%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:48:36 EDT 2022

% Result   : Theorem 5.62s 1.94s
% Output   : Proof 9.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : SEU296+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 20:22:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.58/0.61          ____       _                          
% 0.58/0.61    ___  / __ \_____(_)___  ________  __________
% 0.58/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.61  
% 0.58/0.61  A Theorem Prover for First-Order Logic
% 0.58/0.61  (ePrincess v.1.0)
% 0.58/0.61  
% 0.58/0.61  (c) Philipp Rümmer, 2009-2015
% 0.58/0.61  (c) Peter Backeman, 2014-2015
% 0.58/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.61  Bug reports to peter@backeman.se
% 0.58/0.61  
% 0.58/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.61  
% 0.58/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.93/1.04  Prover 0: Preprocessing ...
% 2.99/1.37  Prover 0: Warning: ignoring some quantifiers
% 3.26/1.41  Prover 0: Constructing countermodel ...
% 5.62/1.94  Prover 0: proved (1277ms)
% 5.62/1.94  
% 5.62/1.94  No countermodel exists, formula is valid
% 5.62/1.94  % SZS status Theorem for theBenchmark
% 5.62/1.94  
% 5.62/1.94  Generating proof ... Warning: ignoring some quantifiers
% 8.67/2.68  found it (size 80)
% 8.67/2.68  
% 8.67/2.68  % SZS output start Proof for theBenchmark
% 8.67/2.68  Assumed formulas after preprocessing and simplification: 
% 8.67/2.68  | (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] : (relation_image(v1, v0) = v2 & ordinal_yielding(v12) & being_limit_ordinal(v18) & function_yielding(v21) & relation_non_empty(v3) & transfinite_sequence(v12) & transfinite_sequence(v4) & relation_empty_yielding(v6) & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & one_to_one(v13) & one_to_one(v8) & one_to_one(empty_set) & natural(v23) & natural(v9) & relation(v21) & relation(v20) & relation(v17) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v3) & relation(v1) & relation(empty_set) & function(v21) & function(v20) & function(v14) & function(v13) & function(v12) & function(v8) & function(v5) & function(v4) & function(v3) & function(v1) & function(empty_set) & finite(v22) & finite(v0) & empty(v17) & empty(v16) & empty(v14) & empty(v13) & empty(v9) & empty(empty_set) & epsilon_connected(v23) & epsilon_connected(v19) & epsilon_connected(v18) & epsilon_connected(v15) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v7) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(v23) & epsilon_transitive(v19) & epsilon_transitive(v18) & epsilon_transitive(v15) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v7) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & element(v15, positive_rationals) & element(v9, positive_rationals) & ordinal(v23) & ordinal(v19) & ordinal(v18) & ordinal(v15) & ordinal(v13) & ordinal(v9) & ordinal(v7) & ordinal(empty_set) & ordinal(omega) &  ~ finite(v2) &  ~ empty(v23) &  ~ empty(v22) &  ~ empty(v15) &  ~ empty(v11) &  ~ empty(v10) &  ~ empty(v7) &  ~ empty(positive_rationals) &  ~ empty(omega) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (relation_image(v25, v27) = v28) |  ~ (relation_dom(v25) = v26) |  ~ (set_intersection2(v26, v24) = v27) |  ~ relation(v25) | relation_image(v25, v24) = v28) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : (v25 = v24 |  ~ (relation_image(v27, v26) = v25) |  ~ (relation_image(v27, v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : (v25 = v24 |  ~ (relation_composition(v27, v26) = v25) |  ~ (relation_composition(v27, v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : (v25 = v24 |  ~ (set_intersection2(v27, v26) = v25) |  ~ (set_intersection2(v27, v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (relation_image(v26, v25) = v27) |  ~ (relation_rng(v24) = v25) |  ~ relation(v26) |  ~ relation(v24) |  ? [v28] : (relation_composition(v24, v26) = v28 & relation_rng(v28) = v27)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (relation_composition(v24, v26) = v27) |  ~ (relation_rng(v24) = v25) |  ~ relation(v26) |  ~ relation(v24) |  ? [v28] : (relation_image(v26, v25) = v28 & relation_rng(v27) = v28)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ empty(v26) |  ~ element(v25, v27) |  ~ in(v24, v25)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ element(v25, v27) |  ~ in(v24, v25) | element(v24, v26)) &  ! [v24] :  ! [v25] :  ! [v26] : (v25 = v24 |  ~ (relation_rng(v26) = v25) |  ~ (relation_rng(v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] : (v25 = v24 |  ~ (relation_dom(v26) = v25) |  ~ (relation_dom(v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] : (v25 = v24 |  ~ (powerset(v26) = v25) |  ~ (powerset(v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_image(v25, v24) = v26) |  ~ relation(v25) |  ? [v27] :  ? [v28] : (relation_image(v25, v28) = v26 & relation_dom(v25) = v27 & set_intersection2(v27, v24) = v28)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v25, v24) = v26) |  ~ function_yielding(v24) |  ~ relation(v25) |  ~ relation(v24) |  ~ function(v25) |  ~ function(v24) | function_yielding(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v25, v24) = v26) |  ~ function_yielding(v24) |  ~ relation(v25) |  ~ relation(v24) |  ~ function(v25) |  ~ function(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v25, v24) = v26) |  ~ function_yielding(v24) |  ~ relation(v25) |  ~ relation(v24) |  ~ function(v25) |  ~ function(v24) | function(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v25, v24) = v26) |  ~ relation(v25) |  ~ empty(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v25, v24) = v26) |  ~ relation(v25) |  ~ empty(v24) | empty(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v24, v25) = v26) |  ~ relation(v25) |  ~ relation(v24) |  ~ function(v25) |  ~ function(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v24, v25) = v26) |  ~ relation(v25) |  ~ relation(v24) |  ~ function(v25) |  ~ function(v24) | function(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v24, v25) = v26) |  ~ relation(v25) |  ~ relation(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v24, v25) = v26) |  ~ relation(v25) |  ~ empty(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_composition(v24, v25) = v26) |  ~ relation(v25) |  ~ empty(v24) | empty(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v25, v24) = v26) | set_intersection2(v24, v25) = v26) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v24, v25) = v26) |  ~ relation(v25) |  ~ relation(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v24, v25) = v26) |  ~ finite(v25) | finite(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v24, v25) = v26) |  ~ finite(v24) | finite(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v24, v25) = v26) | set_intersection2(v25, v24) = v26) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_intersection2(v24, v25) = v26) | subset(v26, v24)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ~ subset(v24, v25) | element(v24, v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ~ element(v24, v26) | subset(v24, v25)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v24) = v25) |  ~ finite(v24) |  ~ element(v26, v25) | finite(v26)) &  ? [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_dom(v25) = v26) |  ~ relation(v25) |  ~ function(v25) |  ~ in(v26, omega) | finite(v24) |  ? [v27] : ( ~ (v27 = v24) & relation_rng(v25) = v27)) &  ! [v24] :  ! [v25] : (v25 = v24 |  ~ (set_intersection2(v24, v24) = v25)) &  ! [v24] :  ! [v25] : (v25 = v24 |  ~ empty(v25) |  ~ empty(v24)) &  ! [v24] :  ! [v25] : (v25 = empty_set |  ~ (set_intersection2(v24, empty_set) = v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v25) = v24) |  ~ relation(v25) |  ~ function(v25) | finite(v24) |  ? [v26] : (relation_dom(v25) = v26 &  ~ in(v26, omega))) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v24) = v25) |  ~ relation_non_empty(v24) |  ~ relation(v24) |  ~ function(v24) | with_non_empty_elements(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v24) = v25) |  ~ relation(v24) |  ~ empty(v25) | empty(v24)) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v24) = v25) |  ~ relation(v24) |  ? [v26] : (relation_dom(v24) = v26 &  ! [v27] :  ! [v28] : ( ~ (relation_composition(v24, v27) = v28) |  ~ relation(v27) |  ? [v29] :  ? [v30] : (relation_dom(v28) = v30 & relation_dom(v27) = v29 & (v30 = v26 |  ~ subset(v25, v29)))) &  ! [v27] :  ! [v28] : ( ~ (relation_dom(v27) = v28) |  ~ subset(v25, v28) |  ~ relation(v27) |  ? [v29] : (relation_composition(v24, v27) = v29 & relation_dom(v29) = v26)))) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v24) = v25) |  ~ empty(v24) | relation(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_rng(v24) = v25) |  ~ empty(v24) | empty(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ transfinite_sequence(v24) |  ~ relation(v24) |  ~ function(v24) | epsilon_connected(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ transfinite_sequence(v24) |  ~ relation(v24) |  ~ function(v24) | epsilon_transitive(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ transfinite_sequence(v24) |  ~ relation(v24) |  ~ function(v24) | ordinal(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ relation(v24) |  ~ empty(v25) | empty(v24)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ relation(v24) |  ? [v26] : (relation_rng(v24) = v26 &  ! [v27] :  ! [v28] : ( ~ (relation_composition(v24, v27) = v28) |  ~ relation(v27) |  ? [v29] :  ? [v30] : (relation_dom(v28) = v30 & relation_dom(v27) = v29 & (v30 = v25 |  ~ subset(v26, v29)))) &  ! [v27] :  ! [v28] : ( ~ (relation_dom(v27) = v28) |  ~ subset(v26, v28) |  ~ relation(v27) |  ? [v29] : (relation_composition(v24, v27) = v29 & relation_dom(v29) = v25)))) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ empty(v24) | relation(v25)) &  ! [v24] :  ! [v25] : ( ~ (relation_dom(v24) = v25) |  ~ empty(v24) | empty(v25)) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ~ empty(v25)) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) | empty(v24) |  ? [v26] : (finite(v26) & element(v26, v25) &  ~ empty(v26))) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) | empty(v24) |  ? [v26] : (element(v26, v25) &  ~ empty(v26))) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ? [v26] : (one_to_one(v26) & natural(v26) & relation(v26) & function(v26) & finite(v26) & empty(v26) & epsilon_connected(v26) & epsilon_transitive(v26) & element(v26, v25) & ordinal(v26))) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ? [v26] : (empty(v26) & element(v26, v25))) &  ! [v24] :  ! [v25] : ( ~ empty(v25) |  ~ in(v24, v25)) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | epsilon_connected(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | epsilon_transitive(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | ordinal(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v24, v25) | empty(v25) | in(v24, v25)) &  ! [v24] :  ! [v25] : ( ~ in(v25, v24) |  ~ in(v24, v25)) &  ! [v24] :  ! [v25] : ( ~ in(v24, v25) | element(v24, v25)) &  ! [v24] : (v24 = empty_set |  ~ empty(v24)) &  ! [v24] : ( ~ relation(v24) |  ~ function(v24) |  ~ empty(v24) | one_to_one(v24)) &  ! [v24] : ( ~ finite(v24) |  ? [v25] :  ? [v26] : (relation_rng(v25) = v24 & relation_dom(v25) = v26 & relation(v25) & function(v25) & in(v26, omega))) &  ! [v24] : ( ~ empty(v24) |  ~ ordinal(v24) | natural(v24)) &  ! [v24] : ( ~ empty(v24) |  ~ ordinal(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ empty(v24) |  ~ ordinal(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ empty(v24) | relation(v24)) &  ! [v24] : ( ~ empty(v24) | function(v24)) &  ! [v24] : ( ~ empty(v24) | finite(v24)) &  ! [v24] : ( ~ empty(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ empty(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ empty(v24) | ordinal(v24)) &  ! [v24] : ( ~ epsilon_connected(v24) |  ~ epsilon_transitive(v24) | ordinal(v24)) &  ! [v24] : ( ~ element(v24, positive_rationals) |  ~ ordinal(v24) | natural(v24)) &  ! [v24] : ( ~ element(v24, positive_rationals) |  ~ ordinal(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ element(v24, positive_rationals) |  ~ ordinal(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ element(v24, omega) | natural(v24)) &  ! [v24] : ( ~ element(v24, omega) | epsilon_connected(v24)) &  ! [v24] : ( ~ element(v24, omega) | epsilon_transitive(v24)) &  ! [v24] : ( ~ element(v24, omega) | ordinal(v24)) &  ! [v24] : ( ~ ordinal(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ ordinal(v24) | epsilon_transitive(v24)) &  ? [v24] :  ? [v25] : element(v25, v24) &  ? [v24] : subset(v24, v24))
% 9.09/2.73  | 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 yields:
