%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:46:34 EDT 2022

% Result   : Theorem 9.70s 2.92s
% Output   : Proof 43.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 19:11:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.60          ____       _                          
% 0.20/0.60    ___  / __ \_____(_)___  ________  __________
% 0.20/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.20/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic
% 0.20/0.60  (ePrincess v.1.0)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2015
% 0.20/0.60  (c) Peter Backeman, 2014-2015
% 0.20/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.60  Bug reports to peter@backeman.se
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/1.01  Prover 0: Preprocessing ...
% 2.41/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.53/1.26  Prover 0: Constructing countermodel ...
% 4.08/1.64  Prover 0: gave up
% 4.08/1.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.32/1.70  Prover 1: Preprocessing ...
% 4.77/1.83  Prover 1: Warning: ignoring some quantifiers
% 4.99/1.83  Prover 1: Constructing countermodel ...
% 7.59/2.43  Prover 1: gave up
% 7.59/2.43  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.59/2.47  Prover 2: Preprocessing ...
% 8.07/2.58  Prover 2: Warning: ignoring some quantifiers
% 8.07/2.59  Prover 2: Constructing countermodel ...
% 9.70/2.92  Prover 2: proved (491ms)
% 9.70/2.92  
% 9.70/2.92  No countermodel exists, formula is valid
% 9.70/2.92  % SZS status Theorem for theBenchmark
% 9.70/2.92  
% 9.70/2.92  Generating proof ... Warning: ignoring some quantifiers
% 42.32/20.49  found it (size 265)
% 42.32/20.49  
% 42.32/20.49  % SZS output start Proof for theBenchmark
% 42.32/20.49  Assumed formulas after preprocessing and simplification: 
% 42.32/20.49  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] :  ? [v27] :  ? [v28] :  ? [v29] :  ? [v30] :  ? [v31] :  ? [v32] : ( ~ (v32 = 0) &  ~ (v30 = 0) &  ~ (v22 = 0) &  ~ (v17 = 0) &  ~ (v15 = 0) &  ~ (v11 = 0) &  ~ (v5 = 0) &  ~ (v0 = 0) & relation_inverse_image(v2, v1) = v4 & subset(v1, v3) = 0 & relation_empty_yielding(v9) = 0 & relation_empty_yielding(v8) = 0 & relation_empty_yielding(empty_set) = 0 & transfinite_sequence(v18) = 0 & transfinite_sequence(v7) = 0 & ordinal_yielding(v18) = 0 & being_limit_ordinal(v25) = 0 & function_yielding(v28) = 0 & relation_rng(v2) = v3 & relation_non_empty(v6) = 0 & one_to_one(v19) = 0 & one_to_one(v12) = 0 & one_to_one(empty_set) = 0 & natural(v31) = 0 & natural(v13) = 0 & relation(v28) = 0 & relation(v27) = 0 & relation(v24) = 0 & relation(v20) = 0 & relation(v19) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v12) = 0 & relation(v9) = 0 & relation(v8) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & function(v28) = 0 & function(v27) = 0 & function(v20) = 0 & function(v19) = 0 & function(v18) = 0 & function(v12) = 0 & function(v8) = 0 & function(v7) = 0 & function(v6) = 0 & function(v2) = 0 & function(empty_set) = 0 & finite(v29) = 0 & finite(v4) = 0 & finite(v1) = v5 & empty(v31) = v32 & empty(v29) = v30 & empty(v24) = 0 & empty(v23) = 0 & empty(v21) = v22 & empty(v20) = 0 & empty(v19) = 0 & empty(v16) = v17 & empty(v14) = v15 & empty(v13) = 0 & empty(v10) = v11 & empty(empty_set) = 0 & empty(positive_rationals) = v0 & epsilon_connected(v31) = 0 & epsilon_connected(v26) = 0 & epsilon_connected(v25) = 0 & epsilon_connected(v21) = 0 & epsilon_connected(v19) = 0 & epsilon_connected(v13) = 0 & epsilon_connected(v10) = 0 & epsilon_connected(empty_set) = 0 & element(v21, positive_rationals) = 0 & element(v13, positive_rationals) = 0 & epsilon_transitive(v31) = 0 & epsilon_transitive(v26) = 0 & epsilon_transitive(v25) = 0 & epsilon_transitive(v21) = 0 & epsilon_transitive(v19) = 0 & epsilon_transitive(v13) = 0 & epsilon_transitive(v10) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v31) = 0 & ordinal(v26) = 0 & ordinal(v25) = 0 & ordinal(v21) = 0 & ordinal(v19) = 0 & ordinal(v13) = 0 & ordinal(v10) = 0 & ordinal(empty_set) = 0 &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] :  ! [v37] : (v37 = 0 |  ~ (powerset(v35) = v36) |  ~ (element(v34, v36) = 0) |  ~ (element(v33, v35) = v37) |  ? [v38] : ( ~ (v38 = 0) & in(v33, v34) = v38)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v36 = 0 |  ~ (powerset(v34) = v35) |  ~ (element(v33, v35) = v36) |  ? [v37] : ( ~ (v37 = 0) & subset(v33, v34) = v37)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v36 = 0 |  ~ (powerset(v33) = v34) |  ~ (finite(v35) = v36) |  ? [v37] : (( ~ (v37 = 0) & finite(v33) = v37) | ( ~ (v37 = 0) & element(v35, v34) = v37))) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v36 = 0 |  ~ (element(v33, v35) = v36) |  ~ (in(v33, v34) = 0) |  ? [v37] :  ? [v38] : ( ~ (v38 = 0) & powerset(v35) = v37 & element(v34, v37) = v38)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v34 = v33 |  ~ (relation_inverse_image(v36, v35) = v34) |  ~ (relation_inverse_image(v36, v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v34 = v33 |  ~ (subset(v36, v35) = v34) |  ~ (subset(v36, v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v34 = v33 |  ~ (relation_image(v36, v35) = v34) |  ~ (relation_image(v36, v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v34 = v33 |  ~ (element(v36, v35) = v34) |  ~ (element(v36, v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : (v34 = v33 |  ~ (in(v36, v35) = v34) |  ~ (in(v36, v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : ( ~ (powerset(v35) = v36) |  ~ (element(v34, v36) = 0) |  ~ (in(v33, v34) = 0) | element(v33, v35) = 0) &  ! [v33] :  ! [v34] :  ! [v35] :  ! [v36] : ( ~ (powerset(v35) = v36) |  ~ (element(v34, v36) = 0) |  ~ (in(v33, v34) = 0) |  ? [v37] : ( ~ (v37 = 0) & empty(v35) = v37)) &  ! [v33] :  ! [v34] :  ! [v35] : (v35 = 0 |  ~ (subset(v33, v34) = v35) |  ? [v36] :  ? [v37] : ( ~ (v37 = 0) & powerset(v34) = v36 & element(v33, v36) = v37)) &  ! [v33] :  ! [v34] :  ! [v35] : (v35 = 0 |  ~ (element(v33, v34) = v35) |  ? [v36] : ( ~ (v36 = 0) & in(v33, v34) = v36)) &  ! [v33] :  ! [v34] :  ! [v35] : (v35 = 0 |  ~ (in(v33, v34) = v35) |  ? [v36] : ((v36 = 0 & empty(v34) = 0) | ( ~ (v36 = 0) & element(v33, v34) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (relation_empty_yielding(v35) = v34) |  ~ (relation_empty_yielding(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (transfinite_sequence(v35) = v34) |  ~ (transfinite_sequence(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (ordinal_yielding(v35) = v34) |  ~ (ordinal_yielding(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (being_limit_ordinal(v35) = v34) |  ~ (being_limit_ordinal(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (function_yielding(v35) = v34) |  ~ (function_yielding(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (relation_rng(v35) = v34) |  ~ (relation_rng(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (relation_non_empty(v35) = v34) |  ~ (relation_non_empty(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (with_non_empty_elements(v35) = v34) |  ~ (with_non_empty_elements(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (one_to_one(v35) = v34) |  ~ (one_to_one(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (powerset(v35) = v34) |  ~ (powerset(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (natural(v35) = v34) |  ~ (natural(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (relation(v35) = v34) |  ~ (relation(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (function(v35) = v34) |  ~ (function(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (finite(v35) = v34) |  ~ (finite(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (empty(v35) = v34) |  ~ (empty(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (epsilon_connected(v35) = v34) |  ~ (epsilon_connected(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (epsilon_transitive(v35) = v34) |  ~ (epsilon_transitive(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : (v34 = v33 |  ~ (ordinal(v35) = v34) |  ~ (ordinal(v35) = v33)) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (relation_inverse_image(v34, v33) = v35) |  ? [v36] :  ? [v37] : ((v36 = v33 & relation_image(v34, v35) = v33) | ( ~ (v37 = 0) & subset(v33, v36) = v37 & relation_rng(v34) = v36) | ( ~ (v36 = 0) & relation(v34) = v36) | ( ~ (v36 = 0) & function(v34) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (subset(v33, v35) = 0) |  ~ (relation_rng(v34) = v35) |  ? [v36] :  ? [v37] : ((v37 = v33 & relation_inverse_image(v34, v33) = v36 & relation_image(v34, v36) = v33) | ( ~ (v36 = 0) & relation(v34) = v36) | ( ~ (v36 = 0) & function(v34) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (relation_image(v34, v33) = v35) |  ? [v36] : ((v36 = 0 & finite(v35) = 0) | ( ~ (v36 = 0) & relation(v34) = v36) | ( ~ (v36 = 0) & function(v34) = v36) | ( ~ (v36 = 0) & finite(v33) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (relation_image(v33, v34) = v35) |  ? [v36] : ((v36 = 0 & finite(v35) = 0) | ( ~ (v36 = 0) & relation(v33) = v36) | ( ~ (v36 = 0) & function(v33) = v36) | ( ~ (v36 = 0) & finite(v34) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (powerset(v34) = v35) |  ~ (element(v33, v35) = 0) | subset(v33, v34) = 0) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (powerset(v33) = v34) |  ~ (element(v35, v34) = 0) |  ? [v36] : ((v36 = 0 & finite(v35) = 0) | ( ~ (v36 = 0) & finite(v33) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (empty(v35) = 0) |  ~ (in(v33, v34) = 0) |  ? [v36] :  ? [v37] : ( ~ (v37 = 0) & powerset(v35) = v36 & element(v34, v36) = v37)) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (epsilon_connected(v34) = v35) |  ~ (ordinal(v33) = 0) |  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & epsilon_transitive(v34) = 0 & ordinal(v34) = 0) | ( ~ (v36 = 0) & element(v34, v33) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (epsilon_transitive(v34) = v35) |  ~ (ordinal(v33) = 0) |  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & epsilon_connected(v34) = 0 & ordinal(v34) = 0) | ( ~ (v36 = 0) & element(v34, v33) = v36))) &  ! [v33] :  ! [v34] :  ! [v35] : ( ~ (ordinal(v34) = v35) |  ~ (ordinal(v33) = 0) |  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & epsilon_connected(v34) = 0 & epsilon_transitive(v34) = 0) | ( ~ (v36 = 0) & element(v34, v33) = v36))) &  ! [v33] :  ! [v34] : (v34 = v33 |  ~ (empty(v34) = 0) |  ~ (empty(v33) = 0)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (subset(v33, v33) = v34)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (relation(v33) = v34) |  ? [v35] : ( ~ (v35 = 0) & empty(v33) = v35)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (function(v33) = v34) |  ? [v35] : ( ~ (v35 = 0) & empty(v33) = v35)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (finite(v33) = v34) |  ? [v35] : ( ~ (v35 = 0) & empty(v33) = v35)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (empty(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ( ~ (v37 = 0) & powerset(v33) = v35 & finite(v36) = 0 & empty(v36) = v37 & element(v36, v35) = 0)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (empty(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ( ~ (v37 = 0) & powerset(v33) = v35 & empty(v36) = v37 & element(v36, v35) = 0)) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (empty(v33) = v34) |  ? [v35] :  ? [v36] : (( ~ (v36 = 0) & relation_rng(v33) = v35 & empty(v35) = v36) | ( ~ (v35 = 0) & relation(v33) = v35))) &  ! [v33] :  ! [v34] : (v34 = 0 |  ~ (ordinal(v33) = v34) |  ? [v35] : (( ~ (v35 = 0) & epsilon_connected(v33) = v35) | ( ~ (v35 = 0) & epsilon_transitive(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (subset(v33, v34) = 0) |  ? [v35] : (powerset(v34) = v35 & element(v33, v35) = 0)) &  ! [v33] :  ! [v34] : ( ~ (relation_rng(v33) = v34) |  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & relation(v34) = 0 & empty(v34) = 0) | ( ~ (v35 = 0) & empty(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (relation_rng(v33) = v34) |  ? [v35] : ((v35 = 0 & with_non_empty_elements(v34) = 0) | ( ~ (v35 = 0) & relation_non_empty(v33) = v35) | ( ~ (v35 = 0) & relation(v33) = v35) | ( ~ (v35 = 0) & function(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (relation_rng(v33) = v34) |  ? [v35] : ((v35 = 0 & empty(v33) = 0) | ( ~ (v35 = 0) & relation(v33) = v35) | ( ~ (v35 = 0) & empty(v34) = v35))) &  ! [v33] :  ! [v34] : ( ~ (one_to_one(v33) = v34) |  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & relation(v33) = 0 & function(v33) = 0) | ( ~ (v35 = 0) & relation(v33) = v35) | ( ~ (v35 = 0) & function(v33) = v35) | ( ~ (v35 = 0) & empty(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (powerset(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] :  ? [v38] : ((v38 = 0 & v36 = 0 &  ~ (v37 = 0) & finite(v35) = 0 & empty(v35) = v37 & element(v35, v34) = 0) | (v35 = 0 & empty(v33) = 0))) &  ! [v33] :  ! [v34] : ( ~ (powerset(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v36 = 0 &  ~ (v37 = 0) & empty(v35) = v37 & element(v35, v34) = 0) | (v35 = 0 & empty(v33) = 0))) &  ! [v33] :  ! [v34] : ( ~ (powerset(v33) = v34) |  ? [v35] : ( ~ (v35 = 0) & empty(v34) = v35)) &  ! [v33] :  ! [v34] : ( ~ (powerset(v33) = v34) |  ? [v35] : (one_to_one(v35) = 0 & natural(v35) = 0 & relation(v35) = 0 & function(v35) = 0 & finite(v35) = 0 & empty(v35) = 0 & epsilon_connected(v35) = 0 & element(v35, v34) = 0 & epsilon_transitive(v35) = 0 & ordinal(v35) = 0)) &  ! [v33] :  ! [v34] : ( ~ (powerset(v33) = v34) |  ? [v35] : (empty(v35) = 0 & element(v35, v34) = 0)) &  ! [v33] :  ! [v34] : ( ~ (natural(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (natural(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & element(v33, positive_rationals) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_connected(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_connected(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & element(v33, positive_rationals) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_connected(v33) = v34) |  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_connected(v33) = v34) |  ? [v35] : ((v35 = 0 & v34 = 0 & epsilon_transitive(v33) = 0) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (element(v34, v33) = 0) |  ~ (ordinal(v33) = 0) | (epsilon_connected(v34) = 0 & epsilon_transitive(v34) = 0 & ordinal(v34) = 0)) &  ! [v33] :  ! [v34] : ( ~ (element(v33, v34) = 0) |  ? [v35] : ((v35 = 0 & empty(v34) = 0) | (v35 = 0 & in(v33, v34) = 0))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_transitive(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_transitive(v33) = v34) |  ? [v35] :  ? [v36] :  ? [v37] : ((v37 = 0 & v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & element(v33, positive_rationals) = v35) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_transitive(v33) = v34) |  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & epsilon_connected(v33) = 0 & ordinal(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (epsilon_transitive(v33) = v34) |  ? [v35] : ((v35 = 0 & v34 = 0 & epsilon_connected(v33) = 0) | ( ~ (v35 = 0) & ordinal(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (ordinal(v33) = v34) |  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0) | ( ~ (v35 = 0) & empty(v33) = v35))) &  ! [v33] :  ! [v34] : ( ~ (in(v34, v33) = 0) |  ? [v35] : ( ~ (v35 = 0) & in(v33, v34) = v35)) &  ! [v33] :  ! [v34] : ( ~ (in(v33, v34) = 0) | element(v33, v34) = 0) &  ! [v33] :  ! [v34] : ( ~ (in(v33, v34) = 0) |  ? [v35] : ( ~ (v35 = 0) & empty(v34) = v35)) &  ! [v33] :  ! [v34] : ( ~ (in(v33, v34) = 0) |  ? [v35] : ( ~ (v35 = 0) & in(v34, v33) = v35)) &  ! [v33] : (v33 = empty_set |  ~ (empty(v33) = 0)) &  ! [v33] : ( ~ (relation_non_empty(v33) = 0) |  ? [v34] :  ? [v35] : ((v35 = 0 & relation_rng(v33) = v34 & with_non_empty_elements(v34) = 0) | ( ~ (v34 = 0) & relation(v33) = v34) | ( ~ (v34 = 0) & function(v33) = v34))) &  ! [v33] : ( ~ (relation(v33) = 0) |  ? [v34] :  ? [v35] : ((v35 = 0 & v34 = 0 & one_to_one(v33) = 0 & function(v33) = 0) | ( ~ (v34 = 0) & function(v33) = v34) | ( ~ (v34 = 0) & empty(v33) = v34))) &  ! [v33] : ( ~ (relation(v33) = 0) |  ? [v34] :  ? [v35] : ((v35 = 0 & relation_rng(v33) = v34 & with_non_empty_elements(v34) = 0) | ( ~ (v34 = 0) & relation_non_empty(v33) = v34) | ( ~ (v34 = 0) & function(v33) = v34))) &  ! [v33] : ( ~ (relation(v33) = 0) |  ? [v34] :  ? [v35] : ((v34 = 0 & empty(v33) = 0) | ( ~ (v35 = 0) & relation_rng(v33) = v34 & empty(v34) = v35))) &  ! [v33] : ( ~ (function(v33) = 0) |  ? [v34] :  ? [v35] : ((v35 = 0 & v34 = 0 & one_to_one(v33) = 0 & relation(v33) = 0) | ( ~ (v34 = 0) & relation(v33) = v34) | ( ~ (v34 = 0) & empty(v33) = v34))) &  ! [v33] : ( ~ (function(v33) = 0) |  ? [v34] :  ? [v35] : ((v35 = 0 & relation_rng(v33) = v34 & with_non_empty_elements(v34) = 0) | ( ~ (v34 = 0) & relation_non_empty(v33) = v34) | ( ~ (v34 = 0) & relation(v33) = v34))) &  ! [v33] : ( ~ (finite(v33) = 0) |  ? [v34] : (powerset(v33) = v34 &  ! [v35] :  ! [v36] : (v36 = 0 |  ~ (finite(v35) = v36) |  ? [v37] : ( ~ (v37 = 0) & element(v35, v34) = v37)) &  ! [v35] : ( ~ (element(v35, v34) = 0) | finite(v35) = 0))) &  ! [v33] : ( ~ (empty(v33) = 0) | relation(v33) = 0) &  ! [v33] : ( ~ (empty(v33) = 0) | function(v33) = 0) &  ! [v33] : ( ~ (empty(v33) = 0) | finite(v33) = 0) &  ! [v33] : ( ~ (empty(v33) = 0) |  ? [v34] :  ? [v35] :  ? [v36] :  ? [v37] : (ordinal(v33) = v34 & ( ~ (v34 = 0) | (v37 = 0 & v36 = 0 & v35 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0)))) &  ! [v33] : ( ~ (empty(v33) = 0) |  ? [v34] :  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & one_to_one(v33) = 0 & relation(v33) = 0 & function(v33) = 0) | ( ~ (v34 = 0) & relation(v33) = v34) | ( ~ (v34 = 0) & function(v33) = v34))) &  ! [v33] : ( ~ (empty(v33) = 0) |  ? [v34] : (relation_rng(v33) = v34 & relation(v34) = 0 & empty(v34) = 0)) &  ! [v33] : ( ~ (empty(v33) = 0) | (epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0)) &  ! [v33] : ( ~ (epsilon_connected(v33) = 0) |  ? [v34] : ((v34 = 0 & ordinal(v33) = 0) | ( ~ (v34 = 0) & epsilon_transitive(v33) = v34))) &  ! [v33] : ( ~ (element(v33, positive_rationals) = 0) |  ? [v34] :  ? [v35] :  ? [v36] :  ? [v37] : (ordinal(v33) = v34 & ( ~ (v34 = 0) | (v37 = 0 & v36 = 0 & v35 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0)))) &  ! [v33] : ( ~ (epsilon_transitive(v33) = 0) |  ? [v34] : ((v34 = 0 & ordinal(v33) = 0) | ( ~ (v34 = 0) & epsilon_connected(v33) = v34))) &  ! [v33] : ( ~ (ordinal(v33) = 0) |  ? [v34] :  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0) | ( ~ (v34 = 0) & empty(v33) = v34))) &  ! [v33] : ( ~ (ordinal(v33) = 0) |  ? [v34] :  ? [v35] :  ? [v36] : ((v36 = 0 & v35 = 0 & v34 = 0 & natural(v33) = 0 & epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0) | ( ~ (v34 = 0) & element(v33, positive_rationals) = v34))) &  ! [v33] : ( ~ (ordinal(v33) = 0) | (epsilon_connected(v33) = 0 & epsilon_transitive(v33) = 0)) &  ? [v33] :  ? [v34] :  ? [v35] : relation_inverse_image(v34, v33) = v35 &  ? [v33] :  ? [v34] :  ? [v35] : subset(v34, v33) = v35 &  ? [v33] :  ? [v34] :  ? [v35] : relation_image(v34, v33) = v35 &  ? [v33] :  ? [v34] :  ? [v35] : element(v34, v33) = v35 &  ? [v33] :  ? [v34] :  ? [v35] : in(v34, v33) = v35 &  ? [v33] :  ? [v34] : relation_empty_yielding(v33) = v34 &  ? [v33] :  ? [v34] : transfinite_sequence(v33) = v34 &  ? [v33] :  ? [v34] : ordinal_yielding(v33) = v34 &  ? [v33] :  ? [v34] : being_limit_ordinal(v33) = v34 &  ? [v33] :  ? [v34] : function_yielding(v33) = v34 &  ? [v33] :  ? [v34] : relation_rng(v33) = v34 &  ? [v33] :  ? [v34] : relation_non_empty(v33) = v34 &  ? [v33] :  ? [v34] : with_non_empty_elements(v33) = v34 &  ? [v33] :  ? [v34] : one_to_one(v33) = v34 &  ? [v33] :  ? [v34] : powerset(v33) = v34 &  ? [v33] :  ? [v34] : natural(v33) = v34 &  ? [v33] :  ? [v34] : relation(v33) = v34 &  ? [v33] :  ? [v34] : function(v33) = v34 &  ? [v33] :  ? [v34] : finite(v33) = v34 &  ? [v33] :  ? [v34] : empty(v33) = v34 &  ? [v33] :  ? [v34] : epsilon_connected(v33) = v34 &  ? [v33] :  ? [v34] : element(v34, v33) = 0 &  ? [v33] :  ? [v34] : epsilon_transitive(v33) = v34 &  ? [v33] :  ? [v34] : ordinal(v33) = v34)
% 42.56/20.59  | 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, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30, all_0_31_31, all_0_32_32 yields:
% 42.56/20.59  | (1)  ~ (all_0_0_0 = 0) &  ~ (all_0_2_2 = 0) &  ~ (all_0_10_10 = 0) &  ~ (all_0_15_15 = 0) &  ~ (all_0_17_17 = 0) &  ~ (all_0_21_21 = 0) &  ~ (all_0_27_27 = 0) &  ~ (all_0_32_32 = 0) & relation_inverse_image(all_0_30_30, all_0_31_31) = all_0_28_28 & subset(all_0_31_31, all_0_29_29) = 0 & relation_empty_yielding(all_0_23_23) = 0 & relation_empty_yielding(all_0_24_24) = 0 & relation_empty_yielding(empty_set) = 0 & transfinite_sequence(all_0_14_14) = 0 & transfinite_sequence(all_0_25_25) = 0 & ordinal_yielding(all_0_14_14) = 0 & being_limit_ordinal(all_0_7_7) = 0 & function_yielding(all_0_4_4) = 0 & relation_rng(all_0_30_30) = all_0_29_29 & relation_non_empty(all_0_26_26) = 0 & one_to_one(all_0_13_13) = 0 & one_to_one(all_0_20_20) = 0 & one_to_one(empty_set) = 0 & natural(all_0_1_1) = 0 & natural(all_0_19_19) = 0 & relation(all_0_4_4) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_12_12) = 0 & relation(all_0_13_13) = 0 & relation(all_0_14_14) = 0 & relation(all_0_16_16) = 0 & relation(all_0_20_20) = 0 & relation(all_0_23_23) = 0 & relation(all_0_24_24) = 0 & relation(all_0_25_25) = 0 & relation(all_0_26_26) = 0 & relation(all_0_30_30) = 0 & relation(empty_set) = 0 & function(all_0_4_4) = 0 & function(all_0_5_5) = 0 & function(all_0_12_12) = 0 & function(all_0_13_13) = 0 & function(all_0_14_14) = 0 & function(all_0_20_20) = 0 & function(all_0_24_24) = 0 & function(all_0_25_25) = 0 & function(all_0_26_26) = 0 & function(all_0_30_30) = 0 & function(empty_set) = 0 & finite(all_0_3_3) = 0 & finite(all_0_28_28) = 0 & finite(all_0_31_31) = all_0_27_27 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_8_8) = 0 & empty(all_0_9_9) = 0 & empty(all_0_11_11) = all_0_10_10 & empty(all_0_12_12) = 0 & empty(all_0_13_13) = 0 & empty(all_0_16_16) = all_0_15_15 & empty(all_0_18_18) = all_0_17_17 & empty(all_0_19_19) = 0 & empty(all_0_22_22) = all_0_21_21 & empty(empty_set) = 0 & empty(positive_rationals) = all_0_32_32 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_6_6) = 0 & epsilon_connected(all_0_7_7) = 0 & epsilon_connected(all_0_11_11) = 0 & epsilon_connected(all_0_13_13) = 0 & epsilon_connected(all_0_19_19) = 0 & epsilon_connected(all_0_22_22) = 0 & epsilon_connected(empty_set) = 0 & element(all_0_11_11, positive_rationals) = 0 & element(all_0_19_19, positive_rationals) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_6_6) = 0 & epsilon_transitive(all_0_7_7) = 0 & epsilon_transitive(all_0_11_11) = 0 & epsilon_transitive(all_0_13_13) = 0 & epsilon_transitive(all_0_19_19) = 0 & epsilon_transitive(all_0_22_22) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_6_6) = 0 & ordinal(all_0_7_7) = 0 & ordinal(all_0_11_11) = 0 & ordinal(all_0_13_13) = 0 & ordinal(all_0_19_19) = 0 & ordinal(all_0_22_22) = 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 |  ~ (relation_inverse_image(v3, v2) = v1) |  ~ (relation_inverse_image(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(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 |  ~ (transfinite_sequence(v2) = v1) |  ~ (transfinite_sequence(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal_yielding(v2) = v1) |  ~ (ordinal_yielding(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (being_limit_ordinal(v2) = v1) |  ~ (being_limit_ordinal(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function_yielding(v2) = v1) |  ~ (function_yielding(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(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 |  ~ (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] : ( ~ (relation_inverse_image(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v3 = v0 & relation_image(v1, v2) = v0) | ( ~ (v4 = 0) & subset(v0, v3) = v4 & relation_rng(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v2) = 0) |  ~ (relation_rng(v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = v0 & relation_inverse_image(v1, v0) = v3 & relation_image(v1, v3) = v0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & finite(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3) | ( ~ (v3 = 0) & function(v0) = v3) | ( ~ (v3 = 0) & finite(v1) = v3))) &  ! [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 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) &  ! [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] : ( ~ (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] : ( ~ (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] : ( ~ (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) & element(v0, positive_rationals) = 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] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = 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] :  ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = 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_non_empty(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) &  ! [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 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (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] : ( ~ (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 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(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) |  ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) &  ! [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] : ( ~ (element(v0, positive_rationals) = 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] : ( ~ (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) |  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & element(v0, positive_rationals) = v1))) &  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0)) &  ? [v0] :  ? [v1] :  ? [v2] : relation_inverse_image(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : relation_image(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] : transfinite_sequence(v0) = v1 &  ? [v0] :  ? [v1] : ordinal_yielding(v0) = v1 &  ? [v0] :  ? [v1] : being_limit_ordinal(v0) = v1 &  ? [v0] :  ? [v1] : function_yielding(v0) = v1 &  ? [v0] :  ? [v1] : relation_rng(v0) = v1 &  ? [v0] :  ? [v1] : relation_non_empty(v0) = v1 &  ? [v0] :  ? [v1] : with_non_empty_elements(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
% 42.89/20.62  |
% 42.89/20.62  | Applying alpha-rule on (1) yields:
% 42.89/20.62  | (2)  ? [v0] :  ? [v1] : function_yielding(v0) = v1
% 42.89/20.62  | (3) ordinal(all_0_13_13) = 0
% 42.89/20.62  | (4) relation(all_0_12_12) = 0
% 42.89/20.62  | (5) function(all_0_25_25) = 0
