%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 : Mon Jul 18 08:44:12 EDT 2022

% Result   : Theorem 7.80s 2.52s
% Output   : Proof 13.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jul  7 23:42:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.58/0.57          ____       _                          
% 0.58/0.57    ___  / __ \_____(_)___  ________  __________
% 0.58/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.57  
% 0.58/0.57  A Theorem Prover for First-Order Logic
% 0.58/0.57  (ePrincess v.1.0)
% 0.58/0.57  
% 0.58/0.57  (c) Philipp Rümmer, 2009-2015
% 0.58/0.57  (c) Peter Backeman, 2014-2015
% 0.58/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.57  Bug reports to peter@backeman.se
% 0.58/0.57  
% 0.58/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.57  
% 0.58/0.57  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.95  Prover 0: Preprocessing ...
% 2.36/1.21  Prover 0: Warning: ignoring some quantifiers
% 2.48/1.24  Prover 0: Constructing countermodel ...
% 3.42/1.46  Prover 0: gave up
% 3.42/1.46  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.55/1.51  Prover 1: Preprocessing ...
% 4.20/1.65  Prover 1: Warning: ignoring some quantifiers
% 4.20/1.66  Prover 1: Constructing countermodel ...
% 6.53/2.15  Prover 1: gave up
% 6.53/2.15  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.53/2.18  Prover 2: Preprocessing ...
% 7.24/2.32  Prover 2: Warning: ignoring some quantifiers
% 7.24/2.33  Prover 2: Constructing countermodel ...
% 7.80/2.52  Prover 2: proved (367ms)
% 7.80/2.52  
% 7.80/2.52  No countermodel exists, formula is valid
% 7.80/2.52  % SZS status Theorem for theBenchmark
% 7.80/2.52  
% 7.80/2.52  Generating proof ... Warning: ignoring some quantifiers
% 13.07/3.66  found it (size 110)
% 13.07/3.66  
% 13.07/3.66  % SZS output start Proof for theBenchmark
% 13.07/3.66  Assumed formulas after preprocessing and simplification: 
% 13.07/3.66  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : ( ~ (v12 = 0) &  ~ (v10 = 0) &  ~ (v7 = 0) &  ~ (v1 = 0) & relation_empty_yielding(v5) = 0 & relation_empty_yielding(v4) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(v2) = 0 & transfinite_sequence_of(empty_set, v0) = v1 & transfinite_sequence(v3) = 0 & one_to_one(v13) = 0 & one_to_one(v8) = 0 & one_to_one(empty_set) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(v3) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & epsilon_transitive(v17) = 0 & epsilon_transitive(v13) = 0 & epsilon_transitive(v6) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v17) = 0 & ordinal(v13) = 0 & ordinal(v6) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v17) = 0 & epsilon_connected(v13) = 0 & epsilon_connected(v6) = 0 & epsilon_connected(empty_set) = 0 & function(v18) = 0 & function(v14) = 0 & function(v13) = 0 & function(v8) = 0 & function(v4) = 0 & function(v3) = 0 & function(v2) = 0 & function(empty_set) = 0 & empty(v16) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v11) = v12 & empty(v9) = v10 & empty(v6) = v7 & empty(empty_set) = 0 &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = 0 |  ~ (relation_dom(v19) = v20) |  ~ (ordered_pair(v21, v23) = v24) |  ~ (in(v21, v20) = v22) |  ? [v25] : (( ~ (v25 = 0) & relation(v19) = v25) | ( ~ (v25 = 0) & in(v24, v19) = v25))) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] :  ! [v23] : (v23 = 0 |  ~ (powerset(v21) = v22) |  ~ (element(v20, v22) = 0) |  ~ (element(v19, v21) = v23) |  ? [v24] : ( ~ (v24 = 0) & in(v19, v20) = v24)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v22 = 0 |  ~ (powerset(v20) = v21) |  ~ (element(v19, v21) = v22) |  ? [v23] : ( ~ (v23 = 0) & subset(v19, v20) = v23)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v22 = 0 |  ~ (element(v19, v21) = v22) |  ~ (in(v19, v20) = 0) |  ? [v23] :  ? [v24] : ( ~ (v24 = 0) & powerset(v21) = v23 & element(v20, v23) = v24)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (element(v22, v21) = v20) |  ~ (element(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (subset(v22, v21) = v20) |  ~ (subset(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (transfinite_sequence_of(v22, v21) = v20) |  ~ (transfinite_sequence_of(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (ordered_pair(v22, v21) = v20) |  ~ (ordered_pair(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (unordered_pair(v22, v21) = v20) |  ~ (unordered_pair(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : (v20 = v19 |  ~ (in(v22, v21) = v20) |  ~ (in(v22, v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) |  ~ (element(v20, v22) = 0) |  ~ (in(v19, v20) = 0) | element(v19, v21) = 0) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : ( ~ (powerset(v21) = v22) |  ~ (element(v20, v22) = 0) |  ~ (in(v19, v20) = 0) |  ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) &  ! [v19] :  ! [v20] :  ! [v21] :  ! [v22] : ( ~ (relation_rng(v20) = v21) |  ~ (subset(v21, v19) = v22) |  ? [v23] : (( ~ (v23 = 0) & transfinite_sequence(v20) = v23) | ( ~ (v23 = 0) & relation(v20) = v23) | ( ~ (v23 = 0) & function(v20) = v23) | (( ~ (v22 = 0) | (v23 = 0 & transfinite_sequence_of(v20, v19) = 0)) & (v22 = 0 | ( ~ (v23 = 0) & transfinite_sequence_of(v20, v19) = v23))))) &  ! [v19] :  ! [v20] :  ! [v21] : (v21 = 0 |  ~ (element(v19, v20) = v21) |  ? [v22] : ( ~ (v22 = 0) & in(v19, v20) = v22)) &  ! [v19] :  ! [v20] :  ! [v21] : (v21 = 0 |  ~ (subset(v19, v20) = v21) |  ? [v22] :  ? [v23] : ( ~ (v23 = 0) & powerset(v20) = v22 & element(v19, v22) = v23)) &  ! [v19] :  ! [v20] :  ! [v21] : (v21 = 0 |  ~ (in(v19, v20) = v21) |  ? [v22] : ((v22 = 0 & empty(v20) = 0) | ( ~ (v22 = 0) & element(v19, v20) = v22))) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (powerset(v21) = v20) |  ~ (powerset(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (relation_empty_yielding(v21) = v20) |  ~ (relation_empty_yielding(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (relation_non_empty(v21) = v20) |  ~ (relation_non_empty(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (with_non_empty_elements(v21) = v20) |  ~ (with_non_empty_elements(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (relation_rng(v21) = v20) |  ~ (relation_rng(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (transfinite_sequence(v21) = v20) |  ~ (transfinite_sequence(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (singleton(v21) = v20) |  ~ (singleton(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (relation_dom(v21) = v20) |  ~ (relation_dom(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (one_to_one(v21) = v20) |  ~ (one_to_one(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (relation(v21) = v20) |  ~ (relation(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (epsilon_transitive(v21) = v20) |  ~ (epsilon_transitive(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (ordinal(v21) = v20) |  ~ (ordinal(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (epsilon_connected(v21) = v20) |  ~ (epsilon_connected(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (function(v21) = v20) |  ~ (function(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : (v20 = v19 |  ~ (empty(v21) = v20) |  ~ (empty(v21) = v19)) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (powerset(v20) = v21) |  ~ (element(v19, v21) = 0) | subset(v19, v20) = 0) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (transfinite_sequence_of(v20, v19) = v21) |  ? [v22] :  ? [v23] : (( ~ (v22 = 0) & transfinite_sequence(v20) = v22) | ( ~ (v22 = 0) & relation(v20) = v22) | ( ~ (v22 = 0) & function(v20) = v22) | (( ~ (v21 = 0) | (v23 = 0 & relation_rng(v20) = v22 & subset(v22, v19) = 0)) & (v21 = 0 | ( ~ (v23 = 0) & relation_rng(v20) = v22 & subset(v22, v19) = v23))))) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (relation_dom(v19) = v20) |  ~ (in(v21, v20) = 0) |  ? [v22] :  ? [v23] :  ? [v24] : ((v24 = 0 & ordered_pair(v21, v22) = v23 & in(v23, v19) = 0) | ( ~ (v22 = 0) & relation(v19) = v22))) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) |  ? [v22] :  ? [v23] : (singleton(v19) = v23 & unordered_pair(v22, v23) = v21 & unordered_pair(v19, v20) = v22)) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) |  ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (unordered_pair(v20, v19) = v21) | unordered_pair(v19, v20) = v21) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (unordered_pair(v19, v20) = v21) | unordered_pair(v20, v19) = v21) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (unordered_pair(v19, v20) = v21) |  ? [v22] :  ? [v23] : (singleton(v19) = v23 & ordered_pair(v19, v20) = v22 & unordered_pair(v21, v23) = v22)) &  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (empty(v21) = 0) |  ~ (in(v19, v20) = 0) |  ? [v22] :  ? [v23] : ( ~ (v23 = 0) & powerset(v21) = v22 & element(v20, v22) = v23)) &  ? [v19] :  ! [v20] :  ! [v21] : (v21 = v19 |  ~ (relation_dom(v20) = v21) |  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] : (( ~ (v22 = 0) & relation(v20) = v22) | (( ! [v27] :  ! [v28] : ( ~ (ordered_pair(v22, v27) = v28) |  ? [v29] : ( ~ (v29 = 0) & in(v28, v20) = v29)) | ( ~ (v23 = 0) & in(v22, v19) = v23)) & ((v26 = 0 & ordered_pair(v22, v24) = v25 & in(v25, v20) = 0) | (v23 = 0 & in(v22, v19) = 0))))) &  ! [v19] :  ! [v20] : (v20 = v19 |  ~ (empty(v20) = 0) |  ~ (empty(v19) = 0)) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (subset(v19, v19) = v20)) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (subset(empty_set, v19) = v20)) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (relation(v19) = v20) |  ? [v21] : ( ~ (v21 = 0) & empty(v19) = v21)) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (ordinal(v19) = v20) |  ? [v21] : (( ~ (v21 = 0) & epsilon_transitive(v19) = v21) | ( ~ (v21 = 0) & epsilon_connected(v19) = v21))) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (function(v19) = v20) |  ? [v21] : ( ~ (v21 = 0) & empty(v19) = v21)) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (empty(v19) = v20) |  ? [v21] :  ? [v22] : (( ~ (v22 = 0) & relation_rng(v19) = v21 & empty(v21) = v22) | ( ~ (v21 = 0) & relation(v19) = v21))) &  ! [v19] :  ! [v20] : (v20 = 0 |  ~ (empty(v19) = v20) |  ? [v21] :  ? [v22] : (( ~ (v22 = 0) & relation_dom(v19) = v21 & empty(v21) = v22) | ( ~ (v21 = 0) & relation(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (element(v19, v20) = 0) |  ? [v21] : ((v21 = 0 & empty(v20) = 0) | (v21 = 0 & in(v19, v20) = 0))) &  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & relation(v20) = 0 & empty(v20) = 0) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ? [v21] : ((v21 = 0 & with_non_empty_elements(v20) = 0) | ( ~ (v21 = 0) & relation_non_empty(v19) = v21) | ( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & function(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ? [v21] : ((v21 = 0 & empty(v19) = 0) | ( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & empty(v20) = v21))) &  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ? [v21] : (( ~ (v21 = 0) & relation(v19) = v21) | (( ~ (v20 = empty_set) | (v21 = empty_set & relation_dom(v19) = empty_set)) & (v20 = empty_set | ( ~ (v21 = empty_set) & relation_dom(v19) = v21))))) &  ! [v19] :  ! [v20] : ( ~ (subset(v19, v20) = 0) |  ? [v21] : (powerset(v20) = v21 & element(v19, v21) = 0)) &  ! [v19] :  ! [v20] : ( ~ (transfinite_sequence_of(v20, v19) = 0) | (transfinite_sequence(v20) = 0 & relation(v20) = 0 & function(v20) = 0)) &  ! [v19] :  ! [v20] : ( ~ (transfinite_sequence(v19) = v20) |  ? [v21] :  ? [v22] : (( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & function(v19) = v21) | (( ~ (v20 = 0) | (v22 = 0 & relation_dom(v19) = v21 & ordinal(v21) = 0)) & (v20 = 0 | ( ~ (v22 = 0) & relation_dom(v19) = v21 & ordinal(v21) = v22))))) &  ! [v19] :  ! [v20] : ( ~ (relation_dom(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & relation(v20) = 0 & empty(v20) = 0) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (relation_dom(v19) = v20) |  ? [v21] :  ? [v22] : (( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & function(v19) = v21) | (((v22 = 0 & ordinal(v20) = 0) | ( ~ (v21 = 0) & transfinite_sequence(v19) = v21)) & ((v21 = 0 & transfinite_sequence(v19) = 0) | ( ~ (v22 = 0) & ordinal(v20) = v22))))) &  ! [v19] :  ! [v20] : ( ~ (relation_dom(v19) = v20) |  ? [v21] : ((v21 = 0 & empty(v19) = 0) | ( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & empty(v20) = v21))) &  ! [v19] :  ! [v20] : ( ~ (relation_dom(v19) = v20) |  ? [v21] : (( ~ (v21 = 0) & relation(v19) = v21) | (( ~ (v20 = empty_set) | (v21 = empty_set & relation_rng(v19) = empty_set)) & (v20 = empty_set | ( ~ (v21 = empty_set) & relation_rng(v19) = v21))))) &  ! [v19] :  ! [v20] : ( ~ (one_to_one(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & relation(v19) = 0 & function(v19) = 0) | ( ~ (v21 = 0) & relation(v19) = v21) | ( ~ (v21 = 0) & function(v19) = v21) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (epsilon_transitive(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & ordinal(v19) = 0 & epsilon_connected(v19) = 0) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (epsilon_transitive(v19) = v20) |  ? [v21] : ((v21 = 0 & v20 = 0 & epsilon_connected(v19) = 0) | ( ~ (v21 = 0) & ordinal(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (ordinal(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & epsilon_transitive(v19) = 0 & epsilon_connected(v19) = 0) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (epsilon_connected(v19) = v20) |  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & epsilon_transitive(v19) = 0 & ordinal(v19) = 0) | ( ~ (v21 = 0) & empty(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (epsilon_connected(v19) = v20) |  ? [v21] : ((v21 = 0 & v20 = 0 & epsilon_transitive(v19) = 0) | ( ~ (v21 = 0) & ordinal(v19) = v21))) &  ! [v19] :  ! [v20] : ( ~ (in(v20, v19) = 0) |  ? [v21] : ( ~ (v21 = 0) & in(v19, v20) = v21)) &  ! [v19] :  ! [v20] : ( ~ (in(v19, v20) = 0) | element(v19, v20) = 0) &  ! [v19] :  ! [v20] : ( ~ (in(v19, v20) = 0) |  ? [v21] : ( ~ (v21 = 0) & empty(v20) = v21)) &  ! [v19] :  ! [v20] : ( ~ (in(v19, v20) = 0) |  ? [v21] : ( ~ (v21 = 0) & in(v20, v19) = v21)) &  ! [v19] : (v19 = empty_set |  ~ (empty(v19) = 0)) &  ! [v19] : ( ~ (relation_non_empty(v19) = 0) |  ? [v20] :  ? [v21] : ((v21 = 0 & with_non_empty_elements(v20) = 0 & relation_rng(v19) = v20) | ( ~ (v20 = 0) & relation(v19) = v20) | ( ~ (v20 = 0) & function(v19) = v20))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] :  ? [v22] : (( ~ (v20 = 0) & function(v19) = v20) | (((v22 = 0 & relation_dom(v19) = v21 & ordinal(v21) = 0) | ( ~ (v20 = 0) & transfinite_sequence(v19) = v20)) & ((v20 = 0 & transfinite_sequence(v19) = 0) | ( ~ (v22 = 0) & relation_dom(v19) = v21 & ordinal(v21) = v22))))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] : (((v21 = empty_set & relation_rng(v19) = empty_set) | ( ~ (v20 = empty_set) & relation_dom(v19) = v20)) & ((v20 = empty_set & relation_dom(v19) = empty_set) | ( ~ (v21 = empty_set) & relation_rng(v19) = v21)))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] : ((v21 = 0 & v20 = 0 & one_to_one(v19) = 0 & function(v19) = 0) | ( ~ (v20 = 0) & function(v19) = v20) | ( ~ (v20 = 0) & empty(v19) = v20))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] : ((v21 = 0 & with_non_empty_elements(v20) = 0 & relation_rng(v19) = v20) | ( ~ (v20 = 0) & relation_non_empty(v19) = v20) | ( ~ (v20 = 0) & function(v19) = v20))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] : ((v20 = 0 & empty(v19) = 0) | ( ~ (v21 = 0) & relation_rng(v19) = v20 & empty(v20) = v21))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] :  ? [v21] : ((v20 = 0 & empty(v19) = 0) | ( ~ (v21 = 0) & relation_dom(v19) = v20 & empty(v20) = v21))) &  ! [v19] : ( ~ (relation(v19) = 0) |  ? [v20] : (relation_dom(v19) = v20 &  ! [v21] :  ! [v22] :  ! [v23] :  ! [v24] : (v22 = 0 |  ~ (ordered_pair(v21, v23) = v24) |  ~ (in(v21, v20) = v22) |  ? [v25] : ( ~ (v25 = 0) & in(v24, v19) = v25)) &  ! [v21] : ( ~ (in(v21, v20) = 0) |  ? [v22] :  ? [v23] : (ordered_pair(v21, v22) = v23 & in(v23, v19) = 0)) &  ? [v21] : (v21 = v20 |  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] : (( ! [v27] :  ! [v28] : ( ~ (ordered_pair(v22, v27) = v28) |  ? [v29] : ( ~ (v29 = 