%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU090+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 08:46:33 EDT 2022

% Result   : Theorem 3.35s 1.44s
% Output   : Proof 5.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU090+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n021.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 08:41:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.54/0.59          ____       _                          
% 0.54/0.59    ___  / __ \_____(_)___  ________  __________
% 0.54/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.59  
% 0.54/0.59  A Theorem Prover for First-Order Logic
% 0.54/0.59  (ePrincess v.1.0)
% 0.54/0.59  
% 0.54/0.59  (c) Philipp Rümmer, 2009-2015
% 0.54/0.59  (c) Peter Backeman, 2014-2015
% 0.54/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59  Bug reports to peter@backeman.se
% 0.54/0.59  
% 0.54/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59  
% 0.54/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/0.99  Prover 0: Preprocessing ...
% 2.81/1.23  Prover 0: Warning: ignoring some quantifiers
% 2.87/1.26  Prover 0: Constructing countermodel ...
% 3.35/1.44  Prover 0: proved (802ms)
% 3.35/1.44  
% 3.35/1.44  No countermodel exists, formula is valid
% 3.35/1.44  % SZS status Theorem for theBenchmark
% 3.35/1.44  
% 3.35/1.44  Generating proof ... Warning: ignoring some quantifiers
% 5.15/1.77  found it (size 8)
% 5.15/1.77  
% 5.15/1.77  % SZS output start Proof for theBenchmark
% 5.15/1.77  Assumed formulas after preprocessing and simplification: 
% 5.15/1.77  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] : (cartesian_product4(v0, v1, v2, v3) = v4 & relation_non_empty(v5) & ordinal_yielding(v14) & transfinite_sequence(v14) & transfinite_sequence(v6) & being_limit_ordinal(v20) & function_yielding(v23) & relation_empty_yielding(v8) & relation_empty_yielding(v7) & relation_empty_yielding(empty_set) & one_to_one(v15) & one_to_one(v10) & one_to_one(empty_set) & natural(v25) & natural(v11) & relation(v23) & relation(v22) & relation(v19) & relation(v16) & relation(v15) & relation(v14) & relation(v13) & relation(v10) & relation(v8) & relation(v7) & relation(v6) & relation(v5) & relation(empty_set) & function(v23) & function(v22) & function(v16) & function(v15) & function(v14) & function(v10) & function(v7) & function(v6) & function(v5) & function(empty_set) & finite(v24) & finite(v3) & finite(v2) & finite(v1) & finite(v0) & empty(v19) & empty(v18) & empty(v16) & empty(v15) & empty(v11) & empty(empty_set) & epsilon_connected(v25) & epsilon_connected(v21) & epsilon_connected(v20) & epsilon_connected(v17) & epsilon_connected(v15) & epsilon_connected(v11) & epsilon_connected(v9) & epsilon_connected(empty_set) & epsilon_transitive(v25) & epsilon_transitive(v21) & epsilon_transitive(v20) & epsilon_transitive(v17) & epsilon_transitive(v15) & epsilon_transitive(v11) & epsilon_transitive(v9) & epsilon_transitive(empty_set) & element(v17, positive_rationals) & element(v11, positive_rationals) & ordinal(v25) & ordinal(v21) & ordinal(v20) & ordinal(v17) & ordinal(v15) & ordinal(v11) & ordinal(v9) & ordinal(empty_set) &  ~ finite(v4) &  ~ empty(v25) &  ~ empty(v24) &  ~ empty(v17) &  ~ empty(v13) &  ~ empty(v12) &  ~ empty(v9) &  ~ empty(positive_rationals) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : (v27 = v26 |  ~ (cartesian_product4(v31, v30, v29, v28) = v27) |  ~ (cartesian_product4(v31, v30, v29, v28) = v26)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] :  ! [v30] :  ! [v31] : ( ~ (cartesian_product3(v26, v27, v28) = v30) |  ~ (cartesian_product2(v30, v29) = v31) | cartesian_product4(v26, v27, v28, v29) = v31) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] :  ! [v30] : (v27 = v26 |  ~ (cartesian_product3(v30, v29, v28) = v27) |  ~ (cartesian_product3(v30, v29, v28) = v26)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] :  ! [v30] : ( ~ (cartesian_product4(v26, v27, v28, v29) = v30) |  ~ empty(v30) | empty(v29) | empty(v28) | empty(v27) | empty(v26)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] :  ! [v30] : ( ~ (cartesian_product4(v26, v27, v28, v29) = v30) |  ? [v31] : (cartesian_product3(v26, v27, v28) = v31 & cartesian_product2(v31, v29) = v30)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : (v27 = v26 |  ~ (cartesian_product2(v29, v28) = v27) |  ~ (cartesian_product2(v29, v28) = v26)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (cartesian_product3(v26, v27, v28) = v29) |  ~ finite(v28) |  ~ finite(v27) |  ~ finite(v26) | finite(v29)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (cartesian_product3(v26, v27, v28) = v29) |  ~ empty(v29) | empty(v28) | empty(v27) | empty(v26)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (powerset(v28) = v29) |  ~ empty(v28) |  ~ element(v27, v29) |  ~ in(v26, v27)) &  ! [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (powerset(v28) = v29) |  ~ element(v27, v29) |  ~ in(v26, v27) | element(v26, v28)) &  ? [v26] :  ! [v27] :  ! [v28] :  ! [v29] : ( ~ (cartesian_product2(v27, v28) = v29) | relation(v26) |  ? [v30] : (powerset(v29) = v30 &  ~ element(v26, v30))) &  ! [v26] :  ! [v27] :  ! [v28] : (v27 = v26 |  ~ (powerset(v28) = v27) |  ~ (powerset(v28) = v26)) &  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (cartesian_product2(v26, v27) = v28) |  ~ finite(v27) |  ~ finite(v26) | finite(v28)) &  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (cartesian_product2(v26, v27) = v28) |  ~ empty(v28) | empty(v27) | empty(v26)) &  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (powerset(v27) = v28) |  ~ subset(v26, v27) | element(v26, v28)) &  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (powerset(v27) = v28) |  ~ element(v26, v28) | subset(v26, v27)) &  ! [v26] :  ! [v27] :  ! [v28] : ( ~ (powerset(v26) = v27) |  ~ finite(v26) |  ~ element(v28, v27) | finite(v28)) &  ! [v26] :  ! [v27] : (v27 = v26 |  ~ empty(v27) |  ~ empty(v26)) &  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ~ empty(v27)) &  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) | empty(v26) |  ? [v28] : (finite(v28) & element(v28, v27) &  ~ empty(v28))) &  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) | empty(v26) |  ? [v28] : (element(v28, v27) &  ~ empty(v28))) &  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ? [v28] : (one_to_one(v28) & natural(v28) & relation(v28) & function(v28) & finite(v28) & empty(v28) & epsilon_connected(v28) & epsilon_transitive(v28) & element(v28, v27) & ordinal(v28))) &  ! [v26] :  ! [v27] : ( ~ (powerset(v26) = v27) |  ? [v28] : (empty(v28) & element(v28, v27))) &  ! [v26] :  ! [v27] : ( ~ empty(v27) |  ~ in(v26, v27)) &  ! [v26] :  ! [v27] : ( ~ element(v27, v26) |  ~ ordinal(v26) | epsilon_connected(v27)) &  ! [v26] :  ! [v27] : ( ~ element(v27, v26) |  ~ ordinal(v26) | epsilon_transitive(v27)) &  ! [v26] :  ! [v27] : ( ~ element(v27, v26) |  ~ ordinal(v26) | ordinal(v27)) &  ! [v26] :  ! [v27] : ( ~ element(v26, v27) | empty(v27) | in(v26, v27)) &  ! [v26] :  ! [v27] : ( ~ in(v27, v26) |  ~ in(v26, v27)) &  ! [v26] :  ! [v27] : ( ~ in(v26, v27) | element(v26, v27)) &  ! [v26] : (v26 = empty_set |  ~ empty(v26)) &  ! [v26] : ( ~ relation(v26) |  ~ function(v26) |  ~ empty(v26) | one_to_one(v26)) &  ! [v26] : ( ~ empty(v26) |  ~ ordinal(v26) | natural(v26)) &  ! [v26] : ( ~ empty(v26) |  ~ ordinal(v26) | epsilon_connected(v26)) &  ! [v26] : ( ~ empty(v26) |  ~ ordinal(v26) | epsilon_transitive(v26)) &  ! [v26] : ( ~ empty(v26) | relation(v26)) &  ! [v26] : ( ~ empty(v26) | function(v26)) &  ! [v26] : ( ~ empty(v26) | finite(v26)) &  ! [v26] : ( ~ empty(v26) | epsilon_connected(v26)) &  ! [v26] : ( ~ empty(v26) | epsilon_transitive(v26)) &  ! [v26] : ( ~ empty(v26) | ordinal(v26)) &  ! [v26] : ( ~ epsilon_connected(v26) |  ~ epsilon_transitive(v26) | ordinal(v26)) &  ! [v26] : ( ~ element(v26, positive_rationals) |  ~ ordinal(v26) | natural(v26)) &  ! [v26] : ( ~ element(v26, positive_rationals) |  ~ ordinal(v26) | epsilon_connected(v26)) &  ! [v26] : ( ~ element(v26, positive_rationals) |  ~ ordinal(v26) | epsilon_transitive(v26)) &  ! [v26] : ( ~ ordinal(v26) | epsilon_connected(v26)) &  ! [v26] : ( ~ ordinal(v26) | epsilon_transitive(v26)) &  ? [v26] :  ? [v27] : element(v27, v26) &  ? [v26] : subset(v26, v26))
