%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:46:31 EDT 2022

% Result   : Theorem 3.08s 1.60s
% Output   : Proof 5.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.36  % Computer : n020.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 600
% 0.13/0.36  % DateTime : Sun Jun 19 08:19:18 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.60/0.65          ____       _                          
% 0.60/0.65    ___  / __ \_____(_)___  ________  __________
% 0.60/0.65   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.65  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.60/0.65  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.60/0.65  
% 0.60/0.65  A Theorem Prover for First-Order Logic
% 0.60/0.66  (ePrincess v.1.0)
% 0.60/0.66  
% 0.60/0.66  (c) Philipp Rümmer, 2009-2015
% 0.60/0.66  (c) Peter Backeman, 2014-2015
% 0.60/0.66  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.66  Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.66  Bug reports to peter@backeman.se
% 0.60/0.66  
% 0.60/0.66  For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.66  
% 0.60/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.72  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/1.06  Prover 0: Preprocessing ...
% 2.37/1.36  Prover 0: Warning: ignoring some quantifiers
% 2.37/1.39  Prover 0: Constructing countermodel ...
% 3.08/1.60  Prover 0: proved (874ms)
% 3.08/1.60  
% 3.08/1.60  No countermodel exists, formula is valid
% 3.08/1.60  % SZS status Theorem for theBenchmark
% 3.08/1.60  
% 3.08/1.60  Generating proof ... Warning: ignoring some quantifiers
% 4.76/1.92  found it (size 4)
% 4.76/1.92  
% 4.76/1.92  % SZS output start Proof for theBenchmark
% 4.76/1.92  Assumed formulas after preprocessing and simplification: 
% 4.76/1.92  | (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] : (set_union2(v0, v1) = v2 & function_yielding(v3) & ordinal_yielding(v16) & transfinite_sequence(v16) & transfinite_sequence(v6) & being_limit_ordinal(v17) & relation_non_empty(v18) & natural(v12) & natural(v10) & finite(v23) & finite(v1) & finite(v0) & element(v11, positive_rationals) & element(v10, positive_rationals) & ordinal(v17) & ordinal(v12) & ordinal(v11) & ordinal(v10) & ordinal(v9) & ordinal(v8) & ordinal(v7) & ordinal(empty_set) & epsilon_connected(v17) & epsilon_connected(v12) & epsilon_connected(v11) & epsilon_connected(v10) & epsilon_connected(v9) & epsilon_connected(v8) & epsilon_connected(v7) & epsilon_connected(empty_set) & epsilon_transitive(v17) & epsilon_transitive(v12) & epsilon_transitive(v11) & epsilon_transitive(v10) & epsilon_transitive(v9) & epsilon_transitive(v8) & epsilon_transitive(v7) & epsilon_transitive(empty_set) & one_to_one(v20) & one_to_one(v8) & one_to_one(empty_set) & function(v22) & function(v21) & function(v20) & function(v19) & function(v18) & function(v16) & function(v8) & function(v6) & function(v3) & function(empty_set) & relation_empty_yielding(v19) & relation_empty_yielding(v13) & relation_empty_yielding(empty_set) & relation(v22) & relation(v21) & relation(v20) & relation(v19) & relation(v18) & relation(v16) & relation(v15) & relation(v14) & relation(v13) & relation(v8) & relation(v6) & relation(v3) & relation(empty_set) & empty(v21) & empty(v15) & empty(v10) & empty(v8) & empty(v5) & empty(empty_set) &  ~ finite(v2) &  ~ empty(v23) &  ~ empty(v14) &  ~ empty(v12) &  ~ empty(v11) &  ~ empty(v7) &  ~ empty(v4) &  ~ empty(positive_rationals) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : (v25 = v24 |  ~ (set_union2(v27, v26) = v25) |  ~ (set_union2(v27, v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ element(v25, v27) |  ~ empty(v26) |  ~ in(v24, v25)) &  ! [v24] :  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ element(v25, v27) |  ~ in(v24, v25) | element(v24, v26)) &  ! [v24] :  ! [v25] :  ! [v26] : (v25 = v24 |  ~ (powerset(v26) = v25) |  ~ (powerset(v26) = v24)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ~ element(v24, v26) | subset(v24, v25)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ~ subset(v24, v25) | element(v24, v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (powerset(v24) = v25) |  ~ finite(v24) |  ~ element(v26, v25) | finite(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v25, v24) = v26) |  ~ empty(v26) | empty(v24)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v25, v24) = v26) | set_union2(v24, v25) = v26) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v24, v25) = v26) |  ~ finite(v25) |  ~ finite(v24) | finite(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v24, v25) = v26) |  ~ relation(v25) |  ~ relation(v24) | relation(v26)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v24, v25) = v26) |  ~ empty(v26) | empty(v24)) &  ! [v24] :  ! [v25] :  ! [v26] : ( ~ (set_union2(v24, v25) = v26) | set_union2(v25, v24) = v26) &  ! [v24] :  ! [v25] : (v25 = v24 |  ~ (set_union2(v24, v24) = v25)) &  ! [v24] :  ! [v25] : (v25 = v24 |  ~ (set_union2(v24, empty_set) = v25)) &  ! [v24] :  ! [v25] : (v25 = v24 |  ~ empty(v25) |  ~ empty(v24)) &  ! [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] : (natural(v26) & finite(v26) & element(v26, v25) & ordinal(v26) & epsilon_connected(v26) & epsilon_transitive(v26) & one_to_one(v26) & function(v26) & relation(v26) & empty(v26))) &  ! [v24] :  ! [v25] : ( ~ (powerset(v24) = v25) |  ? [v26] : (element(v26, v25) & empty(v26))) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | ordinal(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | epsilon_connected(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v25, v24) |  ~ ordinal(v24) | epsilon_transitive(v25)) &  ! [v24] :  ! [v25] : ( ~ element(v24, v25) | empty(v25) | in(v24, v25)) &  ! [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] : ( ~ 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) |  ~ empty(v24) | natural(v24)) &  ! [v24] : ( ~ ordinal(v24) |  ~ empty(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ ordinal(v24) |  ~ empty(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ ordinal(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ ordinal(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ epsilon_connected(v24) |  ~ epsilon_transitive(v24) | ordinal(v24)) &  ! [v24] : ( ~ function(v24) |  ~ relation(v24) |  ~ empty(v24) | one_to_one(v24)) &  ! [v24] : ( ~ empty(v24) | finite(v24)) &  ! [v24] : ( ~ empty(v24) | ordinal(v24)) &  ! [v24] : ( ~ empty(v24) | epsilon_connected(v24)) &  ! [v24] : ( ~ empty(v24) | epsilon_transitive(v24)) &  ! [v24] : ( ~ empty(v24) | function(v24)) &  ! [v24] : ( ~ empty(v24) | relation(v24)) &  ? [v24] :  ? [v25] : element(v25, v24) &  ? [v24] : subset(v24, v24))
% 4.76/1.97  | 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:
% 4.76/1.97  | (1) set_union2(all_0_23_23, all_0_22_22) = all_0_21_21 & function_yielding(all_0_20_20) & ordinal_yielding(all_0_7_7) & transfinite_sequence(all_0_7_7) & transfinite_sequence(all_0_17_17) & being_limit_ordinal(all_0_6_6) & relation_non_empty(all_0_5_5) & natural(all_0_11_11) & natural(all_0_13_13) & finite(all_0_0_0) & finite(all_0_22_22) & finite(all_0_23_23) & element(all_0_12_12, positive_rationals) & element(all_0_13_13, positive_rationals) & ordinal(all_0_6_6) & ordinal(all_0_11_11) & ordinal(all_0_12_12) & ordinal(all_0_13_13) & ordinal(all_0_14_14) & ordinal(all_0_15_15) & ordinal(all_0_16_16) & ordinal(empty_set) & epsilon_connected(all_0_6_6) & epsilon_connected(all_0_11_11) & epsilon_connected(all_0_12_12) & epsilon_connected(all_0_13_13) & epsilon_connected(all_0_14_14) & epsilon_connected(all_0_15_15) & epsilon_connected(all_0_16_16) & epsilon_connected(empty_set) & epsilon_transitive(all_0_6_6) & epsilon_transitive(all_0_11_11) & epsilon_transitive(all_0_12_12) & epsilon_transitive(all_0_13_13) & epsilon_transitive(all_0_14_14) & epsilon_transitive(all_0_15_15) & epsilon_transitive(all_0_16_16) & epsilon_transitive(empty_set) & one_to_one(all_0_3_3) & one_to_one(all_0_15_15) & one_to_one(empty_set) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_3_3) & function(all_0_4_4) & function(all_0_5_5) & function(all_0_7_7) & function(all_0_15_15) & function(all_0_17_17) & function(all_0_20_20) & function(empty_set) & relation_empty_yielding(all_0_4_4) & relation_empty_yielding(all_0_10_10) & relation_empty_yielding(empty_set) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_9_9) & relation(all_0_10_10) & relation(all_0_15_15) & relation(all_0_17_17) & relation(all_0_20_20) & relation(empty_set) & empty(all_0_2_2) & empty(all_0_8_8) & empty(all_0_13_13) & empty(all_0_15_15) & empty(all_0_18_18) & empty(empty_set) &  ~ finite(all_0_21_21) &  ~ empty(all_0_0_0) &  ~ empty(all_0_9_9) &  ~ empty(all_0_11_11) &  ~ empty(all_0_12_12) &  ~ empty(all_0_16_16) &  ~ empty(all_0_19_19) &  ~ empty(positive_rationals) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [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] : (natural(v2) & finite(v2) & element(v2, v1) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2))) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) &  ! [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] : ( ~ 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) |  ~ empty(v0) | natural(v0)) &  ! [v0] : ( ~ ordinal(v0) |  ~ empty(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) |  ~ empty(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0)) &  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | finite(v0)) &  ! [v0] : ( ~ empty(v0) | ordinal(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 4.76/1.99  |
% 4.76/1.99  | Applying alpha-rule on (1) yields:
% 4.76/1.99  | (2) relation(all_0_20_20)
% 4.76/1.99  | (3)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.76/1.99  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 4.76/1.99  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 4.76/1.99  | (6) ordinal(empty_set)
% 4.76/1.99  | (7) relation(all_0_5_5)
% 4.76/1.99  | (8) being_limit_ordinal(all_0_6_6)
% 4.76/1.99  | (9) transfinite_sequence(all_0_7_7)
% 4.76/1.99  | (10) ordinal(all_0_12_12)
% 4.76/1.99  | (11) epsilon_connected(all_0_12_12)
% 4.76/1.99  | (12) element(all_0_12_12, positive_rationals)
% 4.76/1.99  | (13)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.76/1.99  | (14)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.76/1.99  | (15) epsilon_connected(all_0_14_14)
% 4.76/1.99  | (16)  ~ empty(all_0_11_11)
% 4.76/1.99  | (17) finite(all_0_23_23)
% 4.76/1.99  | (18) finite(all_0_0_0)
% 4.76/1.99  | (19) epsilon_transitive(all_0_14_14)
% 4.76/1.99  | (20) empty(all_0_15_15)
% 4.76/1.99  | (21)  ? [v0] : subset(v0, v0)
% 4.76/1.99  | (22)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0))
% 4.76/1.99  | (23)  ~ empty(all_0_16_16)
% 4.76/1.99  | (24) epsilon_connected(all_0_11_11)
% 4.76/1.99  | (25) natural(all_0_13_13)
% 4.76/1.99  | (26)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 4.76/1.99  | (27) function_yielding(all_0_20_20)
% 4.76/1.99  | (28) ordinal(all_0_13_13)
% 4.76/1.99  | (29)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.11/1.99  | (30) one_to_one(all_0_3_3)
% 5.11/1.99  | (31)  ! [v0] : ( ~ ordinal(v0) |  ~ empty(v0) | epsilon_connected(v0))
% 5.11/1.99  | (32) one_to_one(all_0_15_15)
% 5.11/1.99  | (33) relation(all_0_1_1)
% 5.11/1.99  | (34)  ~ empty(positive_rationals)
% 5.11/1.99  | (35) epsilon_connected(all_0_6_6)
% 5.11/1.99  | (36) relation(all_0_15_15)
% 5.11/1.99  | (37) relation(all_0_2_2)
% 5.11/1.99  | (38) relation(empty_set)
% 5.11/1.99  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.11/1.99  | (40)  ! [v0] : ( ~ ordinal(v0) |  ~ empty(v0) | epsilon_transitive(v0))
% 5.11/1.99  | (41)  ~ empty(all_0_12_12)
% 5.11/1.99  | (42) epsilon_connected(all_0_13_13)
% 5.11/1.99  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 5.11/1.99  | (44) relation(all_0_8_8)
% 5.11/1.99  | (45) ordinal_yielding(all_0_7_7)
% 5.11/1.99  | (46)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 5.11/1.99  | (47) function(all_0_1_1)
% 5.11/1.99  | (48) relation(all_0_10_10)
% 5.11/1.99  | (49)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.11/1.99  | (50)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.11/1.99  | (51) epsilon_connected(all_0_16_16)
% 5.11/1.99  | (52)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1))
% 5.11/1.99  | (53) epsilon_transitive(all_0_13_13)
% 5.11/1.99  | (54)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.11/2.00  | (55)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 5.11/2.00  | (56) one_to_one(empty_set)
% 5.11/2.00  | (57)  ~ empty(all_0_19_19)
% 5.11/2.00  | (58) relation(all_0_4_4)
% 5.11/2.00  | (59) epsilon_transitive(all_0_6_6)
% 5.11/2.00  | (60) empty(all_0_18_18)
% 5.11/2.00  | (61) ordinal(all_0_15_15)
% 5.11/2.00  | (62)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 5.11/2.00  | (63) epsilon_connected(empty_set)
