%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n018.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 08:47:50 EDT 2022

% Result   : Theorem 2.46s 1.33s
% Output   : Proof 4.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.31  % Computer : n018.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Sun Jun 19 09:47:34 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.15/0.56          ____       _                          
% 0.15/0.56    ___  / __ \_____(_)___  ________  __________
% 0.15/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.15/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.15/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.15/0.56  
% 0.15/0.56  A Theorem Prover for First-Order Logic
% 0.15/0.56  (ePrincess v.1.0)
% 0.15/0.56  
% 0.15/0.56  (c) Philipp Rümmer, 2009-2015
% 0.15/0.56  (c) Peter Backeman, 2014-2015
% 0.15/0.56  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.15/0.56  Free software under GNU Lesser General Public License (LGPL).
% 0.15/0.56  Bug reports to peter@backeman.se
% 0.15/0.56  
% 0.15/0.56  For more information, visit http://user.uu.se/~petba168/breu/
% 0.15/0.56  
% 0.15/0.56  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.61  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.93  Prover 0: Preprocessing ...
% 1.99/1.15  Prover 0: Warning: ignoring some quantifiers
% 2.23/1.17  Prover 0: Constructing countermodel ...
% 2.46/1.32  Prover 0: proved (713ms)
% 2.46/1.33  
% 2.46/1.33  No countermodel exists, formula is valid
% 2.46/1.33  % SZS status Theorem for theBenchmark
% 2.46/1.33  
% 2.46/1.33  Generating proof ... Warning: ignoring some quantifiers
% 3.69/1.60  found it (size 11)
% 3.69/1.60  
% 3.69/1.60  % SZS output start Proof for theBenchmark
% 3.69/1.60  Assumed formulas after preprocessing and simplification: 
% 3.69/1.60  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v6 = v5) & apply(v3, v1) = v5 & apply(v2, v1) = v6 & relation_dom(v3) = v4 & relation_dom_restriction(v2, v0) = v3 & in(v1, v4) & empty(v12) & empty(v11) & empty(v9) & empty(empty_set) & one_to_one(v13) & function(v13) & function(v12) & function(v7) & function(v2) & relation_empty_yielding(v14) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v7) & relation(v2) & relation(empty_set) &  ~ empty(v10) &  ~ empty(v8) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom(v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ (set_intersection2(v19, v15) = v20) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : (relation_dom_restriction(v18, v15) = v21 & ( ~ (v21 = v16) | (v20 = v17 &  ! [v25] :  ! [v26] : ( ~ (apply(v18, v25) = v26) |  ~ in(v25, v17) | apply(v16, v25) = v26) &  ! [v25] :  ! [v26] : ( ~ (apply(v16, v25) = v26) |  ~ in(v25, v17) | apply(v18, v25) = v26))) & ( ~ (v20 = v17) | v21 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))))) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (relation_dom(v16) = v17) |  ~ (relation_dom_restriction(v18, v15) = v19) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : (relation_dom(v18) = v20 & set_intersection2(v20, v15) = v21 & ( ~ (v21 = v17) | v19 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))) & ( ~ (v19 = v16) | (v21 = v17 &  ! [v25] :  ! [v26] : ( ~ (apply(v18, v25) = v26) |  ~ in(v25, v17) | apply(v16, v25) = v26) &  ! [v25] :  ! [v26] : ( ~ (apply(v16, v25) = v26) |  ~ in(v25, v17) | apply(v18, v25) = v26))))) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (apply(v18, v17) = v16) |  ~ (apply(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (set_intersection2(v18, v17) = v16) |  ~ (set_intersection2(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_dom_restriction(v18, v17) = v16) |  ~ (relation_dom_restriction(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (relation_dom(v17) = v16) |  ~ (relation_dom(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (set_intersection2(v16, v15) = v17) | set_intersection2(v15, v16) = v17) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) |  ~ relation(v16) |  ~ relation(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | set_intersection2(v16, v15) = v17) &  ! [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] : (v16 = v15 |  ~ (set_intersection2(v15, v15) = v16)) &  ! [v15] :  ! [v16] : (v16 = v15 |  ~ empty(v16) |  ~ empty(v15)) &  ! [v15] :  ! [v16] : (v16 = empty_set |  ~ (set_intersection2(v15, empty_set) = v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v16) |  ~ relation(v15) | empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | relation(v16)) &  ! [v15] :  ! [v16] : ( ~ in(v16, v15) |  ~ in(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) |  ~ empty(v16)) &  ! [v15] :  ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) &  ! [v15] :  ! [v16] : ( ~ element(v15, v16) | in(v15, v16) | empty(v16)) &  ! [v15] : (v15 = empty_set |  ~ empty(v15)) &  ! [v15] : ( ~ empty(v15) |  ~ function(v15) |  ~ relation(v15) | one_to_one(v15)) &  ! [v15] : ( ~ empty(v15) | function(v15)) &  ! [v15] : ( ~ empty(v15) | relation(v15)) &  ? [v15] :  ? [v16] : element(v16, v15))
% 4.10/1.65  | 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:
% 4.10/1.65  | (1)  ~ (all_0_8_8 = all_0_9_9) & apply(all_0_11_11, all_0_13_13) = all_0_9_9 & apply(all_0_12_12, all_0_13_13) = all_0_8_8 & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11 & in(all_0_13_13, all_0_10_10) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_5_5) & empty(empty_set) & one_to_one(all_0_1_1) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_7_7) & function(all_0_12_12) & relation_empty_yielding(all_0_0_0) & 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_7_7) & relation(all_0_12_12) & relation(empty_set) &  ~ empty(all_0_4_4) &  ~ empty(all_0_6_6) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v4, v0) = v5) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 &  ! [v10] :  ! [v11] : ( ~ (apply(v3, v10) = v11) |  ~ in(v10, v2) | apply(v1, v10) = v11) &  ! [v10] :  ! [v11] : ( ~ (apply(v1, v10) = v11) |  ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v1) = v2) |  ~ (relation_dom_restriction(v3, v0) = v4) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 &  ! [v10] :  ! [v11] : ( ~ (apply(v3, v10) = v11) |  ~ in(v10, v2) | apply(v1, v10) = v11) &  ! [v10] :  ! [v11] : ( ~ (apply(v1, v10) = v11) |  ~ in(v10, v2) | apply(v3, v10) = v11))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [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] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v1) |  ~ relation(v0) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v0, v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) &  ! [v0] : (v0 = empty_set |  ~ empty(v0)) &  ! [v0] : ( ~ empty(v0) |  ~ function(v0) |  ~ relation(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ? [v0] :  ? [v1] : element(v1, v0)
% 4.10/1.65  |
% 4.10/1.65  | Applying alpha-rule on (1) yields:
% 4.10/1.66  | (2) function(all_0_1_1)
% 4.10/1.66  | (3) empty(all_0_2_2)
% 4.10/1.66  | (4) relation_dom(all_0_11_11) = all_0_10_10
% 4.10/1.66  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 4.10/1.66  | (6)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 4.10/1.66  | (7) one_to_one(all_0_1_1)
% 4.10/1.66  | (8)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 4.10/1.66  | (9)  ! [v0] : ( ~ empty(v0) |  ~ function(v0) |  ~ relation(v0) | one_to_one(v0))
% 4.10/1.66  | (10)  ~ empty(all_0_4_4)
% 4.10/1.66  | (11)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1))
% 4.10/1.66  | (12) empty(all_0_5_5)
% 4.10/1.66  | (13)  ! [v0] : ( ~ empty(v0) | function(v0))
% 4.10/1.66  | (14) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11
% 4.10/1.66  | (15) relation(all_0_4_4)
% 4.10/1.66  | (16)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 4.10/1.66  | (17)  ~ (all_0_8_8 = all_0_9_9)
% 4.10/1.66  | (18) relation_empty_yielding(all_0_0_0)
% 4.10/1.66  | (19) relation(all_0_3_3)
% 4.10/1.66  | (20)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 4.10/1.66  | (21) relation(all_0_12_12)
% 4.10/1.66  | (22)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v1) |  ~ relation(v0) | empty(v0))
% 4.10/1.66  | (23) empty(empty_set)
% 4.10/1.66  | (24) function(all_0_2_2)
% 4.10/1.66  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 4.10/1.66  | (26)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 4.10/1.66  | (27) relation(all_0_7_7)
% 4.10/1.66  | (28)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 4.10/1.66  | (29) apply(all_0_12_12, all_0_13_13) = all_0_8_8
% 4.10/1.66  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | function(v2))
