] :  ! [v23] : ( ~ (in(v22, v23) = 0) | element(v22, v23) = 0) &  ! [v22] :  ! [v23] : ( ~ (in(v22, v23) = 0) |  ? [v24] : ( ~ (v24 = 0) & empty(v23) = v24)) &  ! [v22] :  ! [v23] : ( ~ (in(v22, v23) = 0) |  ? [v24] : ( ~ (v24 = 0) & in(v23, v22) = v24)) &  ! [v22] : (v22 = empty_set |  ~ (empty(v22) = 0)) &  ! [v22] : ( ~ (relation(v22) = 0) |  ? [v23] :  ? [v24] : ((v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & function(v22) = 0) | ( ~ (v23 = 0) & function(v22) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) &  ! [v22] : ( ~ (function(v22) = 0) |  ? [v23] :  ? [v24] : ((v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & relation(v22) = 0) | ( ~ (v23 = 0) & relation(v22) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) &  ! [v22] : ( ~ (finite(v22) = 0) |  ? [v23] : (powerset(v22) = v23 &  ! [v24] :  ! [v25] : (v25 = 0 |  ~ (finite(v24) = v25) |  ? [v26] : ( ~ (v26 = 0) & element(v24, v23) = v26)) &  ! [v24] : ( ~ (element(v24, v23) = 0) | finite(v24) = 0))) &  ! [v22] : ( ~ (empty(v22) = 0) | relation(v22) = 0) &  ! [v22] : ( ~ (empty(v22) = 0) | function(v22) = 0) &  ! [v22] : ( ~ (empty(v22) = 0) | finite(v22) = 0) &  ! [v22] : ( ~ (empty(v22) = 0) |  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] : (ordinal(v22) = v23 & ( ~ (v23 = 0) | (v26 = 0 & v25 = 0 & v24 = 0 & natural(v22) = 0 & epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0)))) &  ! [v22] : ( ~ (empty(v22) = 0) |  ? [v23] :  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & relation(v22) = 0 & function(v22) = 0) | ( ~ (v23 = 0) & relation(v22) = v23) | ( ~ (v23 = 0) & function(v22) = v23))) &  ! [v22] : ( ~ (empty(v22) = 0) | (epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0 & ordinal(v22) = 0)) &  ! [v22] : ( ~ (epsilon_connected(v22) = 0) |  ? [v23] : ((v23 = 0 & ordinal(v22) = 0) | ( ~ (v23 = 0) & epsilon_transitive(v22) = v23))) &  ! [v22] : ( ~ (epsilon_transitive(v22) = 0) |  ? [v23] : ((v23 = 0 & ordinal(v22) = 0) | ( ~ (v23 = 0) & epsilon_connected(v22) = v23))) &  ! [v22] : ( ~ (ordinal(v22) = 0) |  ? [v23] :  ? [v24] :  ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & natural(v22) = 0 & epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0) | ( ~ (v23 = 0) & empty(v22) = v23))) &  ! [v22] : ( ~ (ordinal(v22) = 0) | (epsilon_connected(v22) = 0 & epsilon_transitive(v22) = 0)) &  ? [v22] :  ? [v23] :  ? [v24] : subset(v23, v22) = v24 &  ? [v22] :  ? [v23] :  ? [v24] : element(v23, v22) = v24 &  ? [v22] :  ? [v23] :  ? [v24] : in(v23, v22) = v24 &  ? [v22] :  ? [v23] : relation_empty_yielding(v22) = v23 &  ? [v22] :  ? [v23] : one_to_one(v22) = v23 &  ? [v22] :  ? [v23] : powerset(v22) = v23 &  ? [v22] :  ? [v23] : natural(v22) = v23 &  ? [v22] :  ? [v23] : relation(v22) = v23 &  ? [v22] :  ? [v23] : function(v22) = v23 &  ? [v22] :  ? [v23] : finite(v22) = v23 &  ? [v22] :  ? [v23] : empty(v22) = v23 &  ? [v22] :  ? [v23] : epsilon_connected(v22) = v23 &  ? [v22] :  ? [v23] : element(v23, v22) = 0 &  ? [v22] :  ? [v23] : epsilon_transitive(v22) = v23 &  ? [v22] :  ? [v23] : ordinal(v22) = v23)
% 20.68/5.67  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21 yields:
% 20.68/5.67  | (1)  ~ (all_0_0_0 = 0) &  ~ (all_0_2_2 = 0) &  ~ (all_0_10_10 = 0) &  ~ (all_0_12_12 = 0) &  ~ (all_0_15_15 = 0) &  ~ (all_0_19_19 = 0) & subset(all_0_21_21, all_0_20_20) = 0 & relation_empty_yielding(all_0_17_17) = 0 & relation_empty_yielding(all_0_18_18) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(all_0_9_9) = 0 & one_to_one(all_0_14_14) = 0 & one_to_one(empty_set) = 0 & natural(all_0_1_1) = 0 & relation(all_0_4_4) = 0 & relation(all_0_6_6) = 0 & relation(all_0_8_8) = 0 & relation(all_0_9_9) = 0 & relation(all_0_11_11) = 0 & relation(all_0_14_14) = 0 & relation(all_0_17_17) = 0 & relation(all_0_18_18) = 0 & relation(empty_set) = 0 & function(all_0_4_4) = 0 & function(all_0_8_8) = 0 & function(all_0_9_9) = 0 & function(all_0_14_14) = 0 & function(all_0_18_18) = 0 & function(empty_set) = 0 & finite(all_0_3_3) = 0 & finite(all_0_20_20) = 0 & finite(all_0_21_21) = all_0_19_19 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_6_6) = 0 & empty(all_0_7_7) = 0 & empty(all_0_8_8) = 0 & empty(all_0_9_9) = 0 & empty(all_0_11_11) = all_0_10_10 & empty(all_0_13_13) = all_0_12_12 & empty(all_0_16_16) = all_0_15_15 & empty(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_5_5) = 0 & epsilon_connected(all_0_9_9) = 0 & epsilon_connected(all_0_16_16) = 0 & epsilon_connected(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_5_5) = 0 & epsilon_transitive(all_0_9_9) = 0 & epsilon_transitive(all_0_16_16) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_5_5) = 0 & ordinal(all_0_9_9) = 0 & ordinal(all_0_16_16) = 0 & ordinal(empty_set) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (element(v0, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (finite(v2) = v3) |  ? [v4] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, 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 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(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 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [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 |  ~ (relation_empty_yielding(v2) = v1) |  ~ (relation_empty_yielding(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (one_to_one(v2) = v1) |  ~ (one_to_one(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (natural(v2) = v1) |  ~ (natural(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (finite(v2) = v1) |  ~ (finite(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_connected(v2) = v1) |  ~ (epsilon_connected(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] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (element(v2, v1) = 0) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (epsilon_connected(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (epsilon_transitive(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordinal(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & finite(v3) = 0 & empty(v3) = v4 & element(v3, v2) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_connected(v0) = v2) | ( ~ (v2 = 0) & epsilon_transitive(v0) = v2))) &  ! [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] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & v3 = 0 &  ~ (v4 = 0) & finite(v2) = 0 & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (one_to_one(v2) = 0 & natural(v2) = 0 & relation(v2) = 0 & function(v2) = 0 & finite(v2) = 0 & empty(v2) = 0 & epsilon_connected(v2) = 0 & element(v2, v1) = 0 & epsilon_transitive(v2) = 0 & ordinal(v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (natural(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(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] : ( ~ (element(v1, v0) = 0) |  ~ (ordinal(v0) = 0) | (epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) &  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & ordinal(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_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & empty(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] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(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] : ( ~ (finite(v0) = 0) |  ? [v1] : (powerset(v0) = v1 &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (finite(v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) &  ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) &  ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) &  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) &  ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0) &  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(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_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0)) &  ! [v0] : ( ~ (epsilon_connected(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) &  ! [v0] : ( ~ (epsilon_transitive(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) &  ! [v0] : ( ~ (ordinal(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & empty(v0) = v1))) &  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0)) &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2 &  ? [v0] :  ? [v1] : relation_empty_yielding(v0) = v1 &  ? [v0] :  ? [v1] : one_to_one(v0) = v1 &  ? [v0] :  ? [v1] : powerset(v0) = v1 &  ? [v0] :  ? [v1] : natural(v0) = v1 &  ? [v0] :  ? [v1] : relation(v0) = v1 &  ? [v0] :  ? [v1] : function(v0) = v1 &  ? [v0] :  ? [v1] : finite(v0) = v1 &  ? [v0] :  ? [v1] : empty(v0) = v1 &  ? [v0] :  ? [v1] : epsilon_connected(v0) = v1 &  ? [v0] :  ? [v1] : element(v1, v0) = 0 &  ? [v0] :  ? [v1] : epsilon_transitive(v0) = v1 &  ? [v0] :  ? [v1] : ordinal(v0) = v1
