%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU180+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.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 08:47:22 EDT 2022

% Result   : Theorem 2.86s 1.40s
% Output   : Proof 4.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SEU180+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jun 19 05:03:43 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.62/0.60          ____       _                          
% 0.62/0.60    ___  / __ \_____(_)___  ________  __________
% 0.62/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.62/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.62/0.60  
% 0.62/0.60  A Theorem Prover for First-Order Logic
% 0.62/0.60  (ePrincess v.1.0)
% 0.62/0.60  
% 0.62/0.60  (c) Philipp Rümmer, 2009-2015
% 0.62/0.60  (c) Peter Backeman, 2014-2015
% 0.62/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.60  Bug reports to peter@backeman.se
% 0.62/0.60  
% 0.62/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.60  
% 0.62/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.94  Prover 0: Preprocessing ...
% 2.24/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.24/1.21  Prover 0: Constructing countermodel ...
% 2.86/1.39  Prover 0: proved (747ms)
% 2.86/1.40  
% 2.86/1.40  No countermodel exists, formula is valid
% 2.86/1.40  % SZS status Theorem for theBenchmark
% 2.86/1.40  
% 2.86/1.40  Generating proof ... Warning: ignoring some quantifiers
% 4.22/1.65  found it (size 15)
% 4.22/1.65  
% 4.22/1.65  % SZS output start Proof for theBenchmark
% 4.22/1.65  Assumed formulas after preprocessing and simplification: 
% 4.22/1.65  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (relation_field(v2) = v4 & ordered_pair(v0, v1) = v3 & empty(v7) & empty(v6) & empty(empty_set) & relation(v7) & relation(v2) & in(v3, v2) &  ~ empty(v5) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (singleton(v8) = v11) |  ~ (unordered_pair(v10, v11) = v12) |  ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (relation_rng(v8) = v9) |  ~ (ordered_pair(v11, v10) = v12) |  ~ relation(v8) |  ~ in(v12, v8) | in(v10, v9)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (relation_dom(v8) = v9) |  ~ (ordered_pair(v10, v11) = v12) |  ~ relation(v8) |  ~ in(v12, v8) | in(v10, v9)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (ordered_pair(v11, v10) = v9) |  ~ (ordered_pair(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (set_union2(v11, v10) = v9) |  ~ (set_union2(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (unordered_pair(v11, v10) = v9) |  ~ (unordered_pair(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (relation_rng(v8) = v10) |  ~ (relation_dom(v8) = v9) |  ~ (set_union2(v9, v10) = v11) |  ~ relation(v8) | relation_field(v8) = v11) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_union2(v8, v9) = v10) |  ~ in(v11, v10) | in(v11, v9) | in(v11, v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_union2(v8, v9) = v10) |  ~ in(v11, v9) | in(v11, v10)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_union2(v8, v9) = v10) |  ~ in(v11, v8) | in(v11, v10)) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_union2(v9, v10) = v11) |  ? [v12] : (( ~ in(v12, v8) | ( ~ in(v12, v10) &  ~ in(v12, v9))) & (in(v12, v10) | in(v12, v9) | in(v12, v8)))) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (relation_field(v10) = v9) |  ~ (relation_field(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (singleton(v10) = v9) |  ~ (singleton(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (relation_rng(v10) = v9) |  ~ (relation_rng(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (relation_dom(v10) = v9) |  ~ (relation_dom(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (relation_rng(v8) = v9) |  ~ relation(v8) |  ~ in(v10, v9) |  ? [v11] :  ? [v12] : (ordered_pair(v11, v10) = v12 & in(v12, v8))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (relation_dom(v8) = v9) |  ~ relation(v8) |  ~ in(v10, v9) |  ? [v11] :  ? [v12] : (ordered_pair(v10, v11) = v12 & in(v12, v8))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) |  ~ empty(v10)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) |  ? [v11] :  ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v9, v8) = v10) |  ~ empty(v10) | empty(v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v8, v9) = v10) |  ~ empty(v10) | empty(v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v8, v9) = v10) |  ~ relation(v9) |  ~ relation(v8) | relation(v10)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) |  ~ empty(v10)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) &  ? [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (relation_rng(v9) = v10) |  ~ relation(v9) |  ? [v11] :  ? [v12] :  ? [v13] : (( ~ in(v11, v8) |  ! [v14] :  ! [v15] : ( ~ (ordered_pair(v14, v11) = v15) |  ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v12, v11) = v13 & in(v13, v9))))) &  ? [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (relation_dom(v9) = v10) |  ~ relation(v9) |  ? [v11] :  ? [v12] :  ? [v13] : (( ~ in(v11, v8) |  ! [v14] :  ! [v15] : ( ~ (ordered_pair(v11, v14) = v15) |  ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v11, v12) = v13 & in(v13, v9))))) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ empty(v9) |  ~ empty(v8)) &  ! [v8] :  ! [v9] : ( ~ (relation_field(v8) = v9) |  ~ relation(v8) |  ? [v10] :  ? [v11] : (relation_rng(v8) = v11 & relation_dom(v8) = v10 & set_union2(v10, v11) = v9)) &  ! [v8] :  ! [v9] : ( ~ (singleton(v8) = v9) |  ~ empty(v9)) &  ! [v8] :  ! [v9] : ( ~ empty(v9) |  ~ in(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ element(v8, v9) | empty(v9) | in(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ in(v9, v8) |  ~ in(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ in(v8, v9) | element(v8, v9)) &  ! [v8] : (v8 = empty_set |  ~ empty(v8)) &  ? [v8] :  ? [v9] : element(v9, v8) & ( ~ in(v1, v4) |  ~ in(v0, v4)))
% 4.22/1.70  | 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 yields:
% 4.22/1.70  | (1) relation_field(all_0_5_5) = all_0_3_3 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & relation(all_0_0_0) & relation(all_0_5_5) & in(all_0_4_4, all_0_5_5) &  ~ empty(all_0_2_2) &  ! [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] : ( ~ (relation_rng(v0) = v1) |  ~ (ordered_pair(v3, v2) = v4) |  ~ relation(v0) |  ~ in(v4, v0) | in(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v3) = v4) |  ~ relation(v0) |  ~ in(v4, v0) | in(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_rng(v0) = v2) |  ~ (relation_dom(v0) = v1) |  ~ (set_union2(v1, v2) = v3) |  ~ relation(v0) | relation_field(v0) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v1) | in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) &  ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_field(v2) = v1) |  ~ (relation_field(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(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] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ in(v2, v1) |  ? [v3] :  ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ in(v2, v1) |  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) &  ! [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] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [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] :  ! [v2] : (v2 = v0 |  ~ (relation_rng(v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ in(v3, v0) |  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) |  ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ in(v3, v0) |  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) |  ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ element(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] :  ? [v1] : element(v1, v0) & ( ~ in(all_0_6_6, all_0_3_3) |  ~ in(all_0_7_7, all_0_3_3))
% 4.22/1.71  |
% 4.22/1.71  | Applying alpha-rule on (1) yields:
% 4.22/1.71  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 4.22/1.71  | (3)  ~ in(all_0_6_6, all_0_3_3) |  ~ in(all_0_7_7, all_0_3_3)
% 4.22/1.71  | (4)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 4.22/1.71  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ in(v2, v1) |  ? [v3] :  ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 4.22/1.71  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ in(v2, v1) |  ? [v3] :  ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 4.22/1.71  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v3) = v4) |  ~ relation(v0) |  ~ in(v4, v0) | in(v2, v1))
% 4.22/1.71  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 4.22/1.71  | (9)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.22/1.71  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 4.22/1.71  | (11)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.22/1.71  | (12)  ! [v0] :  ! [v1] : ( ~ (relation_field(v0) = v1) |  ~ relation(v0) |  ? [v2] :  ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 4.22/1.71  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 4.22/1.71  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 4.22/1.71  | (15)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_dom(v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ in(v3, v0) |  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) |  ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1)))))
% 4.22/1.71  | (16)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.22/1.71  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.22/1.71  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 4.22/1.71  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 4.22/1.71  | (20) in(all_0_4_4, all_0_5_5)
% 4.22/1.71  | (21) empty(all_0_0_0)
% 4.22/1.71  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 4.22/1.72  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 4.22/1.72  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_field(v2) = v1) |  ~ (relation_field(v2) = v0))
