%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n003.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 5.26s 2.07s
% Output   : Proof 8.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU039+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 13:18:14 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.70/0.68          ____       _                          
% 0.70/0.68    ___  / __ \_____(_)___  ________  __________
% 0.70/0.68   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.70/0.68  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.70/0.68  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.70/0.68  
% 0.70/0.68  A Theorem Prover for First-Order Logic
% 0.70/0.69  (ePrincess v.1.0)
% 0.70/0.69  
% 0.70/0.69  (c) Philipp Rümmer, 2009-2015
% 0.70/0.69  (c) Peter Backeman, 2014-2015
% 0.70/0.69  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.70/0.69  Free software under GNU Lesser General Public License (LGPL).
% 0.70/0.69  Bug reports to peter@backeman.se
% 0.70/0.69  
% 0.70/0.69  For more information, visit http://user.uu.se/~petba168/breu/
% 0.70/0.69  
% 0.70/0.69  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.82/0.75  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/1.16  Prover 0: Preprocessing ...
% 3.29/1.58  Prover 0: Warning: ignoring some quantifiers
% 3.29/1.62  Prover 0: Constructing countermodel ...
% 5.26/2.06  Prover 0: proved (1312ms)
% 5.26/2.07  
% 5.26/2.07  No countermodel exists, formula is valid
% 5.26/2.07  % SZS status Theorem for theBenchmark
% 5.26/2.07  
% 5.26/2.07  Generating proof ... Warning: ignoring some quantifiers
% 7.50/2.57  found it (size 40)
% 7.50/2.57  
% 7.50/2.57  % SZS output start Proof for theBenchmark
% 7.50/2.57  Assumed formulas after preprocessing and simplification: 
% 7.50/2.57  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (relation_dom_restriction(v2, v0) = v5 & relation_rng(v5) = v6 & relation_dom(v2) = v3 & apply(v2, v1) = v4 & relation_empty_yielding(v7) & relation_empty_yielding(empty_set) & one_to_one(v8) & relation(v14) & relation(v13) & relation(v11) & relation(v10) & relation(v8) & relation(v7) & relation(v2) & relation(empty_set) & function(v14) & function(v11) & function(v8) & function(v2) & empty(v13) & empty(v12) & empty(v11) & empty(empty_set) & in(v1, v3) & in(v1, v0) &  ~ empty(v10) &  ~ empty(v9) &  ~ in(v4, v6) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] :  ! [v20] : ( ~ (relation_dom(v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ (set_intersection2(v19, v15) = v20) |  ~ relation(v18) |  ~ relation(v16) |  ~ function(v18) |  ~ function(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_restriction(v18, v15) = v19) |  ~ (relation_dom(v16) = v17) |  ~ relation(v18) |  ~ relation(v16) |  ~ function(v18) |  ~ function(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] :  ! [v19] : ( ~ (relation_dom_restriction(v17, v15) = v18) |  ~ (apply(v18, v16) = v19) |  ~ relation(v17) |  ~ function(v17) |  ~ in(v16, v15) | apply(v17, v16) = v19) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_dom_restriction(v18, v17) = v16) |  ~ (relation_dom_restriction(v18, v17) = v15)) &  ! [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] : ( ~ (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] :  ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) |  ~ in(v18, v17) | in(v18, v16)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) |  ~ in(v18, v17) | in(v18, v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) |  ~ in(v18, v16) |  ~ in(v18, v15) | in(v18, v17)) &  ? [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v18 = v15 |  ~ (set_intersection2(v16, v17) = v18) |  ? [v19] : (( ~ in(v19, v17) |  ~ in(v19, v16) |  ~ in(v19, v15)) & (in(v19, v15) | (in(v19, v17) & in(v19, v16))))) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (powerset(v17) = v16) |  ~ (powerset(v17) = v15)) &  ! [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] : ( ~ (powerset(v16) = v17) |  ~ subset(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) | subset(v15, v16)) &  ! [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) |  ~ function(v15) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation(v15) |  ~ function(v15) | function(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) |  ~ relation(v15) | relation(v17)) &  ! [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] : (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] : ( ~ (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] : ( ~ (relation_rng(v15) = v16) |  ~ relation(v15) |  ~ function(v15) |  ? [v17] : (relation_dom(v15) = v17 &  ! [v18] :  ! [v19] : ( ~ (apply(v15, v19) = v18) |  ~ in(v19, v17) | in(v18, v16)) &  ! [v18] : ( ~ in(v18, v16) |  ? [v19] : (apply(v15, v19) = v18 & in(v19, v17))) &  ? [v18] : (v18 = v16 |  ? [v19] :  ? [v20] :  ? [v21] : (( ~ in(v19, v18) |  ! [v22] : ( ~ (apply(v15, v22) = v19) |  ~ in(v22, v17))) & (in(v19, v18) | (v21 = v19 & apply(v15, v20) = v19 & in(v20, v17))))))) &  ! [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) |  ~ function(v15) |  ? [v17] : (relation_rng(v15) = v17 &  ! [v18] :  ! [v19] : ( ~ (apply(v15, v19) = v18) |  ~ in(v19, v16) | in(v18, v17)) &  ! [v18] : ( ~ in(v18, v17) |  ? [v19] : (apply(v15, v19) = v18 & in(v19, v16))) &  ? [v18] : (v18 = v17 |  ? [v19] :  ? [v20] :  ? [v21] : (( ~ in(v19, v18) |  ! [v22] : ( ~ (apply(v15, v22) = v19) |  ~ in(v22, v16))) & (in(v19, v18) | (v21 = v19 & apply(v15, v20) = v19 & in(v20, 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] : ( ~ 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] : ( ~ relation(v15) |  ~ function(v15) |  ~ empty(v15) | one_to_one(v15)) &  ! [v15] : ( ~ empty(v15) | relation(v15)) &  ! [v15] : ( ~ empty(v15) | function(v15)) &  ? [v15] :  ? [v16] : element(v16, v15) &  ? [v15] : subset(v15, v15))
% 7.76/2.63  | 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:
% 7.76/2.63  | (1) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9 & relation_rng(all_0_9_9) = all_0_8_8 & relation_dom(all_0_12_12) = all_0_11_11 & apply(all_0_12_12, all_0_13_13) = all_0_10_10 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_12_12) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_12_12) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & in(all_0_13_13, all_0_11_11) & in(all_0_13_13, all_0_14_14) &  ~ empty(all_0_4_4) &  ~ empty(all_0_5_5) &  ~ in(all_0_10_10, all_0_8_8) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v4, v0) = v5) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(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_restriction(v3, v0) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(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] :  ! [v4] : ( ~ (relation_dom_restriction(v2, v0) = v3) |  ~ (apply(v3, v1) = v4) |  ~ relation(v2) |  ~ function(v2) |  ~ in(v1, v0) | apply(v2, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0)) &  ! [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] : ( ~ (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] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(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] : ( ~ (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_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) |  ~ function(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2)) &  ! [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] : (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] : ( ~ (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] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v2) | in(v3, v1)) &  ! [v3] : ( ~ in(v3, v1) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) &  ? [v3] : (v3 = v1 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) &  ! [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) |  ~ function(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v1) | in(v3, v2)) &  ! [v3] : ( ~ in(v3, v2) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) &  ? [v3] : (v3 = v2 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, 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] : ( ~ 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] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0)