% 9.09/2.73  | (1) relation_image(all_0_22_22, all_0_23_23) = all_0_21_21 & ordinal_yielding(all_0_11_11) & being_limit_ordinal(all_0_5_5) & function_yielding(all_0_2_2) & relation_non_empty(all_0_20_20) & transfinite_sequence(all_0_11_11) & transfinite_sequence(all_0_19_19) & relation_empty_yielding(all_0_17_17) & relation_empty_yielding(all_0_18_18) & relation_empty_yielding(empty_set) & one_to_one(all_0_10_10) & one_to_one(all_0_15_15) & one_to_one(empty_set) & natural(all_0_0_0) & natural(all_0_14_14) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_6_6) & relation(all_0_9_9) & relation(all_0_10_10) & relation(all_0_11_11) & relation(all_0_12_12) & relation(all_0_15_15) & relation(all_0_17_17) & relation(all_0_18_18) & relation(all_0_19_19) & relation(all_0_20_20) & relation(all_0_22_22) & relation(empty_set) & function(all_0_2_2) & function(all_0_3_3) & function(all_0_9_9) & function(all_0_10_10) & function(all_0_11_11) & function(all_0_15_15) & function(all_0_18_18) & function(all_0_19_19) & function(all_0_20_20) & function(all_0_22_22) & function(empty_set) & finite(all_0_1_1) & finite(all_0_23_23) & empty(all_0_6_6) & empty(all_0_7_7) & empty(all_0_9_9) & empty(all_0_10_10) & empty(all_0_14_14) & empty(empty_set) & epsilon_connected(all_0_0_0) & epsilon_connected(all_0_4_4) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_8_8) & epsilon_connected(all_0_10_10) & epsilon_connected(all_0_14_14) & epsilon_connected(all_0_16_16) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(all_0_0_0) & epsilon_transitive(all_0_4_4) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_8_8) & epsilon_transitive(all_0_10_10) & epsilon_transitive(all_0_14_14) & epsilon_transitive(all_0_16_16) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & element(all_0_8_8, positive_rationals) & element(all_0_14_14, positive_rationals) & ordinal(all_0_0_0) & ordinal(all_0_4_4) & ordinal(all_0_5_5) & ordinal(all_0_8_8) & ordinal(all_0_10_10) & ordinal(all_0_14_14) & ordinal(all_0_16_16) & ordinal(empty_set) & ordinal(omega) &  ~ finite(all_0_21_21) &  ~ empty(all_0_0_0) &  ~ empty(all_0_1_1) &  ~ empty(all_0_8_8) &  ~ empty(all_0_12_12) &  ~ empty(all_0_13_13) &  ~ empty(all_0_16_16) &  ~ empty(positive_rationals) &  ~ empty(omega) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_image(v1, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v2, v0) = v3) |  ~ relation(v1) | relation_image(v1, v0) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_image(v2, v1) = v3) |  ~ (relation_rng(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_composition(v0, v2) = v3) |  ~ (relation_rng(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ? [v4] : (relation_image(v2, v1) = v4 & relation_rng(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_image(v1, v4) = v2 & relation_dom(v1) = v3 & set_intersection2(v3, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function_yielding(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ finite(v1) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ relation(v1) |  ~ function(v1) |  ~ in(v2, omega) | finite(v0) |  ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v1) = v0) |  ~ relation(v1) |  ~ function(v1) | finite(v0) |  ? [v2] : (relation_dom(v1) = v2 &  ~ in(v2, omega))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation_non_empty(v0) |  ~ relation(v0) |  ~ function(v0) | with_non_empty_elements(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_composition(v0, v3) = v4) |  ~ relation(v3) |  ? [v5] :  ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 |  ~ subset(v1, v5)))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v1, v4) |  ~ relation(v3) |  ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_connected(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_transitive(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | ordinal(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_composition(v0, v3) = v4) |  ~ relation(v3) |  ? [v5] :  ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 |  ~ subset(v2, v5)))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v2, v4) |  ~ relation(v3) |  ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1))) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) &  ! [v0] : (v0 = empty_set |  ~ empty(v0)) &  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ finite(v0) |  ? [v1] :  ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega))) &  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | natural(v0)) &  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | finite(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | ordinal(v0)) &  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0)) &  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0)) &  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ element(v0, omega) | natural(v0)) &  ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0)) &  ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0)) &  ! [v0] : ( ~ element(v0, omega) | ordinal(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 9.09/2.74  |
% 9.09/2.75  | Applying alpha-rule on (1) yields:
% 9.09/2.75  | (2)  ~ empty(omega)
% 9.09/2.75  | (3) ordinal(all_0_8_8)
% 9.09/2.75  | (4) ordinal(all_0_0_0)
% 9.09/2.75  | (5)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 9.09/2.75  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_composition(v0, v2) = v3) |  ~ (relation_rng(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ? [v4] : (relation_image(v2, v1) = v4 & relation_rng(v3) = v4))
% 9.09/2.75  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 9.09/2.75  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 9.09/2.75  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 9.09/2.75  | (10)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2)))
% 9.09/2.75  | (11)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 9.09/2.75  | (12) empty(empty_set)
% 9.09/2.75  | (13) relation(empty_set)
% 9.09/2.75  | (14) one_to_one(empty_set)
% 9.09/2.75  | (15) epsilon_connected(all_0_10_10)
% 9.09/2.75  | (16) finite(all_0_1_1)
% 9.09/2.75  | (17)  ~ empty(all_0_16_16)
% 9.09/2.75  | (18)  ! [v0] : ( ~ element(v0, omega) | natural(v0))
% 9.09/2.75  | (19)  ? [v0] : subset(v0, v0)
% 9.09/2.75  | (20)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_composition(v0, v3) = v4) |  ~ relation(v3) |  ? [v5] :  ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 |  ~ subset(v1, v5)))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v1, v4) |  ~ relation(v3) |  ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2))))
% 9.09/2.75  | (21)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0))
% 9.09/2.75  | (22)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 9.09/2.75  | (23) function(all_0_11_11)
% 9.09/2.75  | (24) relation(all_0_15_15)
% 9.09/2.75  | (25)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 9.09/2.75  | (26)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_connected(v1))
% 9.09/2.75  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function_yielding(v2))
% 9.09/2.75  | (28) epsilon_connected(all_0_16_16)
