%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 00:23:41 EDT 2022

% Result   : Theorem 3.25s 1.46s
% Output   : Proof 5.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET995+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n027.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 : Sat Jul  9 17:43:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.48/0.58          ____       _                          
% 0.48/0.58    ___  / __ \_____(_)___  ________  __________
% 0.48/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.48/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.48/0.58  
% 0.48/0.58  A Theorem Prover for First-Order Logic
% 0.48/0.58  (ePrincess v.1.0)
% 0.48/0.58  
% 0.48/0.58  (c) Philipp Rümmer, 2009-2015
% 0.48/0.58  (c) Peter Backeman, 2014-2015
% 0.48/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.58  Bug reports to peter@backeman.se
% 0.48/0.58  
% 0.48/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.58  
% 0.48/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.96  Prover 0: Preprocessing ...
% 2.38/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.38/1.26  Prover 0: Constructing countermodel ...
% 3.25/1.45  Prover 0: proved (823ms)
% 3.25/1.46  
% 3.25/1.46  No countermodel exists, formula is valid
% 3.25/1.46  % SZS status Theorem for theBenchmark
% 3.25/1.46  
% 3.25/1.46  Generating proof ... Warning: ignoring some quantifiers
% 4.82/1.84  found it (size 24)
% 4.82/1.84  
% 4.82/1.84  % SZS output start Proof for theBenchmark
% 4.82/1.84  Assumed formulas after preprocessing and simplification: 
% 4.82/1.84  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v4 = v1) & relation_rng(v4) = v3 & relation_rng(v1) = v3 & relation_dom(v4) = v2 & relation_dom(v1) = v2 & singleton(v0) = v3 & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & relation(v10) & relation(v9) & relation(v7) & relation(v5) & relation(v4) & relation(v1) & relation(empty_set) & function(v10) & function(v4) & function(v1) & empty(v9) & empty(v8) & empty(empty_set) &  ~ empty(v7) &  ~ empty(v6) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (apply(v14, v13) = v12) |  ~ (apply(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (powerset(v13) = v14) |  ~ element(v12, v14) |  ~ empty(v13) |  ~ in(v11, v12)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (powerset(v13) = v14) |  ~ element(v12, v14) |  ~ in(v11, v12) | element(v11, v13)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (relation_dom(v13) = v12) |  ~ (relation_dom(v11) = v12) |  ~ relation(v13) |  ~ relation(v11) |  ~ function(v13) |  ~ function(v11) |  ? [v14] :  ? [v15] :  ? [v16] : ( ~ (v16 = v15) & apply(v13, v14) = v16 & apply(v11, v14) = v15 & in(v14, v12))) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (singleton(v11) = v12) |  ~ in(v13, v12)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (powerset(v13) = v12) |  ~ (powerset(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (relation_rng(v13) = v12) |  ~ (relation_rng(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (relation_dom(v13) = v12) |  ~ (relation_dom(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (singleton(v13) = v12) |  ~ (singleton(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (powerset(v12) = v13) |  ~ subset(v11, v12) | element(v11, v13)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (powerset(v12) = v13) |  ~ element(v11, v13) | subset(v11, v12)) &  ? [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (singleton(v12) = v13) |  ? [v14] : (( ~ (v14 = v12) |  ~ in(v12, v11)) & (v14 = v12 | in(v14, v11)))) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ empty(v12) |  ~ empty(v11)) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ~ empty(v12)) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) |  ? [v13] : (element(v13, v12) &  ~ empty(v13))) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] : (element(v13, v12) & empty(v13))) &  ! [v11] :  ! [v12] : ( ~ (relation_rng(v11) = v12) |  ~ relation(v11) |  ~ function(v11) |  ? [v13] : (relation_dom(v11) = v13 &  ! [v14] :  ! [v15] : ( ~ (apply(v11, v15) = v14) |  ~ in(v15, v13) | in(v14, v12)) &  ! [v14] : ( ~ in(v14, v12) |  ? [v15] : (apply(v11, v15) = v14 & in(v15, v13))) &  ? [v14] : (v14 = v12 |  ? [v15] :  ? [v16] :  ? [v17] : (( ~ in(v15, v14) |  ! [v18] : ( ~ (apply(v11, v18) = v15) |  ~ in(v18, v13))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v13))))))) &  ! [v11] :  ! [v12] : ( ~ (relation_rng(v11) = v12) |  ~ relation(v11) |  ~ empty(v12) | empty(v11)) &  ! [v11] :  ! [v12] : ( ~ (relation_rng(v11) = v12) |  ~ empty(v11) | relation(v12)) &  ! [v11] :  ! [v12] : ( ~ (relation_rng(v11) = v12) |  ~ empty(v11) | empty(v12)) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ~ relation(v11) |  ~ function(v11) |  ? [v13] : (relation_rng(v11) = v13 &  ! [v14] :  ! [v15] : ( ~ (apply(v11, v15) = v14) |  ~ in(v15, v12) | in(v14, v13)) &  ! [v14] : ( ~ in(v14, v13) |  ? [v15] : (apply(v11, v15) = v14 & in(v15, v12))) &  ? [v14] : (v14 = v13 |  ? [v15] :  ? [v16] :  ? [v17] : (( ~ in(v15, v14) |  ! [v18] : ( ~ (apply(v11, v18) = v15) |  ~ in(v18, v12))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v12))))))) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ~ relation(v11) |  ~ empty(v12) | empty(v11)) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ~ empty(v11) | relation(v12)) &  ! [v11] :  ! [v12] : ( ~ (relation_dom(v11) = v12) |  ~ empty(v11) | empty(v12)) &  ! [v11] :  ! [v12] : ( ~ (singleton(v11) = v12) |  ~ empty(v12)) &  ! [v11] :  ! [v12] : ( ~ (singleton(v11) = v12) | in(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ empty(v12) |  ~ in(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ in(v12, v11) |  ~ in(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) &  ! [v11] : (v11 = empty_set |  ~ empty(v11)) &  ! [v11] : ( ~ empty(v11) | relation(v11)) &  ! [v11] : ( ~ empty(v11) | function(v11)) &  ? [v11] :  ? [v12] : element(v12, v11) &  ? [v11] : subset(v11, v11))
% 5.03/1.89  | 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 yields:
% 5.03/1.89  | (1)  ~ (all_0_6_6 = all_0_9_9) & relation_rng(all_0_6_6) = all_0_7_7 & relation_rng(all_0_9_9) = all_0_7_7 & relation_dom(all_0_6_6) = all_0_8_8 & relation_dom(all_0_9_9) = all_0_8_8 & singleton(all_0_10_10) = all_0_7_7 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_6_6) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_6_6) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) &  ~ empty(all_0_3_3) &  ~ empty(all_0_4_4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(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] : (v2 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ~ function(v2) |  ~ function(v0) |  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ in(v2, v1)) &  ! [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] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = 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] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] : (( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v2) | in(v3, v1)) &  ! [v3] : ( ~ in(v3, v1) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) &  ? [v3] : (v3 = v1 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) &  ! [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] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v1) | in(v3, v2)) &  ! [v3] : ( ~ in(v3, v2) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) &  ? [v3] : (v3 = v2 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, 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] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 5.03/1.90  |
% 5.03/1.90  | Applying alpha-rule on (1) yields:
% 5.03/1.90  | (2)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.03/1.90  | (3) relation_dom(all_0_6_6) = all_0_8_8
% 5.03/1.90  | (4)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v2) | in(v3, v1)) &  ! [v3] : ( ~ in(v3, v1) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) &  ? [v3] : (v3 = v1 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 5.03/1.90  | (5)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 5.03/1.90  | (6) relation_dom(all_0_9_9) = all_0_8_8
% 5.03/1.90  | (7)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.03/1.91  | (8)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.03/1.91  | (9) relation(all_0_0_0)
% 5.03/1.91  | (10) relation(all_0_5_5)
% 5.03/1.91  | (11) relation_empty_yielding(all_0_5_5)
% 5.03/1.91  | (12)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.03/1.91  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v1) | in(v3, v2)) &  ! [v3] : ( ~ in(v3, v2) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) &  ? [v3] : (v3 = v2 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 5.03/1.91  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 5.03/1.91  | (15) relation(empty_set)
% 5.03/1.91  | (16)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.03/1.91  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 5.03/1.91  | (18)  ~ empty(all_0_3_3)
% 5.03/1.91  | (19)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.03/1.91  | (20) relation_empty_yielding(empty_set)
% 5.03/1.91  | (21) empty(all_0_2_2)
% 5.03/1.91  | (22)  ~ (all_0_6_6 = all_0_9_9)
% 5.03/1.91  | (23)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] : (( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 5.03/1.91  | (24) relation_rng(all_0_9_9) = all_0_7_7
% 5.03/1.91  | (25) empty(empty_set)
% 5.03/1.91  | (26)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 5.03/1.91  | (27)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.03/1.91  | (28) relation_rng(all_0_6_6) = all_0_7_7
% 5.03/1.91  | (29) relation(all_0_9_9)
% 5.03/1.91  | (30)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.03/1.91  | (31) empty(all_0_1_1)
% 5.03/1.91  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.03/1.91  | (33) relation(all_0_1_1)
% 5.03/1.91  | (34)  ? [v0] :  ? [v1] : element(v1, v0)
% 5.03/1.91  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.03/1.91  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.03/1.91  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 5.03/1.91  | (38)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.03/1.91  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 5.03/1.91  | (40) function(all_0_6_6)
% 5.03/1.92  | (41)  ! [v0] : ( ~ empty(v0) | function(v0))
% 5.03/1.92  | (42)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 5.03/1.92  | (43)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.03/1.92  | (44)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 5.03/1.92  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 5.03/1.92  | (46)  ? [v0] : subset(v0, v0)
% 5.03/1.92  | (47)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.03/1.92  | (48)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.03/1.92  | (49) function(all_0_9_9)
% 5.03/1.92  | (50) function(all_0_0_0)
% 5.03/1.92  | (51)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ~ function(v2) |  ~ function(v0) |  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1)))
% 5.03/1.92  | (52) relation(all_0_6_6)
% 5.03/1.92  | (53)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ in(v2, v1))
% 5.03/1.92  | (54)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.03/1.92  | (55)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.03/1.92  | (56)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.03/1.92  | (57) singleton(all_0_10_10) = all_0_7_7
% 5.03/1.92  | (58) relation(all_0_3_3)
% 5.03/1.92  | (59)  ~ empty(all_0_4_4)