% 5.40/1.82  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25 yields:
% 5.40/1.82  | (1) cartesian_product4(all_0_25_25, 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) & finite(all_0_25_25) & 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] :  ! [v5] : (v1 = v0 |  ~ (cartesian_product4(v5, v4, v3, v2) = v1) |  ~ (cartesian_product4(v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product3(v0, v1, v2) = v4) |  ~ (cartesian_product2(v4, v3) = v5) | cartesian_product4(v0, v1, v2, v3) = v5) &  ! [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_product4(v0, v1, v2, v3) = v4) |  ~ empty(v4) | empty(v3) | empty(v2) | empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product4(v0, v1, v2, v3) = v4) |  ? [v5] : (cartesian_product3(v0, v1, v2) = v5 & cartesian_product2(v5, v3) = 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) |  ~ finite(v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ~ empty(v3) | empty(v2) | empty(v1) | empty(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] :  ! [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)
% 5.40/1.83  |
% 5.40/1.83  | Applying alpha-rule on (1) yields:
% 5.40/1.83  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (cartesian_product4(v5, v4, v3, v2) = v1) |  ~ (cartesian_product4(v5, v4, v3, v2) = v0))
% 5.40/1.83  | (3)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.40/1.83  | (4)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 5.49/1.83  | (5)  ~ empty(positive_rationals)
% 5.49/1.83  | (6) relation_empty_yielding(all_0_18_18)
% 5.49/1.83  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ finite(v0) |  ~ element(v2, v1) | finite(v2))
% 5.49/1.83  | (8) relation(all_0_20_20)
% 5.49/1.83  | (9)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.49/1.83  | (10) relation(all_0_6_6)
% 5.49/1.83  | (11)  ~ empty(all_0_12_12)
% 5.49/1.83  | (12)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 5.49/1.83  | (13) natural(all_0_0_0)
% 5.49/1.83  | (14) element(all_0_14_14, positive_rationals)
% 5.49/1.83  | (15) function(all_0_15_15)
% 5.49/1.83  | (16) empty(all_0_10_10)
% 5.49/1.83  | (17) epsilon_connected(all_0_0_0)
% 5.49/1.83  | (18) relation_empty_yielding(all_0_17_17)
% 5.49/1.83  | (19) epsilon_transitive(empty_set)
% 5.49/1.83  | (20) relation(all_0_15_15)
% 5.49/1.83  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ empty(v2) | empty(v1) | empty(v0))
% 5.49/1.84  | (22)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_connected(v0))
% 5.49/1.84  | (23) epsilon_connected(all_0_4_4)
% 5.49/1.84  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product4(v0, v1, v2, v3) = v4) |  ? [v5] : (cartesian_product3(v0, v1, v2) = v5 & cartesian_product2(v5, v3) = v4))
% 5.49/1.84  | (25) function(all_0_19_19)
% 5.49/1.84  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product3(v0, v1, v2) = v4) |  ~ (cartesian_product2(v4, v3) = v5) | cartesian_product4(v0, v1, v2, v3) = v5)
% 5.49/1.84  | (27) relation(all_0_10_10)
% 5.49/1.84  | (28) empty(all_0_7_7)
% 5.49/1.84  | (29)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (finite(v2) & element(v2, v1) &  ~ empty(v2)))
% 5.49/1.84  | (30)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.49/1.84  | (31) epsilon_transitive(all_0_0_0)