% 21.04/5.69  |
% 21.04/5.69  | Applying alpha-rule on (1) yields:
% 21.04/5.69  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 21.04/5.69  | (3)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 21.04/5.69  | (4)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & v3 = 0 &  ~ (v4 = 0) & finite(v2) = 0 & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 21.04/5.69  | (5)  ~ (all_0_15_15 = 0)
% 21.04/5.69  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 21.04/5.69  | (7)  ! [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)))
% 21.04/5.69  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 21.04/5.69  | (9) ordinal(empty_set) = 0
% 21.04/5.69  | (10)  ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0)
% 21.04/5.69  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 21.04/5.69  | (12)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 21.04/5.69  | (13) relation_empty_yielding(all_0_18_18) = 0
% 21.04/5.69  | (14)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 21.04/5.70  | (15) epsilon_transitive(all_0_1_1) = 0
% 21.04/5.70  | (16)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 21.04/5.70  | (17)  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2
% 21.04/5.70  | (18) empty(all_0_6_6) = 0
% 21.04/5.70  | (19) empty(empty_set) = 0
% 21.04/5.70  | (20)  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 21.04/5.70  | (21) empty(all_0_1_1) = all_0_0_0
% 21.04/5.70  | (22)  ? [v0] :  ? [v1] : ordinal(v0) = v1
% 21.04/5.70  | (23)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 21.04/5.70  | (24) relation(all_0_6_6) = 0
% 21.04/5.70  | (25)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 21.04/5.70  | (26)  ? [v0] :  ? [v1] : relation(v0) = v1
% 21.04/5.70  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_transitive(v2) = v1) |  ~ (epsilon_transitive(v2) = v0))
% 21.04/5.70  | (28) one_to_one(all_0_14_14) = 0
% 21.04/5.70  | (29)  ! [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)))
% 21.04/5.70  | (30) ordinal(all_0_9_9) = 0
% 21.04/5.70  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (natural(v2) = v1) |  ~ (natural(v2) = v0))
% 21.04/5.70  | (32)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 21.04/5.70  | (33) epsilon_transitive(empty_set) = 0
% 21.04/5.70  | (34)  ! [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)))
% 21.04/5.70  | (35)  ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 21.04/5.70  | (36) epsilon_transitive(all_0_16_16) = 0
% 21.04/5.70  | (37)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 21.04/5.70  | (38) relation(all_0_14_14) = 0
% 21.04/5.70  | (39) empty(all_0_8_8) = 0
% 21.04/5.70  | (40) natural(all_0_1_1) = 0
% 21.04/5.70  | (41) empty(all_0_7_7) = 0
% 21.04/5.70  | (42)  ? [v0] :  ? [v1] : relation_empty_yielding(v0) = v1
% 21.04/5.70  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 21.04/5.70  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (finite(v2) = v1) |  ~ (finite(v2) = v0))
% 21.04/5.70  | (45)  ! [v0] :  ! [v1] : ( ~ (element(v1, v0) = 0) |  ~ (ordinal(v0) = 0) | (epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0))
% 21.04/5.70  | (46)  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))))
% 21.04/5.70  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 21.04/5.70  | (48)  ! [v0] :  ! [v1] : ( ~ (ordinal(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 21.04/5.70  | (49) empty(all_0_13_13) = all_0_12_12
% 21.04/5.70  | (50)  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2
% 21.04/5.70  | (51) epsilon_connected(all_0_9_9) = 0
% 21.04/5.70  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 21.04/5.70  | (53) finite(all_0_21_21) = all_0_19_19
% 21.04/5.70  | (54)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (element(v2, v1) = 0) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 21.04/5.70  | (55) function(all_0_18_18) = 0
% 21.04/5.70  | (56) relation(all_0_9_9) = 0
% 21.04/5.70  | (57)  ? [v0] :  ? [v1] : function(v0) = v1
% 21.04/5.70  | (58) subset(all_0_21_21, all_0_20_20) = 0
% 21.04/5.70  | (59)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 21.04/5.70  | (60)  ! [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)))