% 5.03/1.92  |
% 5.03/1.92  | Instantiating formula (13) with all_0_8_8, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_8_8, relation(all_0_6_6), function(all_0_6_6), yields:
% 5.03/1.92  | (60)  ? [v0] : (relation_rng(all_0_6_6) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_6_6, v2) = v1) |  ~ in(v2, all_0_8_8) | in(v1, v0)) &  ! [v1] : ( ~ in(v1, v0) |  ? [v2] : (apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8))) &  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ in(v2, v1) |  ! [v5] : ( ~ (apply(all_0_6_6, v5) = v2) |  ~ in(v5, all_0_8_8))) & (in(v2, v1) | (v4 = v2 & apply(all_0_6_6, v3) = v2 & in(v3, all_0_8_8))))))
% 5.03/1.92  |
% 5.03/1.92  | Instantiating formula (51) with all_0_9_9, all_0_8_8, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_8_8, relation_dom(all_0_9_9) = all_0_8_8, relation(all_0_6_6), relation(all_0_9_9), function(all_0_6_6), function(all_0_9_9), yields:
% 5.03/1.92  | (61) all_0_6_6 = all_0_9_9 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0) = v1 & apply(all_0_9_9, v0) = v2 & in(v0, all_0_8_8))
% 5.03/1.92  |
% 5.03/1.92  | Instantiating formula (13) with all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields:
% 5.03/1.93  | (62)  ? [v0] : (relation_rng(all_0_9_9) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_9_9, v2) = v1) |  ~ in(v2, all_0_8_8) | in(v1, v0)) &  ! [v1] : ( ~ in(v1, v0) |  ? [v2] : (apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8))) &  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ in(v2, v1) |  ! [v5] : ( ~ (apply(all_0_9_9, v5) = v2) |  ~ in(v5, all_0_8_8))) & (in(v2, v1) | (v4 = v2 & apply(all_0_9_9, v3) = v2 & in(v3, all_0_8_8))))))
% 5.03/1.93  |
% 5.03/1.93  | Instantiating (60) with all_19_0_15 yields:
% 5.03/1.93  | (63) relation_rng(all_0_6_6) = all_19_0_15 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_6_6, v1) = v0) |  ~ in(v1, all_0_8_8) | in(v0, all_19_0_15)) &  ! [v0] : ( ~ in(v0, all_19_0_15) |  ? [v1] : (apply(all_0_6_6, v1) = v0 & in(v1, all_0_8_8))) &  ? [v0] : (v0 = all_19_0_15 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_6_6, v4) = v1) |  ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93  |
% 5.03/1.93  | Applying alpha-rule on (63) yields:
% 5.03/1.93  | (64) relation_rng(all_0_6_6) = all_19_0_15
% 5.03/1.93  | (65)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_6_6, v1) = v0) |  ~ in(v1, all_0_8_8) | in(v0, all_19_0_15))
% 5.03/1.93  | (66)  ! [v0] : ( ~ in(v0, all_19_0_15) |  ? [v1] : (apply(all_0_6_6, v1) = v0 & in(v1, all_0_8_8)))
% 5.03/1.93  | (67)  ? [v0] : (v0 = all_19_0_15 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_6_6, v4) = v1) |  ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_6_6, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93  |
% 5.03/1.93  | Instantiating (62) with all_22_0_16 yields:
% 5.03/1.93  | (68) relation_rng(all_0_9_9) = all_22_0_16 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) |  ~ in(v1, all_0_8_8) | in(v0, all_22_0_16)) &  ! [v0] : ( ~ in(v0, all_22_0_16) |  ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8))) &  ? [v0] : (v0 = all_22_0_16 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) |  ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93  |
% 5.03/1.93  | Applying alpha-rule on (68) yields:
% 5.03/1.93  | (69) relation_rng(all_0_9_9) = all_22_0_16
% 5.03/1.93  | (70)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) |  ~ in(v1, all_0_8_8) | in(v0, all_22_0_16))
% 5.03/1.93  | (71)  ! [v0] : ( ~ in(v0, all_22_0_16) |  ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8)))
% 5.03/1.93  | (72)  ? [v0] : (v0 = all_22_0_16 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) |  ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8)))))
% 5.03/1.93  |
% 5.03/1.93  +-Applying beta-rule and splitting (61), into two cases.