% 8.09/2.66  |
% 8.09/2.66  | Applying alpha-rule on (1) yields:
% 8.09/2.66  | (2)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 8.09/2.66  | (3) relation(all_0_6_6)
% 8.09/2.66  | (4)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 8.09/2.66  | (5) empty(all_0_3_3)
% 8.09/2.66  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 8.09/2.66  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0))
% 8.09/2.66  | (8) relation_empty_yielding(all_0_7_7)
% 8.09/2.66  | (9) in(all_0_13_13, all_0_11_11)
% 8.09/2.66  | (10)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 8.09/2.66  | (11)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 8.09/2.66  | (12) relation(all_0_0_0)
% 8.09/2.66  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 8.09/2.66  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 8.09/2.66  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation(v2))
% 8.09/2.66  | (16)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 8.09/2.66  | (17)  ~ empty(all_0_5_5)
% 8.09/2.66  | (18)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 8.09/2.67  | (19)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 8.09/2.67  | (20) apply(all_0_12_12, all_0_13_13) = all_0_10_10
% 8.09/2.67  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom_restriction(v2, v0) = v3) |  ~ (apply(v3, v1) = v4) |  ~ relation(v2) |  ~ function(v2) |  ~ in(v1, v0) | apply(v2, v1) = v4)
% 8.09/2.67  | (22) relation(all_0_4_4)
% 8.09/2.67  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 8.18/2.67  | (24) relation(all_0_7_7)
% 8.18/2.67  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 8.18/2.67  | (26) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9
% 8.18/2.67  | (27) relation(all_0_1_1)
% 8.18/2.67  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom_restriction(v3, v0) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(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)))))
% 8.18/2.67  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation_empty_yielding(v0) |  ~ relation(v0) | relation_empty_yielding(v2))
% 8.18/2.67  | (30)  ! [v0] : ( ~ empty(v0) | function(v0))
% 8.18/2.67  | (31) relation(all_0_3_3)
% 8.18/2.67  | (32)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 8.18/2.67  | (33)  ! [v0] : ( ~ relation(v0) |  ~ function(v0) |  ~ empty(v0) | one_to_one(v0))
% 8.18/2.67  | (34) one_to_one(all_0_6_6)
% 8.18/2.67  | (35)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 8.18/2.67  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 8.18/2.67  | (37)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 8.18/2.68  | (38)  ~ empty(all_0_4_4)
% 8.18/2.68  | (39) relation_dom(all_0_12_12) = all_0_11_11
% 8.18/2.68  | (40) in(all_0_13_13, all_0_14_14)
% 8.18/2.68  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | function(v2))
% 8.18/2.68  | (42)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 8.18/2.68  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2))
% 8.18/2.68  | (44)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 8.18/2.68  | (45) empty(all_0_1_1)
% 8.18/2.68  | (46)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 8.18/2.68  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 8.18/2.68  | (48)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_dom(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v2) | in(v3, v1)) &  ! [v3] : ( ~ in(v3, v1) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) &  ? [v3] : (v3 = v1 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 8.18/2.68  | (49) function(all_0_12_12)
% 8.18/2.68  | (50)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 8.18/2.68  | (51) relation(empty_set)
% 8.18/2.68  | (52) function(all_0_3_3)
% 8.18/2.68  | (53)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 8.18/2.68  | (54) relation_rng(all_0_9_9) = all_0_8_8
