%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n013.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 : Mon Jul 18 08:44:13 EDT 2022

% Result   : Theorem 3.12s 1.40s
% Output   : Proof 4.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n013.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 : Wed Jul  6 19:06:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59          ____       _                          
% 0.19/0.59    ___  / __ \_____(_)___  ________  __________
% 0.19/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic
% 0.19/0.59  (ePrincess v.1.0)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2015
% 0.19/0.59  (c) Peter Backeman, 2014-2015
% 0.19/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59  Bug reports to peter@backeman.se
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.96  Prover 0: Preprocessing ...
% 2.28/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.39/1.22  Prover 0: Constructing countermodel ...
% 3.12/1.40  Prover 0: proved (758ms)
% 3.12/1.40  
% 3.12/1.40  No countermodel exists, formula is valid
% 3.12/1.40  % SZS status Theorem for theBenchmark
% 3.12/1.40  
% 3.12/1.40  Generating proof ... Warning: ignoring some quantifiers
% 4.50/1.71  found it (size 11)
% 4.50/1.71  
% 4.50/1.71  % SZS output start Proof for theBenchmark
% 4.50/1.71  Assumed formulas after preprocessing and simplification: 
% 4.50/1.71  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (tseq_dom_restriction(v1, v2) = v3 & relation_non_empty(v4) & relation_empty_yielding(v7) & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & transfinite_sequence_of(v1, v0) & transfinite_sequence(v5) & one_to_one(v12) & one_to_one(v9) & one_to_one(empty_set) & relation(v17) & relation(v15) & relation(v13) & relation(v12) & relation(v11) & relation(v9) & relation(v7) & relation(v6) & relation(v5) & relation(v4) & relation(empty_set) & epsilon_connected(v16) & epsilon_connected(v12) & epsilon_connected(v8) & epsilon_connected(empty_set) & epsilon_transitive(v16) & epsilon_transitive(v12) & epsilon_transitive(v8) & epsilon_transitive(empty_set) & ordinal(v16) & ordinal(v12) & ordinal(v8) & ordinal(v2) & ordinal(empty_set) & function(v17) & function(v13) & function(v12) & function(v9) & function(v6) & function(v5) & function(v4) & function(empty_set) & empty(v15) & empty(v14) & empty(v13) & empty(v12) & empty(empty_set) &  ~ transfinite_sequence_of(v3, v0) &  ~ empty(v11) &  ~ empty(v10) &  ~ empty(v8) &  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : (v19 = v18 |  ~ (relation_dom_restriction(v21, v20) = v19) |  ~ (relation_dom_restriction(v21, v20) = v18)) &  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : (v19 = v18 |  ~ (tseq_dom_restriction(v21, v20) = v19) |  ~ (tseq_dom_restriction(v21, v20) = v18)) &  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (powerset(v20) = v21) |  ~ element(v19, v21) |  ~ empty(v20) |  ~ in(v18, v19)) &  ! [v18] :  ! [v19] :  ! [v20] :  ! [v21] : ( ~ (powerset(v20) = v21) |  ~ element(v19, v21) |  ~ in(v18, v19) | element(v18, v20)) &  ! [v18] :  ! [v19] :  ! [v20] : (v19 = v18 |  ~ (powerset(v20) = v19) |  ~ (powerset(v20) = v18)) &  ! [v18] :  ! [v19] :  ! [v20] : (v19 = v18 |  ~ (relation_rng(v20) = v19) |  ~ (relation_rng(v20) = v18)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (powerset(v19) = v20) |  ~ element(v18, v20) | subset(v18, v19)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (powerset(v19) = v20) |  ~ subset(v18, v19) | element(v18, v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ relation_empty_yielding(v18) |  ~ relation(v18) | relation_empty_yielding(v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ relation_empty_yielding(v18) |  ~ relation(v18) | relation(v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ transfinite_sequence(v18) |  ~ relation(v18) |  ~ ordinal(v19) |  ~ function(v18) | tseq_dom_restriction(v18, v19) = v20) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ relation(v18) |  ~ function(v18) | relation(v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ relation(v18) |  ~ function(v18) | function(v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom_restriction(v18, v19) = v20) |  ~ relation(v18) | relation(v20)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (tseq_dom_restriction(v18, v19) = v20) |  ~ transfinite_sequence(v18) |  ~ relation(v18) |  ~ ordinal(v19) |  ~ function(v18) | relation_dom_restriction(v18, v19) = v20) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (tseq_dom_restriction(v18, v19) = v20) |  ~ transfinite_sequence(v18) |  ~ relation(v18) |  ~ ordinal(v19) |  ~ function(v18) |  ? [v21] : (relation_rng(v18) = v21 & transfinite_sequence_of(v20, v21))) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ~ subset(v20, v18) |  ~ transfinite_sequence(v19) |  ~ relation(v19) |  ~ function(v19) | transfinite_sequence_of(v19, v18)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_rng(v19) = v20) |  ~ transfinite_sequence_of(v19, v18) |  ~ transfinite_sequence(v19) |  ~ relation(v19) |  ~ function(v19) | subset(v20, v18)) &  ! [v18] :  ! [v19] :  ! [v20] : ( ~ subset(v18, v19) |  ~ transfinite_sequence_of(v20, v18) | transfinite_sequence_of(v20, v19)) &  ! [v18] :  ! [v19] : (v19 = v18 |  ~ empty(v19) |  ~ empty(v18)) &  ! [v18] :  ! [v19] : ( ~ (relation_rng(v18) = v19) |  ~ relation_non_empty(v18) |  ~ relation(v18) |  ~ function(v18) | with_non_empty_elements(v19)) &  ! [v18] :  ! [v19] : ( ~ (relation_rng(v18) = v19) |  ~ relation(v18) |  ~ empty(v19) | empty(v18)) &  ! [v18] :  ! [v19] : ( ~ (relation_rng(v18) = v19) |  ~ empty(v18) | relation(v19)) &  ! [v18] :  ! [v19] : ( ~ (relation_rng(v18) = v19) |  ~ empty(v18) | empty(v19)) &  ! [v18] :  ! [v19] : ( ~ element(v18, v19) | empty(v19) | in(v18, v19)) &  ! [v18] :  ! [v19] : ( ~ transfinite_sequence_of(v19, v18) | transfinite_sequence(v19)) &  ! [v18] :  ! [v19] : ( ~ transfinite_sequence_of(v19, v18) | relation(v19)) &  ! [v18] :  ! [v19] : ( ~ transfinite_sequence_of(v19, v18) | function(v19)) &  ! [v18] :  ! [v19] : ( ~ empty(v19) |  ~ in(v18, v19)) &  ! [v18] :  ! [v19] : ( ~ in(v19, v18) |  ~ in(v18, v19)) &  ! [v18] :  ! [v19] : ( ~ in(v18, v19) | element(v18, v19)) &  ! [v18] : (v18 = empty_set |  ~ empty(v18)) &  ! [v18] : ( ~ relation(v18) |  ~ function(v18) |  ~ empty(v18) | one_to_one(v18)) &  ! [v18] : ( ~ epsilon_connected(v18) |  ~ epsilon_transitive(v18) | ordinal(v18)) &  ! [v18] : ( ~ ordinal(v18) | epsilon_connected(v18)) &  ! [v18] : ( ~ ordinal(v18) | epsilon_transitive(v18)) &  ! [v18] : ( ~ empty(v18) | relation(v18)) &  ! [v18] : ( ~ empty(v18) | epsilon_connected(v18)) &  ! [v18] : ( ~ empty(v18) | epsilon_transitive(v18)) &  ! [v18] : ( ~ empty(v18) | ordinal(v18)) &  ! [v18] : ( ~ empty(v18) | function(v18)) &  ? [v18] :  ? [v19] : element(v19, v18) &  ? [v18] :  ? [v19] : transfinite_sequence_of(v19, v18) &  ? [v18] : subset(v18, v18))
% 4.50/1.76  | 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 yields:
% 4.50/1.76  | (1) tseq_dom_restriction(all_0_16_16, all_0_15_15) = all_0_14_14 & relation_non_empty(all_0_13_13) & relation_empty_yielding(all_0_10_10) & relation_empty_yielding(all_0_11_11) & relation_empty_yielding(empty_set) & transfinite_sequence_of(all_0_16_16, all_0_17_17) & transfinite_sequence(all_0_12_12) & one_to_one(all_0_5_5) & one_to_one(all_0_8_8) & one_to_one(empty_set) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_6_6) & relation(all_0_8_8) & relation(all_0_10_10) & relation(all_0_11_11) & relation(all_0_12_12) & relation(all_0_13_13) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_9_9) & epsilon_connected(empty_set) & epsilon_transitive(all_0_1_1) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_9_9) & epsilon_transitive(empty_set) & ordinal(all_0_1_1) & ordinal(all_0_5_5) & ordinal(all_0_9_9) & ordinal(all_0_15_15) & ordinal(empty_set) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_5_5) & function(all_0_8_8) & function(all_0_11_11) & function(all_0_12_12) & function(all_0_13_13) & function(empty_set) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(all_0_5_5) & empty(empty_set) &  ~ transfinite_sequence_of(all_0_14_14, all_0_17_17) &  ~ empty(all_0_6_6) &  ~ empty(all_0_7_7) &  ~ empty(all_0_9_9) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (tseq_dom_restriction(v3, v2) = v1) |  ~ (tseq_dom_restriction(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] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(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] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) | tseq_dom_restriction(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tseq_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) | relation_dom_restriction(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tseq_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) |  ? [v3] : (relation_rng(v0) = v3 & transfinite_sequence_of(v2, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ subset(v2, v0) |  ~ transfinite_sequence(v1) |  ~ relation(v1) |  ~ function(v1) | transfinite_sequence_of(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ transfinite_sequence_of(v1, v0) |  ~ transfinite_sequence(v1) |  ~ relation(v1) |  ~ function(v1) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ transfinite_sequence_of(v2, v0) | transfinite_sequence_of(v2, v1)) &  ! [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) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | transfinite_sequence(v1)) &  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | function(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] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) &  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) &  ! [v0] : ( ~ empty(v0) | ordinal(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] :  ? [v1] : transfinite_sequence_of(v1, v0) &  ? [v0] : subset(v0, v0)
% 4.89/1.77  |
% 4.89/1.77  | Applying alpha-rule on (1) yields:
% 4.89/1.77  | (2) relation(all_0_12_12)
% 4.89/1.77  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2))
% 4.89/1.77  | (4) relation(all_0_10_10)
% 4.89/1.77  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) | tseq_dom_restriction(v0, v1) = v2)
% 4.89/1.77  | (6)  ! [v0] : ( ~ empty(v0) | epsilon_connected(v0))
% 4.89/1.77  | (7) transfinite_sequence_of(all_0_16_16, all_0_17_17)
% 4.89/1.77  | (8) ordinal(all_0_9_9)
% 4.89/1.77  | (9)  ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0))
% 4.89/1.77  | (10) function(empty_set)
% 4.89/1.77  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 4.89/1.77  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0))
% 4.89/1.77  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 4.89/1.78  | (14)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.89/1.78  | (15)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 4.89/1.78  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2))
% 4.89/1.78  | (17) epsilon_transitive(all_0_9_9)
% 4.89/1.78  | (18) epsilon_transitive(all_0_1_1)
% 4.89/1.78  | (19)  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | relation(v1))