% 4.22/1.72  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.58/1.72  | (26)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) &  ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 4.58/1.72  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 4.58/1.72  | (28) ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4
% 4.58/1.72  | (29)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 4.58/1.72  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 4.58/1.72  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_rng(v0) = v2) |  ~ (relation_dom(v0) = v1) |  ~ (set_union2(v1, v2) = v3) |  ~ relation(v0) | relation_field(v0) = v3)
% 4.58/1.72  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2))
% 4.58/1.72  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 4.58/1.72  | (34)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 4.58/1.72  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 4.58/1.72  | (36)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.58/1.72  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v1) | in(v3, v2))
% 4.58/1.72  | (38)  ~ empty(all_0_2_2)
% 4.58/1.72  | (39) relation(all_0_5_5)
% 4.58/1.72  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 4.58/1.72  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 4.58/1.72  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 4.58/1.72  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_rng(v0) = v1) |  ~ (ordered_pair(v3, v2) = v4) |  ~ relation(v0) |  ~ in(v4, v0) | in(v2, v1))
% 4.58/1.72  | (44)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (relation_rng(v1) = v2) |  ~ relation(v1) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ in(v3, v0) |  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) |  ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1)))))
% 4.58/1.72  | (45) relation_field(all_0_5_5) = all_0_3_3
% 4.58/1.72  | (46)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.58/1.72  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 4.58/1.72  | (48) empty(all_0_1_1)
% 4.58/1.72  | (49) relation(all_0_0_0)
% 4.58/1.72  | (50) empty(empty_set)
% 4.58/1.72  | (51)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.58/1.72  |
% 4.58/1.73  | Instantiating formula (12) with all_0_3_3, all_0_5_5 and discharging atoms relation_field(all_0_5_5) = all_0_3_3, relation(all_0_5_5), yields:
% 4.58/1.73  | (52)  ? [v0] :  ? [v1] : (relation_rng(all_0_5_5) = v1 & relation_dom(all_0_5_5) = v0 & set_union2(v0, v1) = all_0_3_3)
% 4.58/1.73  |
% 4.58/1.73  | Instantiating (52) with all_21_0_13, all_21_1_14 yields:
% 4.58/1.73  | (53) relation_rng(all_0_5_5) = all_21_0_13 & relation_dom(all_0_5_5) = all_21_1_14 & set_union2(all_21_1_14, all_21_0_13) = all_0_3_3
% 4.58/1.73  |
% 4.58/1.73  | Applying alpha-rule on (53) yields:
% 4.58/1.73  | (54) relation_rng(all_0_5_5) = all_21_0_13
% 4.58/1.73  | (55) relation_dom(all_0_5_5) = all_21_1_14
% 4.58/1.73  | (56) set_union2(all_21_1_14, all_21_0_13) = all_0_3_3
% 4.58/1.73  |
% 4.58/1.73  | Instantiating formula (43) with all_0_4_4, all_0_7_7, all_0_6_6, all_21_0_13, all_0_5_5 and discharging atoms relation_rng(all_0_5_5) = all_21_0_13, ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, relation(all_0_5_5), in(all_0_4_4, all_0_5_5), yields:
% 4.58/1.73  | (57) in(all_0_6_6, all_21_0_13)
% 4.58/1.73  |
% 4.58/1.73  | Instantiating formula (7) with all_0_4_4, all_0_6_6, all_0_7_7, all_21_1_14, all_0_5_5 and discharging atoms relation_dom(all_0_5_5) = all_21_1_14, ordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, relation(all_0_5_5), in(all_0_4_4, all_0_5_5), yields:
% 4.58/1.73  | (58) in(all_0_7_7, all_21_1_14)
% 4.58/1.73  |
% 4.58/1.73  | Instantiating formula (42) with all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_1_14, all_21_0_13) = all_0_3_3, yields:
% 4.58/1.73  | (59) set_union2(all_21_0_13, all_21_1_14) = all_0_3_3
% 4.58/1.73  |
% 4.58/1.73  | Instantiating formula (32) with all_0_6_6, all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_0_13, all_21_1_14) = all_0_3_3, in(all_0_6_6, all_21_0_13), yields:
% 4.58/1.73  | (60) in(all_0_6_6, all_0_3_3)
% 4.58/1.73  |
% 4.58/1.73  | Instantiating formula (37) with all_0_7_7, all_0_3_3, all_21_1_14, all_21_0_13 and discharging atoms set_union2(all_21_0_13, all_21_1_14) = all_0_3_3, in(all_0_7_7, all_21_1_14), yields:
% 4.58/1.73  | (61) in(all_0_7_7, all_0_3_3)
% 4.58/1.73  |
% 4.58/1.73  +-Applying beta-rule and splitting (3), into two cases.
% 4.58/1.73  |-Branch one:
% 4.58/1.73  | (62)  ~ in(all_0_6_6, all_0_3_3)
% 4.58/1.73  |
% 4.58/1.73  	| Using (60) and (62) yields:
% 4.58/1.73  	| (63) $false
% 4.58/1.73  	|
% 4.58/1.73  	|-The branch is then unsatisfiable
% 4.58/1.73  |-Branch two:
% 4.58/1.73  | (60) in(all_0_6_6, all_0_3_3)
% 4.58/1.73  | (65)  ~ in(all_0_7_7, all_0_3_3)
% 4.58/1.73  |
% 4.58/1.73  	| Using (61) and (65) yields:
% 4.58/1.73  	| (63) $false
% 4.58/1.73  	|
% 4.58/1.73  	|-The branch is then unsatisfiable
% 4.58/1.73  % SZS output end Proof for theBenchmark
% 4.58/1.73  
% 4.58/1.73  1124ms
%------------------------------------------------------------------------------