%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n014.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 08:46:32 EDT 2022

% Result   : Theorem 3.38s 1.48s
% Output   : Proof 4.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 04:17:33 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.64/0.64          ____       _                          
% 0.64/0.64    ___  / __ \_____(_)___  ________  __________
% 0.64/0.64   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.64  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.64/0.64  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.64/0.64  
% 0.64/0.64  A Theorem Prover for First-Order Logic
% 0.64/0.65  (ePrincess v.1.0)
% 0.64/0.65  
% 0.64/0.65  (c) Philipp Rümmer, 2009-2015
% 0.64/0.65  (c) Peter Backeman, 2014-2015
% 0.64/0.65  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.65  Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.65  Bug reports to peter@backeman.se
% 0.64/0.65  
% 0.64/0.65  For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.65  
% 0.64/0.65  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.70  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.06  Prover 0: Preprocessing ...
% 2.46/1.29  Prover 0: Warning: ignoring some quantifiers
% 2.70/1.31  Prover 0: Constructing countermodel ...
% 3.38/1.48  Prover 0: proved (783ms)
% 3.38/1.48  
% 3.38/1.48  No countermodel exists, formula is valid
% 3.38/1.48  % SZS status Theorem for theBenchmark
% 3.38/1.48  
% 3.38/1.48  Generating proof ... Warning: ignoring some quantifiers
% 4.80/1.80  found it (size 8)
% 4.80/1.80  
% 4.80/1.80  % SZS output start Proof for theBenchmark
% 4.80/1.80  Assumed formulas after preprocessing and simplification: 
% 4.80/1.80  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : (cartesian_product3(v0, v1, v2) = v3 & relation_non_empty(v4) & ordinal_yielding(v13) & transfinite_sequence(v13) & transfinite_sequence(v5) & being_limit_ordinal(v19) & function_yielding(v22) & relation_empty_yielding(v7) & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v14) & one_to_one(v9) & one_to_one(empty_set) & natural(v24) & natural(v10) & relation(v22) & relation(v21) & relation(v18) & relation(v15) & relation(v14) & relation(v13) & relation(v12) & relation(v9) & relation(v7) & relation(v6) & relation(v5) & relation(v4) & relation(empty_set) & function(v22) & function(v21) & function(v15) & function(v14) & function(v13) & function(v9) & function(v6) & function(v5) & function(v4) & function(empty_set) & finite(v23) & finite(v2) & finite(v1) & finite(v0) & empty(v18) & empty(v17) & empty(v15) & empty(v14) & empty(v10) & empty(empty_set) & epsilon_connected(v24) & epsilon_connected(v20) & epsilon_connected(v19) & epsilon_connected(v16) & epsilon_connected(v14) & epsilon_connected(v10) & epsilon_connected(v8) & epsilon_connected(empty_set) & epsilon_transitive(v24) & epsilon_transitive(v20) & epsilon_transitive(v19) & epsilon_transitive(v16) & epsilon_transitive(v14) & epsilon_transitive(v10) & epsilon_transitive(v8) & epsilon_transitive(empty_set) & element(v16, positive_rationals) & element(v10, positive_rationals) & ordinal(v24) & ordinal(v20) & ordinal(v19) & ordinal(v16) & ordinal(v14) & ordinal(v10) & ordinal(v8) & ordinal(empty_set) &  ~ finite(v3) &  ~ empty(v24) &  ~ empty(v23) &  ~ empty(v16) &  ~ empty(v12) &  ~ empty(v11) &  ~ empty(v8) &  ~ empty(positive_rationals) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : (v26 = v25 |  ~ (cartesian_product3(v29, v28, v27) = v26) |  ~ (cartesian_product3(v29, v28, v27) = v25)) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (cartesian_product2(v28, v27) = v29) |  ~ (cartesian_product2(v25, v26) = v28) | cartesian_product3(v25, v26, v27) = v29) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : (v26 = v25 |  ~ (cartesian_product2(v28, v27) = v26) |  ~ (cartesian_product2(v28, v27) = v25)) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (cartesian_product3(v25, v26, v27) = v28) |  ~ empty(v28) | empty(v27) | empty(v26) | empty(v25)) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (cartesian_product3(v25, v26, v27) = v28) |  ? [v29] : (cartesian_product2(v29, v27) = v28 & cartesian_product2(v25, v26) = v29)) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (powerset(v27) = v28) |  ~ empty(v27) |  ~ element(v26, v28) |  ~ in(v25, v26)) &  ! [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (powerset(v27) = v28) |  ~ element(v26, v28) |  ~ in(v25, v26) | element(v25, v27)) &  ? [v25] :  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (cartesian_product2(v26, v27) = v28) | relation(v25) |  ? [v29] : (powerset(v28) = v29 &  ~ element(v25, v29))) &  ! [v25] :  ! [v26] :  ! [v27] : (v26 = v25 |  ~ (powerset(v27) = v26) |  ~ (powerset(v27) = v25)) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (cartesian_product2(v25, v26) = v27) |  ~ finite(v26) |  ~ finite(v25) | finite(v27)) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (cartesian_product2(v25, v26) = v27) |  ~ empty(v27) | empty(v26) | empty(v25)) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ subset(v25, v26) | element(v25, v27)) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ element(v25, v27) | subset(v25, v26)) &  ! [v25] :  ! [v26] :  ! [v27] : ( ~ (powerset(v25) = v26) |  ~ finite(v25) |  ~ element(v27, v26) | finite(v27)) &  ! [v25] :  ! [v26] : (v26 = v25 |  ~ empty(v26) |  ~ empty(v25)) &  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ~ empty(v26)) &  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) | empty(v25) |  ? [v27] : (finite(v27) & element(v27, v26) &  ~ empty(v27))) &  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) | empty(v25) |  ? [v27] : (element(v27, v26) &  ~ empty(v27))) &  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ? [v27] : (one_to_one(v27) & natural(v27) & relation(v27) & function(v27) & finite(v27) & empty(v27) & epsilon_connected(v27) & epsilon_transitive(v27) & element(v27, v26) & ordinal(v27))) &  ! [v25] :  ! [v26] : ( ~ (powerset(v25) = v26) |  ? [v27] : (empty(v27) & element(v27, v26))) &  ! [v25] :  ! [v26] : ( ~ empty(v26) |  ~ in(v25, v26)) &  ! [v25] :  ! [v26] : ( ~ element(v26, v25) |  ~ ordinal(v25) | epsilon_connected(v26)) &  ! [v25] :  ! [v26] : ( ~ element(v26, v25) |  ~ ordinal(v25) | epsilon_transitive(v26)) &  ! [v25] :  ! [v26] : ( ~ element(v26, v25) |  ~ ordinal(v25) | ordinal(v26)) &  ! [v25] :  ! [v26] : ( ~ element(v25, v26) | empty(v26) | in(v25, v26)) &  ! [v25] :  ! [v26] : ( ~ in(v26, v25) |  ~ in(v25, v26)) &  ! [v25] :  ! [v26] : ( ~ in(v25, v26) | element(v25, v26)) &  ! [v25] : (v25 = empty_set |  ~ empty(v25)) &  ! [v25] : ( ~ relation(v25) |  ~ function(v25) |  ~ empty(v25) | one_to_one(v25)) &  ! [v25] : ( ~ empty(v25) |  ~ ordinal(v25) | natural(v25)) &  ! [v25] : ( ~ empty(v25) |  ~ ordinal(v25) | epsilon_connected(v25)) &  ! [v25] : ( ~ empty(v25) |  ~ ordinal(v25) | epsilon_transitive(v25)) &  ! [v25] : ( ~ empty(v25) | relation(v25)) &  ! [v25] : ( ~ empty(v25) | function(v25)) &  ! [v25] : ( ~ empty(v25) | finite(v25)) &  ! [v25] : ( ~ empty(v25) | epsilon_connected(v25)) &  ! [v25] : ( ~ empty(v25) | epsilon_transitive(v25)) &  ! [v25] : ( ~ empty(v25) | ordinal(v25)) &  ! [v25] : ( ~ epsilon_connected(v25) |  ~ epsilon_transitive(v25) | ordinal(v25)) &  ! [v25] : ( ~ element(v25, positive_rationals) |  ~ ordinal(v25) | natural(v25)) &  ! [v25] : ( ~ element(v25, positive_rationals) |  ~ ordinal(v25) | epsilon_connected(v25)) &  ! [v25] : ( ~ element(v25, positive_rationals) |  ~ ordinal(v25) | epsilon_transitive(v25)) &  ! [v25] : ( ~ ordinal(v25) | epsilon_connected(v25)) &  ! [v25] : ( ~ ordinal(v25) | epsilon_transitive(v25)) &  ? [v25] :  ? [v26] : element(v26, v25) &  ? [v25] : subset(v25, v25))