% 9.09/2.75  | (29) being_limit_ordinal(all_0_5_5)
% 9.09/2.75  | (30) epsilon_connected(omega)
% 9.09/2.75  | (31)  ~ empty(all_0_13_13)
% 9.09/2.75  | (32) relation(all_0_11_11)
% 9.09/2.75  | (33) relation(all_0_17_17)
% 9.09/2.75  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 9.09/2.75  | (35)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 9.09/2.75  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_image(v1, v4) = v2 & relation_dom(v1) = v3 & set_intersection2(v3, v0) = v4))
% 9.09/2.75  | (37) epsilon_transitive(all_0_10_10)
% 9.09/2.75  | (38) function(all_0_20_20)
% 9.09/2.75  | (39)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 9.09/2.75  | (40) epsilon_transitive(omega)
% 9.09/2.75  | (41) epsilon_transitive(all_0_14_14)
% 9.09/2.75  | (42)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1))
% 9.09/2.75  | (43)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v1) = v0) |  ~ relation(v1) |  ~ function(v1) | finite(v0) |  ? [v2] : (relation_dom(v1) = v2 &  ~ in(v2, omega)))
% 9.09/2.76  | (44)  ~ empty(all_0_8_8)
% 9.09/2.76  | (45)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 9.09/2.76  | (46) epsilon_transitive(all_0_0_0)
% 9.09/2.76  | (47) relation_empty_yielding(all_0_17_17)
% 9.09/2.76  | (48) relation(all_0_2_2)
% 9.09/2.76  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 9.09/2.76  | (50) finite(all_0_23_23)
% 9.09/2.76  | (51) epsilon_connected(all_0_4_4)
% 9.09/2.76  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2))
% 9.09/2.76  | (53) function(all_0_2_2)
% 9.09/2.76  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_image(v1, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v2, v0) = v3) |  ~ relation(v1) | relation_image(v1, v0) = v4)
% 9.09/2.76  | (55)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 9.09/2.76  | (56) transfinite_sequence(all_0_19_19)
% 9.09/2.76  | (57) relation(all_0_19_19)
% 9.09/2.76  | (58)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 9.09/2.76  | (59) epsilon_transitive(all_0_5_5)
% 9.09/2.76  | (60) ordinal_yielding(all_0_11_11)
% 9.09/2.76  | (61) epsilon_transitive(empty_set)
% 9.09/2.76  | (62) empty(all_0_14_14)
% 9.09/2.76  | (63) epsilon_connected(all_0_8_8)
% 9.09/2.76  | (64)  ! [v0] : ( ~ finite(v0) |  ? [v1] :  ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega)))
% 9.09/2.76  | (65)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | natural(v0))
% 9.09/2.76  | (66)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 9.09/2.76  | (67)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_connected(v0))
% 9.09/2.76  | (68) transfinite_sequence(all_0_11_11)
% 9.09/2.76  | (69) relation(all_0_6_6)
% 9.09/2.76  | (70) function(all_0_9_9)
% 9.09/2.76  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0))
% 9.09/2.76  | (72) function(all_0_19_19)
% 9.09/2.76  | (73) ordinal(all_0_16_16)
% 9.09/2.76  | (74)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 9.09/2.76  | (75)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 9.09/2.76  | (76)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 9.09/2.76  | (77)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 9.09/2.76  | (78)  ~ empty(all_0_12_12)
% 9.09/2.76  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ finite(v0) | finite(v2))
% 9.09/2.76  | (80)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 9.09/2.76  | (81)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 9.09/2.76  | (82)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 9.09/2.76  | (83) relation(all_0_12_12)
% 9.09/2.76  | (84)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1)))
% 9.09/2.76  | (85) relation_empty_yielding(all_0_18_18)
% 9.09/2.76  | (86)  ! [v0] : ( ~ element(v0, omega) | ordinal(v0))
% 9.09/2.76  | (87) epsilon_transitive(all_0_4_4)
% 9.09/2.76  | (88) function(all_0_15_15)
% 9.09/2.76  | (89)  ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0))
% 9.09/2.76  | (90)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 9.09/2.76  | (91) one_to_one(all_0_10_10)
% 9.09/2.76  | (92)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1))
% 9.09/2.76  | (93) function(all_0_10_10)
% 9.09/2.76  | (94) ordinal(omega)
% 9.09/2.76  | (95) relation(all_0_3_3)
% 9.09/2.76  | (96)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 9.09/2.77  | (97) epsilon_transitive(all_0_8_8)
% 9.09/2.77  | (98)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0))
% 9.09/2.77  | (99) relation(all_0_9_9)
% 9.09/2.77  | (100) empty(all_0_10_10)
% 9.09/2.77  | (101)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 9.09/2.77  | (102)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 9.09/2.77  | (103) relation_image(all_0_22_22, all_0_23_23) = all_0_21_21
% 9.09/2.77  | (104)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_transitive(v1))
% 9.09/2.77  | (105)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2))
% 9.09/2.77  | (106)  ! [v0] : ( ~ empty(v0) | function(v0))
% 9.09/2.77  | (107)  ~ finite(all_0_21_21)
% 9.09/2.77  | (108) epsilon_connected(all_0_14_14)
% 9.09/2.77  | (109) ordinal(all_0_4_4)
% 9.09/2.77  | (110)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 9.09/2.77  | (111)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 9.09/2.77  | (112) function(all_0_18_18)
% 9.09/2.77  | (113)  ~ empty(all_0_0_0)
% 9.09/2.77  | (114)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 9.09/2.77  | (115)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 9.09/2.77  | (116)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 9.09/2.77  | (117)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 9.09/2.77  | (118)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 9.09/2.77  | (119)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 9.09/2.77  | (120)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1))
% 9.09/2.77  | (121) epsilon_connected(all_0_0_0)
% 9.09/2.77  | (122) function(all_0_22_22)
% 9.09/2.77  | (123) element(all_0_8_8, positive_rationals)
% 9.09/2.77  | (124) natural(all_0_14_14)
% 9.09/2.77  | (125) empty(all_0_7_7)
% 9.09/2.77  | (126)  ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0))
% 9.09/2.77  | (127) function(all_0_3_3)
% 9.09/2.77  | (128)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) = v0))
% 9.09/2.77  | (129) empty(all_0_9_9)
% 9.09/2.77  | (130)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation_non_empty(v0) |  ~ relation(v0) |  ~ function(v0) | with_non_empty_elements(v1))
% 9.09/2.77  | (131) function(empty_set)
% 9.09/2.77  | (132) function_yielding(all_0_2_2)
% 9.09/2.77  | (133)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 9.09/2.77  | (134) relation(all_0_22_22)
