%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU200+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n008.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 08:47:34 EDT 2022

% Result   : Theorem 2.49s 1.30s
% Output   : Proof 4.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU200+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.32  % Computer : n008.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Mon Jun 20 13:38:52 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.17/0.56          ____       _                          
% 0.17/0.56    ___  / __ \_____(_)___  ________  __________
% 0.17/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.17/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.17/0.56  
% 0.17/0.56  A Theorem Prover for First-Order Logic
% 0.17/0.56  (ePrincess v.1.0)
% 0.17/0.56  
% 0.17/0.56  (c) Philipp Rümmer, 2009-2015
% 0.17/0.56  (c) Peter Backeman, 2014-2015
% 0.17/0.56  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.56  Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.56  Bug reports to peter@backeman.se
% 0.17/0.56  
% 0.17/0.56  For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.56  
% 0.17/0.56  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.61  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.91  Prover 0: Preprocessing ...
% 1.97/1.10  Prover 0: Warning: ignoring some quantifiers
% 1.97/1.13  Prover 0: Constructing countermodel ...
% 2.49/1.30  Prover 0: proved (693ms)
% 2.49/1.30  
% 2.49/1.30  No countermodel exists, formula is valid
% 2.49/1.30  % SZS status Theorem for theBenchmark
% 2.49/1.30  
% 2.49/1.30  Generating proof ... Warning: ignoring some quantifiers
% 3.84/1.55  found it (size 9)
% 3.84/1.55  
% 3.84/1.55  % SZS output start Proof for theBenchmark
% 3.84/1.55  Assumed formulas after preprocessing and simplification: 
% 3.84/1.56  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & relation_rng_restriction(v0, v1) = v2 & relation(v8) & relation(v6) & relation(v1) & relation(empty_set) & empty(v8) & empty(v7) & empty(empty_set) &  ~ subset(v3, v4) &  ~ empty(v6) &  ~ empty(v5) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (relation_rng_restriction(v12, v11) = v10) |  ~ (relation_rng_restriction(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ~ element(v10, v12) |  ~ empty(v11) |  ~ in(v9, v10)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ~ element(v10, v12) |  ~ in(v9, v10) | element(v9, v11)) &  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (relation_rng(v11) = v10) |  ~ (relation_rng(v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (relation_dom(v11) = v10) |  ~ (relation_dom(v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (powerset(v11) = v10) |  ~ (powerset(v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (powerset(v10) = v11) |  ~ subset(v9, v10) | element(v9, v11)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (powerset(v10) = v11) |  ~ element(v9, v11) | subset(v9, v10)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (relation_rng_restriction(v9, v10) = v11) |  ~ relation(v10) | subset(v11, v10)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (relation_rng_restriction(v9, v10) = v11) |  ~ relation(v10) | relation(v11)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ empty(v10) |  ~ empty(v9)) &  ! [v9] :  ! [v10] : ( ~ (relation_rng(v9) = v10) |  ~ relation(v9) |  ~ empty(v10) | empty(v9)) &  ! [v9] :  ! [v10] : ( ~ (relation_rng(v9) = v10) |  ~ relation(v9) |  ? [v11] : (relation_dom(v9) = v11 &  ! [v12] :  ! [v13] : ( ~ (relation_rng(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) | subset(v10, v13)) &  ! [v12] :  ! [v13] : ( ~ (relation_rng(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) |  ? [v14] : (relation_dom(v12) = v14 & subset(v11, v14))) &  ! [v12] :  ! [v13] : ( ~ (relation_dom(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) | subset(v11, v13)) &  ! [v12] :  ! [v13] : ( ~ (relation_dom(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) |  ? [v14] : (relation_rng(v12) = v14 & subset(v10, v14))))) &  ! [v9] :  ! [v10] : ( ~ (relation_rng(v9) = v10) |  ~ empty(v9) | relation(v10)) &  ! [v9] :  ! [v10] : ( ~ (relation_rng(v9) = v10) |  ~ empty(v9) | empty(v10)) &  ! [v9] :  ! [v10] : ( ~ (relation_dom(v9) = v10) |  ~ relation(v9) |  ~ empty(v10) | empty(v9)) &  ! [v9] :  ! [v10] : ( ~ (relation_dom(v9) = v10) |  ~ relation(v9) |  ? [v11] : (relation_rng(v9) = v11 &  ! [v12] :  ! [v13] : ( ~ (relation_rng(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) | subset(v11, v13)) &  ! [v12] :  ! [v13] : ( ~ (relation_rng(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) |  ? [v14] : (relation_dom(v12) = v14 & subset(v10, v14))) &  ! [v12] :  ! [v13] : ( ~ (relation_dom(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) | subset(v10, v13)) &  ! [v12] :  ! [v13] : ( ~ (relation_dom(v12) = v13) |  ~ subset(v9, v12) |  ~ relation(v12) |  ? [v14] : (relation_rng(v12) = v14 & subset(v11, v14))))) &  ! [v9] :  ! [v10] : ( ~ (relation_dom(v9) = v10) |  ~ empty(v9) | relation(v10)) &  ! [v9] :  ! [v10] : ( ~ (relation_dom(v9) = v10) |  ~ empty(v9) | empty(v10)) &  ! [v9] :  ! [v10] : ( ~ (powerset(v9) = v10) |  ~ empty(v10)) &  ! [v9] :  ! [v10] : ( ~ (powerset(v9) = v10) | empty(v9) |  ? [v11] : (element(v11, v10) &  ~ empty(v11))) &  ! [v9] :  ! [v10] : ( ~ (powerset(v9) = v10) |  ? [v11] : (element(v11, v10) & empty(v11))) &  ! [v9] :  ! [v10] : ( ~ element(v9, v10) | empty(v10) | in(v9, v10)) &  ! [v9] :  ! [v10] : ( ~ empty(v10) |  ~ in(v9, v10)) &  ! [v9] :  ! [v10] : ( ~ in(v10, v9) |  ~ in(v9, v10)) &  ! [v9] :  ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) &  ! [v9] : (v9 = empty_set |  ~ empty(v9)) &  ! [v9] : ( ~ empty(v9) | relation(v9)) &  ? [v9] :  ? [v10] : element(v10, v9) &  ? [v9] : subset(v9, v9))
% 3.84/1.60  | 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 yields:
% 3.84/1.60  | (1) relation_rng(all_0_6_6) = all_0_5_5 & relation_rng(all_0_7_7) = all_0_4_4 & relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_7_7) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) &  ~ subset(all_0_5_5, all_0_4_4) &  ~ empty(all_0_2_2) &  ~ empty(all_0_3_3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_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 |  ~ (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 |  ~ (powerset(v2) = v1) |  ~ (powerset(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] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | subset(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v1, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v2, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) &  ! [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) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v2, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v1, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [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] : ( ~ 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] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 3.84/1.61  |
% 3.84/1.61  | Applying alpha-rule on (1) yields:
% 3.84/1.61  | (2)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.84/1.61  | (3)  ~ empty(all_0_2_2)
% 3.84/1.61  | (4)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v2, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v1, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5)))))
% 3.84/1.61  | (5)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 3.84/1.61  | (6)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 3.84/1.61  | (7) relation_rng(all_0_7_7) = all_0_4_4
% 3.84/1.61  | (8)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 3.84/1.61  | (9)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 3.84/1.61  | (10) relation(all_0_2_2)
% 3.84/1.61  | (11)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 3.84/1.61  | (12) empty(empty_set)
% 3.84/1.61  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 3.84/1.61  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 3.84/1.61  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 3.84/1.61  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0))
% 3.84/1.61  | (17)  ? [v0] : subset(v0, v0)
% 3.84/1.61  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2))
% 3.84/1.61  | (19)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 3.84/1.61  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | subset(v2, v1))
