%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU040+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 08:46:19 EDT 2022

% Result   : Theorem 2.77s 1.30s
% Output   : Proof 3.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU040+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.12  % 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 Jun 18 22:11:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.58          ____       _                          
% 0.18/0.58    ___  / __ \_____(_)___  ________  __________
% 0.18/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.58  
% 0.18/0.58  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.95  Prover 0: Preprocessing ...
% 1.98/1.14  Prover 0: Warning: ignoring some quantifiers
% 1.98/1.17  Prover 0: Constructing countermodel ...
% 2.77/1.30  Prover 0: proved (669ms)
% 2.77/1.30  
% 2.77/1.30  No countermodel exists, formula is valid
% 2.77/1.30  % SZS status Theorem for theBenchmark
% 2.77/1.30  
% 2.77/1.30  Generating proof ... Warning: ignoring some quantifiers
% 3.58/1.53  found it (size 19)
% 3.58/1.53  
% 3.58/1.53  % SZS output start Proof for theBenchmark
% 3.58/1.53  Assumed formulas after preprocessing and simplification: 
% 3.68/1.53  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (relation_dom_restriction(v1, v0) = v2 & relation_rng(v2) = v5 & relation_rng(v1) = v6 & relation_dom(v2) = v3 & relation_dom(v1) = v4 & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v1) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v1) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) &  ~ empty(v10) &  ~ empty(v7) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_dom_restriction(v18, v17) = v16) |  ~ (relation_dom_restriction(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ element(v16, v18) |  ~ empty(v17) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ element(v16, v18) |  ~ in(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (relation_rng(v17) = v16) |  ~ (relation_rng(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (relation_dom(v17) = v16) |  ~ (relation_dom(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (powerset(v17) = v16) |  ~ (powerset(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) |  ~ relation(v16) |  ? [v18] :  ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) |  ~ relation(v16) |  ? [v18] :  ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & subset(v18, v19))) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ function(v15) |  ~ relation(v15) | function(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ function(v15) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation_empty_yielding(v15) |  ~ relation(v15) | relation_empty_yielding(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation_empty_yielding(v15) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ subset(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) | subset(v15, v16)) &  ! [v15] :  ! [v16] : (v16 = v15 |  ~ empty(v16) |  ~ empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_rng(v15) = v16) |  ~ relation(v15) |  ~ empty(v16) | empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_rng(v15) = v16) |  ~ empty(v15) | relation(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_rng(v15) = v16) |  ~ empty(v15) | empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ relation(v15) |  ~ empty(v16) | empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | relation(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) |  ? [v17] : (element(v17, v16) &  ~ empty(v17))) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ? [v17] : (element(v17, v16) & empty(v17))) &  ! [v15] :  ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ empty(v16) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v16, v15) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) &  ! [v15] : (v15 = empty_set |  ~ empty(v15)) &  ! [v15] : ( ~ function(v15) |  ~ relation(v15) |  ~ empty(v15) | one_to_one(v15)) &  ! [v15] : ( ~ empty(v15) | function(v15)) &  ! [v15] : ( ~ empty(v15) | relation(v15)) &  ? [v15] :  ? [v16] : element(v16, v15) &  ? [v15] : subset(v15, v15) & ( ~ subset(v5, v6) |  ~ subset(v3, v4)))
% 3.68/1.57  | 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 yields:
% 3.68/1.57  | (1) relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12 & relation_rng(all_0_12_12) = all_0_9_9 & relation_rng(all_0_13_13) = all_0_8_8 & relation_dom(all_0_12_12) = all_0_11_11 & relation_dom(all_0_13_13) = all_0_10_10 & one_to_one(all_0_2_2) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_13_13) & 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_2_2) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_13_13) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_3_3) & empty(all_0_6_6) & empty(empty_set) &  ~ empty(all_0_4_4) &  ~ empty(all_0_7_7) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_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 |  ~ (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] : ( ~ (relation_dom_restriction(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | relation(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) |  ~ relation(v0) | relation(v2)) &  ! [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] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [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) |  ~ 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] : ( ~ (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] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) & ( ~ subset(all_0_9_9, all_0_8_8) |  ~ subset(all_0_11_11, all_0_10_10))
% 3.68/1.58  |
% 3.68/1.58  | Applying alpha-rule on (1) yields:
% 3.68/1.58  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 3.68/1.58  | (3) relation(all_0_13_13)
% 3.68/1.58  | (4) function(all_0_1_1)
% 3.68/1.58  | (5) relation(all_0_2_2)
% 3.68/1.58  | (6)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 3.68/1.58  | (7) function(all_0_2_2)
% 3.68/1.58  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2))
% 3.68/1.58  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 3.68/1.58  | (10)  ? [v0] :  ? [v1] : element(v1, v0)
% 3.68/1.58  | (11)  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0))
% 3.68/1.58  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 3.68/1.58  | (13) relation_empty_yielding(all_0_5_5)
% 3.68/1.58  | (14)  ~ empty(all_0_4_4)
% 3.68/1.58  | (15)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 3.68/1.58  | (16)  ! [v0] : ( ~ empty(v0) | function(v0))
% 3.68/1.58  | (17)  ? [v0] : subset(v0, v0)
% 3.68/1.58  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 3.68/1.58  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 3.68/1.58  | (20)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 3.68/1.58  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | relation(v2))
% 3.68/1.58  | (22) relation_dom(all_0_12_12) = all_0_11_11
% 3.68/1.58  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0))
% 3.68/1.58  | (24) relation(all_0_5_5)
% 3.68/1.58  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2))
% 3.68/1.58  | (26) relation(all_0_0_0)
% 3.68/1.58  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 3.68/1.58  | (28)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 3.68/1.59  | (29)  ~ subset(all_0_9_9, all_0_8_8) |  ~ subset(all_0_11_11, all_0_10_10)
% 3.68/1.59  | (30)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.68/1.59  | (31)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.68/1.59  | (32) function(all_0_13_13)
% 3.68/1.59  | (33)  ~ empty(all_0_7_7)
% 3.68/1.59  | (34)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 3.68/1.59  | (35)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 3.68/1.59  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 3.68/1.59  | (37)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 3.68/1.59  | (38) relation(all_0_1_1)
% 3.68/1.59  | (39) relation_rng(all_0_12_12) = all_0_9_9
% 3.68/1.59  | (40) relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12
% 3.68/1.59  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 3.68/1.59  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 3.68/1.59  | (43) relation(empty_set)
% 3.68/1.59  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4)))
% 3.68/1.59  | (45)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 3.68/1.59  | (46) empty(all_0_3_3)
% 3.68/1.59  | (47) relation(all_0_4_4)
% 3.68/1.59  | (48)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 3.68/1.59  | (49) one_to_one(all_0_2_2)