% 4.89/1.78  | (20) epsilon_transitive(empty_set)
% 4.89/1.78  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 4.89/1.78  | (22) relation(all_0_0_0)
% 4.89/1.78  | (23)  ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0))
% 4.89/1.78  | (24) epsilon_connected(all_0_5_5)
% 4.89/1.78  | (25) epsilon_connected(empty_set)
% 4.89/1.78  | (26)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.89/1.78  | (27) ordinal(all_0_15_15)
% 4.89/1.78  | (28)  ~ empty(all_0_6_6)
% 4.89/1.78  | (29) relation_empty_yielding(all_0_11_11)
% 4.89/1.78  | (30) relation(empty_set)
% 4.89/1.78  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ transfinite_sequence_of(v1, v0) |  ~ transfinite_sequence(v1) |  ~ relation(v1) |  ~ function(v1) | subset(v2, v0))
% 4.89/1.78  | (32) function(all_0_8_8)
% 4.89/1.78  | (33) relation(all_0_8_8)
% 4.89/1.78  | (34)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 4.89/1.78  | (35) empty(all_0_3_3)
% 4.89/1.78  | (36) ordinal(all_0_1_1)
% 4.89/1.78  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | relation(v2))
% 4.89/1.78  | (38) epsilon_connected(all_0_1_1)
% 4.89/1.78  | (39) relation(all_0_4_4)
% 4.89/1.78  | (40)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 4.97/1.78  | (41)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.97/1.78  | (42)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.97/1.78  | (43) function(all_0_4_4)
% 4.97/1.78  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2))
% 4.97/1.78  | (45)  ~ empty(all_0_7_7)
% 4.97/1.78  | (46)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.97/1.78  | (47) function(all_0_5_5)
% 4.97/1.78  | (48) ordinal(empty_set)
% 4.97/1.78  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (tseq_dom_restriction(v3, v2) = v1) |  ~ (tseq_dom_restriction(v3, v2) = v0))
% 4.97/1.78  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.97/1.78  | (51)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.97/1.78  | (52) relation_empty_yielding(all_0_10_10)
% 4.97/1.78  | (53) relation(all_0_2_2)
% 4.97/1.78  | (54) epsilon_transitive(all_0_5_5)
% 4.97/1.78  | (55)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tseq_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) |  ? [v3] : (relation_rng(v0) = v3 & transfinite_sequence_of(v2, v3)))
% 4.97/1.79  | (56)  ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0))
% 4.97/1.79  | (57)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.97/1.79  | (58) empty(all_0_4_4)
% 4.97/1.79  | (59) relation(all_0_5_5)
% 4.97/1.79  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 4.97/1.79  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 4.97/1.79  | (62) transfinite_sequence(all_0_12_12)
% 4.97/1.79  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ transfinite_sequence_of(v2, v0) | transfinite_sequence_of(v2, v1))
% 4.97/1.79  | (64) tseq_dom_restriction(all_0_16_16, all_0_15_15) = all_0_14_14
% 4.97/1.79  | (65) function(all_0_0_0)
% 4.97/1.79  | (66) relation(all_0_11_11)
% 4.97/1.79  | (67)  ~ transfinite_sequence_of(all_0_14_14, all_0_17_17)
% 4.97/1.79  | (68) relation_non_empty(all_0_13_13)
% 4.97/1.79  | (69)  ! [v0] : ( ~ epsilon_connected(v0) |  ~ epsilon_transitive(v0) | ordinal(v0))
% 4.97/1.79  | (70)  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | transfinite_sequence(v1))
% 4.97/1.79  | (71) one_to_one(all_0_8_8)
% 4.97/1.79  | (72)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | function(v2))
% 4.97/1.79  | (73) relation_empty_yielding(empty_set)
% 4.97/1.79  | (74)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 4.97/1.79  | (75) function(all_0_12_12)
% 4.97/1.79  | (76) one_to_one(empty_set)
% 4.97/1.79  | (77)  ? [v0] : subset(v0, v0)