% 5.49/1.84  | (32) epsilon_transitive(all_0_10_10)
% 5.49/1.84  | (33) ordinal_yielding(all_0_11_11)
% 5.49/1.84  | (34)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) |  ? [v4] : (powerset(v3) = v4 &  ~ element(v0, v4)))
% 5.49/1.84  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 5.49/1.84  | (36) finite(all_0_24_24)
% 5.49/1.84  | (37)  ~ empty(all_0_0_0)
% 5.49/1.84  | (38)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_connected(v1))
% 5.49/1.84  | (39)  ! [v0] : ( ~ empty(v0) | finite(v0))
% 5.49/1.84  | (40) epsilon_connected(all_0_5_5)
% 5.49/1.84  | (41) cartesian_product4(all_0_25_25, all_0_24_24, all_0_23_23, all_0_22_22) = all_0_21_21
% 5.49/1.84  | (42) function(all_0_9_9)
% 5.49/1.84  | (43) epsilon_connected(all_0_8_8)
% 5.49/1.84  | (44) empty(all_0_6_6)
% 5.49/1.84  | (45) function(all_0_3_3)
% 5.49/1.84  | (46) epsilon_connected(all_0_10_10)
% 5.49/1.84  | (47) epsilon_transitive(all_0_14_14)
% 5.49/1.84  | (48) function(all_0_18_18)
% 5.49/1.84  | (49) epsilon_connected(all_0_14_14)
% 5.49/1.84  | (50) function(empty_set)
% 5.49/1.84  | (51) relation(all_0_2_2)
% 5.49/1.84  | (52)  ? [v0] : subset(v0, v0)
% 5.49/1.84  | (53) ordinal(all_0_5_5)
% 5.49/1.84  | (54) function(all_0_20_20)
% 5.49/1.84  | (55)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_connected(v0))
% 5.49/1.84  | (56)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 5.49/1.84  | (57)  ~ empty(all_0_16_16)
% 5.49/1.84  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ empty(v2) |  ~ element(v1, v3) |  ~ in(v0, v1))
% 5.49/1.84  | (59)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 5.49/1.84  | (60)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 5.49/1.84  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ~ empty(v3) | empty(v2) | empty(v1) | empty(v0))
% 5.49/1.84  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 5.49/1.84  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.49/1.84  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.49/1.84  | (65) transfinite_sequence(all_0_19_19)
% 5.49/1.84  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.49/1.84  | (67) one_to_one(empty_set)
% 5.49/1.85  | (68) epsilon_transitive(all_0_5_5)
% 5.49/1.85  | (69)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.49/1.85  | (70) relation(all_0_3_3)
% 5.49/1.85  | (71) ordinal(empty_set)
% 5.49/1.85  | (72) epsilon_transitive(all_0_4_4)
% 5.49/1.85  | (73)  ~ empty(all_0_1_1)
% 5.49/1.85  | (74) transfinite_sequence(all_0_11_11)
% 5.49/1.85  | (75)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 5.49/1.85  | (76)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | epsilon_transitive(v1))
% 5.49/1.85  | (77) natural(all_0_14_14)
% 5.49/1.85  | (78) epsilon_transitive(all_0_8_8)
% 5.49/1.85  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v2))
% 5.49/1.85  | (80)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.49/1.85  | (81) empty(all_0_9_9)
% 5.49/1.85  | (82) ordinal(all_0_10_10)
% 5.49/1.85  | (83)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 5.49/1.85  | (84) relation_non_empty(all_0_20_20)
% 5.49/1.85  | (85) empty(empty_set)
% 5.49/1.85  | (86) relation(all_0_18_18)
% 5.49/1.85  | (87)  ! [v0] : ( ~ empty(v0) | function(v0))
% 5.49/1.85  | (88)  ! [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)))
% 5.49/1.85  | (89)  ! [v0] : ( ~ element(v0, positive_rationals) |  ~ ordinal(v0) | natural(v0))
% 5.49/1.85  | (90) epsilon_connected(empty_set)
% 5.49/1.85  | (91) epsilon_connected(all_0_16_16)
% 5.49/1.85  | (92) function(all_0_11_11)
% 5.49/1.85  | (93)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.49/1.85  | (94)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | natural(v0))
% 5.49/1.85  | (95)  ! [v0] :  ! [v1] : ( ~ element(v1, v0) |  ~ ordinal(v0) | ordinal(v1))
% 5.49/1.85  | (96)  ~ empty(all_0_13_13)
% 5.49/1.85  | (97) function(all_0_10_10)