% 4.95/1.84  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24 yields:
% 4.95/1.84  | (1) cartesian_product3(all_0_24_24, all_0_23_23, all_0_22_22) = all_0_21_21 & relation_non_empty(all_0_20_20) & ordinal_yielding(all_0_11_11) & transfinite_sequence(all_0_11_11) & transfinite_sequence(all_0_19_19) & being_limit_ordinal(all_0_5_5) & function_yielding(all_0_2_2) & 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(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(empty_set) & finite(all_0_1_1) & finite(all_0_22_22) & finite(all_0_23_23) & finite(all_0_24_24) & 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] :  ! [v4] : (v1 = v0 |  ~ (cartesian_product3(v4, v3, v2) = v1) |  ~ (cartesian_product3(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) |  ~ (cartesian_product2(v0, v1) = v3) | cartesian_product3(v0, v1, v2) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ~ empty(v3) | empty(v2) | empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ? [v4] : (cartesian_product2(v4, v2) = v3 & cartesian_product2(v0, v1) = 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] :  ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) |  ? [v4] : (powerset(v3) = v4 &  ~ element(v0, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ empty(v2) | empty(v1) | empty(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] : (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] : (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)
% 4.95/1.86  |
% 4.95/1.86  | Applying alpha-rule on (1) yields:
% 4.95/1.86  | (2) relation(all_0_12_12)
% 4.95/1.86  | (3) relation(all_0_15_15)
% 4.95/1.86  | (4)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 4.95/1.86  | (5) empty(all_0_10_10)
% 4.95/1.86  | (6)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.95/1.86  | (7)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 4.95/1.86  | (8) epsilon_transitive(all_0_5_5)
% 4.95/1.86  | (9) ordinal(all_0_16_16)
% 4.95/1.86  | (10)  ~ empty(all_0_16_16)
% 4.95/1.86  | (11)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 4.95/1.86  | (12)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0))
% 4.95/1.86  | (13) function(all_0_2_2)
% 4.95/1.86  | (14) epsilon_transitive(all_0_4_4)
% 4.95/1.86  | (15) epsilon_transitive(all_0_10_10)
% 4.95/1.86  | (16) epsilon_transitive(all_0_16_16)
% 4.95/1.86  | (17) epsilon_connected(all_0_4_4)
% 4.95/1.86  | (18) ordinal_yielding(all_0_11_11)
% 4.95/1.86  | (19) relation(all_0_19_19)
% 4.95/1.86  | (20) finite(all_0_24_24)
% 4.95/1.86  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.95/1.86  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.95/1.86  | (23) epsilon_connected(all_0_16_16)
% 4.95/1.86  | (24)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 4.95/1.86  | (25) being_limit_ordinal(all_0_5_5)
% 4.95/1.86  | (26) natural(all_0_14_14)
% 4.95/1.86  | (27)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1))
% 4.95/1.86  | (28)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 4.95/1.86  | (29) epsilon_connected(all_0_5_5)
% 4.95/1.86  | (30) element(all_0_8_8, positive_rationals)
% 4.95/1.86  | (31)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1)))