0) & in(v28, v19) = v29)) | ( ~ (v23 = 0) & in(v22, v21) = v23)) & ((v26 = 0 & ordered_pair(v22, v24) = v25 & in(v25, v19) = 0) | (v23 = 0 & in(v22, v21) = 0)))))) &  ! [v19] : ( ~ (epsilon_transitive(v19) = 0) |  ? [v20] : ((v20 = 0 & ordinal(v19) = 0) | ( ~ (v20 = 0) & epsilon_connected(v19) = v20))) &  ! [v19] : ( ~ (ordinal(v19) = 0) | (epsilon_transitive(v19) = 0 & epsilon_connected(v19) = 0)) &  ! [v19] : ( ~ (epsilon_connected(v19) = 0) |  ? [v20] : ((v20 = 0 & ordinal(v19) = 0) | ( ~ (v20 = 0) & epsilon_transitive(v19) = v20))) &  ! [v19] : ( ~ (function(v19) = 0) |  ? [v20] :  ? [v21] :  ? [v22] : (( ~ (v20 = 0) & relation(v19) = v20) | (((v22 = 0 & relation_dom(v19) = v21 & ordinal(v21) = 0) | ( ~ (v20 = 0) & transfinite_sequence(v19) = v20)) & ((v20 = 0 & transfinite_sequence(v19) = 0) | ( ~ (v22 = 0) & relation_dom(v19) = v21 & ordinal(v21) = v22))))) &  ! [v19] : ( ~ (function(v19) = 0) |  ? [v20] :  ? [v21] : ((v21 = 0 & v20 = 0 & one_to_one(v19) = 0 & relation(v19) = 0) | ( ~ (v20 = 0) & relation(v19) = v20) | ( ~ (v20 = 0) & empty(v19) = v20))) &  ! [v19] : ( ~ (function(v19) = 0) |  ? [v20] :  ? [v21] : ((v21 = 0 & with_non_empty_elements(v20) = 0 & relation_rng(v19) = v20) | ( ~ (v20 = 0) & relation_non_empty(v19) = v20) | ( ~ (v20 = 0) & relation(v19) = v20))) &  ! [v19] : ( ~ (empty(v19) = 0) | relation(v19) = 0) &  ! [v19] : ( ~ (empty(v19) = 0) | function(v19) = 0) &  ! [v19] : ( ~ (empty(v19) = 0) |  ? [v20] :  ? [v21] :  ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & one_to_one(v19) = 0 & relation(v19) = 0 & function(v19) = 0) | ( ~ (v20 = 0) & relation(v19) = v20) | ( ~ (v20 = 0) & function(v19) = v20))) &  ! [v19] : ( ~ (empty(v19) = 0) |  ? [v20] : (relation_rng(v19) = v20 & relation(v20) = 0 & empty(v20) = 0)) &  ! [v19] : ( ~ (empty(v19) = 0) |  ? [v20] : (relation_dom(v19) = v20 & relation(v20) = 0 & empty(v20) = 0)) &  ! [v19] : ( ~ (empty(v19) = 0) | (epsilon_transitive(v19) = 0 & ordinal(v19) = 0 & epsilon_connected(v19) = 0)) &  ? [v19] :  ? [v20] :  ? [v21] : element(v20, v19) = v21 &  ? [v19] :  ? [v20] :  ? [v21] : subset(v20, v19) = v21 &  ? [v19] :  ? [v20] :  ? [v21] : transfinite_sequence_of(v20, v19) = v21 &  ? [v19] :  ? [v20] :  ? [v21] : ordered_pair(v20, v19) = v21 &  ? [v19] :  ? [v20] :  ? [v21] : unordered_pair(v20, v19) = v21 &  ? [v19] :  ? [v20] :  ? [v21] : in(v20, v19) = v21 &  ? [v19] :  ? [v20] : powerset(v19) = v20 &  ? [v19] :  ? [v20] : relation_empty_yielding(v19) = v20 &  ? [v19] :  ? [v20] : relation_non_empty(v19) = v20 &  ? [v19] :  ? [v20] : with_non_empty_elements(v19) = v20 &  ? [v19] :  ? [v20] : element(v20, v19) = 0 &  ? [v19] :  ? [v20] : relation_rng(v19) = v20 &  ? [v19] :  ? [v20] : transfinite_sequence_of(v20, v19) = 0 &  ? [v19] :  ? [v20] : transfinite_sequence(v19) = v20 &  ? [v19] :  ? [v20] : singleton(v19) = v20 &  ? [v19] :  ? [v20] : relation_dom(v19) = v20 &  ? [v19] :  ? [v20] : one_to_one(v19) = v20 &  ? [v19] :  ? [v20] : relation(v19) = v20 &  ? [v19] :  ? [v20] : epsilon_transitive(v19) = v20 &  ? [v19] :  ? [v20] : ordinal(v19) = v20 &  ? [v19] :  ? [v20] : epsilon_connected(v19) = v20 &  ? [v19] :  ? [v20] : function(v19) = v20 &  ? [v19] :  ? [v20] : empty(v19) = v20)
% 13.35/3.72  | 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 yields:
% 13.35/3.72  | (1)  ~ (all_0_6_6 = 0) &  ~ (all_0_8_8 = 0) &  ~ (all_0_11_11 = 0) &  ~ (all_0_17_17 = 0) & relation_empty_yielding(all_0_13_13) = 0 & relation_empty_yielding(all_0_14_14) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(all_0_16_16) = 0 & transfinite_sequence_of(empty_set, all_0_18_18) = all_0_17_17 & transfinite_sequence(all_0_15_15) = 0 & one_to_one(all_0_5_5) = 0 & one_to_one(all_0_10_10) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_5_5) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(all_0_13_13) = 0 & relation(all_0_14_14) = 0 & relation(all_0_15_15) = 0 & relation(all_0_16_16) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_5_5) = 0 & epsilon_transitive(all_0_12_12) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_5_5) = 0 & ordinal(all_0_12_12) = 0 & ordinal(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_5_5) = 0 & epsilon_connected(all_0_12_12) = 0 & epsilon_connected(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_4_4) = 0 & function(all_0_5_5) = 0 & function(all_0_10_10) = 0 & function(all_0_14_14) = 0 & function(all_0_15_15) = 0 & function(all_0_16_16) = 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_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(all_0_9_9) = all_0_8_8 & empty(all_0_12_12) = all_0_11_11 & empty(empty_set) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v2, v1) = v3) |  ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) &  ! [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 |  ~ (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 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (transfinite_sequence_of(v3, v2) = v1) |  ~ (transfinite_sequence_of(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 |  ~ (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] :  ! [v3] : ( ~ (relation_rng(v1) = v2) |  ~ (subset(v2, v0) = v3) |  ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (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_non_empty(v2) = v1) |  ~ (relation_non_empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (with_non_empty_elements(v2) = v1) |  ~ (with_non_empty_elements(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (transfinite_sequence(v2) = v1) |  ~ (transfinite_sequence(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(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] : ( ~ (transfinite_sequence_of(v1, v0) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = 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] : ( ~ (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] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) &  ! [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] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = empty_set) | (v2 = empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_dom(v0) = v2))))) &  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (transfinite_sequence(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (((v3 = 0 & ordinal(v1) = 0) | ( ~ (v2 = 0) & transfinite_sequence(v0) = v2)) & ((v2 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3))))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = empty_set) | (v2 = empty_set & relation_rng(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_rng(v0) = v2))))) &  ! [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_non_empty(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ (v1 = 0) & function(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : (((v2 = empty_set & relation_rng(v0) = empty_set) | ( ~ (v1 = empty_set) & relation_dom(v0) = v1)) & ((v1 = empty_set & relation_dom(v0) = empty_set) | ( ~ (v2 = empty_set) & relation_rng(v0) = v2)))) &  ! [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] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2))) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2))) &  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] : (relation_dom(v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v2, v1) = v3) |  ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) &  ! [v2] : ( ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) &  ? [v2] : (v2 = v1 |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0)))))) &  ! [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] :  ? [v3] : (( ~ (v1 = 0) & relation(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) &  ! [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] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))) &  ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) &  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) &  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) &  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) &  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) &  ! [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] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : transfinite_sequence_of(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(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] : relation_non_empty(v0) = v1 &  ? [v0] :  ? [v1] : with_non_empty_elements(v0) = v1 &  ? [v0] :  ? [v1] : element(v1, v0) = 0 &  ? [v0] :  ? [v1] : relation_rng(v0) = v1 &  ? [v0] :  ? [v1] : transfinite_sequence_of(v1, v0) = 0 &  ? [v0] :  ? [v1] : transfinite_sequence(v0) = v1 &  ? [v0] :  ? [v1] : singleton(v0) = v1 &  ? [v0] :  ? [v1] : relation_dom(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