% 42.89/20.62  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 42.89/20.62  | (7)  ! [v0] : ( ~ (element(v0, positive_rationals) = 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))))
% 42.89/20.62  | (8)  ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0)
% 42.89/20.62  | (9)  ? [v0] :  ? [v1] : ordinal(v0) = v1
% 42.89/20.62  | (10) relation(all_0_8_8) = 0
% 42.89/20.62  | (11)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (natural(v2) = v1) |  ~ (natural(v2) = v0))
% 42.89/20.62  | (12) relation_empty_yielding(empty_set) = 0
% 42.89/20.63  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 42.89/20.63  | (14)  ! [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)))
% 42.89/20.63  | (15)  ! [v0] : ( ~ (empty(v0) = 0) |  ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 42.89/20.63  | (16)  ! [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)))
% 42.89/20.63  | (17) relation(all_0_16_16) = 0
% 42.89/20.63  | (18)  ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 42.89/20.63  | (19)  ! [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)))
% 42.89/20.63  | (20)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 42.89/20.63  | (21) empty(all_0_22_22) = all_0_21_21
% 42.89/20.63  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 42.89/20.63  | (23) epsilon_transitive(all_0_19_19) = 0
% 42.89/20.63  | (24) finite(all_0_31_31) = all_0_27_27
% 42.89/20.63  | (25) ordinal(all_0_1_1) = 0
% 42.89/20.63  | (26) epsilon_transitive(all_0_6_6) = 0
% 42.89/20.63  | (27)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 42.89/20.63  | (28) relation(all_0_24_24) = 0
% 42.89/20.63  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (with_non_empty_elements(v2) = v1) |  ~ (with_non_empty_elements(v2) = v0))
% 42.89/20.63  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function_yielding(v2) = v1) |  ~ (function_yielding(v2) = v0))
% 42.89/20.63  | (31)  ~ (all_0_10_10 = 0)
% 42.89/20.63  | (32)  ! [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)))
% 42.89/20.63  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_connected(v2) = v1) |  ~ (epsilon_connected(v2) = v0))
% 42.89/20.63  | (34) empty(all_0_1_1) = all_0_0_0
% 42.89/20.63  | (35) epsilon_connected(empty_set) = 0
% 42.89/20.63  | (36) function(empty_set) = 0
% 42.89/20.63  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 42.89/20.63  | (38) relation(all_0_20_20) = 0
% 42.89/20.63  | (39)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 42.89/20.63  | (40) function(all_0_30_30) = 0
% 42.89/20.63  | (41) one_to_one(empty_set) = 0
% 42.89/20.63  | (42)  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2
% 42.89/20.63  | (43)  ~ (all_0_0_0 = 0)
% 42.89/20.63  | (44) ordinal(all_0_7_7) = 0
% 42.89/20.63  | (45)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (finite(v2) = v1) |  ~ (finite(v2) = v0))
% 42.89/20.63  | (46) epsilon_connected(all_0_1_1) = 0
% 42.89/20.63  | (47) empty(all_0_11_11) = all_0_10_10
% 42.89/20.63  | (48) epsilon_connected(all_0_11_11) = 0
% 42.89/20.63  | (49)  ! [v0] :  ! [v1] : ( ~ (epsilon_transitive(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 42.89/20.63  | (50)  ? [v0] :  ? [v1] : finite(v0) = v1
% 42.89/20.63  | (51)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 42.89/20.63  | (52)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 42.89/20.63  | (53) relation(all_0_5_5) = 0
% 42.89/20.63  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 42.89/20.63  | (55) empty(all_0_12_12) = 0
% 42.89/20.63  | (56)  ! [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)))
% 42.89/20.63  | (57)  ? [v0] :  ? [v1] : natural(v0) = v1
% 42.89/20.63  | (58) ordinal(all_0_6_6) = 0
% 42.89/20.63  | (59)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 42.89/20.63  | (60)  ? [v0] :  ? [v1] : epsilon_connected(v0) = v1
% 42.89/20.64  | (61)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 42.89/20.64  | (62)  ! [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) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 42.89/20.64  | (63)  ? [v0] :  ? [v1] : one_to_one(v0) = v1
% 42.89/20.64  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 42.89/20.64  | (65)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 42.89/20.64  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 42.89/20.64  | (67) epsilon_transitive(empty_set) = 0
% 42.89/20.64  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (in(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 42.89/20.64  | (69) epsilon_transitive(all_0_13_13) = 0
% 42.89/20.64  | (70) function(all_0_5_5) = 0
% 42.89/20.64  | (71) empty(all_0_16_16) = all_0_15_15
% 42.89/20.64  | (72)  ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0))
% 42.89/20.64  | (73)  ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))
% 42.89/20.64  | (74) subset(all_0_31_31, all_0_29_29) = 0
% 42.89/20.64  | (75)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3) | ( ~ (v3 = 0) & function(v0) = v3) | ( ~ (v3 = 0) & finite(v1) = v3)))
% 42.89/20.64  | (76) one_to_one(all_0_13_13) = 0
% 42.89/20.64  | (77)  ? [v0] :  ? [v1] : powerset(v0) = v1
% 42.89/20.64  | (78)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal(v2) = v1) |  ~ (ordinal(v2) = v0))
% 42.89/20.64  | (79) finite(all_0_28_28) = 0
% 42.89/20.64  | (80) function(all_0_14_14) = 0
% 42.89/20.64  | (81)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 42.89/20.64  | (82) relation_empty_yielding(all_0_24_24) = 0
% 42.89/20.64  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (element(v2, v1) = 0) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 42.89/20.64  | (84)  ! [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))))
% 42.89/20.64  | (85)  ! [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)))
% 42.89/20.64  | (86) ordinal(empty_set) = 0
% 42.89/20.64  | (87)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 42.89/20.64  | (88)  ! [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))
% 42.89/20.64  | (89)  ! [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))
% 42.89/20.64  | (90)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_non_empty(v2) = v1) |  ~ (relation_non_empty(v2) = v0))
% 42.89/20.64  | (91)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (transfinite_sequence(v2) = v1) |  ~ (transfinite_sequence(v2) = v0))
% 42.89/20.64  | (92) relation(all_0_14_14) = 0
% 42.89/20.65  | (93)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 42.89/20.65  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v2) = 0) |  ~ (in(v0, v1) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 42.89/20.65  | (95) relation(all_0_25_25) = 0
% 42.89/20.65  | (96)  ? [v0] :  ? [v1] : transfinite_sequence(v0) = v1
% 42.89/20.65  | (97)  ? [v0] :  ? [v1] : relation_non_empty(v0) = v1
% 42.89/20.65  | (98)  ? [v0] :  ? [v1] : relation_rng(v0) = v1
% 42.89/20.65  | (99)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (finite(v2) = v3) |  ? [v4] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 42.89/20.65  | (100) one_to_one(all_0_20_20) = 0
% 42.89/20.65  | (101)  ! [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)))
% 42.89/20.65  | (102) epsilon_transitive(all_0_11_11) = 0
% 42.89/20.65  | (103)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 42.89/20.65  | (104)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 42.89/20.65  | (105) ordinal(all_0_11_11) = 0
% 42.89/20.65  | (106)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 42.89/20.65  | (107)  ? [v0] :  ? [v1] : function(v0) = v1
% 42.89/20.65  | (108)  ? [v0] :  ? [v1] :  ? [v2] : relation_inverse_image(v1, v0) = v2
% 42.89/20.65  | (109) relation_rng(all_0_30_30) = all_0_29_29
% 42.89/20.65  | (110) epsilon_connected(all_0_13_13) = 0
% 42.89/20.65  | (111)  ! [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)))
% 42.89/20.65  | (112) empty(all_0_18_18) = all_0_17_17
% 42.89/20.65  | (113) empty(all_0_13_13) = 0
% 42.89/20.65  | (114) epsilon_connected(all_0_19_19) = 0
% 42.89/20.65  | (115)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (ordinal_yielding(v2) = v1) |  ~ (ordinal_yielding(v2) = v0))
% 42.89/20.65  | (116)  ? [v0] :  ? [v1] :  ? [v2] : element(v1, v0) = v2
% 42.89/20.65  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0))
% 42.89/20.65  | (118)  ? [v0] :  ? [v1] :  ? [v2] : relation_image(v1, v0) = v2
% 42.89/20.65  | (119)  ! [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) & element(v0, positive_rationals) = v1)))
% 42.89/20.66  | (120)  ! [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)))
% 42.89/20.66  | (121) epsilon_connected(all_0_6_6) = 0
% 42.89/20.66  | (122)  ? [v0] :  ? [v1] : epsilon_transitive(v0) = v1
% 42.89/20.66  | (123)  ! [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)))
% 42.89/20.66  | (124)  ~ (all_0_15_15 = 0)
% 42.89/20.66  | (125) function(all_0_20_20) = 0
% 42.89/20.66  | (126) empty(empty_set) = 0
% 42.89/20.66  | (127)  ~ (all_0_17_17 = 0)
% 42.89/20.66  | (128) empty(all_0_19_19) = 0
% 42.89/20.66  | (129)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 42.89/20.66  | (130)  ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 42.89/20.66  | (131)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0))
% 42.89/20.66  | (132)  ! [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)))
% 42.89/20.66  | (133) empty(all_0_9_9) = 0
% 42.89/20.66  | (134)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2)))
% 42.89/20.66  | (135) natural(all_0_1_1) = 0
% 42.89/20.66  | (136)  ~ (all_0_2_2 = 0)
% 42.89/20.66  | (137)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 42.89/20.66  | (138) function(all_0_13_13) = 0
% 42.89/20.66  | (139)  ! [v0] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 42.89/20.66  | (140)  ! [v0] : ( ~ (relation(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 42.89/20.66  | (141) function(all_0_12_12) = 0
% 42.89/20.66  | (142) relation(all_0_13_13) = 0
% 42.89/20.67  | (143)  ~ (all_0_32_32 = 0)
% 42.89/20.67  | (144) relation(all_0_4_4) = 0
% 42.89/20.67  | (145)  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 42.89/20.67  | (146)  ~ (all_0_21_21 = 0)
% 42.89/20.67  | (147)  ! [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) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 43.14/20.67  | (148)  ! [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)))
% 43.14/20.67  | (149) ordinal(all_0_22_22) = 0
% 43.14/20.67  | (150) relation(empty_set) = 0
% 43.14/20.67  | (151)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (epsilon_transitive(v2) = v1) |  ~ (epsilon_transitive(v2) = v0))
% 43.14/20.67  | (152)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (ordinal(v0) = v1) |  ? [v2] : (( ~ (v2 = 0) & epsilon_connected(v0) = v2) | ( ~ (v2 = 0) & epsilon_transitive(v0) = v2)))
% 43.14/20.67  | (153)  ! [v0] :  ! [v1] : ( ~ (epsilon_connected(v0) = v1) |  ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 43.14/20.67  | (154)  ! [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)))
% 43.14/20.67  | (155)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 43.14/20.67  | (156) epsilon_transitive(all_0_22_22) = 0
% 43.14/20.67  | (157)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (being_limit_ordinal(v2) = v1) |  ~ (being_limit_ordinal(v2) = v0))
% 43.14/20.67  | (158) epsilon_connected(all_0_7_7) = 0
% 43.14/20.67  | (159)  ! [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))
% 43.14/20.67  | (160)  ! [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)))
% 43.14/20.67  | (161)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 43.14/20.67  | (162)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 43.14/20.67  | (163) function(all_0_4_4) = 0
% 43.14/20.68  | (164)  ! [v0] :  ! [v1] : ( ~ (element(v1, v0) = 0) |  ~ (ordinal(v0) = 0) | (epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0))
% 43.14/20.68  | (165) being_limit_ordinal(all_0_7_7) = 0
% 43.14/20.68  | (166) function(all_0_24_24) = 0
% 43.14/20.68  | (167)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 43.14/20.68  | (168)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 43.14/20.68  | (169)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v3 = v0 & relation_image(v1, v2) = v0) | ( ~ (v4 = 0) & subset(v0, v3) = v4 & relation_rng(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3)))
% 43.14/20.68  | (170)  ? [v0] :  ? [v1] : relation(v0) = v1
% 43.14/20.68  | (171)  ! [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)))
% 43.14/20.68  | (172) element(all_0_11_11, positive_rationals) = 0
% 43.14/20.68  | (173)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_inverse_image(v3, v2) = v1) |  ~ (relation_inverse_image(v3, v2) = v0))
% 43.14/20.68  | (174)  ! [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)))
% 43.14/20.68  | (175)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 43.14/20.68  | (176)  ! [v0] : ( ~ (relation_non_empty(v0) = 0) |  ? [v1] :  ? [v2] : ((v2 = 0 & relation_rng(v0) = v1 & with_non_empty_elements(v1) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 43.14/20.68  | (177) epsilon_transitive(all_0_1_1) = 0
% 43.14/20.68  | (178)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v2) = 0) |  ~ (relation_rng(v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = v0 & relation_inverse_image(v1, v0) = v3 & relation_image(v1, v3) = v0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3)))