% 5.11/2.00  | (64) relation(all_0_7_7)
% 5.11/2.00  | (65) relation(all_0_3_3)
% 5.11/2.00  | (66) epsilon_transitive(all_0_11_11)
% 5.11/2.00  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 5.11/2.00  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 5.11/2.00  | (69) ordinal(all_0_6_6)
% 5.11/2.00  | (70)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.11/2.00  | (71) function(all_0_3_3)
% 5.11/2.00  | (72)  ~ finite(all_0_21_21)
% 5.11/2.00  | (73) relation_empty_yielding(empty_set)
% 5.11/2.00  | (74) element(all_0_13_13, positive_rationals)
% 5.11/2.00  | (75) empty(all_0_13_13)
% 5.11/2.00  | (76) transfinite_sequence(all_0_17_17)
% 5.11/2.00  | (77) relation_empty_yielding(all_0_10_10)
% 5.11/2.00  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.11/2.00  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 5.11/2.00  | (80)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.11/2.00  | (81) finite(all_0_22_22)
% 5.11/2.00  | (82) empty(all_0_2_2)
% 5.11/2.00  | (83) function(all_0_17_17)
% 5.11/2.00  | (84)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0))
% 5.11/2.00  | (85)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.11/2.00  | (86)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 5.11/2.00  | (87) function(all_0_7_7)
% 5.11/2.00  | (88)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 5.11/2.00  | (89) relation_empty_yielding(all_0_4_4)
% 5.11/2.00  | (90)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 5.11/2.00  | (91)  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0))
% 5.11/2.00  | (92) function(all_0_15_15)
% 5.11/2.00  | (93) function(all_0_2_2)
% 5.11/2.00  | (94) epsilon_connected(all_0_15_15)
% 5.11/2.00  | (95)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.11/2.00  | (96)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.11/2.00  | (97)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 5.11/2.01  | (98)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 5.11/2.01  | (99) relation(all_0_17_17)
% 5.11/2.01  | (100)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 5.11/2.01  | (101) natural(all_0_11_11)
% 5.11/2.02  | (102) epsilon_transitive(empty_set)
% 5.11/2.02  | (103) epsilon_transitive(all_0_12_12)
% 5.11/2.02  | (104) empty(empty_set)
% 5.11/2.02  | (105) ordinal(all_0_16_16)
% 5.11/2.02  | (106)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1))
% 5.11/2.02  | (107) ordinal(all_0_14_14)
% 5.11/2.02  | (108)  ~ empty(all_0_9_9)
% 5.11/2.02  | (109)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 5.11/2.02  | (110) epsilon_transitive(all_0_16_16)
% 5.11/2.02  | (111) relation(all_0_9_9)
% 5.11/2.02  | (112)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1))
% 5.11/2.02  | (113) relation_non_empty(all_0_5_5)
% 5.11/2.02  | (114) set_union2(all_0_23_23, all_0_22_22) = all_0_21_21
% 5.11/2.02  | (115)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 5.11/2.02  | (116) ordinal(all_0_11_11)
% 5.11/2.02  | (117) empty(all_0_8_8)
% 5.11/2.02  | (118)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.11/2.02  | (119)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 5.11/2.02  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 5.11/2.02  | (121)  ~ empty(all_0_0_0)
% 5.11/2.02  | (122)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (natural(v2) & finite(v2) & element(v2, v1) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & empty(v2)))
% 5.11/2.02  | (123) function(empty_set)
% 5.11/2.02  | (124) epsilon_transitive(all_0_15_15)
% 5.11/2.02  | (125)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2))
% 5.11/2.02  | (126) function(all_0_5_5)
% 5.11/2.02  | (127) function(all_0_20_20)
% 5.11/2.02  | (128) function(all_0_4_4)
% 5.11/2.02  | (129)  ! [v0] : ( ~ ordinal(v0) |  ~ empty(v0) | natural(v0))
% 5.11/2.02  |
% 5.11/2.02  | Instantiating formula (125) with all_0_21_21, all_0_22_22, all_0_23_23 and discharging atoms set_union2(all_0_23_23, all_0_22_22) = all_0_21_21, finite(all_0_22_22), finite(all_0_23_23),  ~ finite(all_0_21_21), yields:
% 5.11/2.02  | (130) $false
% 5.11/2.02  |
% 5.11/2.02  |-The branch is then unsatisfiable
% 5.11/2.02  % SZS output end Proof for theBenchmark
% 5.11/2.02  
% 5.11/2.02  1350ms
%------------------------------------------------------------------------------