% 9.09/2.77  | (135)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 9.09/2.77  | (136)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 9.09/2.77  | (137) relation_empty_yielding(empty_set)
% 9.09/2.77  | (138) natural(all_0_0_0)
% 9.09/2.77  | (139) ordinal(all_0_14_14)
% 9.09/2.77  | (140)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 9.09/2.77  | (141) relation(all_0_20_20)
% 9.09/2.77  | (142)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_composition(v0, v3) = v4) |  ~ relation(v3) |  ? [v5] :  ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 |  ~ subset(v2, v5)))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v2, v4) |  ~ relation(v3) |  ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1))))
% 9.09/2.78  | (143)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 9.09/2.78  | (144)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 9.09/2.78  | (145) ordinal(all_0_5_5)
% 9.09/2.78  | (146) element(all_0_14_14, positive_rationals)
% 9.09/2.78  | (147)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1))
% 9.09/2.78  | (148)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 9.09/2.78  | (149)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2))
% 9.09/2.78  | (150)  ~ empty(all_0_1_1)
% 9.09/2.78  | (151) ordinal(all_0_10_10)
% 9.09/2.78  | (152)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 9.09/2.78  | (153) relation(all_0_18_18)
% 9.09/2.78  | (154) relation_non_empty(all_0_20_20)
% 9.09/2.78  | (155)  ? [v0] :  ? [v1] : element(v1, v0)
% 9.09/2.78  | (156)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ relation(v1) |  ~ function(v1) |  ~ in(v2, omega) | finite(v0) |  ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3))
% 9.09/2.78  | (157) epsilon_connected(all_0_5_5)
% 9.09/2.78  | (158) epsilon_connected(empty_set)
% 9.09/2.78  | (159) ordinal(empty_set)
% 9.09/2.78  | (160)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ function_yielding(v0) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2))
% 9.09/2.78  | (161)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 9.09/2.78  | (162)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 9.09/2.78  | (163) empty(all_0_6_6)
% 9.09/2.78  | (164)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ finite(v1) | finite(v2))
% 9.09/2.78  | (165) epsilon_transitive(all_0_16_16)
% 9.09/2.78  | (166) one_to_one(all_0_15_15)
% 9.09/2.78  | (167)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_image(v2, v1) = v3) |  ~ (relation_rng(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3))
% 9.09/2.78  | (168)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | ordinal(v1))
% 9.09/2.78  | (169) relation(all_0_10_10)
% 9.09/2.78  | (170)  ~ empty(positive_rationals)
% 9.09/2.78  | (171)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 9.09/2.78  |
% 9.09/2.78  | Instantiating formula (36) with all_0_21_21, all_0_22_22, all_0_23_23 and discharging atoms relation_image(all_0_22_22, all_0_23_23) = all_0_21_21, relation(all_0_22_22), yields:
% 9.09/2.78  | (172)  ? [v0] :  ? [v1] : (relation_image(all_0_22_22, v1) = all_0_21_21 & relation_dom(all_0_22_22) = v0 & set_intersection2(v0, all_0_23_23) = v1)
% 9.09/2.78  |
% 9.09/2.78  | Instantiating formula (64) with all_0_23_23 and discharging atoms finite(all_0_23_23), yields:
% 9.09/2.78  | (173)  ? [v0] :  ? [v1] : (relation_rng(v0) = all_0_23_23 & relation_dom(v0) = v1 & relation(v0) & function(v0) & in(v1, omega))
% 9.09/2.78  |
% 9.09/2.78  | Instantiating (172) with all_21_0_30, all_21_1_31 yields:
% 9.09/2.78  | (174) relation_image(all_0_22_22, all_21_0_30) = all_0_21_21 & relation_dom(all_0_22_22) = all_21_1_31 & set_intersection2(all_21_1_31, all_0_23_23) = all_21_0_30
% 9.09/2.78  |
% 9.09/2.78  | Applying alpha-rule on (174) yields:
% 9.09/2.78  | (175) relation_image(all_0_22_22, all_21_0_30) = all_0_21_21
% 9.09/2.78  | (176) relation_dom(all_0_22_22) = all_21_1_31
% 9.09/2.79  | (177) set_intersection2(all_21_1_31, all_0_23_23) = all_21_0_30
% 9.09/2.79  |
% 9.09/2.79  | Instantiating (173) with all_23_0_32, all_23_1_33 yields:
% 9.09/2.79  | (178) relation_rng(all_23_1_33) = all_0_23_23 & relation_dom(all_23_1_33) = all_23_0_32 & relation(all_23_1_33) & function(all_23_1_33) & in(all_23_0_32, omega)
% 9.09/2.79  |
% 9.09/2.79  | Applying alpha-rule on (178) yields:
% 9.09/2.79  | (179) function(all_23_1_33)
% 9.09/2.79  | (180) relation_rng(all_23_1_33) = all_0_23_23
% 9.09/2.79  | (181) relation(all_23_1_33)
% 9.09/2.79  | (182) relation_dom(all_23_1_33) = all_23_0_32
% 9.09/2.79  | (183) in(all_23_0_32, omega)
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (36) with all_0_21_21, all_0_22_22, all_21_0_30 and discharging atoms relation_image(all_0_22_22, all_21_0_30) = all_0_21_21, relation(all_0_22_22), yields:
% 9.09/2.79  | (184)  ? [v0] :  ? [v1] : (relation_image(all_0_22_22, v1) = all_0_21_21 & relation_dom(all_0_22_22) = v0 & set_intersection2(v0, all_21_0_30) = v1)
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (142) with all_21_1_31, all_0_22_22 and discharging atoms relation_dom(all_0_22_22) = all_21_1_31, relation(all_0_22_22), yields:
% 9.09/2.79  | (185)  ? [v0] : (relation_rng(all_0_22_22) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_0_22_22, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_21_1_31 |  ~ subset(v0, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(v0, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_0_22_22, v1) = v3 & relation_dom(v3) = all_21_1_31)))
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (164) with all_21_0_30, all_0_23_23, all_21_1_31 and discharging atoms set_intersection2(all_21_1_31, all_0_23_23) = all_21_0_30, finite(all_0_23_23), yields:
% 9.09/2.79  | (186) finite(all_21_0_30)
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (115) with all_21_0_30, all_0_23_23, all_21_1_31 and discharging atoms set_intersection2(all_21_1_31, all_0_23_23) = all_21_0_30, yields:
% 9.09/2.79  | (187) subset(all_21_0_30, all_21_1_31)
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (167) with all_0_21_21, all_0_22_22, all_0_23_23, all_23_1_33 and discharging atoms relation_image(all_0_22_22, all_0_23_23) = all_0_21_21, relation_rng(all_23_1_33) = all_0_23_23, relation(all_23_1_33), relation(all_0_22_22), yields:
% 9.09/2.79  | (188)  ? [v0] : (relation_composition(all_23_1_33, all_0_22_22) = v0 & relation_rng(v0) = all_0_21_21)
% 9.09/2.79  |
% 9.09/2.79  | Instantiating formula (20) with all_0_23_23, all_23_1_33 and discharging atoms relation_rng(all_23_1_33) = all_0_23_23, relation(all_23_1_33), yields:
% 9.09/2.79  | (189)  ? [v0] : (relation_dom(all_23_1_33) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_23_1_33, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 |  ~ subset(all_0_23_23, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_0_23_23, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_23_1_33, v1) = v3 & relation_dom(v3) = v0)))
% 9.53/2.79  |
% 9.53/2.79  | Instantiating formula (142) with all_23_0_32, all_23_1_33 and discharging atoms relation_dom(all_23_1_33) = all_23_0_32, relation(all_23_1_33), yields:
% 9.53/2.79  | (190)  ? [v0] : (relation_rng(all_23_1_33) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_23_1_33, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_23_0_32 |  ~ subset(v0, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(v0, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_23_1_33, v1) = v3 & relation_dom(v3) = all_23_0_32)))
% 9.53/2.79  |
% 9.53/2.79  | Instantiating (185) with all_36_0_37 yields:
% 9.53/2.79  | (191) relation_rng(all_0_22_22) = all_36_0_37 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_0_22_22, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_21_1_31 |  ~ subset(all_36_0_37, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_36_0_37, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_0_22_22, v0) = v2 & relation_dom(v2) = all_21_1_31))
% 9.53/2.79  |
% 9.53/2.79  | Applying alpha-rule on (191) yields:
% 9.53/2.79  | (192) relation_rng(all_0_22_22) = all_36_0_37
% 9.53/2.79  | (193)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_0_22_22, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_21_1_31 |  ~ subset(all_36_0_37, v2))))
% 9.53/2.79  | (194)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_36_0_37, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_0_22_22, v0) = v2 & relation_dom(v2) = all_21_1_31))
% 9.53/2.79  |
% 9.53/2.79  | Instantiating (189) with all_42_0_39 yields:
% 9.53/2.79  | (195) relation_dom(all_23_1_33) = all_42_0_39 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_23_1_33, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_42_0_39 |  ~ subset(all_0_23_23, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_23_23, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_23_1_33, v0) = v2 & relation_dom(v2) = all_42_0_39))
% 9.53/2.79  |
% 9.53/2.80  | Applying alpha-rule on (195) yields:
% 9.53/2.80  | (196) relation_dom(all_23_1_33) = all_42_0_39
% 9.53/2.80  | (197)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_23_1_33, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_42_0_39 |  ~ subset(all_0_23_23, v2))))
% 9.53/2.80  | (198)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_23_23, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_23_1_33, v0) = v2 & relation_dom(v2) = all_42_0_39))
% 9.53/2.80  |
% 9.53/2.80  | Instantiating (188) with all_45_0_40 yields:
% 9.53/2.80  | (199) relation_composition(all_23_1_33, all_0_22_22) = all_45_0_40 & relation_rng(all_45_0_40) = all_0_21_21
% 9.53/2.80  |
% 9.53/2.80  | Applying alpha-rule on (199) yields:
% 9.53/2.80  | (200) relation_composition(all_23_1_33, all_0_22_22) = all_45_0_40
% 9.53/2.80  | (201) relation_rng(all_45_0_40) = all_0_21_21
% 9.53/2.80  |
% 9.53/2.80  | Instantiating (190) with all_47_0_41 yields:
% 9.53/2.80  | (202) relation_rng(all_23_1_33) = all_47_0_41 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_23_1_33, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_23_0_32 |  ~ subset(all_47_0_41, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_47_0_41, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_23_1_33, v0) = v2 & relation_dom(v2) = all_23_0_32))
% 9.53/2.80  |
% 9.53/2.80  | Applying alpha-rule on (202) yields:
% 9.53/2.80  | (203) relation_rng(all_23_1_33) = all_47_0_41
% 9.53/2.80  | (204)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_23_1_33, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_23_0_32 |  ~ subset(all_47_0_41, v2))))
% 9.53/2.80  | (205)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_47_0_41, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_23_1_33, v0) = v2 & relation_dom(v2) = all_23_0_32))
% 9.53/2.80  |
% 9.53/2.80  | Instantiating (184) with all_50_0_42, all_50_1_43 yields:
% 9.53/2.80  | (206) relation_image(all_0_22_22, all_50_0_42) = all_0_21_21 & relation_dom(all_0_22_22) = all_50_1_43 & set_intersection2(all_50_1_43, all_21_0_30) = all_50_0_42
% 9.53/2.80  |
% 9.53/2.80  | Applying alpha-rule on (206) yields:
% 9.53/2.80  | (207) relation_image(all_0_22_22, all_50_0_42) = all_0_21_21
% 9.53/2.80  | (208) relation_dom(all_0_22_22) = all_50_1_43
% 9.53/2.80  | (209) set_intersection2(all_50_1_43, all_21_0_30) = all_50_0_42
% 9.53/2.80  |
% 9.53/2.80  | Instantiating formula (116) with all_0_22_22, all_50_1_43, all_21_1_31 and discharging atoms relation_dom(all_0_22_22) = all_50_1_43, relation_dom(all_0_22_22) = all_21_1_31, yields:
% 9.53/2.80  | (210) all_50_1_43 = all_21_1_31
% 9.53/2.80  |
% 9.53/2.80  | From (210) and (208) follows:
% 9.53/2.80  | (176) relation_dom(all_0_22_22) = all_21_1_31
% 9.53/2.80  |
% 9.53/2.80  | Instantiating formula (36) with all_0_21_21, all_0_22_22, all_50_0_42 and discharging atoms relation_image(all_0_22_22, all_50_0_42) = all_0_21_21, relation(all_0_22_22), yields:
% 9.53/2.80  | (212)  ? [v0] :  ? [v1] : (relation_image(all_0_22_22, v1) = all_0_21_21 & relation_dom(all_0_22_22) = v0 & set_intersection2(v0, all_50_0_42) = v1)
% 9.53/2.80  |
% 9.53/2.80  | Instantiating formula (197) with all_45_0_40, all_0_22_22 and discharging atoms relation_composition(all_23_1_33, all_0_22_22) = all_45_0_40, relation(all_0_22_22), yields:
% 9.53/2.80  | (213)  ? [v0] :  ? [v1] : (relation_dom(all_45_0_40) = v1 & relation_dom(all_0_22_22) = v0 & (v1 = all_42_0_39 |  ~ subset(all_0_23_23, v0)))
% 9.53/2.80  |
% 9.53/2.80  | Instantiating formula (204) with all_45_0_40, all_0_22_22 and discharging atoms relation_composition(all_23_1_33, all_0_22_22) = all_45_0_40, relation(all_0_22_22), yields:
% 9.53/2.81  | (214)  ? [v0] :  ? [v1] : (relation_dom(all_45_0_40) = v1 & relation_dom(all_0_22_22) = v0 & (v1 = all_23_0_32 |  ~ subset(all_47_0_41, v0)))
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (20) with all_36_0_37, all_0_22_22 and discharging atoms relation_rng(all_0_22_22) = all_36_0_37, relation(all_0_22_22), yields:
% 9.53/2.81  | (215)  ? [v0] : (relation_dom(all_0_22_22) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_0_22_22, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 |  ~ subset(all_36_0_37, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_36_0_37, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_0_22_22, v1) = v3 & relation_dom(v3) = v0)))