% 13.35/3.75  |
% 13.35/3.75  | Applying alpha-rule on (1) yields:
% 13.35/3.75  | (2)  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2
% 13.35/3.75  | (3)  ? [v0] :  ? [v1] : singleton(v0) = v1
% 13.35/3.75  | (4) function(all_0_10_10) = 0
% 13.35/3.75  | (5)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (((v3 = 0 & ordinal(v1) = 0) | ( ~ (v2 = 0) & transfinite_sequence(v0) = v2)) & ((v2 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3)))))
% 13.35/3.75  | (6) one_to_one(all_0_10_10) = 0
% 13.35/3.75  | (7)  ? [v0] :  ? [v1] : relation(v0) = v1
% 13.35/3.75  | (8)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 13.35/3.75  | (9) ordinal(empty_set) = 0
% 13.35/3.75  | (10) transfinite_sequence(all_0_15_15) = 0
% 13.35/3.75  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 13.35/3.75  | (12) empty(all_0_7_7) = all_0_6_6
% 13.35/3.75  | (13) function(all_0_0_0) = 0
% 13.35/3.75  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 13.35/3.75  | (15) relation(all_0_7_7) = 0
% 13.35/3.75  | (16)  ! [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))
% 13.35/3.75  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 13.35/3.75  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 13.35/3.75  | (19)  ! [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)))
% 13.35/3.75  | (20) ordinal(all_0_1_1) = 0
% 13.35/3.75  | (21) function(all_0_16_16) = 0
% 13.35/3.75  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 13.35/3.75  | (23)  ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 13.35/3.75  | (24) empty(all_0_3_3) = 0
% 13.35/3.75  | (25) function(empty_set) = 0
% 13.35/3.75  | (26)  ? [v0] :  ? [v1] : epsilon_transitive(v0) = v1
% 13.35/3.75  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 13.35/3.75  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 13.35/3.75  | (29)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] : (relation_dom(v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v2, v1) = v3) |  ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) &  ! [v2] : ( ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) &  ? [v2] : (v2 = v1 |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0))))))
% 13.56/3.76  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 13.56/3.76  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_empty_yielding(v2) = v1) |  ~ (relation_empty_yielding(v2) = v0))
% 13.56/3.76  | (32)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 13.56/3.76  | (33)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = empty_set) | (v2 = empty_set & relation_rng(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_rng(v0) = v2)))))
% 13.56/3.76  | (34)  ! [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)))
% 13.56/3.76  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 13.56/3.76  | (36)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 13.56/3.76  | (37) relation(empty_set) = 0
% 13.56/3.76  | (38)  ? [v0] :  ? [v1] : transfinite_sequence_of(v1, v0) = 0
% 13.56/3.76  | (39)  ? [v0] :  ? [v1] : with_non_empty_elements(v0) = v1
% 13.56/3.76  | (40)  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 13.56/3.76  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_rng(v1) = v2) |  ~ (subset(v2, v0) = v3) |  ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4)))))
% 13.56/3.76  | (42)  ! [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)))
% 13.56/3.76  | (43)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
% 13.56/3.76  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (one_to_one(v2) = v1) |  ~ (one_to_one(v2) = v0))
% 13.56/3.76  | (45)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] :  ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))))
% 13.56/3.76  | (46)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 13.56/3.76  | (47)  ! [v0] : ( ~ (relation_non_empty(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 13.56/3.76  | (48)  ? [v0] :  ? [v1] : relation_empty_yielding(v0) = v1
% 13.56/3.76  | (49)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = empty_set) | (v2 = empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_dom(v0) = v2)))))
% 13.56/3.76  | (50)  ? [v0] :  ? [v1] : powerset(v0) = v1
% 13.56/3.76  | (51)  ! [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)))
% 13.56/3.76  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (transfinite_sequence_of(v1, v0) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4)))))
% 13.56/3.76  | (53) empty(empty_set) = 0
% 13.56/3.76  | (54)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_connected(v2) = v1) |  ~ (epsilon_connected(v2) = v0))
% 13.56/3.77  | (55) one_to_one(all_0_5_5) = 0
% 13.56/3.77  | (56) epsilon_transitive(all_0_5_5) = 0
% 13.56/3.77  | (57)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 13.56/3.77  | (58)  ? [v0] :  ? [v1] : transfinite_sequence(v0) = v1
% 13.56/3.77  | (59)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 13.56/3.77  | (60)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 13.56/3.77  | (61)  ! [v0] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 13.56/3.77  | (62)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 13.56/3.77  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 13.56/3.77  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (in(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 13.56/3.77  | (65)  ? [v0] :  ? [v1] : ordinal(v0) = v1
% 13.56/3.77  | (66) relation(all_0_15_15) = 0
% 13.56/3.77  | (67)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 13.56/3.77  | (68)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 13.56/3.77  | (69)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 13.56/3.77  | (70)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal(v2) = v1) |  ~ (ordinal(v2) = v0))
% 13.56/3.77  | (71)  ! [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)))
% 13.56/3.77  | (72)  ~ (all_0_6_6 = 0)
% 13.56/3.77  | (73) epsilon_connected(all_0_12_12) = 0
% 13.56/3.77  | (74) epsilon_connected(all_0_1_1) = 0
% 13.56/3.77  | (75)  ? [v0] :  ? [v1] : relation_non_empty(v0) = v1
% 13.56/3.77  | (76)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 13.56/3.77  | (77)  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(v1, v0) = v2
% 13.56/3.77  | (78)  ? [v0] :  ? [v1] : function(v0) = v1
% 13.56/3.77  | (79)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_non_empty(v2) = v1) |  ~ (relation_non_empty(v2) = v0))
% 13.56/3.77  | (80)  ~ (all_0_17_17 = 0)
% 13.56/3.77  | (81)  ? [v0] :  ? [v1] : relation_dom(v0) = v1
% 13.56/3.77  | (82) function(all_0_15_15) = 0
% 13.56/3.77  | (83)  ~ (all_0_11_11 = 0)
% 13.56/3.77  | (84) one_to_one(empty_set) = 0
% 13.56/3.77  | (85) relation_empty_yielding(all_0_13_13) = 0
% 13.56/3.77  | (86)  ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 13.56/3.77  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 13.56/3.77  | (88)  ? [v0] :  ? [v1] : epsilon_connected(v0) = v1
% 13.56/3.77  | (89) relation_non_empty(all_0_16_16) = 0
% 13.56/3.77  | (90)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2)))
% 13.56/3.77  | (91)  ! [v0] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ (v1 = 0) & relation(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 13.56/3.77  | (92) epsilon_transitive(all_0_1_1) = 0
% 13.56/3.77  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 13.56/3.77  | (94)  ? [v0] :  ? [v1] : one_to_one(v0) = v1
% 13.56/3.77  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (transfinite_sequence_of(v3, v2) = v1) |  ~ (transfinite_sequence_of(v3, v2) = v0))