% 5.49/1.85  | (98) finite(all_0_25_25)
% 5.49/1.85  | (99)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.49/1.85  | (100)  ~ finite(all_0_21_21)
% 5.49/1.85  | (101)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (empty(v2) & element(v2, v1)))
% 5.49/1.85  | (102) function_yielding(all_0_2_2)
% 5.49/1.85  | (103) finite(all_0_23_23)
% 5.49/1.85  | (104) element(all_0_8_8, positive_rationals)
% 5.49/1.85  | (105) ordinal(all_0_16_16)
% 5.49/1.85  | (106)  ! [v0] : ( ~ empty(v0) |  ~ ordinal(v0) | epsilon_transitive(v0))
% 5.49/1.85  | (107)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.49/1.85  | (108) empty(all_0_14_14)
% 5.49/1.85  | (109)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (cartesian_product3(v4, v3, v2) = v1) |  ~ (cartesian_product3(v4, v3, v2) = v0))
% 5.49/1.85  | (110) relation(all_0_19_19)
% 5.49/1.85  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (cartesian_product4(v0, v1, v2, v3) = v4) |  ~ empty(v4) | empty(v3) | empty(v2) | empty(v1) | empty(v0))
% 5.49/1.86  | (112) ordinal(all_0_8_8)
% 5.49/1.86  | (113) one_to_one(all_0_15_15)
% 5.49/1.86  | (114) epsilon_transitive(all_0_16_16)
% 5.49/1.86  | (115) relation(all_0_12_12)
% 5.49/1.86  | (116) one_to_one(all_0_10_10)
% 5.49/1.86  | (117)  ~ empty(all_0_8_8)
% 5.49/1.86  | (118) relation(all_0_17_17)
% 5.49/1.86  | (119) being_limit_ordinal(all_0_5_5)
% 5.49/1.86  | (120) relation(empty_set)
% 5.49/1.86  | (121) relation(all_0_11_11)
% 5.49/1.86  | (122) ordinal(all_0_4_4)
% 5.49/1.86  | (123) ordinal(all_0_0_0)
% 5.49/1.86  | (124)  ? [v0] :  ? [v1] : element(v1, v0)
% 5.49/1.86  | (125) function(all_0_2_2)
% 5.49/1.86  | (126) finite(all_0_22_22)
% 5.49/1.86  | (127)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 5.49/1.86  | (128)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product3(v0, v1, v2) = v3) |  ~ finite(v2) |  ~ finite(v1) |  ~ finite(v0) | finite(v3))
% 5.49/1.86  | (129) relation_empty_yielding(empty_set)
% 5.49/1.86  | (130) finite(all_0_1_1)
% 5.49/1.86  | (131) relation(all_0_9_9)
% 5.49/1.86  | (132)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.49/1.86  | (133) ordinal(all_0_14_14)
% 5.49/1.86  |
% 5.49/1.86  | Instantiating formula (24) with all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25 and discharging atoms cartesian_product4(all_0_25_25, all_0_24_24, all_0_23_23, all_0_22_22) = all_0_21_21, yields:
% 5.49/1.86  | (134)  ? [v0] : (cartesian_product3(all_0_25_25, all_0_24_24, all_0_23_23) = v0 & cartesian_product2(v0, all_0_22_22) = all_0_21_21)
% 5.49/1.86  |
% 5.49/1.86  | Instantiating (134) with all_19_0_30 yields:
% 5.49/1.86  | (135) cartesian_product3(all_0_25_25, all_0_24_24, all_0_23_23) = all_19_0_30 & cartesian_product2(all_19_0_30, all_0_22_22) = all_0_21_21
% 5.49/1.86  |
% 5.49/1.86  | Applying alpha-rule on (135) yields:
% 5.49/1.86  | (136) cartesian_product3(all_0_25_25, all_0_24_24, all_0_23_23) = all_19_0_30
% 5.49/1.86  | (137) cartesian_product2(all_19_0_30, all_0_22_22) = all_0_21_21
% 5.49/1.86  |
% 5.49/1.86  | Instantiating formula (128) with all_19_0_30, all_0_23_23, all_0_24_24, all_0_25_25 and discharging atoms cartesian_product3(all_0_25_25, all_0_24_24, all_0_23_23) = all_19_0_30, finite(all_0_23_23), finite(all_0_24_24), finite(all_0_25_25), yields:
% 5.49/1.86  | (138) finite(all_19_0_30)
% 5.49/1.86  |
% 5.49/1.86  | Instantiating formula (79) with all_0_21_21, all_0_22_22, all_19_0_30 and discharging atoms cartesian_product2(all_19_0_30, all_0_22_22) = all_0_21_21, finite(all_19_0_30), finite(all_0_22_22),  ~ finite(all_0_21_21), yields:
% 5.49/1.86  | (139) $false
% 5.49/1.86  |
% 5.49/1.87  |-The branch is then unsatisfiable
% 5.49/1.87  % SZS output end Proof for theBenchmark
% 5.49/1.87  
% 5.49/1.87  1267ms
%------------------------------------------------------------------------------