% 8.18/2.68  | (55)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 8.18/2.68  | (56)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ function(v0) |  ? [v2] : (relation_rng(v0) = v2 &  ! [v3] :  ! [v4] : ( ~ (apply(v0, v4) = v3) |  ~ in(v4, v1) | in(v3, v2)) &  ! [v3] : ( ~ in(v3, v2) |  ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) &  ? [v3] : (v3 = v2 |  ? [v4] :  ? [v5] :  ? [v6] : (( ~ in(v4, v3) |  ! [v7] : ( ~ (apply(v0, v7) = v4) |  ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 8.18/2.69  | (57)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | relation(v1))
% 8.18/2.69  | (58)  ~ in(all_0_10_10, all_0_8_8)
% 8.18/2.69  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_dom_restriction(v3, v2) = v1) |  ~ (relation_dom_restriction(v3, v2) = v0))
% 8.18/2.69  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 8.18/2.69  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) | relation(v2))
% 8.18/2.69  | (62) relation(all_0_12_12)
% 8.18/2.69  | (63)  ? [v0] :  ? [v1] : element(v1, v0)
% 8.18/2.69  | (64) relation_empty_yielding(empty_set)
% 8.18/2.69  | (65) empty(all_0_2_2)
% 8.18/2.69  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) |  ~ relation(v0) |  ~ function(v0) | relation(v2))
% 8.18/2.69  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 8.18/2.69  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 8.18/2.69  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ (set_intersection2(v4, v0) = v5) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(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)))))
% 8.18/2.69  | (70) empty(empty_set)
% 8.18/2.69  | (71)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 8.18/2.69  | (72) function(all_0_6_6)
% 8.18/2.69  | (73)  ? [v0] : subset(v0, v0)
% 8.18/2.69  | (74)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 8.18/2.69  | (75) function(all_0_0_0)
% 8.18/2.69  | (76)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 8.18/2.69  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1))
% 8.18/2.69  | (78)  ! [v0] :  ! [v1] : ( ~ (relation_rng(v0) = v1) |  ~ empty(v0) | empty(v1))
% 8.18/2.70  |
% 8.18/2.70  | Instantiating formula (56) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.70  | (79)  ? [v0] : (relation_rng(all_0_12_12) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v2) = v1) |  ~ in(v2, all_0_11_11) | in(v1, v0)) &  ! [v1] : ( ~ in(v1, v0) |  ? [v2] : (apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11))) &  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ in(v2, v1) |  ! [v5] : ( ~ (apply(all_0_12_12, v5) = v2) |  ~ in(v5, all_0_11_11))) & (in(v2, v1) | (v4 = v2 & apply(all_0_12_12, v3) = v2 & in(v3, all_0_11_11))))))
% 8.18/2.70  |
% 8.18/2.70  | Instantiating formula (28) with all_0_9_9, all_0_12_12, all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.70  | (80)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (relation_dom(all_0_12_12) = v0 & set_intersection2(v0, all_0_14_14) = v1 & ( ~ (v1 = all_0_11_11) | all_0_9_9 = all_0_12_12 | ( ~ (v4 = v3) & apply(all_0_12_12, v2) = v4 & apply(all_0_12_12, v2) = v3 & in(v2, all_0_11_11))) & ( ~ (all_0_9_9 = all_0_12_12) | v1 = all_0_11_11))
% 8.18/2.70  |
% 8.18/2.70  | Instantiating formula (66) with all_0_9_9, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.70  | (81) relation(all_0_9_9)
% 8.18/2.70  |
% 8.18/2.70  | Instantiating formula (41) with all_0_9_9, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.70  | (82) function(all_0_9_9)
% 8.18/2.70  |
% 8.18/2.70  | Instantiating (80) with all_19_0_19, all_19_1_20, all_19_2_21, all_19_3_22, all_19_4_23 yields:
% 8.18/2.70  | (83) relation_dom(all_0_12_12) = all_19_4_23 & set_intersection2(all_19_4_23, all_0_14_14) = all_19_3_22 & ( ~ (all_19_3_22 = all_0_11_11) | all_0_9_9 = all_0_12_12 | ( ~ (all_19_0_19 = all_19_1_20) & apply(all_0_12_12, all_19_2_21) = all_19_0_19 & apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_11_11))) & ( ~ (all_0_9_9 = all_0_12_12) | all_19_3_22 = all_0_11_11)
% 8.18/2.70  |
% 8.18/2.70  | Applying alpha-rule on (83) yields:
% 8.18/2.70  | (84) relation_dom(all_0_12_12) = all_19_4_23
% 8.18/2.70  | (85) set_intersection2(all_19_4_23, all_0_14_14) = all_19_3_22