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (64) with all_21_0_30 and discharging atoms finite(all_21_0_30), yields:
% 9.53/2.81  | (216)  ? [v0] :  ? [v1] : (relation_rng(v0) = all_21_0_30 & relation_dom(v0) = v1 & relation(v0) & function(v0) & in(v1, omega))
% 9.53/2.81  |
% 9.53/2.81  | Instantiating (212) with all_65_0_45, all_65_1_46 yields:
% 9.53/2.81  | (217) relation_image(all_0_22_22, all_65_0_45) = all_0_21_21 & relation_dom(all_0_22_22) = all_65_1_46 & set_intersection2(all_65_1_46, all_50_0_42) = all_65_0_45
% 9.53/2.81  |
% 9.53/2.81  | Applying alpha-rule on (217) yields:
% 9.53/2.81  | (218) relation_image(all_0_22_22, all_65_0_45) = all_0_21_21
% 9.53/2.81  | (219) relation_dom(all_0_22_22) = all_65_1_46
% 9.53/2.81  | (220) set_intersection2(all_65_1_46, all_50_0_42) = all_65_0_45
% 9.53/2.81  |
% 9.53/2.81  | Instantiating (216) with all_70_0_48, all_70_1_49 yields:
% 9.53/2.81  | (221) relation_rng(all_70_1_49) = all_21_0_30 & relation_dom(all_70_1_49) = all_70_0_48 & relation(all_70_1_49) & function(all_70_1_49) & in(all_70_0_48, omega)
% 9.53/2.81  |
% 9.53/2.81  | Applying alpha-rule on (221) yields:
% 9.53/2.81  | (222) relation(all_70_1_49)
% 9.53/2.81  | (223) relation_rng(all_70_1_49) = all_21_0_30
% 9.53/2.81  | (224) relation_dom(all_70_1_49) = all_70_0_48
% 9.53/2.81  | (225) function(all_70_1_49)
% 9.53/2.81  | (226) in(all_70_0_48, omega)
% 9.53/2.81  |
% 9.53/2.81  | Instantiating (215) with all_72_0_50 yields:
% 9.53/2.81  | (227) relation_dom(all_0_22_22) = all_72_0_50 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_0_22_22, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_72_0_50 |  ~ subset(all_36_0_37, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_36_0_37, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_0_22_22, v0) = v2 & relation_dom(v2) = all_72_0_50))
% 9.53/2.81  |
% 9.53/2.81  | Applying alpha-rule on (227) yields:
% 9.53/2.81  | (228) relation_dom(all_0_22_22) = all_72_0_50
% 9.53/2.81  | (229)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_0_22_22, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_72_0_50 |  ~ subset(all_36_0_37, v2))))
% 9.53/2.81  | (230)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_36_0_37, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_0_22_22, v0) = v2 & relation_dom(v2) = all_72_0_50))
% 9.53/2.81  |
% 9.53/2.81  | Instantiating (214) with all_75_0_51, all_75_1_52 yields:
% 9.53/2.81  | (231) relation_dom(all_45_0_40) = all_75_0_51 & relation_dom(all_0_22_22) = all_75_1_52 & (all_75_0_51 = all_23_0_32 |  ~ subset(all_47_0_41, all_75_1_52))
% 9.53/2.81  |
% 9.53/2.81  | Applying alpha-rule on (231) yields:
% 9.53/2.81  | (232) relation_dom(all_45_0_40) = all_75_0_51
% 9.53/2.81  | (233) relation_dom(all_0_22_22) = all_75_1_52
% 9.53/2.81  | (234) all_75_0_51 = all_23_0_32 |  ~ subset(all_47_0_41, all_75_1_52)
% 9.53/2.81  |
% 9.53/2.81  | Instantiating (213) with all_77_0_53, all_77_1_54 yields:
% 9.53/2.81  | (235) relation_dom(all_45_0_40) = all_77_0_53 & relation_dom(all_0_22_22) = all_77_1_54 & (all_77_0_53 = all_42_0_39 |  ~ subset(all_0_23_23, all_77_1_54))
% 9.53/2.81  |
% 9.53/2.81  | Applying alpha-rule on (235) yields:
% 9.53/2.81  | (236) relation_dom(all_45_0_40) = all_77_0_53
% 9.53/2.81  | (237) relation_dom(all_0_22_22) = all_77_1_54
% 9.53/2.81  | (238) all_77_0_53 = all_42_0_39 |  ~ subset(all_0_23_23, all_77_1_54)
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (116) with all_0_22_22, all_75_1_52, all_21_1_31 and discharging atoms relation_dom(all_0_22_22) = all_75_1_52, relation_dom(all_0_22_22) = all_21_1_31, yields:
% 9.53/2.81  | (239) all_75_1_52 = all_21_1_31
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (116) with all_0_22_22, all_75_1_52, all_77_1_54 and discharging atoms relation_dom(all_0_22_22) = all_77_1_54, relation_dom(all_0_22_22) = all_75_1_52, yields:
% 9.53/2.81  | (240) all_77_1_54 = all_75_1_52
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (116) with all_0_22_22, all_72_0_50, all_77_1_54 and discharging atoms relation_dom(all_0_22_22) = all_77_1_54, relation_dom(all_0_22_22) = all_72_0_50, yields:
% 9.53/2.81  | (241) all_77_1_54 = all_72_0_50
% 9.53/2.81  |
% 9.53/2.81  | Instantiating formula (116) with all_0_22_22, all_65_1_46, all_77_1_54 and discharging atoms relation_dom(all_0_22_22) = all_77_1_54, relation_dom(all_0_22_22) = all_65_1_46, yields:
% 9.53/2.81  | (242) all_77_1_54 = all_65_1_46
% 9.53/2.81  |
% 9.53/2.81  | Combining equations (240,241) yields a new equation:
% 9.53/2.81  | (243) all_75_1_52 = all_72_0_50
% 9.53/2.81  |
% 9.53/2.81  | Simplifying 243 yields:
% 9.53/2.81  | (244) all_75_1_52 = all_72_0_50
% 9.53/2.81  |
% 9.53/2.81  | Combining equations (242,241) yields a new equation:
% 9.53/2.81  | (245) all_72_0_50 = all_65_1_46
% 9.53/2.81  |
% 9.53/2.81  | Combining equations (244,239) yields a new equation:
% 9.53/2.81  | (246) all_72_0_50 = all_21_1_31
% 9.53/2.81  |
% 9.53/2.81  | Simplifying 246 yields:
% 9.53/2.81  | (247) all_72_0_50 = all_21_1_31
% 9.53/2.81  |
% 9.53/2.81  | Combining equations (247,245) yields a new equation:
% 9.53/2.81  | (248) all_65_1_46 = all_21_1_31
% 9.53/2.81  |
% 9.53/2.81  | From (248) and (219) follows:
% 9.53/2.81  | (176) relation_dom(all_0_22_22) = all_21_1_31
% 9.53/2.81  |
% 9.53/2.82  | Instantiating formula (167) with all_0_21_21, all_0_22_22, all_21_0_30, all_70_1_49 and discharging atoms relation_image(all_0_22_22, all_21_0_30) = all_0_21_21, relation_rng(all_70_1_49) = all_21_0_30, relation(all_70_1_49), relation(all_0_22_22), yields:
% 9.53/2.82  | (250)  ? [v0] : (relation_composition(all_70_1_49, all_0_22_22) = v0 & relation_rng(v0) = all_0_21_21)
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (20) with all_21_0_30, all_70_1_49 and discharging atoms relation_rng(all_70_1_49) = all_21_0_30, relation(all_70_1_49), yields:
% 9.53/2.82  | (251)  ? [v0] : (relation_dom(all_70_1_49) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_70_1_49, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 |  ~ subset(all_21_0_30, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_21_0_30, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_70_1_49, v1) = v3 & relation_dom(v3) = v0)))
% 9.53/2.82  |
% 9.53/2.82  | Instantiating (251) with all_102_0_61 yields:
% 9.53/2.82  | (252) relation_dom(all_70_1_49) = all_102_0_61 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_70_1_49, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_102_0_61 |  ~ subset(all_21_0_30, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_21_0_30, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_70_1_49, v0) = v2 & relation_dom(v2) = all_102_0_61))
% 9.53/2.82  |
% 9.53/2.82  | Applying alpha-rule on (252) yields:
% 9.53/2.82  | (253) relation_dom(all_70_1_49) = all_102_0_61
% 9.53/2.82  | (254)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_70_1_49, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_102_0_61 |  ~ subset(all_21_0_30, v2))))
% 9.53/2.82  | (255)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_21_0_30, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_70_1_49, v0) = v2 & relation_dom(v2) = all_102_0_61))
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (255) with all_21_1_31, all_0_22_22 and discharging atoms relation_dom(all_0_22_22) = all_21_1_31, subset(all_21_0_30, all_21_1_31), relation(all_0_22_22), yields:
% 9.53/2.82  | (256)  ? [v0] : (relation_composition(all_70_1_49, all_0_22_22) = v0 & relation_dom(v0) = all_102_0_61)
% 9.53/2.82  |
% 9.53/2.82  | Instantiating (250) with all_105_0_62 yields:
% 9.53/2.82  | (257) relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62 & relation_rng(all_105_0_62) = all_0_21_21
% 9.53/2.82  |
% 9.53/2.82  | Applying alpha-rule on (257) yields:
% 9.53/2.82  | (258) relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62
% 9.53/2.82  | (259) relation_rng(all_105_0_62) = all_0_21_21
% 9.53/2.82  |
% 9.53/2.82  | Instantiating (256) with all_109_0_65 yields:
% 9.53/2.82  | (260) relation_composition(all_70_1_49, all_0_22_22) = all_109_0_65 & relation_dom(all_109_0_65) = all_102_0_61
% 9.53/2.82  |
% 9.53/2.82  | Applying alpha-rule on (260) yields:
% 9.53/2.82  | (261) relation_composition(all_70_1_49, all_0_22_22) = all_109_0_65
% 9.53/2.82  | (262) relation_dom(all_109_0_65) = all_102_0_61
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (128) with all_70_1_49, all_0_22_22, all_105_0_62, all_109_0_65 and discharging atoms relation_composition(all_70_1_49, all_0_22_22) = all_109_0_65, relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62, yields:
% 9.53/2.82  | (263) all_109_0_65 = all_105_0_62
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (116) with all_70_1_49, all_102_0_61, all_70_0_48 and discharging atoms relation_dom(all_70_1_49) = all_102_0_61, relation_dom(all_70_1_49) = all_70_0_48, yields:
% 9.53/2.82  | (264) all_102_0_61 = all_70_0_48
% 9.53/2.82  |
% 9.53/2.82  | From (263) and (261) follows:
% 9.53/2.82  | (258) relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62
% 9.53/2.82  |
% 9.53/2.82  | From (263)(264) and (262) follows:
% 9.53/2.82  | (266) relation_dom(all_105_0_62) = all_70_0_48
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (105) with all_105_0_62, all_0_22_22, all_70_1_49 and discharging atoms relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62, relation(all_70_1_49), relation(all_0_22_22), function(all_70_1_49), function(all_0_22_22), yields:
% 9.53/2.82  | (267) function(all_105_0_62)
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (152) with all_105_0_62, all_0_22_22, all_70_1_49 and discharging atoms relation_composition(all_70_1_49, all_0_22_22) = all_105_0_62, relation(all_70_1_49), relation(all_0_22_22), yields:
% 9.53/2.82  | (268) relation(all_105_0_62)
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (20) with all_0_21_21, all_105_0_62 and discharging atoms relation_rng(all_105_0_62) = all_0_21_21, relation(all_105_0_62), yields:
% 9.53/2.82  | (269)  ? [v0] : (relation_dom(all_105_0_62) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_composition(all_105_0_62, v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 |  ~ subset(all_0_21_21, v3)))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_0_21_21, v2) |  ~ relation(v1) |  ? [v3] : (relation_composition(all_105_0_62, v1) = v3 & relation_dom(v3) = v0)))
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (43) with all_105_0_62, all_0_21_21 and discharging atoms relation_rng(all_105_0_62) = all_0_21_21, relation(all_105_0_62), function(all_105_0_62),  ~ finite(all_0_21_21), yields:
% 9.53/2.82  | (270)  ? [v0] : (relation_dom(all_105_0_62) = v0 &  ~ in(v0, omega))
% 9.53/2.82  |
% 9.53/2.82  | Instantiating (270) with all_162_0_79 yields:
% 9.53/2.82  | (271) relation_dom(all_105_0_62) = all_162_0_79 &  ~ in(all_162_0_79, omega)
% 9.53/2.82  |
% 9.53/2.82  | Applying alpha-rule on (271) yields:
% 9.53/2.82  | (272) relation_dom(all_105_0_62) = all_162_0_79
% 9.53/2.82  | (273)  ~ in(all_162_0_79, omega)
% 9.53/2.82  |
% 9.53/2.82  | Instantiating (269) with all_167_0_81 yields:
% 9.53/2.82  | (274) relation_dom(all_105_0_62) = all_167_0_81 &  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_105_0_62, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_167_0_81 |  ~ subset(all_0_21_21, v2)))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_21_21, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_105_0_62, v0) = v2 & relation_dom(v2) = all_167_0_81))
% 9.53/2.82  |
% 9.53/2.82  | Applying alpha-rule on (274) yields:
% 9.53/2.82  | (275) relation_dom(all_105_0_62) = all_167_0_81
% 9.53/2.82  | (276)  ! [v0] :  ! [v1] : ( ~ (relation_composition(all_105_0_62, v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_167_0_81 |  ~ subset(all_0_21_21, v2))))
% 9.53/2.82  | (277)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_21_21, v1) |  ~ relation(v0) |  ? [v2] : (relation_composition(all_105_0_62, v0) = v2 & relation_dom(v2) = all_167_0_81))
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (116) with all_105_0_62, all_167_0_81, all_70_0_48 and discharging atoms relation_dom(all_105_0_62) = all_167_0_81, relation_dom(all_105_0_62) = all_70_0_48, yields:
% 9.53/2.82  | (278) all_167_0_81 = all_70_0_48
% 9.53/2.82  |
% 9.53/2.82  | Instantiating formula (116) with all_105_0_62, all_162_0_79, all_167_0_81 and discharging atoms relation_dom(all_105_0_62) = all_167_0_81, relation_dom(all_105_0_62) = all_162_0_79, yields:
% 9.53/2.82  | (279) all_167_0_81 = all_162_0_79
% 9.53/2.82  |
% 9.53/2.82  | Combining equations (278,279) yields a new equation:
% 9.53/2.82  | (280) all_162_0_79 = all_70_0_48
% 9.53/2.82  |
% 9.53/2.82  | From (280) and (273) follows:
% 9.53/2.82  | (281)  ~ in(all_70_0_48, omega)
% 9.53/2.82  |
% 9.53/2.82  | Using (226) and (281) yields:
% 9.53/2.82  | (282) $false
% 9.53/2.82  |
% 9.53/2.82  |-The branch is then unsatisfiable
% 9.53/2.82  % SZS output end Proof for theBenchmark
% 9.53/2.82  
% 9.53/2.82  2202ms
%------------------------------------------------------------------------------