% 43.14/20.68  | (179)  ? [v0] :  ? [v1] : with_non_empty_elements(v0) = v1
% 43.14/20.68  | (180) empty(all_0_8_8) = 0
% 43.14/20.68  | (181) element(all_0_19_19, positive_rationals) = 0
% 43.14/20.68  | (182)  ! [v0] : ( ~ (epsilon_transitive(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 43.14/20.69  | (183)  ! [v0] : ( ~ (epsilon_connected(v0) = 0) |  ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 43.14/20.69  | (184)  ? [v0] :  ? [v1] : being_limit_ordinal(v0) = v1
% 43.14/20.69  | (185)  ! [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) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 43.14/20.69  | (186)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (one_to_one(v2) = v1) |  ~ (one_to_one(v2) = v0))
% 43.14/20.69  | (187)  ? [v0] :  ? [v1] : relation_empty_yielding(v0) = v1
% 43.14/20.69  | (188) function_yielding(all_0_4_4) = 0
% 43.14/20.69  | (189) relation_inverse_image(all_0_30_30, all_0_31_31) = all_0_28_28
% 43.14/20.69  | (190) epsilon_connected(all_0_22_22) = 0
% 43.14/20.69  | (191)  ? [v0] :  ? [v1] : empty(v0) = v1
% 43.14/20.69  | (192) relation_non_empty(all_0_26_26) = 0
% 43.14/20.69  | (193)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 43.14/20.69  | (194)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (relation(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 43.14/20.69  | (195)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_empty_yielding(v2) = v1) |  ~ (relation_empty_yielding(v2) = v0))
% 43.14/20.69  | (196) function(all_0_26_26) = 0
% 43.14/20.69  | (197) ordinal_yielding(all_0_14_14) = 0
% 43.14/20.69  | (198)  ~ (all_0_27_27 = 0)
% 43.14/20.69  | (199) transfinite_sequence(all_0_14_14) = 0
% 43.14/20.69  | (200)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ (element(v1, v3) = 0) |  ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 43.14/20.69  | (201)  ! [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))
% 43.14/20.69  | (202) relation_empty_yielding(all_0_23_23) = 0
% 43.14/20.69  | (203) relation(all_0_26_26) = 0
% 43.14/20.69  | (204) empty(all_0_3_3) = all_0_2_2
% 43.14/20.69  | (205) transfinite_sequence(all_0_25_25) = 0
% 43.14/20.69  | (206) relation(all_0_23_23) = 0
% 43.14/20.69  | (207) epsilon_transitive(all_0_7_7) = 0
% 43.14/20.69  | (208) finite(all_0_3_3) = 0
% 43.14/20.69  | (209) relation(all_0_30_30) = 0
% 43.14/20.69  | (210) empty(positive_rationals) = all_0_32_32
% 43.14/20.69  | (211)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 43.14/20.69  | (212)  ! [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)))
% 43.14/20.70  | (213)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 43.14/20.70  | (214)  ? [v0] :  ? [v1] : ordinal_yielding(v0) = v1
% 43.14/20.70  | (215) natural(all_0_19_19) = 0
% 43.14/20.70  | (216) ordinal(all_0_19_19) = 0
% 43.14/20.70  |
% 43.14/20.70  | Instantiating formula (87) with all_0_12_12, all_0_8_8 and discharging atoms empty(all_0_8_8) = 0, empty(all_0_12_12) = 0, yields:
% 43.14/20.70  | (217) all_0_8_8 = all_0_12_12
% 43.14/20.70  |
% 43.14/20.70  | Instantiating formula (87) with all_0_12_12, all_0_9_9 and discharging atoms empty(all_0_9_9) = 0, empty(all_0_12_12) = 0, yields:
% 43.14/20.70  | (218) all_0_9_9 = all_0_12_12
% 43.14/20.70  |
% 43.14/20.70  | Instantiating formula (87) with all_0_13_13, all_0_8_8 and discharging atoms empty(all_0_8_8) = 0, empty(all_0_13_13) = 0, yields:
% 43.14/20.70  | (219) all_0_8_8 = all_0_13_13
% 43.14/20.70  |
% 43.14/20.70  | Instantiating formula (87) with all_0_19_19, all_0_8_8 and discharging atoms empty(all_0_8_8) = 0, empty(all_0_19_19) = 0, yields:
% 43.14/20.70  | (220) all_0_8_8 = all_0_19_19
% 43.14/20.70  |
% 43.14/20.70  | Instantiating formula (87) with empty_set, all_0_9_9 and discharging atoms empty(all_0_9_9) = 0, empty(empty_set) = 0, yields:
% 43.14/20.70  | (221) all_0_9_9 = empty_set
% 43.14/20.70  |
% 43.14/20.70  | Combining equations (217,219) yields a new equation:
% 43.14/20.70  | (222) all_0_12_12 = all_0_13_13
% 43.14/20.70  |
% 43.14/20.70  | Simplifying 222 yields:
% 43.14/20.70  | (223) all_0_12_12 = all_0_13_13
% 43.14/20.70  |
% 43.14/20.71  | Combining equations (220,219) yields a new equation:
% 43.14/20.71  | (224) all_0_13_13 = all_0_19_19
% 43.14/20.71  |
% 43.14/20.71  | Combining equations (218,221) yields a new equation:
% 43.14/20.71  | (225) all_0_12_12 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | Simplifying 225 yields:
% 43.14/20.71  | (226) all_0_12_12 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | Combining equations (223,226) yields a new equation:
% 43.14/20.71  | (227) all_0_13_13 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | Simplifying 227 yields:
% 43.14/20.71  | (228) all_0_13_13 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | Combining equations (224,228) yields a new equation:
% 43.14/20.71  | (229) all_0_19_19 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | Simplifying 229 yields:
% 43.14/20.71  | (230) all_0_19_19 = empty_set
% 43.14/20.71  |
% 43.14/20.71  | From (230) and (128) follows:
% 43.14/20.71  | (126) empty(empty_set) = 0
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (51) with all_0_29_29, all_0_31_31 and discharging atoms subset(all_0_31_31, all_0_29_29) = 0, yields:
% 43.14/20.71  | (232)  ? [v0] : (powerset(all_0_29_29) = v0 & element(all_0_31_31, v0) = 0)
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (178) with all_0_29_29, all_0_30_30, all_0_31_31 and discharging atoms subset(all_0_31_31, all_0_29_29) = 0, relation_rng(all_0_30_30) = all_0_29_29, yields:
% 43.14/20.71  | (233)  ? [v0] :  ? [v1] : ((v1 = all_0_31_31 & relation_inverse_image(all_0_30_30, all_0_31_31) = v0 & relation_image(all_0_30_30, v0) = all_0_31_31) | ( ~ (v0 = 0) & relation(all_0_30_30) = v0) | ( ~ (v0 = 0) & function(all_0_30_30) = v0))
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (174) with all_0_3_3 and discharging atoms finite(all_0_3_3) = 0, yields:
% 43.14/20.71  | (234)  ? [v0] : (powerset(all_0_3_3) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (174) with all_0_28_28 and discharging atoms finite(all_0_28_28) = 0, yields:
% 43.14/20.71  | (235)  ? [v0] : (powerset(all_0_28_28) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (167) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.71  | (236) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & empty(all_0_31_31) = v0)
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (201) with all_0_0_0, all_0_1_1 and discharging atoms empty(all_0_1_1) = all_0_0_0, yields:
% 43.14/20.71  | (237) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_1_1) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.71  |
% 43.14/20.71  | Instantiating formula (131) with all_0_0_0, all_0_1_1 and discharging atoms empty(all_0_1_1) = all_0_0_0, yields:
% 43.14/20.72  | (238) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_1_1) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_2_2, all_0_3_3 and discharging atoms empty(all_0_3_3) = all_0_2_2, yields:
% 43.14/20.72  | (239) all_0_2_2 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_3_3) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_2_2, all_0_3_3 and discharging atoms empty(all_0_3_3) = all_0_2_2, yields:
% 43.14/20.72  | (240) all_0_2_2 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_3_3) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_10_10, all_0_11_11 and discharging atoms empty(all_0_11_11) = all_0_10_10, yields:
% 43.14/20.72  | (241) all_0_10_10 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_11_11) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_10_10, all_0_11_11 and discharging atoms empty(all_0_11_11) = all_0_10_10, yields:
% 43.14/20.72  | (242) all_0_10_10 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_11_11) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_15_15, all_0_16_16 and discharging atoms empty(all_0_16_16) = all_0_15_15, yields:
% 43.14/20.72  | (243) all_0_15_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_16_16) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_15_15, all_0_16_16 and discharging atoms empty(all_0_16_16) = all_0_15_15, yields:
% 43.14/20.72  | (244) all_0_15_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_16_16) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (175) with all_0_15_15, all_0_16_16 and discharging atoms empty(all_0_16_16) = all_0_15_15, yields:
% 43.14/20.72  | (245) all_0_15_15 = 0 |  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(all_0_16_16) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(all_0_16_16) = v0))
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_17_17, all_0_18_18 and discharging atoms empty(all_0_18_18) = all_0_17_17, yields:
% 43.14/20.72  | (246) all_0_17_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_18_18) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_17_17, all_0_18_18 and discharging atoms empty(all_0_18_18) = all_0_17_17, yields:
% 43.14/20.72  | (247) all_0_17_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_18_18) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_21_21, all_0_22_22 and discharging atoms empty(all_0_22_22) = all_0_21_21, yields:
% 43.14/20.72  | (248) all_0_21_21 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_22_22) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_21_21, all_0_22_22 and discharging atoms empty(all_0_22_22) = all_0_21_21, yields:
% 43.14/20.72  | (249) all_0_21_21 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_22_22) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (175) with all_0_21_21, all_0_22_22 and discharging atoms empty(all_0_22_22) = all_0_21_21, yields:
% 43.14/20.72  | (250) all_0_21_21 = 0 |  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(all_0_22_22) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(all_0_22_22) = v0))
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (8) with empty_set and discharging atoms empty(empty_set) = 0, yields:
% 43.14/20.72  | (251) finite(empty_set) = 0
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (201) with all_0_32_32, positive_rationals and discharging atoms empty(positive_rationals) = all_0_32_32, yields:
% 43.14/20.72  | (252) all_0_32_32 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(positive_rationals) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (131) with all_0_32_32, positive_rationals and discharging atoms empty(positive_rationals) = all_0_32_32, yields:
% 43.14/20.72  | (253) all_0_32_32 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(positive_rationals) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (175) with all_0_32_32, positive_rationals and discharging atoms empty(positive_rationals) = all_0_32_32, yields:
% 43.14/20.72  | (254) all_0_32_32 = 0 |  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(positive_rationals) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(positive_rationals) = v0))
% 43.14/20.72  |
% 43.14/20.72  | Instantiating (235) with all_80_0_130 yields:
% 43.14/20.72  | (255) powerset(all_0_28_28) = all_80_0_130 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_80_0_130) = v2)) &  ! [v0] : ( ~ (element(v0, all_80_0_130) = 0) | finite(v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Applying alpha-rule on (255) yields:
% 43.14/20.72  | (256) powerset(all_0_28_28) = all_80_0_130
% 43.14/20.72  | (257)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_80_0_130) = v2))
% 43.14/20.72  | (258)  ! [v0] : ( ~ (element(v0, all_80_0_130) = 0) | finite(v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating formula (257) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.72  | (259) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_80_0_130) = v0)
% 43.14/20.72  |
% 43.14/20.72  | Instantiating (234) with all_83_0_131 yields:
% 43.14/20.72  | (260) powerset(all_0_3_3) = all_83_0_131 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_83_0_131) = v2)) &  ! [v0] : ( ~ (element(v0, all_83_0_131) = 0) | finite(v0) = 0)
% 43.14/20.72  |
% 43.14/20.72  | Applying alpha-rule on (260) yields:
% 43.14/20.72  | (261) powerset(all_0_3_3) = all_83_0_131
% 43.14/20.73  | (262)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_83_0_131) = v2))
% 43.14/20.73  | (263)  ! [v0] : ( ~ (element(v0, all_83_0_131) = 0) | finite(v0) = 0)
% 43.14/20.73  |
% 43.14/20.73  | Instantiating formula (262) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.73  | (264) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_83_0_131) = v0)
% 43.14/20.73  |
% 43.14/20.73  | Instantiating (233) with all_134_0_231, all_134_1_232 yields:
% 43.14/20.73  | (265) (all_134_0_231 = all_0_31_31 & relation_inverse_image(all_0_30_30, all_0_31_31) = all_134_1_232 & relation_image(all_0_30_30, all_134_1_232) = all_0_31_31) | ( ~ (all_134_1_232 = 0) & relation(all_0_30_30) = all_134_1_232) | ( ~ (all_134_1_232 = 0) & function(all_0_30_30) = all_134_1_232)
% 43.14/20.73  |
% 43.14/20.73  | Instantiating (232) with all_256_0_486 yields:
% 43.14/20.73  | (266) powerset(all_0_29_29) = all_256_0_486 & element(all_0_31_31, all_256_0_486) = 0
% 43.14/20.73  |
% 43.14/20.73  | Applying alpha-rule on (266) yields:
% 43.14/20.73  | (267) powerset(all_0_29_29) = all_256_0_486
% 43.14/20.73  | (268) element(all_0_31_31, all_256_0_486) = 0
% 43.14/20.73  |
% 43.14/20.73  +-Applying beta-rule and splitting (254), into two cases.