% 4.95/1.86  | (32) relation_empty_yielding(empty_set)
% 4.95/1.86  | (33) function(empty_set)
% 4.95/1.87  | (34) epsilon_connected(all_0_8_8)
% 4.95/1.87  | (35) relation_empty_yielding(all_0_17_17)
% 4.95/1.87  | (36) epsilon_transitive(all_0_14_14)
% 4.95/1.87  | (37) one_to_one(all_0_15_15)
% 4.95/1.87  | (38) one_to_one(empty_set)
% 4.95/1.87  | (39) epsilon_transitive(empty_set)
% 4.95/1.87  | (40)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_connected(v0))
% 4.95/1.87  | (41) relation(all_0_17_17)
% 4.95/1.87  | (42) one_to_one(all_0_10_10)
% 4.95/1.87  | (43)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0))
% 4.95/1.87  | (44)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 4.95/1.87  | (45)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 4.95/1.87  | (46)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 4.95/1.87  | (47) relation_empty_yielding(all_0_18_18)
% 4.95/1.87  | (48)  ? [v0] : subset(v0, v0)
% 4.95/1.87  | (49)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 4.95/1.87  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ? [v4] : (cartesian_product2(v4, v2) = v3 & cartesian_product2(v0, v1) = v4))
% 4.95/1.87  | (51)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 4.95/1.87  | (52) function(all_0_15_15)
% 4.95/1.87  | (53) function(all_0_10_10)
% 4.95/1.87  | (54)  ~ empty(positive_rationals)
% 4.95/1.87  | (55) function(all_0_18_18)
% 4.95/1.87  | (56) function(all_0_3_3)
% 4.95/1.87  | (57)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.95/1.87  | (58) relation(all_0_11_11)
% 4.95/1.87  | (59) empty(all_0_9_9)
% 4.95/1.87  | (60) ordinal(all_0_5_5)
% 4.95/1.87  | (61) empty(all_0_14_14)
% 4.95/1.87  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 4.95/1.87  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 4.95/1.87  | (64) ordinal(all_0_0_0)
% 4.95/1.87  | (65) epsilon_connected(all_0_10_10)
% 4.95/1.87  | (66) function(all_0_20_20)
% 4.95/1.87  | (67) finite(all_0_22_22)
% 4.95/1.87  | (68)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 4.95/1.87  | (69)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1))
% 4.95/1.87  | (70) empty(all_0_6_6)
% 4.95/1.87  | (71) relation(all_0_18_18)
% 4.95/1.87  | (72) function(all_0_19_19)
% 4.95/1.87  | (73) ordinal(all_0_14_14)
% 4.95/1.87  | (74) epsilon_connected(all_0_14_14)
% 4.95/1.87  | (75) transfinite_sequence(all_0_19_19)
% 4.95/1.87  | (76)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 4.95/1.87  | (77)  ~ empty(all_0_0_0)
% 4.95/1.87  | (78)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.95/1.88  | (79) epsilon_transitive(all_0_0_0)
% 4.95/1.88  | (80) relation(all_0_2_2)
% 4.95/1.88  | (81) cartesian_product3(all_0_24_24, all_0_23_23, all_0_22_22) = all_0_21_21
% 4.95/1.88  | (82)  ! [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)))
% 4.95/1.88  | (83) transfinite_sequence(all_0_11_11)
% 4.95/1.88  | (84)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.95/1.88  | (85)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | natural(v0))
% 4.95/1.88  | (86)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1))
% 4.95/1.88  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1))
% 4.95/1.88  | (88) ordinal(empty_set)
% 4.95/1.88  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ~ empty(v3) | empty(v2) | empty(v1) | empty(v0))
% 4.95/1.88  | (90)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 4.95/1.88  | (91)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ empty(v2) | empty(v1) | empty(v0))
% 4.95/1.88  | (92) epsilon_transitive(all_0_8_8)
% 4.95/1.88  | (93)  ~ finite(all_0_21_21)