% 21.04/5.70  | (61)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 21.04/5.70  | (62)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 21.04/5.70  | (63)  ~ (all_0_0_0 = 0)
% 21.04/5.70  | (64) function(all_0_4_4) = 0
% 21.04/5.70  | (65)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 21.04/5.70  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (epsilon_transitive(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 21.04/5.70  | (67)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 21.04/5.70  | (68)  ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0))
% 21.04/5.70  | (69)  ! [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))
% 21.04/5.70  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 21.04/5.70  | (71)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & finite(v3) = 0 & empty(v3) = v4 & element(v3, v2) = 0))
% 21.04/5.70  | (72)  ~ (all_0_12_12 = 0)
% 21.04/5.70  | (73) ordinal(all_0_5_5) = 0
% 21.04/5.70  | (74) epsilon_connected(empty_set) = 0
% 21.04/5.70  | (75) function(all_0_14_14) = 0
% 21.04/5.70  | (76)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 21.04/5.70  | (77)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (in(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 21.04/5.70  | (78)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 21.04/5.70  | (79)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0))
% 21.04/5.70  | (80)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 21.04/5.70  | (81) empty(all_0_9_9) = 0
% 21.04/5.70  | (82)  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 21.04/5.70  | (83)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 21.04/5.70  | (84) relation(empty_set) = 0
% 21.04/5.70  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 21.04/5.70  | (86)  ? [v0] :  ? [v1] : powerset(v0) = v1
% 21.04/5.70  | (87)  ? [v0] :  ? [v1] : one_to_one(v0) = v1
% 21.04/5.70  | (88) ordinal(all_0_16_16) = 0
% 21.04/5.70  | (89) epsilon_transitive(all_0_5_5) = 0
% 21.04/5.70  | (90) function(all_0_8_8) = 0
% 21.04/5.70  | (91) epsilon_transitive(all_0_9_9) = 0
% 21.04/5.70  | (92)  ~ (all_0_10_10 = 0)
% 21.04/5.70  | (93) relation(all_0_18_18) = 0
% 21.04/5.70  | (94)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 21.04/5.70  | (95) relation_empty_yielding(all_0_17_17) = 0
% 21.04/5.70  | (96)  ~ (all_0_2_2 = 0)
% 21.04/5.71  | (97)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 21.04/5.71  | (98)  ~ (all_0_19_19 = 0)
% 21.04/5.71  | (99) epsilon_connected(all_0_1_1) = 0
% 21.04/5.71  | (100)  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))
% 21.04/5.71  | (101) epsilon_connected(all_0_16_16) = 0
% 21.04/5.71  | (102)  ? [v0] :  ? [v1] : epsilon_connected(v0) = v1
% 21.04/5.71  | (103)  ? [v0] :  ? [v1] : finite(v0) = v1
% 21.04/5.71  | (104)  ! [v0] :  ! [v1] : ( ~ (natural(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 21.04/5.71  | (105) empty(all_0_11_11) = all_0_10_10
% 21.04/5.71  | (106)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordinal(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 21.04/5.71  | (107)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 21.04/5.71  | (108) one_to_one(all_0_9_9) = 0
% 21.04/5.71  | (109) one_to_one(empty_set) = 0
% 21.04/5.71  | (110)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 21.04/5.71  | (111)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 21.04/5.71  | (112)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (finite(v2) = v3) |  ? [v4] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 21.04/5.71  | (113) ordinal(all_0_1_1) = 0
% 21.04/5.71  | (114)  ! [v0] : ( ~ (epsilon_transitive(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 21.04/5.71  | (115)  ! [v0] : ( ~ (epsilon_connected(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 21.04/5.71  | (116) relation_empty_yielding(empty_set) = 0
% 21.04/5.71  | (117)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 21.04/5.71  | (118)  ? [v0] :  ? [v1] : empty(v0) = v1
% 21.04/5.71  | (119) empty(all_0_16_16) = all_0_15_15
% 21.04/5.71  | (120) relation(all_0_11_11) = 0
% 21.04/5.71  | (121)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (one_to_one(v2) = v1) |  ~ (one_to_one(v2) = v0))
% 21.04/5.71  | (122) finite(all_0_20_20) = 0