% 4.10/1.66  | (31)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 4.10/1.66  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v4, v0) = v5) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 &  ! [v10] :  ! [v11] : ( ~ (apply(v3, v10) = v11) |  ~ in(v10, v2) | apply(v1, v10) = v11) &  ! [v10] :  ! [v11] : ( ~ (apply(v1, v10) = v11) |  ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2)))))
% 4.10/1.66  | (33) relation(all_0_0_0)
% 4.10/1.66  | (34) relation_empty_yielding(empty_set)
% 4.10/1.66  | (35)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.10/1.66  | (36) relation(empty_set)
% 4.10/1.66  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 4.10/1.66  | (38) relation(all_0_2_2)
% 4.10/1.66  | (39)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2))
% 4.10/1.66  | (40)  ? [v0] :  ? [v1] : element(v1, v0)
% 4.10/1.66  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ function(v0) |  ~ relation(v0) | relation(v2))
% 4.10/1.66  | (42) empty(all_0_3_3)
% 4.10/1.67  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0))
% 4.10/1.67  | (44) relation(all_0_1_1)
% 4.10/1.67  | (45)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) |  ~ empty(v1))
% 4.10/1.67  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 4.10/1.67  | (47)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 4.10/1.67  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v1) = v2) |  ~ (relation_dom_restriction(v3, v0) = v4) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 &  ! [v10] :  ! [v11] : ( ~ (apply(v3, v10) = v11) |  ~ in(v10, v2) | apply(v1, v10) = v11) &  ! [v10] :  ! [v11] : ( ~ (apply(v1, v10) = v11) |  ~ in(v10, v2) | apply(v3, v10) = v11)))))
% 4.10/1.67  | (49)  ~ empty(all_0_6_6)
% 4.10/1.67  | (50) apply(all_0_11_11, all_0_13_13) = all_0_9_9
% 4.10/1.67  | (51)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2))
% 4.10/1.67  | (52) function(all_0_7_7)
% 4.10/1.67  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2))
% 4.10/1.67  | (54) in(all_0_13_13, all_0_10_10)
% 4.10/1.67  | (55) function(all_0_12_12)
% 4.10/1.67  | (56)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 4.10/1.67  | (57)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 4.10/1.67  |
% 4.10/1.67  | Instantiating formula (30) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, function(all_0_12_12), relation(all_0_12_12), yields:
% 4.10/1.67  | (58) function(all_0_11_11)
% 4.10/1.67  |
% 4.10/1.67  | Instantiating formula (51) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_12_12), yields:
% 4.10/1.67  | (59) relation(all_0_11_11)
% 4.10/1.67  |
% 4.10/1.67  | Instantiating formula (48) with all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_11_11) = all_0_10_10, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields:
% 4.10/1.67  | (60)  ? [v0] : (relation_dom(all_0_12_12) = v0 & set_intersection2(v0, all_0_14_14) = all_0_10_10 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_11_11, v1) = v2) |  ~ in(v1, all_0_10_10) | apply(all_0_12_12, v1) = v2) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | apply(all_0_11_11, v1) = v2))
% 4.10/1.67  |
% 4.10/1.67  | Instantiating (60) with all_20_0_17 yields:
% 4.10/1.67  | (61) relation_dom(all_0_12_12) = all_20_0_17 & set_intersection2(all_20_0_17, all_0_14_14) = all_0_10_10 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 4.10/1.67  |
% 4.10/1.67  | Applying alpha-rule on (61) yields:
% 4.10/1.67  | (62) relation_dom(all_0_12_12) = all_20_0_17
% 4.10/1.67  | (63) set_intersection2(all_20_0_17, all_0_14_14) = all_0_10_10
% 4.10/1.67  | (64)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1)
% 4.10/1.68  | (65)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 4.10/1.68  |
% 4.10/1.68  | Instantiating formula (64) with all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_11_11, all_0_13_13) = all_0_9_9, in(all_0_13_13, all_0_10_10), yields:
% 4.10/1.68  | (66) apply(all_0_12_12, all_0_13_13) = all_0_9_9
% 4.10/1.68  |
% 4.10/1.68  | Instantiating formula (25) with all_0_12_12, all_0_13_13, all_0_9_9, all_0_8_8 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, apply(all_0_12_12, all_0_13_13) = all_0_9_9, yields:
% 4.10/1.68  | (67) all_0_8_8 = all_0_9_9
% 4.10/1.68  |
% 4.10/1.68  | Equations (67) can reduce 17 to:
% 4.10/1.68  | (68) $false
% 4.10/1.68  |
% 4.10/1.68  |-The branch is then unsatisfiable
% 4.10/1.68  % SZS output end Proof for theBenchmark
% 4.10/1.68  
% 4.10/1.68  1106ms
%------------------------------------------------------------------------------