% 4.95/1.88  | (94) epsilon_connected(empty_set)
% 4.95/1.88  | (95)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 4.95/1.88  | (96)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.95/1.88  | (97) relation(all_0_6_6)
% 4.95/1.88  | (98) ordinal(all_0_10_10)
% 4.95/1.88  | (99) relation(all_0_20_20)
% 4.95/1.88  | (100) empty(all_0_7_7)
% 4.95/1.88  | (101) ordinal(all_0_4_4)
% 4.95/1.88  | (102) empty(empty_set)
% 4.95/1.88  | (103)  ~ empty(all_0_13_13)
% 4.95/1.88  | (104) element(all_0_14_14, positive_rationals)
% 4.95/1.88  | (105) relation_non_empty(all_0_20_20)
% 4.95/1.88  | (106) function(all_0_9_9)
% 4.95/1.88  | (107)  ~ empty(all_0_12_12)
% 4.95/1.88  | (108)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.95/1.88  | (109) relation(all_0_9_9)
% 4.95/1.88  | (110)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2))
% 4.95/1.88  | (111) natural(all_0_0_0)
% 4.95/1.88  | (112)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 4.95/1.88  | (113)  ~ empty(all_0_1_1)
% 4.95/1.88  | (114) finite(all_0_23_23)
% 4.95/1.88  | (115) relation(all_0_10_10)
% 4.95/1.89  | (116)  ~ empty(all_0_8_8)
% 4.95/1.89  | (117) ordinal(all_0_8_8)
% 4.95/1.89  | (118) function(all_0_11_11)
% 4.95/1.89  | (119)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.95/1.89  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) |  ~ (cartesian_product2(v0, v1) = v3) | cartesian_product3(v0, v1, v2) = v4)
% 4.95/1.89  | (121) relation(all_0_3_3)
% 4.95/1.89  | (122)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (cartesian_product3(v4, v3, v2) = v1) |  ~ (cartesian_product3(v4, v3, v2) = v0))
% 4.95/1.89  | (123)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) |  ? [v4] : (powerset(v3) = v4 &  ~ element(v0, v4)))
% 4.95/1.89  | (124)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 4.95/1.89  | (125) function_yielding(all_0_2_2)
% 4.95/1.89  | (126) epsilon_connected(all_0_0_0)
% 4.95/1.89  | (127) relation(empty_set)
% 4.95/1.89  | (128) finite(all_0_1_1)
% 4.95/1.89  | (129)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.95/1.89  |
% 4.95/1.89  | Instantiating formula (50) with all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24 and discharging atoms cartesian_product3(all_0_24_24, all_0_23_23, all_0_22_22) = all_0_21_21, yields:
% 4.95/1.89  | (130)  ? [v0] : (cartesian_product2(v0, all_0_22_22) = all_0_21_21 & cartesian_product2(all_0_24_24, all_0_23_23) = v0)
% 4.95/1.89  |
% 4.95/1.89  | Instantiating (130) with all_19_0_29 yields:
% 4.95/1.89  | (131) cartesian_product2(all_19_0_29, all_0_22_22) = all_0_21_21 & cartesian_product2(all_0_24_24, all_0_23_23) = all_19_0_29
% 4.95/1.89  |
% 4.95/1.89  | Applying alpha-rule on (131) yields:
% 4.95/1.89  | (132) cartesian_product2(all_19_0_29, all_0_22_22) = all_0_21_21
% 4.95/1.89  | (133) cartesian_product2(all_0_24_24, all_0_23_23) = all_19_0_29
% 4.95/1.89  |
% 4.95/1.89  | Instantiating formula (110) with all_19_0_29, all_0_23_23, all_0_24_24 and discharging atoms cartesian_product2(all_0_24_24, all_0_23_23) = all_19_0_29, finite(all_0_23_23), finite(all_0_24_24), yields:
% 4.95/1.89  | (134) finite(all_19_0_29)
% 4.95/1.89  |
% 4.95/1.89  | Instantiating formula (110) with all_0_21_21, all_0_22_22, all_19_0_29 and discharging atoms cartesian_product2(all_19_0_29, all_0_22_22) = all_0_21_21, finite(all_19_0_29), finite(all_0_22_22),  ~ finite(all_0_21_21), yields:
% 4.95/1.89  | (135) $false
% 4.95/1.89  |
% 4.95/1.89  |-The branch is then unsatisfiable
% 4.95/1.89  % SZS output end Proof for theBenchmark
% 4.95/1.89  
% 4.95/1.89  1237ms
%------------------------------------------------------------------------------