% 21.04/5.71  | (123) epsilon_connected(all_0_5_5) = 0
% 21.04/5.71  | (124) relation(all_0_4_4) = 0
% 21.04/5.71  | (125) function(all_0_9_9) = 0
% 21.04/5.71  | (126) finite(all_0_3_3) = 0
% 21.04/5.71  | (127)  ! [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))
% 21.04/5.71  | (128)  ! [v0] : ( ~ (ordinal(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 21.04/5.71  | (129)  ? [v0] :  ? [v1] : natural(v0) = v1
% 21.04/5.71  | (130)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 21.04/5.71  | (131) relation(all_0_17_17) = 0
% 21.04/5.71  | (132)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 21.04/5.71  | (133)  ? [v0] :  ? [v1] : epsilon_transitive(v0) = v1
% 21.04/5.71  | (134)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 21.04/5.71  | (135) relation(all_0_8_8) = 0
% 21.04/5.71  | (136)  ! [v0] : ( ~ (finite(v0) = 0) |  ? [v1] : (powerset(v0) = v1 &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (finite(v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) &  ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0)))
% 21.04/5.71  | (137)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (one_to_one(v2) = 0 & natural(v2) = 0 & relation(v2) = 0 & function(v2) = 0 & finite(v2) = 0 & empty(v2) = 0 & epsilon_connected(v2) = 0 & element(v2, v1) = 0 & epsilon_transitive(v2) = 0 & ordinal(v2) = 0))
% 21.04/5.71  | (138)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (epsilon_connected(v1) = v2) |  ~ (ordinal(v0) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 21.04/5.71  | (139)  ! [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)))
% 21.04/5.71  | (140)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_connected(v2) = v1) |  ~ (epsilon_connected(v2) = v0))
% 21.04/5.71  | (141)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal(v2) = v1) |  ~ (ordinal(v2) = v0))
% 21.04/5.71  | (142) empty(all_0_3_3) = all_0_2_2
% 21.04/5.71  | (143)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_connected(v0) = v2) | ( ~ (v2 = 0) & epsilon_transitive(v0) = v2)))
% 21.04/5.71  | (144)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_empty_yielding(v2) = v1) |  ~ (relation_empty_yielding(v2) = v0))
% 21.04/5.71  | (145) function(empty_set) = 0
% 21.04/5.71  |
% 21.04/5.71  | Instantiating formula (61) with all_0_20_20, all_0_21_21 and discharging atoms subset(all_0_21_21, all_0_20_20) = 0, yields:
% 21.04/5.71  | (146)  ? [v0] : (powerset(all_0_20_20) = v0 & element(all_0_21_21, v0) = 0)
% 21.04/5.71  |
% 21.04/5.71  | Instantiating formula (136) with all_0_20_20 and discharging atoms finite(all_0_20_20) = 0, yields:
% 21.04/5.71  | (147)  ? [v0] : (powerset(all_0_20_20) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 21.04/5.71  |
% 21.04/5.71  | Instantiating formula (94) with all_0_19_19, all_0_21_21 and discharging atoms finite(all_0_21_21) = all_0_19_19, yields:
% 21.04/5.71  | (148) all_0_19_19 = 0 |  ? [v0] : ( ~ (v0 = 0) & empty(all_0_21_21) = v0)
% 21.04/5.71  |
% 21.04/5.71  | Instantiating (147) with all_114_0_207 yields:
% 21.04/5.71  | (149) powerset(all_0_20_20) = all_114_0_207 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_114_0_207) = v2)) &  ! [v0] : ( ~ (element(v0, all_114_0_207) = 0) | finite(v0) = 0)
% 21.04/5.71  |
% 21.04/5.71  | Applying alpha-rule on (149) yields:
% 21.04/5.71  | (150) powerset(all_0_20_20) = all_114_0_207
% 21.04/5.71  | (151)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_114_0_207) = v2))
% 21.04/5.71  | (152)  ! [v0] : ( ~ (element(v0, all_114_0_207) = 0) | finite(v0) = 0)
% 21.04/5.71  |
% 21.04/5.71  | Instantiating formula (151) with all_0_19_19, all_0_21_21 and discharging atoms finite(all_0_21_21) = all_0_19_19, yields:
% 21.04/5.71  | (153) all_0_19_19 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_21_21, all_114_0_207) = v0)
% 21.04/5.71  |
% 21.04/5.71  | Instantiating (146) with all_131_0_233 yields:
% 21.04/5.71  | (154) powerset(all_0_20_20) = all_131_0_233 & element(all_0_21_21, all_131_0_233) = 0
% 21.04/5.71  |
% 21.04/5.71  | Applying alpha-rule on (154) yields:
% 21.04/5.71  | (155) powerset(all_0_20_20) = all_131_0_233
% 21.04/5.71  | (156) element(all_0_21_21, all_131_0_233) = 0
% 21.04/5.71  |
% 21.04/5.71  +-Applying beta-rule and splitting (148), into two cases.