% 13.56/3.77  | (96) ordinal(all_0_5_5) = 0
% 13.56/3.77  | (97)  ? [v0] :  ? [v1] :  ? [v2] : transfinite_sequence_of(v1, v0) = v2
% 13.56/3.77  | (98)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 13.56/3.77  | (99)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = 0 |  ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v4) = v5) |  ~ (in(v2, v1) = v3) |  ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 13.56/3.77  | (100)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_transitive(v2) = v1) |  ~ (epsilon_transitive(v2) = v0))
% 13.56/3.77  | (101)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 13.56/3.77  | (102) ordinal(all_0_12_12) = 0
% 13.56/3.78  | (103)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 13.56/3.78  | (104)  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 13.56/3.78  | (105)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : (((v2 = empty_set & relation_rng(v0) = empty_set) | ( ~ (v1 = empty_set) & relation_dom(v0) = v1)) & ((v1 = empty_set & relation_dom(v0) = empty_set) | ( ~ (v2 = empty_set) & relation_rng(v0) = v2))))
% 13.56/3.78  | (106)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 13.56/3.78  | (107)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 13.56/3.78  | (108) empty(all_0_9_9) = all_0_8_8
% 13.56/3.78  | (109) empty(all_0_2_2) = 0
% 13.56/3.78  | (110) empty(all_0_5_5) = 0
% 13.56/3.78  | (111)  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 13.56/3.78  | (112)  ! [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)))
% 13.56/3.78  | (113)  ? [v0] :  ? [v1] : empty(v0) = v1
% 13.56/3.78  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 13.56/3.78  | (115)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 13.56/3.78  | (116)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 13.56/3.78  | (117)  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 13.56/3.78  | (118)  ! [v0] : ( ~ (epsilon_connected(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 13.56/3.78  | (119)  ! [v0] : ( ~ (epsilon_transitive(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 13.56/3.78  | (120)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 13.56/3.78  | (121)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2)))
% 13.56/3.78  | (122) relation_empty_yielding(empty_set) = 0
% 13.56/3.78  | (123)  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2
% 13.56/3.78  | (124)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 13.56/3.78  | (125)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 13.56/3.78  | (126) empty(all_0_4_4) = 0
% 13.56/3.78  | (127) relation(all_0_5_5) = 0
% 13.56/3.78  | (128)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 13.56/3.78  | (129) relation(all_0_0_0) = 0
% 13.56/3.78  | (130)  ! [v0] :  ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 0))
% 13.56/3.78  | (131)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 13.56/3.78  | (132) function(all_0_5_5) = 0
% 13.56/3.78  | (133)  ? [v0] :  ? [v1] : relation_rng(v0) = v1
% 13.56/3.78  | (134)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 13.56/3.78  | (135) relation(all_0_10_10) = 0
% 13.56/3.78  | (136)  ~ (all_0_8_8 = 0)
% 13.56/3.78  | (137)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (with_non_empty_elements(v2) = v1) |  ~ (with_non_empty_elements(v2) = v0))
% 13.56/3.78  | (138)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 13.56/3.78  | (139) relation_empty_yielding(all_0_14_14) = 0
% 13.56/3.78  | (140) empty(all_0_12_12) = all_0_11_11
% 13.56/3.78  | (141) epsilon_connected(empty_set) = 0
% 13.56/3.78  | (142)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 13.56/3.78  | (143) function(all_0_4_4) = 0
% 13.56/3.78  | (144)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 13.56/3.78  | (145) relation(all_0_13_13) = 0
% 13.56/3.78  | (146)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 13.56/3.78  | (147)  ! [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))
% 13.56/3.78  | (148)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 13.56/3.78  | (149)  ! [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)))
% 13.56/3.78  | (150)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (transfinite_sequence(v2) = v1) |  ~ (transfinite_sequence(v2) = v0))
% 13.56/3.78  | (151) epsilon_transitive(all_0_12_12) = 0
% 13.56/3.78  | (152) epsilon_transitive(empty_set) = 0
% 13.56/3.78  | (153)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 13.56/3.79  | (154)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ (v1 = 0) & function(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 13.56/3.79  | (155) epsilon_connected(all_0_5_5) = 0
% 13.56/3.79  | (156) relation(all_0_4_4) = 0
% 13.56/3.79  | (157) relation(all_0_2_2) = 0
% 13.56/3.79  | (158) relation(all_0_16_16) = 0
% 13.56/3.79  | (159)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 13.56/3.79  | (160)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 13.56/3.79  | (161)  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2
% 13.56/3.79  | (162) relation(all_0_14_14) = 0
% 13.56/3.79  | (163)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 13.56/3.79  | (164)  ! [v0] :  ! [v1] : ( ~ (transfinite_sequence(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 13.56/3.79  | (165) transfinite_sequence_of(empty_set, all_0_18_18) = all_0_17_17
% 13.56/3.79  | (166)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 13.56/3.79  | (167) function(all_0_14_14) = 0
% 13.56/3.79  | (168)  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (107) with all_0_4_4, all_0_2_2 and discharging atoms empty(all_0_2_2) = 0, empty(all_0_4_4) = 0, yields:
% 13.56/3.79  | (169) all_0_2_2 = all_0_4_4
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (107) with all_0_4_4, all_0_3_3 and discharging atoms empty(all_0_3_3) = 0, empty(all_0_4_4) = 0, yields:
% 13.56/3.79  | (170) all_0_3_3 = all_0_4_4
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (107) with all_0_5_5, all_0_2_2 and discharging atoms empty(all_0_2_2) = 0, empty(all_0_5_5) = 0, yields:
% 13.56/3.79  | (171) all_0_2_2 = all_0_5_5
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (107) with empty_set, all_0_3_3 and discharging atoms empty(all_0_3_3) = 0, empty(empty_set) = 0, yields:
% 13.56/3.79  | (172) all_0_3_3 = empty_set
% 13.56/3.79  |
% 13.56/3.79  | Combining equations (169,171) yields a new equation:
% 13.56/3.79  | (173) all_0_4_4 = all_0_5_5
% 13.56/3.79  |
% 13.56/3.79  | Simplifying 173 yields:
% 13.56/3.79  | (174) all_0_4_4 = all_0_5_5
% 13.56/3.79  |
% 13.56/3.79  | Combining equations (170,172) yields a new equation:
% 13.56/3.79  | (175) all_0_4_4 = empty_set
% 13.56/3.79  |
% 13.56/3.79  | Simplifying 175 yields:
% 13.56/3.79  | (176) all_0_4_4 = empty_set
% 13.56/3.79  |
% 13.56/3.79  | Combining equations (174,176) yields a new equation:
% 13.56/3.79  | (177) all_0_5_5 = empty_set
% 13.56/3.79  |
% 13.56/3.79  | Simplifying 177 yields:
% 13.56/3.79  | (178) all_0_5_5 = empty_set
% 13.56/3.79  |
% 13.56/3.79  | From (178) and (127) follows:
% 13.56/3.79  | (37) relation(empty_set) = 0
% 13.56/3.79  |
% 13.56/3.79  | From (178) and (96) follows:
% 13.56/3.79  | (9) ordinal(empty_set) = 0
% 13.56/3.79  |
% 13.56/3.79  | From (178) and (132) follows:
% 13.56/3.79  | (25) function(empty_set) = 0
% 13.56/3.79  |
% 13.56/3.79  | From (178) and (110) follows:
% 13.56/3.79  | (53) empty(empty_set) = 0
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (52) with all_0_17_17, empty_set, all_0_18_18 and discharging atoms transfinite_sequence_of(empty_set, all_0_18_18) = all_0_17_17, yields:
% 13.56/3.79  | (183)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & transfinite_sequence(empty_set) = v0) | ( ~ (v0 = 0) & relation(empty_set) = v0) | ( ~ (v0 = 0) & function(empty_set) = v0) | (( ~ (all_0_17_17 = 0) | (v1 = 0 & relation_rng(empty_set) = v0 & subset(v0, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (v1 = 0) & relation_rng(empty_set) = v0 & subset(v0, all_0_18_18) = v1))))
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (154) with empty_set and discharging atoms relation(empty_set) = 0, yields:
% 13.56/3.79  | (184)  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & function(empty_set) = v0) | (((v2 = 0 & relation_dom(empty_set) = v1 & ordinal(v1) = 0) | ( ~ (v0 = 0) & transfinite_sequence(empty_set) = v0)) & ((v0 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (v2 = 0) & relation_dom(empty_set) = v1 & ordinal(v1) = v2))))
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (105) with empty_set and discharging atoms relation(empty_set) = 0, yields:
% 13.56/3.79  | (185)  ? [v0] :  ? [v1] : (((v1 = empty_set & relation_rng(empty_set) = empty_set) | ( ~ (v0 = empty_set) & relation_dom(empty_set) = v0)) & ((v0 = empty_set & relation_dom(empty_set) = empty_set) | ( ~ (v1 = empty_set) & relation_rng(empty_set) = v1)))
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (91) with empty_set and discharging atoms function(empty_set) = 0, yields:
% 13.56/3.79  | (186)  ? [v0] :  ? [v1] :  ? [v2] : (( ~ (v0 = 0) & relation(empty_set) = v0) | (((v2 = 0 & relation_dom(empty_set) = v1 & ordinal(v1) = 0) | ( ~ (v0 = 0) & transfinite_sequence(empty_set) = v0)) & ((v0 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (v2 = 0) & relation_dom(empty_set) = v1 & ordinal(v1) = v2))))
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (168) with empty_set and discharging atoms empty(empty_set) = 0, yields:
% 13.56/3.79  | (187)  ? [v0] : (relation_rng(empty_set) = v0 & relation(v0) = 0 & empty(v0) = 0)
% 13.56/3.79  |
% 13.56/3.79  | Instantiating formula (117) with empty_set and discharging atoms empty(empty_set) = 0, yields:
% 13.56/3.79  | (188)  ? [v0] : (relation_dom(empty_set) = v0 & relation(v0) = 0 & empty(v0) = 0)
% 13.56/3.79  |
% 13.56/3.79  | Instantiating (188) with all_61_0_72 yields:
% 13.56/3.79  | (189) relation_dom(empty_set) = all_61_0_72 & relation(all_61_0_72) = 0 & empty(all_61_0_72) = 0
% 13.56/3.80  |
% 13.56/3.80  | Applying alpha-rule on (189) yields:
% 13.56/3.80  | (190) relation_dom(empty_set) = all_61_0_72
% 13.56/3.80  | (191) relation(all_61_0_72) = 0
% 13.56/3.80  | (192) empty(all_61_0_72) = 0
% 13.56/3.80  |
% 13.56/3.80  | Instantiating (187) with all_63_0_73 yields:
% 13.56/3.80  | (193) relation_rng(empty_set) = all_63_0_73 & relation(all_63_0_73) = 0 & empty(all_63_0_73) = 0
% 13.56/3.80  |
% 13.56/3.80  | Applying alpha-rule on (193) yields:
% 13.56/3.80  | (194) relation_rng(empty_set) = all_63_0_73
% 13.56/3.80  | (195) relation(all_63_0_73) = 0
% 13.56/3.80  | (196) empty(all_63_0_73) = 0
% 13.56/3.80  |
% 13.56/3.80  | Instantiating (186) with all_85_0_111, all_85_1_112, all_85_2_113 yields:
% 13.56/3.80  | (197) ( ~ (all_85_2_113 = 0) & relation(empty_set) = all_85_2_113) | (((all_85_0_111 = 0 & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = 0) | ( ~ (all_85_2_113 = 0) & transfinite_sequence(empty_set) = all_85_2_113)) & ((all_85_2_113 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_85_0_111 = 0) & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = all_85_0_111)))
% 13.56/3.80  |
% 13.56/3.80  | Instantiating (183) with all_100_0_146, all_100_1_147 yields:
% 13.56/3.80  | (198) ( ~ (all_100_1_147 = 0) & transfinite_sequence(empty_set) = all_100_1_147) | ( ~ (all_100_1_147 = 0) & relation(empty_set) = all_100_1_147) | ( ~ (all_100_1_147 = 0) & function(empty_set) = all_100_1_147) | (( ~ (all_0_17_17 = 0) | (all_100_0_146 = 0 & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (all_100_0_146 = 0) & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = all_100_0_146)))
% 13.56/3.80  |
% 13.56/3.80  | Instantiating (185) with all_113_0_168, all_113_1_169 yields:
% 13.56/3.80  | (199) ((all_113_0_168 = empty_set & relation_rng(empty_set) = empty_set) | ( ~ (all_113_1_169 = empty_set) & relation_dom(empty_set) = all_113_1_169)) & ((all_113_1_169 = empty_set & relation_dom(empty_set) = empty_set) | ( ~ (all_113_0_168 = empty_set) & relation_rng(empty_set) = all_113_0_168))
% 13.56/3.80  |
% 13.56/3.80  | Applying alpha-rule on (199) yields:
% 13.56/3.80  | (200) (all_113_0_168 = empty_set & relation_rng(empty_set) = empty_set) | ( ~ (all_113_1_169 = empty_set) & relation_dom(empty_set) = all_113_1_169)
% 13.56/3.80  | (201) (all_113_1_169 = empty_set & relation_dom(empty_set) = empty_set) | ( ~ (all_113_0_168 = empty_set) & relation_rng(empty_set) = all_113_0_168)
% 13.56/3.80  |
% 13.56/3.80  | Instantiating (184) with all_114_0_170, all_114_1_171, all_114_2_172 yields:
% 13.56/3.80  | (202) ( ~ (all_114_2_172 = 0) & function(empty_set) = all_114_2_172) | (((all_114_0_170 = 0 & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = 0) | ( ~ (all_114_2_172 = 0) & transfinite_sequence(empty_set) = all_114_2_172)) & ((all_114_2_172 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_114_0_170 = 0) & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = all_114_0_170)))
% 13.56/3.80  |
% 13.56/3.80  | Instantiating formula (76) with all_63_0_73 and discharging atoms empty(all_63_0_73) = 0, yields:
% 13.56/3.80  | (203) all_63_0_73 = empty_set
% 13.56/3.80  |
% 13.56/3.80  | Instantiating formula (107) with all_61_0_72, all_63_0_73 and discharging atoms empty(all_63_0_73) = 0, empty(all_61_0_72) = 0, yields:
% 13.56/3.80  | (204) all_63_0_73 = all_61_0_72
% 13.56/3.80  |
% 13.56/3.80  | Combining equations (204,203) yields a new equation:
% 13.56/3.80  | (205) all_61_0_72 = empty_set
% 13.56/3.80  |
% 13.56/3.80  | Simplifying 205 yields:
% 13.56/3.80  | (206) all_61_0_72 = empty_set
% 13.56/3.80  |
% 13.56/3.80  | From (206) and (190) follows:
% 13.56/3.80  | (207) relation_dom(empty_set) = empty_set
% 13.56/3.80  |
% 13.56/3.80  | From (206) and (191) follows:
% 13.56/3.80  | (37) relation(empty_set) = 0
% 13.56/3.80  |
% 13.56/3.80  +-Applying beta-rule and splitting (200), into two cases.
% 13.56/3.80  |-Branch one:
% 13.56/3.80  | (209) all_113_0_168 = empty_set & relation_rng(empty_set) = empty_set
% 13.56/3.80  |
% 13.56/3.80  	| Applying alpha-rule on (209) yields:
% 13.56/3.80  	| (210) all_113_0_168 = empty_set
% 13.56/3.80  	| (211) relation_rng(empty_set) = empty_set
% 13.56/3.80  	|
% 13.56/3.80  	+-Applying beta-rule and splitting (197), into two cases.
% 13.56/3.80  	|-Branch one:
% 13.56/3.80  	| (212)  ~ (all_85_2_113 = 0) & relation(empty_set) = all_85_2_113
% 13.56/3.80  	|
% 13.56/3.80  		| Applying alpha-rule on (212) yields:
% 13.56/3.80  		| (213)  ~ (all_85_2_113 = 0)
% 13.56/3.80  		| (214) relation(empty_set) = all_85_2_113
% 13.56/3.80  		|
% 13.56/3.80  		| Instantiating formula (148) with empty_set, all_85_2_113, 0 and discharging atoms relation(empty_set) = all_85_2_113, relation(empty_set) = 0, yields:
% 13.56/3.80  		| (215) all_85_2_113 = 0
% 13.56/3.80  		|
% 13.56/3.80  		| Equations (215) can reduce 213 to:
% 13.56/3.80  		| (216) $false
% 13.56/3.80  		|
% 13.56/3.80  		|-The branch is then unsatisfiable
% 13.56/3.80  	|-Branch two:
% 13.56/3.80  	| (217) ((all_85_0_111 = 0 & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = 0) | ( ~ (all_85_2_113 = 0) & transfinite_sequence(empty_set) = all_85_2_113)) & ((all_85_2_113 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_85_0_111 = 0) & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = all_85_0_111))
% 13.56/3.80  	|
% 13.56/3.80  		| Applying alpha-rule on (217) yields:
% 13.56/3.80  		| (218) (all_85_0_111 = 0 & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = 0) | ( ~ (all_85_2_113 = 0) & transfinite_sequence(empty_set) = all_85_2_113)
% 13.56/3.80  		| (219) (all_85_2_113 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_85_0_111 = 0) & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = all_85_0_111)
% 13.56/3.80  		|
% 13.56/3.80  		+-Applying beta-rule and splitting (219), into two cases.
% 13.56/3.80  		|-Branch one:
% 13.56/3.80  		| (220) all_85_2_113 = 0 & transfinite_sequence(empty_set) = 0
% 13.56/3.80  		|
% 13.56/3.80  			| Applying alpha-rule on (220) yields:
% 13.56/3.80  			| (215) all_85_2_113 = 0
% 13.56/3.80  			| (222) transfinite_sequence(empty_set) = 0
% 13.56/3.80  			|
% 13.56/3.80  			+-Applying beta-rule and splitting (198), into two cases.