% 5.03/1.93  |-Branch one:
% 5.03/1.93  | (73) all_0_6_6 = all_0_9_9
% 5.03/1.93  |
% 5.03/1.93  	| Equations (73) can reduce 22 to:
% 5.03/1.94  	| (74) $false
% 5.03/1.94  	|
% 5.03/1.94  	|-The branch is then unsatisfiable
% 5.03/1.94  |-Branch two:
% 5.03/1.94  | (22)  ~ (all_0_6_6 = all_0_9_9)
% 5.03/1.94  | (76)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0) = v1 & apply(all_0_9_9, v0) = v2 & in(v0, all_0_8_8))
% 5.03/1.94  |
% 5.03/1.94  	| Instantiating (76) with all_39_0_23, all_39_1_24, all_39_2_25 yields:
% 5.03/1.94  	| (77)  ~ (all_39_0_23 = all_39_1_24) & apply(all_0_6_6, all_39_2_25) = all_39_1_24 & apply(all_0_9_9, all_39_2_25) = all_39_0_23 & in(all_39_2_25, all_0_8_8)
% 5.03/1.94  	|
% 5.03/1.94  	| Applying alpha-rule on (77) yields:
% 5.03/1.94  	| (78)  ~ (all_39_0_23 = all_39_1_24)
% 5.03/1.94  	| (79) apply(all_0_6_6, all_39_2_25) = all_39_1_24
% 5.03/1.94  	| (80) apply(all_0_9_9, all_39_2_25) = all_39_0_23
% 5.03/1.94  	| (81) in(all_39_2_25, all_0_8_8)
% 5.03/1.94  	|
% 5.03/1.94  	| Instantiating formula (42) with all_0_6_6, all_19_0_15, all_0_7_7 and discharging atoms relation_rng(all_0_6_6) = all_19_0_15, relation_rng(all_0_6_6) = all_0_7_7, yields:
% 5.03/1.94  	| (82) all_19_0_15 = all_0_7_7
% 5.03/1.94  	|
% 5.03/1.94  	| Instantiating formula (42) with all_0_9_9, all_22_0_16, all_0_7_7 and discharging atoms relation_rng(all_0_9_9) = all_22_0_16, relation_rng(all_0_9_9) = all_0_7_7, yields:
% 5.03/1.94  	| (83) all_22_0_16 = all_0_7_7
% 5.03/1.94  	|
% 5.03/1.94  	| Instantiating formula (65) with all_39_2_25, all_39_1_24 and discharging atoms apply(all_0_6_6, all_39_2_25) = all_39_1_24, in(all_39_2_25, all_0_8_8), yields:
% 5.03/1.94  	| (84) in(all_39_1_24, all_19_0_15)
% 5.03/1.94  	|
% 5.03/1.94  	| Instantiating formula (70) with all_39_2_25, all_39_0_23 and discharging atoms apply(all_0_9_9, all_39_2_25) = all_39_0_23, in(all_39_2_25, all_0_8_8), yields:
% 5.03/1.94  	| (85) in(all_39_0_23, all_22_0_16)
% 5.03/1.94  	|
% 5.03/1.94  	| From (83) and (85) follows:
% 5.37/1.94  	| (86) in(all_39_0_23, all_0_7_7)
% 5.37/1.94  	|
% 5.37/1.94  	| From (82) and (84) follows:
% 5.37/1.94  	| (87) in(all_39_1_24, all_0_7_7)
% 5.37/1.94  	|
% 5.37/1.94  	| Instantiating formula (53) with all_39_0_23, all_0_7_7, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_0_7_7, in(all_39_0_23, all_0_7_7), yields:
% 5.37/1.94  	| (88) all_39_0_23 = all_0_10_10
% 5.37/1.94  	|
% 5.37/1.94  	| Instantiating formula (53) with all_39_1_24, all_0_7_7, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_0_7_7, in(all_39_1_24, all_0_7_7), yields:
% 5.37/1.94  	| (89) all_39_1_24 = all_0_10_10
% 5.37/1.94  	|
% 5.37/1.94  	| Equations (88,89) can reduce 78 to:
% 5.37/1.94  	| (74) $false
% 5.37/1.94  	|
% 5.37/1.94  	|-The branch is then unsatisfiable
% 5.37/1.94  % SZS output end Proof for theBenchmark
% 5.37/1.94  
% 5.37/1.94  1353ms
%------------------------------------------------------------------------------