% 3.84/1.61  | (21)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v1, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_rng(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) | subset(v2, v4)) &  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ subset(v0, v3) |  ~ relation(v3) |  ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5)))))
% 3.84/1.61  | (22)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 3.84/1.62  | (23)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 3.84/1.62  | (24)  ~ subset(all_0_5_5, all_0_4_4)
% 3.84/1.62  | (25)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 3.84/1.62  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 3.84/1.62  | (27) empty(all_0_1_1)
% 3.84/1.62  | (28)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 3.84/1.62  | (29) empty(all_0_0_0)
% 3.84/1.62  | (30)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 3.84/1.62  | (31)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 3.84/1.62  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 3.84/1.62  | (33)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 3.84/1.62  | (34)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.84/1.62  | (35)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 3.84/1.62  | (36) relation(all_0_7_7)
% 3.84/1.62  | (37) relation(empty_set)
% 3.84/1.62  | (38) relation(all_0_0_0)
% 3.84/1.62  | (39) relation_rng(all_0_6_6) = all_0_5_5
% 3.84/1.62  | (40)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.19/1.62  | (41)  ~ empty(all_0_3_3)
% 4.19/1.62  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 4.19/1.62  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 4.19/1.62  | (44) relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6
% 4.19/1.62  |
% 4.19/1.62  | Instantiating formula (20) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields:
% 4.19/1.62  | (45) subset(all_0_6_6, all_0_7_7)
% 4.19/1.62  |
% 4.19/1.62  | Instantiating formula (18) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields:
% 4.19/1.62  | (46) relation(all_0_6_6)
% 4.19/1.62  |
% 4.19/1.62  | Instantiating formula (21) with all_0_5_5, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields:
% 4.19/1.62  | (47)  ? [v0] : (relation_dom(all_0_6_6) = v0 &  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ subset(all_0_6_6, v1) |  ~ relation(v1) | subset(all_0_5_5, v2)) &  ! [v1] :  ! [v2] : ( ~ (relation_rng(v1) = v2) |  ~ subset(all_0_6_6, v1) |  ~ relation(v1) |  ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_0_6_6, v1) |  ~ relation(v1) | subset(v0, v2)) &  ! [v1] :  ! [v2] : ( ~ (relation_dom(v1) = v2) |  ~ subset(all_0_6_6, v1) |  ~ relation(v1) |  ? [v3] : (relation_rng(v1) = v3 & subset(all_0_5_5, v3))))
% 4.19/1.62  |
% 4.19/1.62  | Instantiating (47) with all_25_0_13 yields:
% 4.19/1.62  | (48) relation_dom(all_0_6_6) = all_25_0_13 &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) | subset(all_0_5_5, v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 & subset(all_25_0_13, v2))) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) | subset(all_25_0_13, v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2)))
% 4.19/1.63  |
% 4.19/1.63  | Applying alpha-rule on (48) yields:
% 4.19/1.63  | (49) relation_dom(all_0_6_6) = all_25_0_13
% 4.19/1.63  | (50)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) | subset(all_25_0_13, v1))
% 4.19/1.63  | (51)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) |  ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2)))
% 4.19/1.63  | (52)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) | subset(all_0_5_5, v1))
% 4.19/1.63  | (53)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ subset(all_0_6_6, v0) |  ~ relation(v0) |  ? [v2] : (relation_dom(v0) = v2 & subset(all_25_0_13, v2)))
% 4.19/1.63  |
% 4.19/1.63  | Instantiating formula (52) with all_0_4_4, all_0_7_7 and discharging atoms relation_rng(all_0_7_7) = all_0_4_4, subset(all_0_6_6, all_0_7_7), relation(all_0_7_7),  ~ subset(all_0_5_5, all_0_4_4), yields:
% 4.19/1.63  | (54) $false
% 4.19/1.63  |
% 4.19/1.63  |-The branch is then unsatisfiable
% 4.19/1.63  % SZS output end Proof for theBenchmark
% 4.19/1.63  
% 4.19/1.63  1058ms
%------------------------------------------------------------------------------