% 13.56/3.80  			|-Branch one:
% 13.56/3.80  			| (223) ( ~ (all_100_1_147 = 0) & transfinite_sequence(empty_set) = all_100_1_147) | ( ~ (all_100_1_147 = 0) & relation(empty_set) = all_100_1_147) | ( ~ (all_100_1_147 = 0) & function(empty_set) = all_100_1_147)
% 13.56/3.80  			|
% 13.56/3.80  				+-Applying beta-rule and splitting (223), into two cases.
% 13.56/3.80  				|-Branch one:
% 13.56/3.80  				| (224) ( ~ (all_100_1_147 = 0) & transfinite_sequence(empty_set) = all_100_1_147) | ( ~ (all_100_1_147 = 0) & relation(empty_set) = all_100_1_147)
% 13.56/3.80  				|
% 13.56/3.80  					+-Applying beta-rule and splitting (224), into two cases.
% 13.56/3.80  					|-Branch one:
% 13.56/3.80  					| (225)  ~ (all_100_1_147 = 0) & transfinite_sequence(empty_set) = all_100_1_147
% 13.56/3.80  					|
% 13.56/3.80  						| Applying alpha-rule on (225) yields:
% 13.56/3.80  						| (226)  ~ (all_100_1_147 = 0)
% 13.56/3.80  						| (227) transfinite_sequence(empty_set) = all_100_1_147
% 13.56/3.80  						|
% 13.56/3.80  						| Instantiating formula (150) with empty_set, 0, all_100_1_147 and discharging atoms transfinite_sequence(empty_set) = all_100_1_147, transfinite_sequence(empty_set) = 0, yields:
% 13.56/3.80  						| (228) all_100_1_147 = 0
% 13.56/3.80  						|
% 13.56/3.80  						| Equations (228) can reduce 226 to:
% 13.56/3.80  						| (216) $false
% 13.56/3.80  						|
% 13.56/3.80  						|-The branch is then unsatisfiable
% 13.56/3.80  					|-Branch two:
% 13.56/3.80  					| (230)  ~ (all_100_1_147 = 0) & relation(empty_set) = all_100_1_147
% 13.56/3.80  					|
% 13.56/3.80  						| Applying alpha-rule on (230) yields:
% 13.56/3.80  						| (226)  ~ (all_100_1_147 = 0)
% 13.56/3.80  						| (232) relation(empty_set) = all_100_1_147
% 13.56/3.80  						|
% 13.56/3.80  						| Instantiating formula (148) with empty_set, all_100_1_147, 0 and discharging atoms relation(empty_set) = all_100_1_147, relation(empty_set) = 0, yields:
% 13.56/3.80  						| (228) all_100_1_147 = 0
% 13.56/3.80  						|
% 13.56/3.80  						| Equations (228) can reduce 226 to:
% 13.56/3.80  						| (216) $false
% 13.56/3.80  						|
% 13.56/3.80  						|-The branch is then unsatisfiable
% 13.56/3.80  				|-Branch two:
% 13.56/3.80  				| (235)  ~ (all_100_1_147 = 0) & function(empty_set) = all_100_1_147
% 13.56/3.80  				|
% 13.56/3.80  					| Applying alpha-rule on (235) yields:
% 13.56/3.80  					| (226)  ~ (all_100_1_147 = 0)
% 13.56/3.80  					| (237) function(empty_set) = all_100_1_147
% 13.56/3.81  					|
% 13.56/3.81  					| Instantiating formula (128) with empty_set, all_100_1_147, 0 and discharging atoms function(empty_set) = all_100_1_147, function(empty_set) = 0, yields:
% 13.56/3.81  					| (228) all_100_1_147 = 0
% 13.56/3.81  					|
% 13.56/3.81  					| Equations (228) can reduce 226 to:
% 13.56/3.81  					| (216) $false
% 13.56/3.81  					|
% 13.56/3.81  					|-The branch is then unsatisfiable
% 13.56/3.81  			|-Branch two:
% 13.56/3.81  			| (240) ( ~ (all_0_17_17 = 0) | (all_100_0_146 = 0 & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (all_100_0_146 = 0) & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = all_100_0_146))
% 13.56/3.81  			|
% 13.56/3.81  				| Applying alpha-rule on (240) yields:
% 13.56/3.81  				| (241)  ~ (all_0_17_17 = 0) | (all_100_0_146 = 0 & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = 0)
% 13.56/3.81  				| (242) all_0_17_17 = 0 | ( ~ (all_100_0_146 = 0) & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = all_100_0_146)
% 13.56/3.81  				|
% 13.56/3.81  				+-Applying beta-rule and splitting (242), into two cases.
% 13.56/3.81  				|-Branch one:
% 13.56/3.81  				| (243) all_0_17_17 = 0
% 13.56/3.81  				|
% 13.56/3.81  					| Equations (243) can reduce 80 to:
% 13.56/3.81  					| (216) $false
% 13.56/3.81  					|
% 13.56/3.81  					|-The branch is then unsatisfiable
% 13.56/3.81  				|-Branch two:
% 13.56/3.81  				| (80)  ~ (all_0_17_17 = 0)
% 13.56/3.81  				| (246)  ~ (all_100_0_146 = 0) & relation_rng(empty_set) = all_100_1_147 & subset(all_100_1_147, all_0_18_18) = all_100_0_146
% 13.56/3.81  				|
% 13.56/3.81  					| Applying alpha-rule on (246) yields:
% 13.56/3.81  					| (247)  ~ (all_100_0_146 = 0)
% 13.56/3.81  					| (248) relation_rng(empty_set) = all_100_1_147
% 13.56/3.81  					| (249) subset(all_100_1_147, all_0_18_18) = all_100_0_146
% 13.56/3.81  					|
% 13.56/3.81  					| Instantiating formula (27) with empty_set, empty_set, all_100_1_147 and discharging atoms relation_rng(empty_set) = all_100_1_147, relation_rng(empty_set) = empty_set, yields:
% 13.56/3.81  					| (250) all_100_1_147 = empty_set
% 13.56/3.81  					|
% 13.56/3.81  					| From (250) and (249) follows:
% 13.56/3.81  					| (251) subset(empty_set, all_0_18_18) = all_100_0_146
% 13.56/3.81  					|
% 13.56/3.81  					| Instantiating formula (43) with all_100_0_146, all_0_18_18 and discharging atoms subset(empty_set, all_0_18_18) = all_100_0_146, yields:
% 13.56/3.81  					| (252) all_100_0_146 = 0
% 13.56/3.81  					|
% 13.56/3.81  					| Equations (252) can reduce 247 to:
% 13.56/3.81  					| (216) $false
% 13.56/3.81  					|
% 13.56/3.81  					|-The branch is then unsatisfiable
% 13.56/3.81  		|-Branch two:
% 13.56/3.81  		| (254)  ~ (all_85_0_111 = 0) & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = all_85_0_111
% 13.56/3.81  		|
% 13.56/3.81  			| Applying alpha-rule on (254) yields:
% 13.56/3.81  			| (255)  ~ (all_85_0_111 = 0)
% 13.56/3.81  			| (256) relation_dom(empty_set) = all_85_1_112
% 13.56/3.81  			| (257) ordinal(all_85_1_112) = all_85_0_111
% 13.56/3.81  			|
% 13.56/3.81  			+-Applying beta-rule and splitting (201), into two cases.
% 13.56/3.81  			|-Branch one:
% 13.56/3.81  			| (258) all_113_1_169 = empty_set & relation_dom(empty_set) = empty_set
% 13.56/3.81  			|
% 13.56/3.81  				| Applying alpha-rule on (258) yields:
% 13.56/3.81  				| (259) all_113_1_169 = empty_set
% 13.56/3.81  				| (207) relation_dom(empty_set) = empty_set
% 13.56/3.81  				|
% 13.56/3.81  				+-Applying beta-rule and splitting (202), into two cases.