% 4.97/1.79  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (tseq_dom_restriction(v0, v1) = v2) |  ~ transfinite_sequence(v0) |  ~ relation(v0) |  ~ ordinal(v1) |  ~ function(v0) | relation_dom_restriction(v0, v1) = v2)
% 4.97/1.79  | (79) function(all_0_13_13)
% 4.97/1.79  | (80) empty(all_0_2_2)
% 4.97/1.79  | (81) relation(all_0_6_6)
% 4.97/1.79  | (82)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.97/1.79  | (83) epsilon_connected(all_0_9_9)
% 4.97/1.79  | (84) one_to_one(all_0_5_5)
% 4.97/1.79  | (85)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.97/1.79  | (86) ordinal(all_0_5_5)
% 4.97/1.79  | (87)  ! [v0] :  ! [v1] : ( ~ transfinite_sequence_of(v1, v0) | function(v1))
% 4.97/1.79  | (88)  ! [v0] : ( ~ empty(v0) | ordinal(v0))
% 4.97/1.79  | (89)  ? [v0] :  ? [v1] : transfinite_sequence_of(v1, v0)
% 4.97/1.79  | (90) empty(all_0_5_5)
% 4.97/1.79  | (91)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation_non_empty(v0) |  ~ relation(v0) |  ~ function(v0) | with_non_empty_elements(v1))
% 4.97/1.80  | (92) relation(all_0_13_13)
% 4.97/1.80  | (93) function(all_0_11_11)
% 4.97/1.80  | (94)  ~ empty(all_0_9_9)
% 4.97/1.80  | (95)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ subset(v2, v0) |  ~ transfinite_sequence(v1) |  ~ relation(v1) |  ~ function(v1) | transfinite_sequence_of(v1, v0))
% 4.97/1.80  | (96) empty(empty_set)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (70) with all_0_16_16, all_0_17_17 and discharging atoms transfinite_sequence_of(all_0_16_16, all_0_17_17), yields:
% 4.97/1.80  | (97) transfinite_sequence(all_0_16_16)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (19) with all_0_16_16, all_0_17_17 and discharging atoms transfinite_sequence_of(all_0_16_16, all_0_17_17), yields:
% 4.97/1.80  | (98) relation(all_0_16_16)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (87) with all_0_16_16, all_0_17_17 and discharging atoms transfinite_sequence_of(all_0_16_16, all_0_17_17), yields:
% 4.97/1.80  | (99) function(all_0_16_16)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (55) with all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms tseq_dom_restriction(all_0_16_16, all_0_15_15) = all_0_14_14, transfinite_sequence(all_0_16_16), relation(all_0_16_16), ordinal(all_0_15_15), function(all_0_16_16), yields:
% 4.97/1.80  | (100)  ? [v0] : (relation_rng(all_0_16_16) = v0 & transfinite_sequence_of(all_0_14_14, v0))
% 4.97/1.80  |
% 4.97/1.80  | Instantiating (100) with all_25_0_23 yields:
% 4.97/1.80  | (101) relation_rng(all_0_16_16) = all_25_0_23 & transfinite_sequence_of(all_0_14_14, all_25_0_23)
% 4.97/1.80  |
% 4.97/1.80  | Applying alpha-rule on (101) yields:
% 4.97/1.80  | (102) relation_rng(all_0_16_16) = all_25_0_23
% 4.97/1.80  | (103) transfinite_sequence_of(all_0_14_14, all_25_0_23)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (31) with all_25_0_23, all_0_16_16, all_0_17_17 and discharging atoms relation_rng(all_0_16_16) = all_25_0_23, transfinite_sequence_of(all_0_16_16, all_0_17_17), transfinite_sequence(all_0_16_16), relation(all_0_16_16), function(all_0_16_16), yields:
% 4.97/1.80  | (104) subset(all_25_0_23, all_0_17_17)
% 4.97/1.80  |
% 4.97/1.80  | Instantiating formula (63) with all_0_14_14, all_0_17_17, all_25_0_23 and discharging atoms subset(all_25_0_23, all_0_17_17), transfinite_sequence_of(all_0_14_14, all_25_0_23),  ~ transfinite_sequence_of(all_0_14_14, all_0_17_17), yields:
% 4.97/1.80  | (105) $false
% 4.97/1.80  |
% 4.97/1.80  |-The branch is then unsatisfiable
% 4.97/1.80  % SZS output end Proof for theBenchmark
% 4.97/1.80  
% 4.97/1.80  1199ms
%------------------------------------------------------------------------------