%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n025.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 08:48:40 EDT 2022

% Result   : Theorem 3.57s 1.47s
% Output   : Proof 5.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 19 06:47:58 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.50/0.59          ____       _                          
% 0.50/0.59    ___  / __ \_____(_)___  ________  __________
% 0.50/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.50/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.50/0.59  
% 0.50/0.59  A Theorem Prover for First-Order Logic
% 0.50/0.59  (ePrincess v.1.0)
% 0.50/0.59  
% 0.50/0.59  (c) Philipp Rümmer, 2009-2015
% 0.50/0.59  (c) Peter Backeman, 2014-2015
% 0.50/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59  Bug reports to peter@backeman.se
% 0.50/0.59  
% 0.50/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59  
% 0.50/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.01  Prover 0: Preprocessing ...
% 2.63/1.26  Prover 0: Warning: ignoring some quantifiers
% 2.77/1.29  Prover 0: Constructing countermodel ...
% 3.57/1.47  Prover 0: proved (831ms)
% 3.57/1.47  
% 3.57/1.47  No countermodel exists, formula is valid
% 3.57/1.47  % SZS status Theorem for theBenchmark
% 3.57/1.47  
% 3.57/1.47  Generating proof ... Warning: ignoring some quantifiers
% 4.89/1.81  found it (size 9)
% 4.89/1.81  
% 4.89/1.81  % SZS output start Proof for theBenchmark
% 4.89/1.81  Assumed formulas after preprocessing and simplification: 
% 4.89/1.81  | (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_rng(v0) = v2 & relation_dom(v0) = v1 & 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(v0) & relation(empty_set) & function(v21) & function(v20) & function(v14) & function(v13) & function(v12) & function(v8) & function(v5) & function(v4) & function(v3) & function(v0) & function(empty_set) & finite(v22) & finite(v1) & 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_transitive(v23) & epsilon_transitive(v19) & epsilon_transitive(v18) & epsilon_transitive(v15) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v7) & epsilon_transitive(empty_set) & 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) &  ~ finite(v2) &  ~ empty(v23) &  ~ empty(v22) &  ~ empty(v15) &  ~ empty(v11) &  ~ empty(v10) &  ~ empty(v7) &  ~ empty(positive_rationals) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : (v25 = v24 |  ~ (relation_image(v27, v26) = v25) |  ~ (relation_image(v27, v26) = v24)) &  ! [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_dom(v24) = v25) |  ~ (relation_image(v24, v25) = v26) |  ~ relation(v24) | relation_rng(v24) = v26) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_image(v25, v24) = v26) |  ~ relation(v25) |  ~ function(v25) |  ~ finite(v24) | finite(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (relation_image(v24, v25) = v26) |  ~ relation(v24) |  ~ function(v24) |  ~ finite(v25) | finite(v26)) &  ! [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] : (v25 = v24 |  ~ empty(v25) |  ~ empty(v24)) &  ! [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 & relation_image(v24, v26) = v25)) &  ! [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) |  ~ 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] : ( ~ 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] : ( ~ ordinal(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ ordinal(v24) | epsilon_transitive(v24)) &  ? [v24] :  ? [v25] : element(v25, v24) &  ? [v24] : subset(v24, v24))
% 5.33/1.86  | 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:
% 5.33/1.86  | (1) relation_rng(all_0_23_23) = all_0_21_21 & relation_dom(all_0_23_23) = all_0_22_22 & 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_23_23) & 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_23_23) & function(empty_set) & finite(all_0_1_1) & finite(all_0_22_22) & 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_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) & 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) &  ~ 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) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0)) &  ! [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_dom(v0) = v1) |  ~ (relation_image(v0, v1) = v2) |  ~ relation(v0) | relation_rng(v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ~ relation(v1) |  ~ function(v1) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) |  ~ finite(v1) | finite(v2)) &  ! [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] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [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 & relation_image(v0, v2) = v1)) &  ! [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) |  ~ 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] : ( ~ 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] : ( ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 5.33/1.87  |
