%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 08:47:33 EDT 2022

% Result   : Theorem 2.83s 1.33s
% Output   : Proof 3.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n026.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jun 19 01:30:40 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.57          ____       _                          
% 0.18/0.57    ___  / __ \_____(_)___  ________  __________
% 0.18/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.57  
% 0.18/0.57  A Theorem Prover for First-Order Logic
% 0.18/0.57  (ePrincess v.1.0)
% 0.18/0.57  
% 0.18/0.57  (c) Philipp Rümmer, 2009-2015
% 0.18/0.57  (c) Peter Backeman, 2014-2015
% 0.18/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57  Bug reports to peter@backeman.se
% 0.18/0.57  
% 0.18/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57  
% 0.18/0.57  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.92  Prover 0: Preprocessing ...
% 1.94/1.13  Prover 0: Warning: ignoring some quantifiers
% 1.94/1.15  Prover 0: Constructing countermodel ...
% 2.49/1.33  Prover 0: proved (710ms)
% 2.83/1.33  
% 2.83/1.33  No countermodel exists, formula is valid
% 2.83/1.33  % SZS status Theorem for theBenchmark
% 2.83/1.33  
% 2.83/1.33  Generating proof ... Warning: ignoring some quantifiers
% 3.70/1.53  found it (size 8)
% 3.70/1.53  
% 3.70/1.53  % SZS output start Proof for theBenchmark
% 3.70/1.53  Assumed formulas after preprocessing and simplification: 
% 3.70/1.53  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (relation_rng_restriction(v0, v1) = v2 & relation(v6) & relation(v4) & relation(v1) & relation(empty_set) & empty(v6) & empty(v5) & empty(empty_set) &  ~ subset(v2, v1) &  ~ empty(v4) &  ~ empty(v3) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) |  ~ (ordered_pair(v10, v11) = v12) |  ~ relation(v9) |  ~ relation(v8) |  ~ in(v12, v9) | in(v12, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) |  ~ (ordered_pair(v10, v11) = v12) |  ~ relation(v9) |  ~ relation(v8) |  ~ in(v12, v9) | in(v11, v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) |  ~ (ordered_pair(v10, v11) = v12) |  ~ relation(v9) |  ~ relation(v8) |  ~ in(v12, v8) |  ~ in(v11, v7) | in(v12, v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (singleton(v7) = v10) |  ~ (unordered_pair(v9, v10) = v11) |  ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) |  ~ subset(v7, v8) |  ~ relation(v8) |  ~ relation(v7) |  ~ in(v11, v7) | in(v11, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (relation_rng_restriction(v7, v8) = v9) |  ~ relation(v10) |  ~ relation(v8) |  ? [v11] :  ? [v12] :  ? [v13] : (ordered_pair(v11, v12) = v13 & ( ~ in(v13, v10) |  ~ in(v13, v8) |  ~ in(v12, v7)) & (in(v13, v10) | (in(v13, v8) & in(v12, v7))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (relation_rng_restriction(v10, v9) = v8) |  ~ (relation_rng_restriction(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (ordered_pair(v10, v9) = v8) |  ~ (ordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unordered_pair(v10, v9) = v8) |  ~ (unordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (powerset(v9) = v10) |  ~ element(v8, v10) |  ~ empty(v9) |  ~ in(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (powerset(v9) = v10) |  ~ element(v8, v10) |  ~ in(v7, v8) | element(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (powerset(v9) = v8) |  ~ (powerset(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (singleton(v9) = v8) |  ~ (singleton(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ~ element(v7, v9) | subset(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ~ subset(v7, v8) | element(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (relation_rng_restriction(v7, v8) = v9) |  ~ relation(v8) | relation(v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) |  ~ empty(v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) |  ? [v10] :  ? [v11] : (singleton(v7) = v11 & unordered_pair(v10, v11) = v9 & unordered_pair(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) |  ~ empty(v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ empty(v8) |  ~ empty(v7)) &  ! [v7] :  ! [v8] : ( ~ (powerset(v7) = v8) |  ~ empty(v8)) &  ! [v7] :  ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) |  ? [v9] : (element(v9, v8) &  ~ empty(v9))) &  ! [v7] :  ! [v8] : ( ~ (powerset(v7) = v8) |  ? [v9] : (element(v9, v8) & empty(v9))) &  ! [v7] :  ! [v8] : ( ~ (singleton(v7) = v8) |  ~ empty(v8)) &  ! [v7] :  ! [v8] : ( ~ element(v7, v8) | empty(v8) | in(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ relation(v8) |  ~ relation(v7) | subset(v7, v8) |  ? [v9] :  ? [v10] :  ? [v11] : (ordered_pair(v9, v10) = v11 & in(v11, v7) &  ~ in(v11, v8))) &  ! [v7] :  ! [v8] : ( ~ empty(v8) |  ~ in(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ in(v8, v7) |  ~ in(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) &  ! [v7] : (v7 = empty_set |  ~ empty(v7)) &  ! [v7] : ( ~ empty(v7) | relation(v7)) &  ? [v7] :  ? [v8] : element(v8, v7) &  ? [v7] : subset(v7, v7))
% 3.84/1.57  | 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 yields:
% 3.84/1.57  | (1) relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_5_5) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) &  ~ subset(all_0_4_4, all_0_5_5) &  ~ empty(all_0_2_2) &  ~ empty(all_0_3_3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v2) | in(v5, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v2) | in(v4, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v1) |  ~ in(v4, v0) | in(v5, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ subset(v0, v1) |  ~ relation(v1) |  ~ relation(v0) |  ~ in(v4, v0) | in(v4, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ? [v4] :  ? [v5] :  ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) |  ~ in(v6, v1) |  ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(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 |  ~ (singleton(v2) = v1) |  ~ (singleton(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_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [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] : ( ~ (singleton(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ relation(v1) |  ~ relation(v0) | subset(v0, v1) |  ? [v2] :  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) &  ~ in(v4, 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)
% 3.84/1.58  |
% 3.84/1.58  | Applying alpha-rule on (1) yields:
% 3.84/1.58  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 3.84/1.58  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v1) |  ~ in(v4, v0) | in(v5, v2))
% 3.84/1.58  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 3.84/1.58  | (5) relation(all_0_5_5)
% 3.84/1.58  | (6)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 3.84/1.58  | (7)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 3.84/1.58  | (8) relation(all_0_0_0)
% 3.84/1.58  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 3.84/1.58  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 3.84/1.58  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ? [v4] :  ? [v5] :  ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) |  ~ in(v6, v1) |  ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0)))))
% 3.84/1.58  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 3.84/1.58  | (13)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 3.84/1.58  | (14)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 3.84/1.58  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0))
% 3.84/1.58  | (16)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 3.84/1.58  | (17)  ? [v0] : subset(v0, v0)
% 3.84/1.59  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 3.84/1.59  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 3.84/1.59  | (20)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 3.84/1.59  | (21)  ? [v0] :  ? [v1] : element(v1, v0)
% 3.84/1.59  | (22) relation(empty_set)
% 3.84/1.59  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v2) | in(v5, v1))
% 3.84/1.59  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 3.84/1.59  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 3.84/1.59  | (26)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 3.84/1.59  | (27)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 3.84/1.59  | (28) relation(all_0_2_2)
% 3.84/1.59  | (29)  ! [v0] :  ! [v1] : ( ~ relation(v1) |  ~ relation(v0) | subset(v0, v1) |  ? [v2] :  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) &  ~ in(v4, v1)))
% 3.84/1.59  | (30) empty(all_0_0_0)
% 3.84/1.59  | (31)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 3.84/1.59  | (32)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 3.84/1.59  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 3.84/1.59  | (34) empty(empty_set)
% 3.84/1.59  | (35)  ~ subset(all_0_4_4, all_0_5_5)
% 3.84/1.59  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ (ordered_pair(v3, v4) = v5) |  ~ relation(v2) |  ~ relation(v1) |  ~ in(v5, v2) | in(v4, v0))
% 3.84/1.59  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 3.84/1.59  | (38)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 3.84/1.59  | (39)  ~ empty(all_0_2_2)
% 3.84/1.59  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2))
% 3.84/1.59  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 3.84/1.59  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.84/1.59  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.84/1.59  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ subset(v0, v1) |  ~ relation(v1) |  ~ relation(v0) |  ~ in(v4, v0) | in(v4, v1))
% 3.84/1.59  | (45) empty(all_0_1_1)
% 3.84/1.59  | (46) relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4
% 3.84/1.59  | (47)  ~ empty(all_0_3_3)
% 3.84/1.59  |
% 3.84/1.59  | Instantiating formula (40) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4, relation(all_0_5_5), yields:
% 3.84/1.59  | (48) relation(all_0_4_4)
% 3.84/1.59  |
% 3.84/1.59  | Instantiating formula (29) with all_0_5_5, all_0_4_4 and discharging atoms relation(all_0_4_4), relation(all_0_5_5),  ~ subset(all_0_4_4, all_0_5_5), yields:
% 3.84/1.59  | (49)  ? [v0] :  ? [v1] :  ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_4_4) &  ~ in(v2, all_0_5_5))
% 3.84/1.60  |
% 3.84/1.60  | Instantiating (49) with all_23_0_10, all_23_1_11, all_23_2_12 yields:
% 3.84/1.60  | (50) ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10 & in(all_23_0_10, all_0_4_4) &  ~ in(all_23_0_10, all_0_5_5)
% 3.84/1.60  |
% 3.84/1.60  | Applying alpha-rule on (50) yields:
% 3.84/1.60  | (51) ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10
% 3.84/1.60  | (52) in(all_23_0_10, all_0_4_4)
% 3.84/1.60  | (53)  ~ in(all_23_0_10, all_0_5_5)
% 3.84/1.60  |
% 3.84/1.60  | Instantiating formula (23) with all_23_0_10, all_23_1_11, all_23_2_12, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4, ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10, relation(all_0_4_4), relation(all_0_5_5), in(all_23_0_10, all_0_4_4),  ~ in(all_23_0_10, all_0_5_5), yields:
% 3.84/1.60  | (54) $false
% 3.84/1.60  |
% 3.84/1.60  |-The branch is then unsatisfiable
% 3.84/1.60  % SZS output end Proof for theBenchmark
% 3.84/1.60  
% 3.84/1.60  1019ms
%------------------------------------------------------------------------------