% 43.14/20.73  |-Branch one:
% 43.14/20.73  | (269) all_0_32_32 = 0
% 43.14/20.73  |
% 43.14/20.73  	| Equations (269) can reduce 143 to:
% 43.14/20.73  	| (270) $false
% 43.14/20.73  	|
% 43.14/20.73  	|-The branch is then unsatisfiable
% 43.14/20.73  |-Branch two:
% 43.14/20.73  | (143)  ~ (all_0_32_32 = 0)
% 43.14/20.73  | (272)  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(positive_rationals) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(positive_rationals) = v0))
% 43.14/20.73  |
% 43.14/20.73  	+-Applying beta-rule and splitting (236), into two cases.
% 43.14/20.73  	|-Branch one:
% 43.14/20.73  	| (273) all_0_27_27 = 0
% 43.14/20.73  	|
% 43.14/20.73  		| Equations (273) can reduce 198 to:
% 43.14/20.73  		| (270) $false
% 43.14/20.73  		|
% 43.14/20.73  		|-The branch is then unsatisfiable
% 43.14/20.73  	|-Branch two:
% 43.14/20.73  	| (198)  ~ (all_0_27_27 = 0)
% 43.14/20.73  	| (276)  ? [v0] : ( ~ (v0 = 0) & empty(all_0_31_31) = v0)
% 43.14/20.73  	|
% 43.14/20.73  		+-Applying beta-rule and splitting (237), into two cases.
% 43.14/20.73  		|-Branch one:
% 43.14/20.73  		| (277) all_0_0_0 = 0
% 43.14/20.73  		|
% 43.14/20.73  			| Equations (277) can reduce 43 to:
% 43.14/20.73  			| (270) $false
% 43.14/20.73  			|
% 43.14/20.73  			|-The branch is then unsatisfiable
% 43.14/20.73  		|-Branch two:
% 43.14/20.73  		| (43)  ~ (all_0_0_0 = 0)
% 43.14/20.73  		| (280)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_1_1) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.73  		|
% 43.14/20.73  			| Instantiating (280) with all_311_0_609, all_311_1_610, all_311_2_611 yields:
% 43.14/20.73  			| (281)  ~ (all_311_0_609 = 0) & powerset(all_0_1_1) = all_311_2_611 & finite(all_311_1_610) = 0 & empty(all_311_1_610) = all_311_0_609 & element(all_311_1_610, all_311_2_611) = 0
% 43.14/20.73  			|
% 43.14/20.73  			| Applying alpha-rule on (281) yields:
% 43.14/20.73  			| (282) powerset(all_0_1_1) = all_311_2_611
% 43.14/20.73  			| (283) element(all_311_1_610, all_311_2_611) = 0
% 43.14/20.73  			| (284) finite(all_311_1_610) = 0
% 43.14/20.73  			| (285)  ~ (all_311_0_609 = 0)
% 43.14/20.73  			| (286) empty(all_311_1_610) = all_311_0_609
% 43.14/20.73  			|
% 43.14/20.73  			+-Applying beta-rule and splitting (238), into two cases.
% 43.14/20.73  			|-Branch one:
% 43.14/20.73  			| (277) all_0_0_0 = 0
% 43.14/20.73  			|
% 43.14/20.73  				| Equations (277) can reduce 43 to:
% 43.14/20.73  				| (270) $false
% 43.14/20.73  				|
% 43.14/20.73  				|-The branch is then unsatisfiable
% 43.14/20.73  			|-Branch two:
% 43.14/20.73  			| (43)  ~ (all_0_0_0 = 0)
% 43.14/20.73  			| (290)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_1_1) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.73  			|
% 43.14/20.73  				| Instantiating (290) with all_316_0_612, all_316_1_613, all_316_2_614 yields:
% 43.14/20.73  				| (291)  ~ (all_316_0_612 = 0) & powerset(all_0_1_1) = all_316_2_614 & empty(all_316_1_613) = all_316_0_612 & element(all_316_1_613, all_316_2_614) = 0
% 43.14/20.73  				|
% 43.14/20.73  				| Applying alpha-rule on (291) yields:
% 43.14/20.73  				| (292)  ~ (all_316_0_612 = 0)
% 43.14/20.73  				| (293) powerset(all_0_1_1) = all_316_2_614
% 43.14/20.73  				| (294) empty(all_316_1_613) = all_316_0_612
% 43.14/20.73  				| (295) element(all_316_1_613, all_316_2_614) = 0
% 43.14/20.73  				|
% 43.14/20.73  				+-Applying beta-rule and splitting (264), into two cases.
% 43.14/20.73  				|-Branch one:
% 43.14/20.73  				| (273) all_0_27_27 = 0
% 43.14/20.73  				|
% 43.14/20.73  					| Equations (273) can reduce 198 to:
% 43.14/20.73  					| (270) $false
% 43.14/20.73  					|
% 43.14/20.73  					|-The branch is then unsatisfiable
% 43.14/20.73  				|-Branch two:
% 43.14/20.73  				| (198)  ~ (all_0_27_27 = 0)
% 43.14/20.73  				| (299)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_83_0_131) = v0)
% 43.14/20.73  				|
% 43.14/20.73  					+-Applying beta-rule and splitting (252), into two cases.
% 43.14/20.73  					|-Branch one:
% 43.14/20.73  					| (269) all_0_32_32 = 0
% 43.14/20.73  					|
% 43.14/20.73  						| Equations (269) can reduce 143 to:
% 43.14/20.73  						| (270) $false
% 43.14/20.73  						|
% 43.14/20.73  						|-The branch is then unsatisfiable
% 43.14/20.73  					|-Branch two:
% 43.14/20.73  					| (143)  ~ (all_0_32_32 = 0)
% 43.14/20.73  					| (303)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(positive_rationals) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.73  					|
% 43.14/20.73  						| Instantiating (303) with all_334_0_666, all_334_1_667, all_334_2_668 yields:
% 43.14/20.73  						| (304)  ~ (all_334_0_666 = 0) & powerset(positive_rationals) = all_334_2_668 & finite(all_334_1_667) = 0 & empty(all_334_1_667) = all_334_0_666 & element(all_334_1_667, all_334_2_668) = 0
% 43.14/20.73  						|
% 43.14/20.73  						| Applying alpha-rule on (304) yields:
% 43.14/20.73  						| (305) element(all_334_1_667, all_334_2_668) = 0
% 43.14/20.73  						| (306) finite(all_334_1_667) = 0
% 43.14/20.73  						| (307) powerset(positive_rationals) = all_334_2_668
% 43.14/20.73  						| (308)  ~ (all_334_0_666 = 0)
% 43.14/20.73  						| (309) empty(all_334_1_667) = all_334_0_666
% 43.14/20.73  						|
% 43.14/20.73  						+-Applying beta-rule and splitting (253), into two cases.
% 43.14/20.73  						|-Branch one:
% 43.14/20.73  						| (269) all_0_32_32 = 0
% 43.14/20.73  						|
% 43.14/20.73  							| Equations (269) can reduce 143 to:
% 43.14/20.73  							| (270) $false
% 43.14/20.73  							|
% 43.14/20.73  							|-The branch is then unsatisfiable
% 43.14/20.73  						|-Branch two:
% 43.14/20.73  						| (143)  ~ (all_0_32_32 = 0)
% 43.14/20.73  						| (313)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(positive_rationals) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.73  						|
% 43.14/20.73  							| Instantiating (313) with all_339_0_669, all_339_1_670, all_339_2_671 yields:
% 43.14/20.73  							| (314)  ~ (all_339_0_669 = 0) & powerset(positive_rationals) = all_339_2_671 & empty(all_339_1_670) = all_339_0_669 & element(all_339_1_670, all_339_2_671) = 0
% 43.14/20.74  							|
% 43.14/20.74  							| Applying alpha-rule on (314) yields:
% 43.14/20.74  							| (315)  ~ (all_339_0_669 = 0)
% 43.14/20.74  							| (316) powerset(positive_rationals) = all_339_2_671
% 43.14/20.74  							| (317) empty(all_339_1_670) = all_339_0_669
% 43.14/20.74  							| (318) element(all_339_1_670, all_339_2_671) = 0
% 43.14/20.74  							|
% 43.14/20.74  							+-Applying beta-rule and splitting (246), into two cases.
% 43.14/20.74  							|-Branch one:
% 43.14/20.74  							| (319) all_0_17_17 = 0
% 43.14/20.74  							|
% 43.14/20.74  								| Equations (319) can reduce 127 to:
% 43.14/20.74  								| (270) $false
% 43.14/20.74  								|
% 43.14/20.74  								|-The branch is then unsatisfiable
% 43.14/20.74  							|-Branch two:
% 43.14/20.74  							| (127)  ~ (all_0_17_17 = 0)
% 43.14/20.74  							| (322)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_18_18) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  							|
% 43.14/20.74  								| Instantiating (322) with all_344_0_672, all_344_1_673, all_344_2_674 yields:
% 43.14/20.74  								| (323)  ~ (all_344_0_672 = 0) & powerset(all_0_18_18) = all_344_2_674 & finite(all_344_1_673) = 0 & empty(all_344_1_673) = all_344_0_672 & element(all_344_1_673, all_344_2_674) = 0
% 43.14/20.74  								|
% 43.14/20.74  								| Applying alpha-rule on (323) yields:
% 43.14/20.74  								| (324) finite(all_344_1_673) = 0
% 43.14/20.74  								| (325)  ~ (all_344_0_672 = 0)
% 43.14/20.74  								| (326) element(all_344_1_673, all_344_2_674) = 0
% 43.14/20.74  								| (327) powerset(all_0_18_18) = all_344_2_674
% 43.14/20.74  								| (328) empty(all_344_1_673) = all_344_0_672
% 43.14/20.74  								|
% 43.14/20.74  								+-Applying beta-rule and splitting (244), into two cases.
% 43.14/20.74  								|-Branch one:
% 43.14/20.74  								| (329) all_0_15_15 = 0
% 43.14/20.74  								|
% 43.14/20.74  									| Equations (329) can reduce 124 to:
% 43.14/20.74  									| (270) $false
% 43.14/20.74  									|
% 43.14/20.74  									|-The branch is then unsatisfiable
% 43.14/20.74  								|-Branch two:
% 43.14/20.74  								| (124)  ~ (all_0_15_15 = 0)
% 43.14/20.74  								| (332)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_16_16) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  								|
% 43.14/20.74  									| Instantiating (332) with all_349_0_675, all_349_1_676, all_349_2_677 yields:
% 43.14/20.74  									| (333)  ~ (all_349_0_675 = 0) & powerset(all_0_16_16) = all_349_2_677 & empty(all_349_1_676) = all_349_0_675 & element(all_349_1_676, all_349_2_677) = 0
% 43.14/20.74  									|
% 43.14/20.74  									| Applying alpha-rule on (333) yields:
% 43.14/20.74  									| (334)  ~ (all_349_0_675 = 0)
% 43.14/20.74  									| (335) powerset(all_0_16_16) = all_349_2_677
% 43.14/20.74  									| (336) empty(all_349_1_676) = all_349_0_675
% 43.14/20.74  									| (337) element(all_349_1_676, all_349_2_677) = 0
% 43.14/20.74  									|
% 43.14/20.74  									+-Applying beta-rule and splitting (245), into two cases.
% 43.14/20.74  									|-Branch one:
% 43.14/20.74  									| (329) all_0_15_15 = 0
% 43.14/20.74  									|
% 43.14/20.74  										| Equations (329) can reduce 124 to:
% 43.14/20.74  										| (270) $false
% 43.14/20.74  										|
% 43.14/20.74  										|-The branch is then unsatisfiable
% 43.14/20.74  									|-Branch two:
% 43.14/20.74  									| (124)  ~ (all_0_15_15 = 0)
% 43.14/20.74  									| (341)  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(all_0_16_16) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(all_0_16_16) = v0))
% 43.14/20.74  									|
% 43.14/20.74  										+-Applying beta-rule and splitting (247), into two cases.
% 43.14/20.74  										|-Branch one:
% 43.14/20.74  										| (319) all_0_17_17 = 0
% 43.14/20.74  										|
% 43.14/20.74  											| Equations (319) can reduce 127 to:
% 43.14/20.74  											| (270) $false
% 43.14/20.74  											|
% 43.14/20.74  											|-The branch is then unsatisfiable
% 43.14/20.74  										|-Branch two:
% 43.14/20.74  										| (127)  ~ (all_0_17_17 = 0)
% 43.14/20.74  										| (345)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_18_18) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  										|
% 43.14/20.74  											| Instantiating (345) with all_358_0_680, all_358_1_681, all_358_2_682 yields:
% 43.14/20.74  											| (346)  ~ (all_358_0_680 = 0) & powerset(all_0_18_18) = all_358_2_682 & empty(all_358_1_681) = all_358_0_680 & element(all_358_1_681, all_358_2_682) = 0
% 43.14/20.74  											|
% 43.14/20.74  											| Applying alpha-rule on (346) yields:
% 43.14/20.74  											| (347)  ~ (all_358_0_680 = 0)
% 43.14/20.74  											| (348) powerset(all_0_18_18) = all_358_2_682
% 43.14/20.74  											| (349) empty(all_358_1_681) = all_358_0_680
% 43.14/20.74  											| (350) element(all_358_1_681, all_358_2_682) = 0
% 43.14/20.74  											|
% 43.14/20.74  											+-Applying beta-rule and splitting (249), into two cases.