% 21.04/5.71  |-Branch one:
% 21.04/5.71  | (157) all_0_19_19 = 0
% 21.04/5.71  |
% 21.04/5.71  	| Equations (157) can reduce 98 to:
% 21.04/5.71  	| (158) $false
% 21.04/5.71  	|
% 21.04/5.71  	|-The branch is then unsatisfiable
% 21.04/5.71  |-Branch two:
% 21.04/5.71  | (98)  ~ (all_0_19_19 = 0)
% 21.04/5.71  | (160)  ? [v0] : ( ~ (v0 = 0) & empty(all_0_21_21) = v0)
% 21.04/5.71  |
% 21.04/5.71  	+-Applying beta-rule and splitting (153), into two cases.
% 21.04/5.71  	|-Branch one:
% 21.04/5.71  	| (157) all_0_19_19 = 0
% 21.04/5.71  	|
% 21.04/5.71  		| Equations (157) can reduce 98 to:
% 21.04/5.71  		| (158) $false
% 21.04/5.71  		|
% 21.04/5.71  		|-The branch is then unsatisfiable
% 21.04/5.71  	|-Branch two:
% 21.04/5.71  	| (98)  ~ (all_0_19_19 = 0)
% 21.04/5.71  	| (164)  ? [v0] : ( ~ (v0 = 0) & element(all_0_21_21, all_114_0_207) = v0)
% 21.04/5.72  	|
% 21.04/5.72  		| Instantiating (164) with all_196_0_265 yields:
% 21.04/5.72  		| (165)  ~ (all_196_0_265 = 0) & element(all_0_21_21, all_114_0_207) = all_196_0_265
% 21.04/5.72  		|
% 21.04/5.72  		| Applying alpha-rule on (165) yields:
% 21.04/5.72  		| (166)  ~ (all_196_0_265 = 0)
% 21.04/5.72  		| (167) element(all_0_21_21, all_114_0_207) = all_196_0_265
% 21.04/5.72  		|
% 21.04/5.72  		| Instantiating formula (62) with all_0_20_20, all_114_0_207, all_131_0_233 and discharging atoms powerset(all_0_20_20) = all_131_0_233, powerset(all_0_20_20) = all_114_0_207, yields:
% 21.04/5.72  		| (168) all_131_0_233 = all_114_0_207
% 21.04/5.72  		|
% 21.04/5.72  		| From (168) and (156) follows:
% 21.04/5.72  		| (169) element(all_0_21_21, all_114_0_207) = 0
% 21.04/5.72  		|
% 21.04/5.72  		| Instantiating formula (11) with all_0_21_21, all_114_0_207, 0, all_196_0_265 and discharging atoms element(all_0_21_21, all_114_0_207) = all_196_0_265, element(all_0_21_21, all_114_0_207) = 0, yields:
% 21.04/5.72  		| (170) all_196_0_265 = 0
% 21.04/5.72  		|
% 21.04/5.72  		| Equations (170) can reduce 166 to:
% 21.04/5.72  		| (158) $false
% 21.04/5.72  		|
% 21.04/5.72  		|-The branch is then unsatisfiable
% 21.04/5.72  % SZS output end Proof for theBenchmark
% 21.04/5.72  
% 21.04/5.72  5075ms
%------------------------------------------------------------------------------