% 3.68/1.59  | (50)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 3.68/1.59  | (51) relation_dom(all_0_13_13) = all_0_10_10
% 3.68/1.59  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | function(v2))
% 3.68/1.59  | (53)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 3.68/1.59  | (54) relation_empty_yielding(empty_set)
% 3.68/1.59  | (55) function(all_0_0_0)
% 3.68/1.59  | (56) relation_rng(all_0_13_13) = all_0_8_8
% 3.68/1.59  | (57) empty(all_0_6_6)
% 3.68/1.59  | (58)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 3.68/1.59  | (59) empty(all_0_1_1)
% 3.68/1.59  | (60) empty(empty_set)
% 3.68/1.59  | (61) relation(all_0_3_3)
% 3.68/1.59  | (62)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 3.68/1.59  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2))
% 3.68/1.59  |
% 3.68/1.59  | Instantiating formula (27) with all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12, relation(all_0_13_13), yields:
% 3.68/1.59  | (64)  ? [v0] :  ? [v1] : (relation_rng(all_0_12_12) = v0 & relation_rng(all_0_13_13) = v1 & subset(v0, v1))
% 3.68/1.59  |
% 3.68/1.60  | Instantiating formula (44) with all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12, relation(all_0_13_13), yields:
% 3.68/1.60  | (65)  ? [v0] :  ? [v1] : (relation_dom(all_0_12_12) = v0 & relation_dom(all_0_13_13) = v1 & subset(v0, v1))
% 3.68/1.60  |
% 3.68/1.60  | Instantiating (65) with all_17_0_18, all_17_1_19 yields:
% 3.68/1.60  | (66) relation_dom(all_0_12_12) = all_17_1_19 & relation_dom(all_0_13_13) = all_17_0_18 & subset(all_17_1_19, all_17_0_18)
% 3.68/1.60  |
% 3.68/1.60  | Applying alpha-rule on (66) yields:
% 3.68/1.60  | (67) relation_dom(all_0_12_12) = all_17_1_19
% 3.68/1.60  | (68) relation_dom(all_0_13_13) = all_17_0_18
% 3.68/1.60  | (69) subset(all_17_1_19, all_17_0_18)
% 3.68/1.60  |
% 3.68/1.60  | Instantiating (64) with all_19_0_20, all_19_1_21 yields:
% 3.68/1.60  | (70) relation_rng(all_0_12_12) = all_19_1_21 & relation_rng(all_0_13_13) = all_19_0_20 & subset(all_19_1_21, all_19_0_20)
% 3.68/1.60  |
% 3.68/1.60  | Applying alpha-rule on (70) yields:
% 3.68/1.60  | (71) relation_rng(all_0_12_12) = all_19_1_21
% 3.68/1.60  | (72) relation_rng(all_0_13_13) = all_19_0_20
% 3.68/1.60  | (73) subset(all_19_1_21, all_19_0_20)
% 3.68/1.60  |
% 3.68/1.60  | Instantiating formula (36) with all_0_12_12, all_19_1_21, all_0_9_9 and discharging atoms relation_rng(all_0_12_12) = all_19_1_21, relation_rng(all_0_12_12) = all_0_9_9, yields:
% 3.68/1.60  | (74) all_19_1_21 = all_0_9_9
% 3.68/1.60  |
% 3.68/1.60  | Instantiating formula (36) with all_0_13_13, all_19_0_20, all_0_8_8 and discharging atoms relation_rng(all_0_13_13) = all_19_0_20, relation_rng(all_0_13_13) = all_0_8_8, yields:
% 3.68/1.60  | (75) all_19_0_20 = all_0_8_8
% 3.68/1.60  |
% 3.68/1.60  | Instantiating formula (2) with all_0_12_12, all_17_1_19, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_17_1_19, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 3.68/1.60  | (76) all_17_1_19 = all_0_11_11
% 3.68/1.60  |
% 3.68/1.60  | Instantiating formula (2) with all_0_13_13, all_17_0_18, all_0_10_10 and discharging atoms relation_dom(all_0_13_13) = all_17_0_18, relation_dom(all_0_13_13) = all_0_10_10, yields:
% 3.68/1.60  | (77) all_17_0_18 = all_0_10_10
% 3.68/1.60  |
% 3.95/1.60  | From (74)(75) and (73) follows:
% 3.95/1.60  | (78) subset(all_0_9_9, all_0_8_8)
% 3.95/1.60  |
% 3.95/1.60  | From (76)(77) and (69) follows:
% 3.95/1.60  | (79) subset(all_0_11_11, all_0_10_10)
% 3.95/1.60  |
% 3.95/1.60  +-Applying beta-rule and splitting (29), into two cases.
% 3.95/1.60  |-Branch one:
% 3.95/1.60  | (80)  ~ subset(all_0_9_9, all_0_8_8)
% 3.95/1.60  |
% 3.95/1.60  	| Using (78) and (80) yields:
% 3.95/1.60  	| (81) $false
% 3.95/1.60  	|
% 3.95/1.60  	|-The branch is then unsatisfiable
% 3.95/1.60  |-Branch two:
% 3.95/1.60  | (78) subset(all_0_9_9, all_0_8_8)
% 3.95/1.60  | (83)  ~ subset(all_0_11_11, all_0_10_10)
% 3.95/1.60  |
% 3.95/1.60  	| Using (79) and (83) yields:
% 3.95/1.60  	| (81) $false
% 3.95/1.60  	|
% 3.95/1.60  	|-The branch is then unsatisfiable
% 3.95/1.60  % SZS output end Proof for theBenchmark
% 3.95/1.60  
% 3.95/1.60  1012ms
%------------------------------------------------------------------------------