% 43.14/20.74  											|-Branch one:
% 43.14/20.74  											| (351) all_0_21_21 = 0
% 43.14/20.74  											|
% 43.14/20.74  												| Equations (351) can reduce 146 to:
% 43.14/20.74  												| (270) $false
% 43.14/20.74  												|
% 43.14/20.74  												|-The branch is then unsatisfiable
% 43.14/20.74  											|-Branch two:
% 43.14/20.74  											| (146)  ~ (all_0_21_21 = 0)
% 43.14/20.74  											| (354)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_22_22) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  											|
% 43.14/20.74  												| Instantiating (354) with all_363_0_683, all_363_1_684, all_363_2_685 yields:
% 43.14/20.74  												| (355)  ~ (all_363_0_683 = 0) & powerset(all_0_22_22) = all_363_2_685 & empty(all_363_1_684) = all_363_0_683 & element(all_363_1_684, all_363_2_685) = 0
% 43.14/20.74  												|
% 43.14/20.74  												| Applying alpha-rule on (355) yields:
% 43.14/20.74  												| (356)  ~ (all_363_0_683 = 0)
% 43.14/20.74  												| (357) powerset(all_0_22_22) = all_363_2_685
% 43.14/20.74  												| (358) empty(all_363_1_684) = all_363_0_683
% 43.14/20.74  												| (359) element(all_363_1_684, all_363_2_685) = 0
% 43.14/20.74  												|
% 43.14/20.74  												+-Applying beta-rule and splitting (250), into two cases.
% 43.14/20.74  												|-Branch one:
% 43.14/20.74  												| (351) all_0_21_21 = 0
% 43.14/20.74  												|
% 43.14/20.74  													| Equations (351) can reduce 146 to:
% 43.14/20.74  													| (270) $false
% 43.14/20.74  													|
% 43.14/20.74  													|-The branch is then unsatisfiable
% 43.14/20.74  												|-Branch two:
% 43.14/20.74  												| (146)  ~ (all_0_21_21 = 0)
% 43.14/20.74  												| (363)  ? [v0] :  ? [v1] : (( ~ (v1 = 0) & relation_rng(all_0_22_22) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & relation(all_0_22_22) = v0))
% 43.14/20.74  												|
% 43.14/20.74  													+-Applying beta-rule and splitting (248), into two cases.
% 43.14/20.74  													|-Branch one:
% 43.14/20.74  													| (351) all_0_21_21 = 0
% 43.14/20.74  													|
% 43.14/20.74  														| Equations (351) can reduce 146 to:
% 43.14/20.74  														| (270) $false
% 43.14/20.74  														|
% 43.14/20.74  														|-The branch is then unsatisfiable
% 43.14/20.74  													|-Branch two:
% 43.14/20.74  													| (146)  ~ (all_0_21_21 = 0)
% 43.14/20.74  													| (367)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_22_22) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  													|
% 43.14/20.74  														| Instantiating (367) with all_384_0_690, all_384_1_691, all_384_2_692 yields:
% 43.14/20.74  														| (368)  ~ (all_384_0_690 = 0) & powerset(all_0_22_22) = all_384_2_692 & finite(all_384_1_691) = 0 & empty(all_384_1_691) = all_384_0_690 & element(all_384_1_691, all_384_2_692) = 0
% 43.14/20.74  														|
% 43.14/20.74  														| Applying alpha-rule on (368) yields:
% 43.14/20.74  														| (369) empty(all_384_1_691) = all_384_0_690
% 43.14/20.74  														| (370) powerset(all_0_22_22) = all_384_2_692
% 43.14/20.74  														| (371) element(all_384_1_691, all_384_2_692) = 0
% 43.14/20.74  														| (372)  ~ (all_384_0_690 = 0)
% 43.14/20.74  														| (373) finite(all_384_1_691) = 0
% 43.14/20.74  														|
% 43.14/20.74  														+-Applying beta-rule and splitting (241), into two cases.
% 43.14/20.74  														|-Branch one:
% 43.14/20.74  														| (374) all_0_10_10 = 0
% 43.14/20.74  														|
% 43.14/20.74  															| Equations (374) can reduce 31 to:
% 43.14/20.74  															| (270) $false
% 43.14/20.74  															|
% 43.14/20.74  															|-The branch is then unsatisfiable
% 43.14/20.74  														|-Branch two:
% 43.14/20.74  														| (31)  ~ (all_0_10_10 = 0)
% 43.14/20.74  														| (377)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_11_11) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  														|
% 43.14/20.74  															| Instantiating (377) with all_393_0_693, all_393_1_694, all_393_2_695 yields:
% 43.14/20.74  															| (378)  ~ (all_393_0_693 = 0) & powerset(all_0_11_11) = all_393_2_695 & finite(all_393_1_694) = 0 & empty(all_393_1_694) = all_393_0_693 & element(all_393_1_694, all_393_2_695) = 0
% 43.14/20.74  															|
% 43.14/20.74  															| Applying alpha-rule on (378) yields:
% 43.14/20.74  															| (379) powerset(all_0_11_11) = all_393_2_695
% 43.14/20.74  															| (380) element(all_393_1_694, all_393_2_695) = 0
% 43.14/20.74  															| (381) empty(all_393_1_694) = all_393_0_693
% 43.14/20.74  															| (382)  ~ (all_393_0_693 = 0)
% 43.14/20.74  															| (383) finite(all_393_1_694) = 0
% 43.14/20.74  															|
% 43.14/20.74  															+-Applying beta-rule and splitting (242), into two cases.
% 43.14/20.74  															|-Branch one:
% 43.14/20.74  															| (374) all_0_10_10 = 0
% 43.14/20.74  															|
% 43.14/20.74  																| Equations (374) can reduce 31 to:
% 43.14/20.74  																| (270) $false
% 43.14/20.74  																|
% 43.14/20.74  																|-The branch is then unsatisfiable
% 43.14/20.74  															|-Branch two:
% 43.14/20.74  															| (31)  ~ (all_0_10_10 = 0)
% 43.14/20.74  															| (387)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_11_11) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.74  															|
% 43.14/20.74  																| Instantiating (387) with all_398_0_696, all_398_1_697, all_398_2_698 yields:
% 43.14/20.74  																| (388)  ~ (all_398_0_696 = 0) & powerset(all_0_11_11) = all_398_2_698 & empty(all_398_1_697) = all_398_0_696 & element(all_398_1_697, all_398_2_698) = 0
% 43.14/20.74  																|
% 43.14/20.74  																| Applying alpha-rule on (388) yields:
% 43.14/20.75  																| (389)  ~ (all_398_0_696 = 0)
% 43.14/20.75  																| (390) powerset(all_0_11_11) = all_398_2_698
% 43.14/20.75  																| (391) empty(all_398_1_697) = all_398_0_696
% 43.14/20.75  																| (392) element(all_398_1_697, all_398_2_698) = 0
% 43.14/20.75  																|
% 43.14/20.75  																+-Applying beta-rule and splitting (240), into two cases.
% 43.14/20.75  																|-Branch one:
% 43.14/20.75  																| (393) all_0_2_2 = 0
% 43.14/20.75  																|
% 43.14/20.75  																	| Equations (393) can reduce 136 to:
% 43.14/20.75  																	| (270) $false
% 43.14/20.75  																	|
% 43.14/20.75  																	|-The branch is then unsatisfiable
% 43.14/20.75  																|-Branch two:
% 43.14/20.75  																| (136)  ~ (all_0_2_2 = 0)
% 43.14/20.75  																| (396)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_3_3) = v0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.75  																|
% 43.14/20.75  																	+-Applying beta-rule and splitting (239), into two cases.
% 43.14/20.75  																	|-Branch one:
% 43.14/20.75  																	| (393) all_0_2_2 = 0
% 43.14/20.75  																	|
% 43.14/20.75  																		| Equations (393) can reduce 136 to:
% 43.14/20.75  																		| (270) $false
% 43.14/20.75  																		|
% 43.14/20.75  																		|-The branch is then unsatisfiable
% 43.14/20.75  																	|-Branch two:
% 43.14/20.75  																	| (136)  ~ (all_0_2_2 = 0)
% 43.14/20.75  																	| (400)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_3_3) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.75  																	|
% 43.14/20.75  																		| Instantiating (400) with all_412_0_704, all_412_1_705, all_412_2_706 yields:
% 43.14/20.75  																		| (401)  ~ (all_412_0_704 = 0) & powerset(all_0_3_3) = all_412_2_706 & finite(all_412_1_705) = 0 & empty(all_412_1_705) = all_412_0_704 & element(all_412_1_705, all_412_2_706) = 0
% 43.14/20.75  																		|
% 43.14/20.75  																		| Applying alpha-rule on (401) yields:
% 43.14/20.75  																		| (402) finite(all_412_1_705) = 0
% 43.14/20.75  																		| (403) powerset(all_0_3_3) = all_412_2_706
% 43.14/20.75  																		| (404) empty(all_412_1_705) = all_412_0_704
% 43.14/20.75  																		| (405) element(all_412_1_705, all_412_2_706) = 0
% 43.14/20.75  																		| (406)  ~ (all_412_0_704 = 0)
% 43.14/20.75  																		|
% 43.14/20.75  																		+-Applying beta-rule and splitting (243), into two cases.
% 43.14/20.75  																		|-Branch one:
% 43.14/20.75  																		| (329) all_0_15_15 = 0
% 43.14/20.75  																		|
% 43.14/20.75  																			| Equations (329) can reduce 124 to:
% 43.14/20.75  																			| (270) $false
% 43.14/20.75  																			|
% 43.14/20.75  																			|-The branch is then unsatisfiable
% 43.14/20.75  																		|-Branch two:
% 43.14/20.75  																		| (124)  ~ (all_0_15_15 = 0)
% 43.14/20.75  																		| (410)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & powerset(all_0_16_16) = v0 & finite(v1) = 0 & empty(v1) = v2 & element(v1, v0) = 0)
% 43.14/20.75  																		|
% 43.14/20.75  																			| Instantiating (410) with all_425_0_711, all_425_1_712, all_425_2_713 yields:
% 43.14/20.75  																			| (411)  ~ (all_425_0_711 = 0) & powerset(all_0_16_16) = all_425_2_713 & finite(all_425_1_712) = 0 & empty(all_425_1_712) = all_425_0_711 & element(all_425_1_712, all_425_2_713) = 0
% 43.14/20.75  																			|
% 43.14/20.75  																			| Applying alpha-rule on (411) yields:
% 43.14/20.75  																			| (412) powerset(all_0_16_16) = all_425_2_713
% 43.14/20.75  																			| (413) empty(all_425_1_712) = all_425_0_711
% 43.14/20.75  																			| (414) finite(all_425_1_712) = 0
% 43.14/20.75  																			| (415) element(all_425_1_712, all_425_2_713) = 0
% 43.14/20.75  																			| (416)  ~ (all_425_0_711 = 0)
% 43.14/20.75  																			|
% 43.14/20.75  																			+-Applying beta-rule and splitting (259), into two cases.
% 43.14/20.75  																			|-Branch one:
% 43.14/20.75  																			| (273) all_0_27_27 = 0
% 43.14/20.75  																			|
% 43.14/20.75  																				| Equations (273) can reduce 198 to:
% 43.14/20.75  																				| (270) $false
% 43.14/20.75  																				|
% 43.14/20.75  																				|-The branch is then unsatisfiable
% 43.14/20.75  																			|-Branch two:
% 43.14/20.75  																			| (198)  ~ (all_0_27_27 = 0)
% 43.14/20.75  																			| (420)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_80_0_130) = v0)
% 43.14/20.75  																			|
% 43.14/20.75  																				+-Applying beta-rule and splitting (265), into two cases.
% 43.14/20.75  																				|-Branch one:
% 43.14/20.75  																				| (421) (all_134_0_231 = all_0_31_31 & relation_inverse_image(all_0_30_30, all_0_31_31) = all_134_1_232 & relation_image(all_0_30_30, all_134_1_232) = all_0_31_31) | ( ~ (all_134_1_232 = 0) & relation(all_0_30_30) = all_134_1_232)
% 43.14/20.75  																				|
% 43.14/20.75  																					+-Applying beta-rule and splitting (421), into two cases.