% 5.33/1.87  | Applying alpha-rule on (1) yields:
% 5.33/1.87  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 5.33/1.87  | (3) function(all_0_11_11)
% 5.33/1.87  | (4) finite(all_0_22_22)
% 5.33/1.87  | (5) element(all_0_14_14, positive_rationals)
% 5.33/1.87  | (6) relation_dom(all_0_23_23) = all_0_22_22
% 5.33/1.87  | (7)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.33/1.87  | (8)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.33/1.87  | (9) relation(all_0_2_2)
% 5.33/1.87  | (10) function(all_0_2_2)
% 5.33/1.87  | (11) ordinal(all_0_8_8)
% 5.33/1.87  | (12) transfinite_sequence(all_0_19_19)
% 5.33/1.87  | (13)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 5.33/1.87  | (14) relation(all_0_10_10)
% 5.33/1.87  | (15)  ~ empty(all_0_8_8)
% 5.33/1.87  | (16)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.33/1.87  | (17)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.33/1.87  | (18)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 5.33/1.87  | (19)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.33/1.88  | (20)  ~ empty(all_0_1_1)
% 5.33/1.88  | (21) epsilon_transitive(all_0_8_8)
% 5.33/1.88  | (22) relation_non_empty(all_0_20_20)
% 5.33/1.88  | (23) empty(all_0_14_14)
% 5.33/1.88  | (24) function_yielding(all_0_2_2)
% 5.33/1.88  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 5.33/1.88  | (26)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.33/1.88  | (27)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.33/1.88  | (28)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.33/1.88  | (29) element(all_0_8_8, positive_rationals)
% 5.33/1.88  | (30) ordinal(all_0_4_4)
% 5.33/1.88  | (31)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1)))
% 5.33/1.88  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0))
% 5.33/1.88  | (33)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1))
% 5.33/1.88  | (34) ordinal(empty_set)
% 5.33/1.88  | (35)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation_non_empty(v0) |  ~ relation(v0) |  ~ function(v0) | with_non_empty_elements(v1))
% 5.33/1.88  | (36) being_limit_ordinal(all_0_5_5)
% 5.33/1.88  | (37)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 5.33/1.88  | (38) relation(all_0_19_19)
% 5.33/1.88  | (39)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | ordinal(v1))
% 5.33/1.88  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1))
% 5.33/1.88  | (41)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 5.33/1.88  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 5.33/1.88  | (43)  ~ empty(all_0_16_16)
% 5.33/1.88  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v1, v0) = v2) |  ~ relation(v1) |  ~ function(v1) |  ~ finite(v0) | finite(v2))
% 5.33/1.88  | (45)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_transitive(v1))
% 5.33/1.88  | (46) function(all_0_23_23)
% 5.33/1.88  | (47) empty(all_0_7_7)
% 5.33/1.88  | (48)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 5.33/1.88  | (49) epsilon_transitive(empty_set)
% 5.33/1.88  | (50) relation_empty_yielding(all_0_18_18)
% 5.33/1.88  | (51)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 5.33/1.88  | (52) ordinal(all_0_16_16)
% 5.33/1.88  | (53) relation(all_0_15_15)
% 5.33/1.88  | (54) function(all_0_20_20)
% 5.33/1.88  | (55)  ~ empty(all_0_12_12)
% 5.33/1.88  | (56) epsilon_connected(all_0_16_16)
% 5.33/1.88  | (57) relation(all_0_12_12)
% 5.33/1.88  | (58) epsilon_connected(all_0_10_10)
% 5.33/1.88  | (59) transfinite_sequence(all_0_11_11)
% 5.33/1.88  | (60)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | natural(v0))
% 5.33/1.88  | (61)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.33/1.88  | (62)  ~ empty(all_0_13_13)
% 5.33/1.88  | (63)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_connected(v0))
% 5.33/1.89  | (64)  ! [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)))
% 5.33/1.89  | (65) relation(all_0_6_6)
% 5.33/1.89  | (66)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 5.33/1.89  | (67)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 5.33/1.89  | (68) natural(all_0_14_14)
% 5.33/1.89  | (69) ordinal(all_0_0_0)
% 5.33/1.89  | (70) relation(all_0_9_9)
% 5.33/1.89  | (71)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.33/1.89  | (72) function(all_0_3_3)
% 5.33/1.89  | (73) epsilon_transitive(all_0_5_5)
% 5.33/1.89  | (74)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.33/1.89  | (75) relation(all_0_23_23)
% 5.33/1.89  | (76) one_to_one(empty_set)
% 5.33/1.89  | (77)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.33/1.89  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.33/1.89  | (79)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 5.33/1.89  | (80) one_to_one(all_0_10_10)
% 5.33/1.89  | (81)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1))