% 13.56/3.81  				|-Branch one:
% 13.56/3.81  				| (261)  ~ (all_114_2_172 = 0) & function(empty_set) = all_114_2_172
% 13.56/3.81  				|
% 13.56/3.81  					| Applying alpha-rule on (261) yields:
% 13.56/3.81  					| (262)  ~ (all_114_2_172 = 0)
% 13.56/3.81  					| (263) function(empty_set) = all_114_2_172
% 13.56/3.81  					|
% 13.56/3.81  					| Instantiating formula (128) with empty_set, all_114_2_172, 0 and discharging atoms function(empty_set) = all_114_2_172, function(empty_set) = 0, yields:
% 13.56/3.81  					| (264) all_114_2_172 = 0
% 13.56/3.81  					|
% 13.56/3.81  					| Equations (264) can reduce 262 to:
% 13.56/3.81  					| (216) $false
% 13.56/3.81  					|
% 13.56/3.81  					|-The branch is then unsatisfiable
% 13.56/3.81  				|-Branch two:
% 13.56/3.81  				| (266) ((all_114_0_170 = 0 & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = 0) | ( ~ (all_114_2_172 = 0) & transfinite_sequence(empty_set) = all_114_2_172)) & ((all_114_2_172 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_114_0_170 = 0) & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = all_114_0_170))
% 13.56/3.81  				|
% 13.56/3.81  					| Applying alpha-rule on (266) yields:
% 13.56/3.81  					| (267) (all_114_0_170 = 0 & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = 0) | ( ~ (all_114_2_172 = 0) & transfinite_sequence(empty_set) = all_114_2_172)
% 13.56/3.81  					| (268) (all_114_2_172 = 0 & transfinite_sequence(empty_set) = 0) | ( ~ (all_114_0_170 = 0) & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = all_114_0_170)
% 13.56/3.81  					|
% 13.56/3.81  					+-Applying beta-rule and splitting (218), into two cases.
% 13.56/3.81  					|-Branch one:
% 13.56/3.81  					| (269) all_85_0_111 = 0 & relation_dom(empty_set) = all_85_1_112 & ordinal(all_85_1_112) = 0
% 13.56/3.81  					|
% 13.56/3.81  						| Applying alpha-rule on (269) yields:
% 13.56/3.81  						| (270) all_85_0_111 = 0
% 13.56/3.81  						| (256) relation_dom(empty_set) = all_85_1_112
% 13.56/3.81  						| (272) ordinal(all_85_1_112) = 0
% 13.56/3.81  						|
% 13.56/3.81  						| Equations (270) can reduce 255 to:
% 13.56/3.81  						| (216) $false
% 13.56/3.81  						|
% 13.56/3.81  						|-The branch is then unsatisfiable
% 13.56/3.81  					|-Branch two:
% 13.56/3.81  					| (274)  ~ (all_85_2_113 = 0) & transfinite_sequence(empty_set) = all_85_2_113
% 13.56/3.81  					|
% 13.56/3.81  						| Applying alpha-rule on (274) yields:
% 13.56/3.81  						| (213)  ~ (all_85_2_113 = 0)
% 13.56/3.81  						| (276) transfinite_sequence(empty_set) = all_85_2_113
% 13.56/3.81  						|
% 13.56/3.81  						+-Applying beta-rule and splitting (268), into two cases.
% 13.56/3.81  						|-Branch one:
% 13.56/3.81  						| (277) all_114_2_172 = 0 & transfinite_sequence(empty_set) = 0
% 13.56/3.81  						|
% 13.56/3.81  							| Applying alpha-rule on (277) yields:
% 13.56/3.81  							| (264) all_114_2_172 = 0
% 13.56/3.81  							| (222) transfinite_sequence(empty_set) = 0
% 13.56/3.81  							|
% 13.56/3.81  							| Instantiating formula (150) with empty_set, 0, all_85_2_113 and discharging atoms transfinite_sequence(empty_set) = all_85_2_113, transfinite_sequence(empty_set) = 0, yields:
% 13.56/3.81  							| (215) all_85_2_113 = 0
% 13.56/3.81  							|
% 13.56/3.81  							| Equations (215) can reduce 213 to:
% 13.56/3.81  							| (216) $false
% 13.56/3.81  							|
% 13.56/3.81  							|-The branch is then unsatisfiable
% 13.56/3.81  						|-Branch two:
% 13.56/3.81  						| (282)  ~ (all_114_0_170 = 0) & relation_dom(empty_set) = all_114_1_171 & ordinal(all_114_1_171) = all_114_0_170
% 13.56/3.81  						|
% 13.56/3.81  							| Applying alpha-rule on (282) yields:
% 13.56/3.81  							| (283)  ~ (all_114_0_170 = 0)
% 13.56/3.81  							| (284) relation_dom(empty_set) = all_114_1_171
% 13.56/3.81  							| (285) ordinal(all_114_1_171) = all_114_0_170
% 13.56/3.81  							|
% 13.56/3.81  							| Instantiating formula (124) with empty_set, all_85_1_112, all_114_1_171 and discharging atoms relation_dom(empty_set) = all_114_1_171, relation_dom(empty_set) = all_85_1_112, yields:
% 13.56/3.81  							| (286) all_114_1_171 = all_85_1_112
% 13.56/3.81  							|
% 13.56/3.81  							| Instantiating formula (124) with empty_set, empty_set, all_114_1_171 and discharging atoms relation_dom(empty_set) = all_114_1_171, relation_dom(empty_set) = empty_set, yields:
% 13.56/3.81  							| (287) all_114_1_171 = empty_set
% 13.56/3.81  							|
% 13.56/3.81  							| Combining equations (286,287) yields a new equation:
% 13.56/3.81  							| (288) all_85_1_112 = empty_set
% 13.56/3.81  							|
% 13.56/3.81  							| Simplifying 288 yields:
% 13.56/3.81  							| (289) all_85_1_112 = empty_set
% 13.56/3.81  							|
% 13.56/3.81  							| From (287) and (285) follows:
% 13.56/3.81  							| (290) ordinal(empty_set) = all_114_0_170
% 13.56/3.81  							|
% 13.56/3.81  							| From (289) and (257) follows:
% 13.56/3.81  							| (291) ordinal(empty_set) = all_85_0_111
% 13.56/3.81  							|
% 13.56/3.81  							| Instantiating formula (70) with empty_set, all_114_0_170, 0 and discharging atoms ordinal(empty_set) = all_114_0_170, ordinal(empty_set) = 0, yields:
% 13.56/3.81  							| (292) all_114_0_170 = 0
% 13.56/3.81  							|
% 13.56/3.81  							| Instantiating formula (70) with empty_set, all_85_0_111, all_114_0_170 and discharging atoms ordinal(empty_set) = all_114_0_170, ordinal(empty_set) = all_85_0_111, yields:
% 13.56/3.81  							| (293) all_114_0_170 = all_85_0_111
% 13.56/3.81  							|
% 13.56/3.81  							| Combining equations (292,293) yields a new equation:
% 13.56/3.81  							| (270) all_85_0_111 = 0
% 13.56/3.81  							|
% 13.56/3.81  							| Equations (270) can reduce 255 to:
% 13.56/3.81  							| (216) $false
% 13.56/3.81  							|
% 13.56/3.81  							|-The branch is then unsatisfiable
% 13.56/3.81  			|-Branch two:
% 13.56/3.81  			| (296)  ~ (all_113_0_168 = empty_set) & relation_rng(empty_set) = all_113_0_168
% 13.56/3.81  			|
% 13.56/3.81  				| Applying alpha-rule on (296) yields:
% 13.56/3.81  				| (297)  ~ (all_113_0_168 = empty_set)
% 13.56/3.81  				| (298) relation_rng(empty_set) = all_113_0_168
% 13.56/3.81  				|
% 13.56/3.81  				| Equations (210) can reduce 297 to:
% 13.56/3.81  				| (216) $false
% 13.56/3.81  				|
% 13.56/3.81  				|-The branch is then unsatisfiable
% 13.56/3.81  |-Branch two:
% 13.56/3.81  | (300)  ~ (all_113_1_169 = empty_set) & relation_dom(empty_set) = all_113_1_169
% 13.56/3.81  |
% 13.56/3.81  	| Applying alpha-rule on (300) yields:
% 13.56/3.81  	| (301)  ~ (all_113_1_169 = empty_set)
% 13.56/3.81  	| (302) relation_dom(empty_set) = all_113_1_169
% 13.56/3.81  	|
% 13.56/3.81  	| Instantiating formula (124) with empty_set, empty_set, all_113_1_169 and discharging atoms relation_dom(empty_set) = all_113_1_169, relation_dom(empty_set) = empty_set, yields:
% 13.56/3.81  	| (259) all_113_1_169 = empty_set
% 13.56/3.81  	|
% 13.56/3.81  	| Equations (259) can reduce 301 to:
% 13.56/3.81  	| (216) $false
% 13.56/3.81  	|
% 13.56/3.81  	|-The branch is then unsatisfiable
% 13.56/3.81  % SZS output end Proof for theBenchmark
% 13.56/3.81  
% 13.56/3.81  3230ms
%------------------------------------------------------------------------------