% 43.14/20.75  																					|-Branch one:
% 43.14/20.75  																					| (422) all_134_0_231 = all_0_31_31 & relation_inverse_image(all_0_30_30, all_0_31_31) = all_134_1_232 & relation_image(all_0_30_30, all_134_1_232) = all_0_31_31
% 43.14/20.75  																					|
% 43.14/20.75  																						| Applying alpha-rule on (422) yields:
% 43.14/20.75  																						| (423) all_134_0_231 = all_0_31_31
% 43.14/20.75  																						| (424) relation_inverse_image(all_0_30_30, all_0_31_31) = all_134_1_232
% 43.14/20.75  																						| (425) relation_image(all_0_30_30, all_134_1_232) = all_0_31_31
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (173) with all_0_30_30, all_0_31_31, all_134_1_232, all_0_28_28 and discharging atoms relation_inverse_image(all_0_30_30, all_0_31_31) = all_134_1_232, relation_inverse_image(all_0_30_30, all_0_31_31) = all_0_28_28, yields:
% 43.14/20.75  																						| (426) all_134_1_232 = all_0_28_28
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with all_0_1_1, all_311_2_611, all_316_2_614 and discharging atoms powerset(all_0_1_1) = all_316_2_614, powerset(all_0_1_1) = all_311_2_611, yields:
% 43.14/20.75  																						| (427) all_316_2_614 = all_311_2_611
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with all_0_11_11, all_393_2_695, all_398_2_698 and discharging atoms powerset(all_0_11_11) = all_398_2_698, powerset(all_0_11_11) = all_393_2_695, yields:
% 43.14/20.75  																						| (428) all_398_2_698 = all_393_2_695
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with all_0_16_16, all_349_2_677, all_425_2_713 and discharging atoms powerset(all_0_16_16) = all_425_2_713, powerset(all_0_16_16) = all_349_2_677, yields:
% 43.14/20.75  																						| (429) all_425_2_713 = all_349_2_677
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with all_0_18_18, all_344_2_674, all_358_2_682 and discharging atoms powerset(all_0_18_18) = all_358_2_682, powerset(all_0_18_18) = all_344_2_674, yields:
% 43.14/20.75  																						| (430) all_358_2_682 = all_344_2_674
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with all_0_22_22, all_363_2_685, all_384_2_692 and discharging atoms powerset(all_0_22_22) = all_384_2_692, powerset(all_0_22_22) = all_363_2_685, yields:
% 43.14/20.75  																						| (431) all_384_2_692 = all_363_2_685
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (168) with positive_rationals, all_334_2_668, all_339_2_671 and discharging atoms powerset(positive_rationals) = all_339_2_671, powerset(positive_rationals) = all_334_2_668, yields:
% 43.14/20.75  																						| (432) all_339_2_671 = all_334_2_668
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (426) and (425) follows:
% 43.14/20.75  																						| (433) relation_image(all_0_30_30, all_0_28_28) = all_0_31_31
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (427) and (293) follows:
% 43.14/20.75  																						| (282) powerset(all_0_1_1) = all_311_2_611
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (428) and (390) follows:
% 43.14/20.75  																						| (379) powerset(all_0_11_11) = all_393_2_695
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (429) and (412) follows:
% 43.14/20.75  																						| (335) powerset(all_0_16_16) = all_349_2_677
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (430) and (348) follows:
% 43.14/20.75  																						| (327) powerset(all_0_18_18) = all_344_2_674
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (431) and (370) follows:
% 43.14/20.75  																						| (357) powerset(all_0_22_22) = all_363_2_685
% 43.14/20.75  																						|
% 43.14/20.75  																						| From (432) and (316) follows:
% 43.14/20.75  																						| (307) powerset(positive_rationals) = all_334_2_668
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (106) with all_0_31_31, all_0_30_30, all_0_28_28 and discharging atoms relation_image(all_0_30_30, all_0_28_28) = all_0_31_31, yields:
% 43.14/20.75  																						| (440)  ? [v0] : ((v0 = 0 & finite(all_0_31_31) = 0) | ( ~ (v0 = 0) & relation(all_0_30_30) = v0) | ( ~ (v0 = 0) & function(all_0_30_30) = v0) | ( ~ (v0 = 0) & finite(all_0_28_28) = v0))
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_311_2_611, all_0_1_1 and discharging atoms powerset(all_0_1_1) = all_311_2_611, finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.75  																						| (441) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_1_1) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_311_2_611) = v0))
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_393_2_695, all_0_11_11 and discharging atoms powerset(all_0_11_11) = all_393_2_695, finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.75  																						| (442) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_11_11) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_393_2_695) = v0))
% 43.14/20.75  																						|
% 43.14/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_349_2_677, all_0_16_16 and discharging atoms powerset(all_0_16_16) = all_349_2_677, finite(all_0_31_31) = all_0_27_27, yields:
% 43.14/20.75  																						| (443) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_16_16) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_349_2_677) = v0))
% 43.53/20.75  																						|
% 43.53/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_344_2_674, all_0_18_18 and discharging atoms powerset(all_0_18_18) = all_344_2_674, finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.75  																						| (444) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_18_18) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_344_2_674) = v0))
% 43.53/20.75  																						|
% 43.53/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_363_2_685, all_0_22_22 and discharging atoms powerset(all_0_22_22) = all_363_2_685, finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.75  																						| (445) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_22_22) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_363_2_685) = v0))
% 43.53/20.75  																						|
% 43.53/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_256_0_486, all_0_29_29 and discharging atoms powerset(all_0_29_29) = all_256_0_486, finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.75  																						| (446) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(all_0_29_29) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_256_0_486) = v0))
% 43.53/20.75  																						|
% 43.53/20.75  																						| Instantiating formula (99) with all_0_27_27, all_0_31_31, all_334_2_668, positive_rationals and discharging atoms powerset(positive_rationals) = all_334_2_668, finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (447) all_0_27_27 = 0 |  ? [v0] : (( ~ (v0 = 0) & finite(positive_rationals) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_334_2_668) = v0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_425_1_712 and discharging atoms finite(all_425_1_712) = 0, yields:
% 43.53/20.76  																						| (448)  ? [v0] : (powerset(all_425_1_712) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_412_1_705 and discharging atoms finite(all_412_1_705) = 0, yields:
% 43.53/20.76  																						| (449)  ? [v0] : (powerset(all_412_1_705) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_393_1_694 and discharging atoms finite(all_393_1_694) = 0, yields:
% 43.53/20.76  																						| (450)  ? [v0] : (powerset(all_393_1_694) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_384_1_691 and discharging atoms finite(all_384_1_691) = 0, yields:
% 43.53/20.76  																						| (451)  ? [v0] : (powerset(all_384_1_691) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_344_1_673 and discharging atoms finite(all_344_1_673) = 0, yields:
% 43.53/20.76  																						| (452)  ? [v0] : (powerset(all_344_1_673) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_334_1_667 and discharging atoms finite(all_334_1_667) = 0, yields:
% 43.53/20.76  																						| (453)  ? [v0] : (powerset(all_334_1_667) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with all_311_1_610 and discharging atoms finite(all_311_1_610) = 0, yields:
% 43.53/20.76  																						| (454)  ? [v0] : (powerset(all_311_1_610) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (174) with empty_set and discharging atoms finite(empty_set) = 0, yields:
% 43.53/20.76  																						| (455)  ? [v0] : (powerset(empty_set) = v0 &  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (finite(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) &  ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (453) with all_470_0_716 yields:
% 43.53/20.76  																						| (456) powerset(all_334_1_667) = all_470_0_716 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_470_0_716) = v2)) &  ! [v0] : ( ~ (element(v0, all_470_0_716) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Applying alpha-rule on (456) yields:
% 43.53/20.76  																						| (457) powerset(all_334_1_667) = all_470_0_716
% 43.53/20.76  																						| (458)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_470_0_716) = v2))
% 43.53/20.76  																						| (459)  ! [v0] : ( ~ (element(v0, all_470_0_716) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (458) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (460) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_470_0_716) = v0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (451) with all_473_0_717 yields:
% 43.53/20.76  																						| (461) powerset(all_384_1_691) = all_473_0_717 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_473_0_717) = v2)) &  ! [v0] : ( ~ (element(v0, all_473_0_717) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Applying alpha-rule on (461) yields:
% 43.53/20.76  																						| (462) powerset(all_384_1_691) = all_473_0_717
% 43.53/20.76  																						| (463)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_473_0_717) = v2))
% 43.53/20.76  																						| (464)  ! [v0] : ( ~ (element(v0, all_473_0_717) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (463) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (465) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_473_0_717) = v0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (450) with all_486_0_727 yields:
% 43.53/20.76  																						| (466) powerset(all_393_1_694) = all_486_0_727 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_486_0_727) = v2)) &  ! [v0] : ( ~ (element(v0, all_486_0_727) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Applying alpha-rule on (466) yields:
% 43.53/20.76  																						| (467) powerset(all_393_1_694) = all_486_0_727
% 43.53/20.76  																						| (468)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_486_0_727) = v2))
% 43.53/20.76  																						| (469)  ! [v0] : ( ~ (element(v0, all_486_0_727) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (468) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (470) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_486_0_727) = v0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (455) with all_494_0_735 yields:
% 43.53/20.76  																						| (471) powerset(empty_set) = all_494_0_735 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_494_0_735) = v2)) &  ! [v0] : ( ~ (element(v0, all_494_0_735) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Applying alpha-rule on (471) yields:
% 43.53/20.76  																						| (472) powerset(empty_set) = all_494_0_735
% 43.53/20.76  																						| (473)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_494_0_735) = v2))
% 43.53/20.76  																						| (474)  ! [v0] : ( ~ (element(v0, all_494_0_735) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (473) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (475) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_494_0_735) = v0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (454) with all_497_0_736 yields:
% 43.53/20.76  																						| (476) powerset(all_311_1_610) = all_497_0_736 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_497_0_736) = v2)) &  ! [v0] : ( ~ (element(v0, all_497_0_736) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Applying alpha-rule on (476) yields:
% 43.53/20.76  																						| (477) powerset(all_311_1_610) = all_497_0_736
% 43.53/20.76  																						| (478)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_497_0_736) = v2))
% 43.53/20.76  																						| (479)  ! [v0] : ( ~ (element(v0, all_497_0_736) = 0) | finite(v0) = 0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating formula (478) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.76  																						| (480) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_497_0_736) = v0)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (440) with all_515_0_757 yields:
% 43.53/20.76  																						| (481) (all_515_0_757 = 0 & finite(all_0_31_31) = 0) | ( ~ (all_515_0_757 = 0) & relation(all_0_30_30) = all_515_0_757) | ( ~ (all_515_0_757 = 0) & function(all_0_30_30) = all_515_0_757) | ( ~ (all_515_0_757 = 0) & finite(all_0_28_28) = all_515_0_757)
% 43.53/20.76  																						|
% 43.53/20.76  																						| Instantiating (452) with all_530_0_771 yields:
% 43.53/20.76  																						| (482) powerset(all_344_1_673) = all_530_0_771 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_530_0_771) = v2)) &  ! [v0] : ( ~ (element(v0, all_530_0_771) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Applying alpha-rule on (482) yields:
% 43.53/20.77  																						| (483) powerset(all_344_1_673) = all_530_0_771
% 43.53/20.77  																						| (484)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_530_0_771) = v2))
% 43.53/20.77  																						| (485)  ! [v0] : ( ~ (element(v0, all_530_0_771) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Instantiating formula (484) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.77  																						| (486) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_530_0_771) = v0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Instantiating (449) with all_564_0_809 yields:
% 43.53/20.77  																						| (487) powerset(all_412_1_705) = all_564_0_809 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_564_0_809) = v2)) &  ! [v0] : ( ~ (element(v0, all_564_0_809) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Applying alpha-rule on (487) yields:
% 43.53/20.77  																						| (488) powerset(all_412_1_705) = all_564_0_809
% 43.53/20.77  																						| (489)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_564_0_809) = v2))
% 43.53/20.77  																						| (490)  ! [v0] : ( ~ (element(v0, all_564_0_809) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Instantiating formula (489) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.77  																						| (491) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_564_0_809) = v0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Instantiating (448) with all_567_0_810 yields:
% 43.53/20.77  																						| (492) powerset(all_425_1_712) = all_567_0_810 &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_567_0_810) = v2)) &  ! [v0] : ( ~ (element(v0, all_567_0_810) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Applying alpha-rule on (492) yields:
% 43.53/20.77  																						| (493) powerset(all_425_1_712) = all_567_0_810
% 43.53/20.77  																						| (494)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (finite(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & element(v0, all_567_0_810) = v2))
% 43.53/20.77  																						| (495)  ! [v0] : ( ~ (element(v0, all_567_0_810) = 0) | finite(v0) = 0)
% 43.53/20.77  																						|
% 43.53/20.77  																						| Instantiating formula (494) with all_0_27_27, all_0_31_31 and discharging atoms finite(all_0_31_31) = all_0_27_27, yields:
% 43.53/20.77  																						| (496) all_0_27_27 = 0 |  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_567_0_810) = v0)
% 43.53/20.77  																						|
% 43.53/20.77  																						+-Applying beta-rule and splitting (481), into two cases.
% 43.53/20.77  																						|-Branch one:
% 43.53/20.77  																						| (497) (all_515_0_757 = 0 & finite(all_0_31_31) = 0) | ( ~ (all_515_0_757 = 0) & relation(all_0_30_30) = all_515_0_757) | ( ~ (all_515_0_757 = 0) & function(all_0_30_30) = all_515_0_757)
% 43.53/20.77  																						|
% 43.53/20.77  																							+-Applying beta-rule and splitting (497), into two cases.
% 43.53/20.77  																							|-Branch one:
% 43.53/20.77  																							| (498) (all_515_0_757 = 0 & finite(all_0_31_31) = 0) | ( ~ (all_515_0_757 = 0) & relation(all_0_30_30) = all_515_0_757)
% 43.53/20.77  																							|
% 43.53/20.77  																								+-Applying beta-rule and splitting (498), into two cases.
% 43.53/20.77  																								|-Branch one:
% 43.53/20.77  																								| (499) all_515_0_757 = 0 & finite(all_0_31_31) = 0
% 43.53/20.77  																								|
% 43.53/20.77  																									| Applying alpha-rule on (499) yields:
% 43.53/20.77  																									| (500) all_515_0_757 = 0
% 43.53/20.77  																									| (501) finite(all_0_31_31) = 0
% 43.53/20.77  																									|
% 43.53/20.77  																									+-Applying beta-rule and splitting (460), into two cases.
% 43.53/20.77  																									|-Branch one:
% 43.53/20.77  																									| (273) all_0_27_27 = 0
% 43.53/20.77  																									|
% 43.53/20.77  																										| Equations (273) can reduce 198 to:
% 43.53/20.77  																										| (270) $false
% 43.53/20.77  																										|
% 43.53/20.77  																										|-The branch is then unsatisfiable
% 43.53/20.77  																									|-Branch two:
% 43.53/20.77  																									| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																									| (505)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_470_0_716) = v0)
% 43.53/20.77  																									|
% 43.53/20.77  																										+-Applying beta-rule and splitting (446), into two cases.
% 43.53/20.77  																										|-Branch one:
% 43.53/20.77  																										| (273) all_0_27_27 = 0
% 43.53/20.77  																										|
% 43.53/20.77  																											| Equations (273) can reduce 198 to:
% 43.53/20.77  																											| (270) $false
% 43.53/20.77  																											|
% 43.53/20.77  																											|-The branch is then unsatisfiable
% 43.53/20.77  																										|-Branch two:
% 43.53/20.77  																										| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																										| (509)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_29_29) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_256_0_486) = v0))
% 43.53/20.77  																										|
% 43.53/20.77  																											+-Applying beta-rule and splitting (465), into two cases.
% 43.53/20.77  																											|-Branch one:
% 43.53/20.77  																											| (273) all_0_27_27 = 0
% 43.53/20.77  																											|
% 43.53/20.77  																												| Equations (273) can reduce 198 to:
% 43.53/20.77  																												| (270) $false
% 43.53/20.77  																												|
% 43.53/20.77  																												|-The branch is then unsatisfiable
% 43.53/20.77  																											|-Branch two:
% 43.53/20.77  																											| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																											| (513)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_473_0_717) = v0)
% 43.53/20.77  																											|
% 43.53/20.77  																												+-Applying beta-rule and splitting (475), into two cases.