% 5.33/1.89  | (82) ordinal(all_0_5_5)
% 5.33/1.89  | (83) finite(all_0_1_1)
% 5.33/1.89  | (84)  ~ finite(all_0_21_21)
% 5.33/1.89  | (85)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 5.33/1.89  | (86) function(all_0_10_10)
% 5.33/1.89  | (87)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ (relation_image(v0, v1) = v2) |  ~ relation(v0) | relation_rng(v0) = v2)
% 5.33/1.89  | (88) empty(all_0_9_9)
% 5.33/1.89  | (89)  ! [v0] : ( ~ empty(v0) | function(v0))
% 5.33/1.89  | (90) ordinal(all_0_14_14)
% 5.33/1.89  | (91)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_image(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) |  ~ finite(v1) | finite(v2))
% 5.33/1.89  | (92) epsilon_transitive(all_0_16_16)
% 5.33/1.89  | (93) ordinal(all_0_10_10)
% 5.33/1.89  | (94) relation(empty_set)
% 5.33/1.89  | (95)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.33/1.89  | (96) function(all_0_15_15)
% 5.33/1.89  | (97)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1))
% 5.33/1.89  | (98) epsilon_transitive(all_0_4_4)
% 5.33/1.89  | (99) function(empty_set)
% 5.33/1.89  | (100)  ~ empty(all_0_0_0)
% 5.33/1.89  | (101)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ function(v0) | epsilon_connected(v1))
% 5.33/1.89  | (102) function(all_0_18_18)
% 5.33/1.89  | (103) epsilon_connected(all_0_8_8)
% 5.33/1.89  | (104) epsilon_transitive(all_0_0_0)
% 5.33/1.89  | (105)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.33/1.89  | (106) epsilon_connected(all_0_14_14)
% 5.33/1.89  | (107) natural(all_0_0_0)
% 5.33/1.89  | (108) empty(all_0_6_6)
% 5.33/1.89  | (109)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 5.33/1.90  | (110) ordinal_yielding(all_0_11_11)
% 5.33/1.90  | (111)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.33/1.90  | (112) epsilon_connected(all_0_0_0)
% 5.33/1.90  | (113) epsilon_transitive(all_0_14_14)
% 5.33/1.90  | (114)  ~ empty(positive_rationals)
% 5.33/1.90  | (115) epsilon_transitive(all_0_10_10)
% 5.33/1.90  | (116)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 5.33/1.90  | (117) epsilon_connected(all_0_4_4)
% 5.33/1.90  | (118) relation_empty_yielding(all_0_17_17)
% 5.33/1.90  | (119) relation(all_0_18_18)
% 5.33/1.90  | (120) relation(all_0_17_17)
% 5.33/1.90  | (121) relation(all_0_20_20)
% 5.33/1.90  | (122) function(all_0_19_19)
% 5.33/1.90  | (123)  ? [v0] :  ? [v1] : element(v1, v0)
% 5.33/1.90  | (124) empty(all_0_10_10)
% 5.33/1.90  | (125) relation_rng(all_0_23_23) = all_0_21_21
% 5.33/1.90  | (126) one_to_one(all_0_15_15)
% 5.33/1.90  | (127) epsilon_connected(empty_set)
% 5.33/1.90  | (128) function(all_0_9_9)
% 5.33/1.90  | (129)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0))
% 5.33/1.90  | (130)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 5.33/1.90  | (131) empty(empty_set)
% 5.33/1.90  | (132) relation(all_0_3_3)
% 5.33/1.90  | (133) relation_empty_yielding(empty_set)
% 5.33/1.90  | (134)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0))
% 5.33/1.90  | (135)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.33/1.90  | (136)  ? [v0] : subset(v0, v0)
% 5.33/1.90  | (137) epsilon_connected(all_0_5_5)
% 5.33/1.90  | (138) relation(all_0_11_11)
% 5.33/1.90  | (139)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.33/1.90  |
% 5.33/1.90  | Instantiating formula (41) with all_0_21_21, all_0_23_23 and discharging atoms relation_rng(all_0_23_23) = all_0_21_21, relation(all_0_23_23), yields:
% 5.33/1.90  | (140)  ? [v0] : (relation_dom(all_0_23_23) = v0 & relation_image(all_0_23_23, v0) = all_0_21_21)
% 5.33/1.90  |
% 5.33/1.90  | Instantiating (140) with all_17_0_27 yields:
% 5.33/1.90  | (141) relation_dom(all_0_23_23) = all_17_0_27 & relation_image(all_0_23_23, all_17_0_27) = all_0_21_21
% 5.33/1.90  |
% 5.33/1.90  | Applying alpha-rule on (141) yields:
% 5.33/1.90  | (142) relation_dom(all_0_23_23) = all_17_0_27
% 5.33/1.90  | (143) relation_image(all_0_23_23, all_17_0_27) = all_0_21_21
% 5.33/1.90  |
% 5.33/1.90  | Instantiating formula (2) with all_0_23_23, all_17_0_27, all_0_22_22 and discharging atoms relation_dom(all_0_23_23) = all_17_0_27, relation_dom(all_0_23_23) = all_0_22_22, yields:
% 5.33/1.90  | (144) all_17_0_27 = all_0_22_22
% 5.33/1.91  |
% 5.33/1.91  | From (144) and (143) follows:
% 5.33/1.91  | (145) relation_image(all_0_23_23, all_0_22_22) = all_0_21_21
% 5.33/1.91  |
% 5.33/1.91  | Instantiating formula (44) with all_0_21_21, all_0_23_23, all_0_22_22 and discharging atoms relation_image(all_0_23_23, all_0_22_22) = all_0_21_21, relation(all_0_23_23), function(all_0_23_23), finite(all_0_22_22),  ~ finite(all_0_21_21), yields:
% 5.33/1.91  | (146) $false
% 5.33/1.91  |
% 5.33/1.91  |-The branch is then unsatisfiable
% 5.33/1.91  % SZS output end Proof for theBenchmark
% 5.33/1.91  
% 5.33/1.91  1310ms
%------------------------------------------------------------------------------