% 8.18/2.71  | (86)  ~ (all_19_3_22 = all_0_11_11) | all_0_9_9 = all_0_12_12 | ( ~ (all_19_0_19 = all_19_1_20) & apply(all_0_12_12, all_19_2_21) = all_19_0_19 & apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_11_11))
% 8.18/2.71  | (87)  ~ (all_0_9_9 = all_0_12_12) | all_19_3_22 = all_0_11_11
% 8.18/2.71  |
% 8.18/2.71  | Instantiating (79) with all_21_0_24 yields:
% 8.18/2.71  | (88) relation_rng(all_0_12_12) = all_21_0_24 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) |  ~ in(v1, all_0_11_11) | in(v0, all_21_0_24)) &  ! [v0] : ( ~ in(v0, all_21_0_24) |  ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_0_11_11))) &  ? [v0] : (v0 = all_21_0_24 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) |  ~ in(v4, all_0_11_11))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11)))))
% 8.18/2.71  |
% 8.18/2.71  | Applying alpha-rule on (88) yields:
% 8.18/2.71  | (89) relation_rng(all_0_12_12) = all_21_0_24
% 8.18/2.71  | (90)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) |  ~ in(v1, all_0_11_11) | in(v0, all_21_0_24))
% 8.18/2.71  | (91)  ! [v0] : ( ~ in(v0, all_21_0_24) |  ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_0_11_11)))
% 8.18/2.71  | (92)  ? [v0] : (v0 = all_21_0_24 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) |  ~ in(v4, all_0_11_11))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11)))))
% 8.18/2.71  |
% 8.18/2.71  | Instantiating formula (53) with all_0_12_12, all_19_4_23, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_19_4_23, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 8.18/2.71  | (93) all_19_4_23 = all_0_11_11
% 8.18/2.71  |
% 8.18/2.71  | From (93) and (84) follows:
% 8.18/2.71  | (39) relation_dom(all_0_12_12) = all_0_11_11
% 8.18/2.71  |
% 8.18/2.71  | From (93) and (85) follows:
% 8.18/2.71  | (95) set_intersection2(all_0_11_11, all_0_14_14) = all_19_3_22
% 8.18/2.71  |
% 8.18/2.71  | Instantiating formula (48) with all_21_0_24, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_21_0_24, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.71  | (96)  ? [v0] : (relation_dom(all_0_12_12) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v2) = v1) |  ~ in(v2, v0) | in(v1, all_21_0_24)) &  ! [v1] : ( ~ in(v1, all_21_0_24) |  ? [v2] : (apply(all_0_12_12, v2) = v1 & in(v2, v0))) &  ? [v1] : (v1 = all_21_0_24 |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ in(v2, v1) |  ! [v5] : ( ~ (apply(all_0_12_12, v5) = v2) |  ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_12_12, v3) = v2 & in(v3, v0))))))
% 8.18/2.72  |
% 8.18/2.72  | Instantiating formula (69) with all_19_3_22, all_0_11_11, all_0_12_12, all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, set_intersection2(all_0_11_11, all_0_14_14) = all_19_3_22, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.18/2.72  | (97)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom_restriction(all_0_12_12, all_0_14_14) = v0 & ( ~ (v0 = all_0_12_12) | all_19_3_22 = all_0_11_11) & ( ~ (all_19_3_22 = all_0_11_11) | v0 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_11_11))))
% 8.18/2.72  |
% 8.18/2.72  | Instantiating formula (43) with all_0_13_13, all_19_3_22, all_0_14_14, all_0_11_11 and discharging atoms set_intersection2(all_0_11_11, all_0_14_14) = all_19_3_22, in(all_0_13_13, all_0_11_11), in(all_0_13_13, all_0_14_14), yields:
% 8.18/2.72  | (98) in(all_0_13_13, all_19_3_22)
% 8.18/2.72  |
% 8.18/2.72  | Instantiating formula (48) with all_0_8_8, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields:
% 8.18/2.72  | (99)  ? [v0] : (relation_dom(all_0_9_9) = v0 &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_9_9, v2) = v1) |  ~ in(v2, v0) | in(v1, all_0_8_8)) &  ! [v1] : ( ~ in(v1, all_0_8_8) |  ? [v2] : (apply(all_0_9_9, v2) = v1 & in(v2, v0))) &  ? [v1] : (v1 = all_0_8_8 |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ in(v2, v1) |  ! [v5] : ( ~ (apply(all_0_9_9, v5) = v2) |  ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_9_9, v3) = v2 & in(v3, v0))))))
% 8.18/2.72  |
% 8.18/2.72  | Instantiating (99) with all_36_0_26 yields:
% 8.18/2.72  | (100) relation_dom(all_0_9_9) = all_36_0_26 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) |  ~ in(v1, all_36_0_26) | in(v0, all_0_8_8)) &  ! [v0] : ( ~ in(v0, all_0_8_8) |  ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_36_0_26))) &  ? [v0] : (v0 = all_0_8_8 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) |  ~ in(v4, all_36_0_26))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_36_0_26)))))
% 8.18/2.72  |
% 8.18/2.72  | Applying alpha-rule on (100) yields:
% 8.18/2.72  | (101) relation_dom(all_0_9_9) = all_36_0_26
% 8.18/2.72  | (102)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) |  ~ in(v1, all_36_0_26) | in(v0, all_0_8_8))
% 8.18/2.72  | (103)  ! [v0] : ( ~ in(v0, all_0_8_8) |  ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_36_0_26)))
% 8.18/2.72  | (104)  ? [v0] : (v0 = all_0_8_8 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) |  ~ in(v4, all_36_0_26))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_36_0_26)))))
% 8.18/2.72  |
% 8.18/2.72  | Instantiating (97) with all_41_0_28, all_41_1_29, all_41_2_30, all_41_3_31 yields:
% 8.18/2.72  | (105) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_41_3_31 & ( ~ (all_41_3_31 = all_0_12_12) | all_19_3_22 = all_0_11_11) & ( ~ (all_19_3_22 = all_0_11_11) | all_41_3_31 = all_0_12_12 | ( ~ (all_41_0_28 = all_41_1_29) & apply(all_0_12_12, all_41_2_30) = all_41_0_28 & apply(all_0_12_12, all_41_2_30) = all_41_1_29 & in(all_41_2_30, all_0_11_11)))
% 8.18/2.72  |
% 8.18/2.72  | Applying alpha-rule on (105) yields:
% 8.18/2.72  | (106) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_41_3_31
% 8.18/2.72  | (107)  ~ (all_41_3_31 = all_0_12_12) | all_19_3_22 = all_0_11_11
% 8.18/2.72  | (108)  ~ (all_19_3_22 = all_0_11_11) | all_41_3_31 = all_0_12_12 | ( ~ (all_41_0_28 = all_41_1_29) & apply(all_0_12_12, all_41_2_30) = all_41_0_28 & apply(all_0_12_12, all_41_2_30) = all_41_1_29 & in(all_41_2_30, all_0_11_11))
% 8.18/2.72  |
% 8.18/2.72  | Instantiating (96) with all_43_0_32 yields:
% 8.18/2.72  | (109) relation_dom(all_0_12_12) = all_43_0_32 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) |  ~ in(v1, all_43_0_32) | in(v0, all_21_0_24)) &  ! [v0] : ( ~ in(v0, all_21_0_24) |  ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_43_0_32))) &  ? [v0] : (v0 = all_21_0_24 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) |  ~ in(v4, all_43_0_32))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_43_0_32)))))
% 8.18/2.73  |
% 8.18/2.73  | Applying alpha-rule on (109) yields:
% 8.18/2.73  | (110) relation_dom(all_0_12_12) = all_43_0_32
% 8.18/2.73  | (111)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) |  ~ in(v1, all_43_0_32) | in(v0, all_21_0_24))
% 8.18/2.73  | (112)  ! [v0] : ( ~ in(v0, all_21_0_24) |  ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_43_0_32)))
% 8.18/2.73  | (113)  ? [v0] : (v0 = all_21_0_24 |  ? [v1] :  ? [v2] :  ? [v3] : (( ~ in(v1, v0) |  ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) |  ~ in(v4, all_43_0_32))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_43_0_32)))))
% 8.45/2.73  |
% 8.45/2.73  | Instantiating formula (59) with all_0_12_12, all_0_14_14, all_41_3_31, all_0_9_9 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_41_3_31, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9, yields:
% 8.45/2.73  | (114) all_41_3_31 = all_0_9_9
% 8.45/2.73  |
% 8.45/2.73  | Instantiating formula (53) with all_0_12_12, all_43_0_32, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_43_0_32, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 8.45/2.73  | (115) all_43_0_32 = all_0_11_11
% 8.45/2.73  |
% 8.45/2.73  | From (114) and (106) follows:
% 8.45/2.73  | (26) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9
% 8.45/2.73  |
% 8.45/2.73  | From (115) and (110) follows:
% 8.45/2.73  | (39) relation_dom(all_0_12_12) = all_0_11_11
% 8.45/2.73  |