% 43.53/20.77  																												|-Branch one:
% 43.53/20.77  																												| (273) all_0_27_27 = 0
% 43.53/20.77  																												|
% 43.53/20.77  																													| Equations (273) can reduce 198 to:
% 43.53/20.77  																													| (270) $false
% 43.53/20.77  																													|
% 43.53/20.77  																													|-The branch is then unsatisfiable
% 43.53/20.77  																												|-Branch two:
% 43.53/20.77  																												| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																												| (517)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_494_0_735) = v0)
% 43.53/20.77  																												|
% 43.53/20.77  																													+-Applying beta-rule and splitting (486), into two cases.
% 43.53/20.77  																													|-Branch one:
% 43.53/20.77  																													| (273) all_0_27_27 = 0
% 43.53/20.77  																													|
% 43.53/20.77  																														| Equations (273) can reduce 198 to:
% 43.53/20.77  																														| (270) $false
% 43.53/20.77  																														|
% 43.53/20.77  																														|-The branch is then unsatisfiable
% 43.53/20.77  																													|-Branch two:
% 43.53/20.77  																													| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																													| (521)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_530_0_771) = v0)
% 43.53/20.77  																													|
% 43.53/20.77  																														+-Applying beta-rule and splitting (447), into two cases.
% 43.53/20.77  																														|-Branch one:
% 43.53/20.77  																														| (273) all_0_27_27 = 0
% 43.53/20.77  																														|
% 43.53/20.77  																															| Equations (273) can reduce 198 to:
% 43.53/20.77  																															| (270) $false
% 43.53/20.77  																															|
% 43.53/20.77  																															|-The branch is then unsatisfiable
% 43.53/20.77  																														|-Branch two:
% 43.53/20.77  																														| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																														| (525)  ? [v0] : (( ~ (v0 = 0) & finite(positive_rationals) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_334_2_668) = v0))
% 43.53/20.77  																														|
% 43.53/20.77  																															+-Applying beta-rule and splitting (444), into two cases.
% 43.53/20.77  																															|-Branch one:
% 43.53/20.77  																															| (273) all_0_27_27 = 0
% 43.53/20.77  																															|
% 43.53/20.77  																																| Equations (273) can reduce 198 to:
% 43.53/20.77  																																| (270) $false
% 43.53/20.77  																																|
% 43.53/20.77  																																|-The branch is then unsatisfiable
% 43.53/20.77  																															|-Branch two:
% 43.53/20.77  																															| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																															| (529)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_18_18) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_344_2_674) = v0))
% 43.53/20.77  																															|
% 43.53/20.77  																																+-Applying beta-rule and splitting (441), into two cases.
% 43.53/20.77  																																|-Branch one:
% 43.53/20.77  																																| (273) all_0_27_27 = 0
% 43.53/20.77  																																|
% 43.53/20.77  																																	| Equations (273) can reduce 198 to:
% 43.53/20.77  																																	| (270) $false
% 43.53/20.77  																																	|
% 43.53/20.77  																																	|-The branch is then unsatisfiable
% 43.53/20.77  																																|-Branch two:
% 43.53/20.77  																																| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																| (533)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_1_1) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_311_2_611) = v0))
% 43.53/20.77  																																|
% 43.53/20.77  																																	+-Applying beta-rule and splitting (491), into two cases.
% 43.53/20.77  																																	|-Branch one:
% 43.53/20.77  																																	| (273) all_0_27_27 = 0
% 43.53/20.77  																																	|
% 43.53/20.77  																																		| Equations (273) can reduce 198 to:
% 43.53/20.77  																																		| (270) $false
% 43.53/20.77  																																		|
% 43.53/20.77  																																		|-The branch is then unsatisfiable
% 43.53/20.77  																																	|-Branch two:
% 43.53/20.77  																																	| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																	| (537)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_564_0_809) = v0)
% 43.53/20.77  																																	|
% 43.53/20.77  																																		+-Applying beta-rule and splitting (496), into two cases.
% 43.53/20.77  																																		|-Branch one:
% 43.53/20.77  																																		| (273) all_0_27_27 = 0
% 43.53/20.77  																																		|
% 43.53/20.77  																																			| Equations (273) can reduce 198 to:
% 43.53/20.77  																																			| (270) $false
% 43.53/20.77  																																			|
% 43.53/20.77  																																			|-The branch is then unsatisfiable
% 43.53/20.77  																																		|-Branch two:
% 43.53/20.77  																																		| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																		| (541)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_567_0_810) = v0)
% 43.53/20.77  																																		|
% 43.53/20.77  																																			+-Applying beta-rule and splitting (443), into two cases.
% 43.53/20.77  																																			|-Branch one:
% 43.53/20.77  																																			| (273) all_0_27_27 = 0
% 43.53/20.77  																																			|
% 43.53/20.77  																																				| Equations (273) can reduce 198 to:
% 43.53/20.77  																																				| (270) $false
% 43.53/20.77  																																				|
% 43.53/20.77  																																				|-The branch is then unsatisfiable
% 43.53/20.77  																																			|-Branch two:
% 43.53/20.77  																																			| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																			| (545)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_16_16) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_349_2_677) = v0))
% 43.53/20.77  																																			|
% 43.53/20.77  																																				+-Applying beta-rule and splitting (442), into two cases.
% 43.53/20.77  																																				|-Branch one:
% 43.53/20.77  																																				| (273) all_0_27_27 = 0
% 43.53/20.77  																																				|
% 43.53/20.77  																																					| Equations (273) can reduce 198 to:
% 43.53/20.77  																																					| (270) $false
% 43.53/20.77  																																					|
% 43.53/20.77  																																					|-The branch is then unsatisfiable
% 43.53/20.77  																																				|-Branch two:
% 43.53/20.77  																																				| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																				| (549)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_11_11) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_393_2_695) = v0))
% 43.53/20.77  																																				|
% 43.53/20.77  																																					+-Applying beta-rule and splitting (470), into two cases.
% 43.53/20.77  																																					|-Branch one:
% 43.53/20.77  																																					| (273) all_0_27_27 = 0
% 43.53/20.77  																																					|
% 43.53/20.77  																																						| Equations (273) can reduce 198 to:
% 43.53/20.77  																																						| (270) $false
% 43.53/20.77  																																						|
% 43.53/20.77  																																						|-The branch is then unsatisfiable
% 43.53/20.77  																																					|-Branch two:
% 43.53/20.77  																																					| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.77  																																					| (553)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_486_0_727) = v0)
% 43.53/20.77  																																					|
% 43.53/20.77  																																						+-Applying beta-rule and splitting (445), into two cases.
% 43.53/20.77  																																						|-Branch one:
% 43.53/20.77  																																						| (273) all_0_27_27 = 0
% 43.53/20.77  																																						|
% 43.53/20.77  																																							| Equations (273) can reduce 198 to:
% 43.53/20.77  																																							| (270) $false
% 43.53/20.77  																																							|
% 43.53/20.77  																																							|-The branch is then unsatisfiable
% 43.53/20.77  																																						|-Branch two:
% 43.53/20.77  																																						| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.78  																																						| (557)  ? [v0] : (( ~ (v0 = 0) & finite(all_0_22_22) = v0) | ( ~ (v0 = 0) & element(all_0_31_31, all_363_2_685) = v0))
% 43.53/20.78  																																						|
% 43.53/20.78  																																							+-Applying beta-rule and splitting (480), into two cases.
% 43.53/20.78  																																							|-Branch one:
% 43.53/20.78  																																							| (273) all_0_27_27 = 0
% 43.53/20.78  																																							|
% 43.53/20.78  																																								| Equations (273) can reduce 198 to:
% 43.53/20.78  																																								| (270) $false
% 43.53/20.78  																																								|
% 43.53/20.78  																																								|-The branch is then unsatisfiable
% 43.53/20.78  																																							|-Branch two:
% 43.53/20.78  																																							| (198)  ~ (all_0_27_27 = 0)
% 43.53/20.78  																																							| (561)  ? [v0] : ( ~ (v0 = 0) & element(all_0_31_31, all_497_0_736) = v0)
% 43.53/20.78  																																							|
% 43.53/20.78  																																								| Instantiating formula (45) with all_0_31_31, 0, all_0_27_27 and discharging atoms finite(all_0_31_31) = all_0_27_27, finite(all_0_31_31) = 0, yields:
% 43.53/20.78  																																								| (273) all_0_27_27 = 0
% 43.53/20.78  																																								|
% 43.53/20.78  																																								| Equations (273) can reduce 198 to:
% 43.53/20.78  																																								| (270) $false
% 43.53/20.78  																																								|
% 43.53/20.78  																																								|-The branch is then unsatisfiable
% 43.53/20.78  																								|-Branch two:
% 43.53/20.78  																								| (564)  ~ (all_515_0_757 = 0) & relation(all_0_30_30) = all_515_0_757
% 43.53/20.78  																								|
% 43.53/20.78  																									| Applying alpha-rule on (564) yields:
% 43.53/20.78  																									| (565)  ~ (all_515_0_757 = 0)
% 43.53/20.78  																									| (566) relation(all_0_30_30) = all_515_0_757
% 43.53/20.78  																									|
% 43.53/20.78  																									| Instantiating formula (193) with all_0_30_30, all_515_0_757, 0 and discharging atoms relation(all_0_30_30) = all_515_0_757, relation(all_0_30_30) = 0, yields:
% 43.53/20.78  																									| (500) all_515_0_757 = 0
% 43.53/20.78  																									|
% 43.53/20.78  																									| Equations (500) can reduce 565 to:
% 43.53/20.78  																									| (270) $false
% 43.53/20.78  																									|
% 43.53/20.78  																									|-The branch is then unsatisfiable
% 43.53/20.78  																							|-Branch two:
% 43.53/20.78  																							| (569)  ~ (all_515_0_757 = 0) & function(all_0_30_30) = all_515_0_757
% 43.53/20.78  																							|
% 43.53/20.78  																								| Applying alpha-rule on (569) yields:
% 43.53/20.78  																								| (565)  ~ (all_515_0_757 = 0)
% 43.53/20.78  																								| (571) function(all_0_30_30) = all_515_0_757
% 43.53/20.78  																								|
% 43.53/20.78  																								| Instantiating formula (64) with all_0_30_30, all_515_0_757, 0 and discharging atoms function(all_0_30_30) = all_515_0_757, function(all_0_30_30) = 0, yields:
% 43.53/20.78  																								| (500) all_515_0_757 = 0
% 43.53/20.78  																								|
% 43.53/20.78  																								| Equations (500) can reduce 565 to:
% 43.53/20.78  																								| (270) $false
% 43.53/20.78  																								|
% 43.53/20.78  																								|-The branch is then unsatisfiable
% 43.53/20.78  																						|-Branch two:
% 43.53/20.78  																						| (574)  ~ (all_515_0_757 = 0) & finite(all_0_28_28) = all_515_0_757
% 43.53/20.78  																						|
% 43.53/20.78  																							| Applying alpha-rule on (574) yields:
% 43.53/20.78  																							| (565)  ~ (all_515_0_757 = 0)
% 43.53/20.78  																							| (576) finite(all_0_28_28) = all_515_0_757
% 43.53/20.78  																							|
% 43.53/20.78  																							| Instantiating formula (45) with all_0_28_28, all_515_0_757, 0 and discharging atoms finite(all_0_28_28) = all_515_0_757, finite(all_0_28_28) = 0, yields:
% 43.53/20.78  																							| (500) all_515_0_757 = 0
% 43.53/20.78  																							|
% 43.53/20.78  																							| Equations (500) can reduce 565 to:
% 43.53/20.78  																							| (270) $false
% 43.53/20.78  																							|
% 43.53/20.78  																							|-The branch is then unsatisfiable
% 43.53/20.78  																					|-Branch two:
% 43.53/20.78  																					| (579)  ~ (all_134_1_232 = 0) & relation(all_0_30_30) = all_134_1_232
% 43.53/20.78  																					|
% 43.53/20.78  																						| Applying alpha-rule on (579) yields:
% 43.53/20.78  																						| (580)  ~ (all_134_1_232 = 0)
% 43.53/20.78  																						| (581) relation(all_0_30_30) = all_134_1_232
% 43.53/20.78  																						|
% 43.53/20.78  																						| Instantiating formula (193) with all_0_30_30, all_134_1_232, 0 and discharging atoms relation(all_0_30_30) = all_134_1_232, relation(all_0_30_30) = 0, yields:
% 43.53/20.78  																						| (582) all_134_1_232 = 0
% 43.53/20.78  																						|
% 43.53/20.78  																						| Equations (582) can reduce 580 to:
% 43.53/20.78  																						| (270) $false
% 43.53/20.78  																						|
% 43.53/20.78  																						|-The branch is then unsatisfiable
% 43.53/20.78  																				|-Branch two:
% 43.53/20.78  																				| (584)  ~ (all_134_1_232 = 0) & function(all_0_30_30) = all_134_1_232
% 43.53/20.78  																				|
% 43.53/20.78  																					| Applying alpha-rule on (584) yields:
% 43.53/20.78  																					| (580)  ~ (all_134_1_232 = 0)
% 43.53/20.78  																					| (586) function(all_0_30_30) = all_134_1_232
% 43.53/20.78  																					|
% 43.53/20.78  																					| Instantiating formula (64) with all_0_30_30, all_134_1_232, 0 and discharging atoms function(all_0_30_30) = all_134_1_232, function(all_0_30_30) = 0, yields:
% 43.53/20.78  																					| (582) all_134_1_232 = 0
% 43.53/20.78  																					|
% 43.53/20.78  																					| Equations (582) can reduce 580 to:
% 43.53/20.78  																					| (270) $false
% 43.53/20.78  																					|
% 43.53/20.78  																					|-The branch is then unsatisfiable
% 43.53/20.78  % SZS output end Proof for theBenchmark
% 43.53/20.78  
% 43.53/20.78  20170ms
%------------------------------------------------------------------------------