% 8.45/2.73  | Instantiating formula (69) with all_19_3_22, all_0_11_11, all_0_12_12, all_36_0_26, all_0_9_9, all_0_14_14 and discharging atoms relation_dom(all_0_9_9) = all_36_0_26, relation_dom(all_0_12_12) = all_0_11_11, set_intersection2(all_0_11_11, all_0_14_14) = all_19_3_22, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 8.45/2.73  | (118)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom_restriction(all_0_12_12, all_0_14_14) = v0 & ( ~ (v0 = all_0_9_9) | (all_36_0_26 = all_19_3_22 &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_9_9, v4) = v5) |  ~ in(v4, all_19_3_22) | apply(all_0_12_12, v4) = v5) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_19_3_22) | apply(all_0_9_9, v4) = v5))) & ( ~ (all_36_0_26 = all_19_3_22) | v0 = all_0_9_9 | ( ~ (v3 = v2) & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, v1) = v3 & in(v1, all_19_3_22))))
% 8.45/2.73  |
% 8.45/2.73  | Instantiating (118) with all_66_0_38, all_66_1_39, all_66_2_40, all_66_3_41 yields:
% 8.45/2.73  | (119) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_66_3_41 & ( ~ (all_66_3_41 = all_0_9_9) | (all_36_0_26 = all_19_3_22 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_12_12, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_9_9, v0) = v1))) & ( ~ (all_36_0_26 = all_19_3_22) | all_66_3_41 = all_0_9_9 | ( ~ (all_66_0_38 = all_66_1_39) & apply(all_0_9_9, all_66_2_40) = all_66_1_39 & apply(all_0_12_12, all_66_2_40) = all_66_0_38 & in(all_66_2_40, all_19_3_22)))
% 8.45/2.73  |
% 8.45/2.73  | Applying alpha-rule on (119) yields:
% 8.45/2.73  | (120) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_66_3_41
% 8.45/2.73  | (121)  ~ (all_66_3_41 = all_0_9_9) | (all_36_0_26 = all_19_3_22 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_12_12, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_9_9, v0) = v1))
% 8.45/2.73  | (122)  ~ (all_36_0_26 = all_19_3_22) | all_66_3_41 = all_0_9_9 | ( ~ (all_66_0_38 = all_66_1_39) & apply(all_0_9_9, all_66_2_40) = all_66_1_39 & apply(all_0_12_12, all_66_2_40) = all_66_0_38 & in(all_66_2_40, all_19_3_22))
% 8.45/2.73  |
% 8.45/2.73  | Instantiating formula (59) with all_0_12_12, all_0_14_14, all_66_3_41, all_0_9_9 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_66_3_41, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_9_9, yields:
% 8.45/2.73  | (123) all_66_3_41 = all_0_9_9
% 8.45/2.73  |
% 8.45/2.73  +-Applying beta-rule and splitting (121), into two cases.
% 8.45/2.73  |-Branch one:
% 8.45/2.73  | (124)  ~ (all_66_3_41 = all_0_9_9)
% 8.45/2.73  |
% 8.45/2.74  	| Equations (123) can reduce 124 to:
% 8.45/2.74  	| (125) $false
% 8.45/2.74  	|
% 8.45/2.74  	|-The branch is then unsatisfiable
% 8.45/2.74  |-Branch two:
% 8.45/2.74  | (123) all_66_3_41 = all_0_9_9
% 8.45/2.74  | (127) all_36_0_26 = all_19_3_22 &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_12_12, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_9_9, v0) = v1)
% 8.45/2.74  |
% 8.45/2.74  	| Applying alpha-rule on (127) yields:
% 8.45/2.74  	| (128) all_36_0_26 = all_19_3_22
% 8.45/2.74  	| (129)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_9_9, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_12_12, v0) = v1)
% 8.45/2.74  	| (130)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_19_3_22) | apply(all_0_9_9, v0) = v1)
% 8.45/2.74  	|
% 8.45/2.74  	| Instantiating formula (130) with all_0_10_10, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_10_10, in(all_0_13_13, all_19_3_22), yields:
% 8.45/2.74  	| (131) apply(all_0_9_9, all_0_13_13) = all_0_10_10
% 8.45/2.74  	|
% 8.45/2.74  	| Instantiating formula (102) with all_0_13_13, all_0_10_10 and discharging atoms apply(all_0_9_9, all_0_13_13) = all_0_10_10,  ~ in(all_0_10_10, all_0_8_8), yields:
% 8.45/2.74  	| (132)  ~ in(all_0_13_13, all_36_0_26)
% 8.45/2.74  	|
% 8.45/2.74  	| From (128) and (132) follows:
% 8.45/2.74  	| (133)  ~ in(all_0_13_13, all_19_3_22)
% 8.45/2.74  	|
% 8.45/2.74  	| Using (98) and (133) yields:
% 8.45/2.74  	| (134) $false
% 8.45/2.74  	|
% 8.45/2.74  	|-The branch is then unsatisfiable
% 8.45/2.74  % SZS output end Proof for theBenchmark
% 8.45/2.74  
% 8.45/2.74  2039ms
%------------------------------------------------------------------------------