%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU044+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n004.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 08:46:21 EDT 2022

% Result   : Theorem 3.55s 1.48s
% Output   : Proof 5.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU044+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 20:27:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.53/0.58          ____       _                          
% 0.53/0.58    ___  / __ \_____(_)___  ________  __________
% 0.53/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.58  
% 0.53/0.58  A Theorem Prover for First-Order Logic
% 0.59/0.58  (ePrincess v.1.0)
% 0.59/0.58  
% 0.59/0.58  (c) Philipp Rümmer, 2009-2015
% 0.59/0.58  (c) Peter Backeman, 2014-2015
% 0.59/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58  Bug reports to peter@backeman.se
% 0.59/0.58  
% 0.59/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58  
% 0.59/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.59/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.92  Prover 0: Preprocessing ...
% 2.10/1.15  Prover 0: Warning: ignoring some quantifiers
% 2.33/1.18  Prover 0: Constructing countermodel ...
% 3.55/1.48  Prover 0: proved (854ms)
% 3.55/1.48  
% 3.55/1.48  No countermodel exists, formula is valid
% 3.55/1.48  % SZS status Theorem for theBenchmark
% 3.55/1.48  
% 3.55/1.48  Generating proof ... Warning: ignoring some quantifiers
% 5.19/1.89  found it (size 45)
% 5.19/1.89  
% 5.19/1.89  % SZS output start Proof for theBenchmark
% 5.19/1.89  Assumed formulas after preprocessing and simplification: 
% 5.19/1.89  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v2, v1) = v6 & relation_rng_restriction(v0, v2) = v3 & relation_dom(v3) = v4 & relation_dom(v2) = v5 & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v2) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v2) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) &  ~ empty(v10) &  ~ empty(v7) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (relation_rng_restriction(v15, v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : (relation_dom(v18) = v20 & ( ~ (v19 = v16) | ( ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v25, v15) |  ~ in(v24, v20) | in(v24, v17)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | apply(v16, v24) = v25) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v25, v15)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v24, v20)) &  ! [v24] :  ! [v25] : ( ~ (apply(v16, v24) = v25) |  ~ in(v24, v17) | apply(v18, v24) = v25))) & (v19 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) |  ~ in(v21, v20) |  ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v20))))))) &  ? [v15] :  ! [v16] :  ! [v17] :  ! [v18] :  ! [v19] : ( ~ (relation_dom(v18) = v19) |  ~ (relation_dom(v16) = v17) |  ~ function(v18) |  ~ function(v16) |  ~ relation(v18) |  ~ relation(v16) |  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] : (relation_rng_restriction(v15, v18) = v20 & ( ~ (v20 = v16) | ( ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v25, v15) |  ~ in(v24, v19) | in(v24, v17)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | apply(v16, v24) = v25) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v25, v15)) &  ! [v24] :  ! [v25] : ( ~ (apply(v18, v24) = v25) |  ~ in(v24, v17) | in(v24, v19)) &  ! [v24] :  ! [v25] : ( ~ (apply(v16, v24) = v25) |  ~ in(v24, v17) | apply(v18, v24) = v25))) & (v20 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) |  ~ in(v21, v19) |  ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v19))))))) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (apply(v18, v17) = v16) |  ~ (apply(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : (v16 = v15 |  ~ (relation_rng_restriction(v18, v17) = v16) |  ~ (relation_rng_restriction(v18, v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ in(v15, v16) |  ~ element(v16, v18) |  ~ empty(v17)) &  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (powerset(v17) = v18) |  ~ in(v15, v16) |  ~ element(v16, v18) | element(v15, v17)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (relation_dom(v17) = v16) |  ~ (relation_dom(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : (v16 = v15 |  ~ (powerset(v17) = v16) |  ~ (powerset(v17) = v15)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ function(v16) |  ~ relation(v16) | function(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ function(v16) |  ~ relation(v16) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) |  ~ relation(v16) | relation(v17)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) | subset(v15, v16)) &  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ subset(v15, v16) | element(v15, v17)) &  ! [v15] :  ! [v16] : (v16 = v15 |  ~ empty(v16) |  ~ empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ relation(v15) |  ~ empty(v16) | empty(v15)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | relation(v16)) &  ! [v15] :  ! [v16] : ( ~ (relation_dom(v15) = v16) |  ~ empty(v15) | empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ empty(v16)) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) |  ? [v17] : (element(v17, v16) &  ~ empty(v17))) &  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ? [v17] : (element(v17, v16) & empty(v17))) &  ! [v15] :  ! [v16] : ( ~ 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] : ( ~ function(v15) |  ~ relation(v15) |  ~ empty(v15) | one_to_one(v15)) &  ! [v15] : ( ~ empty(v15) | function(v15)) &  ! [v15] : ( ~ empty(v15) | relation(v15)) &  ? [v15] :  ? [v16] : element(v16, v15) &  ? [v15] : subset(v15, v15) & ((in(v6, v0) & in(v1, v5) &  ~ in(v1, v4)) | (in(v1, v4) & ( ~ in(v6, v0) |  ~ in(v1, v5)))))
% 5.55/1.93  | 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:
% 5.55/1.93  | (1) apply(all_0_12_12, all_0_13_13) = all_0_8_8 & relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11 & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom(all_0_12_12) = all_0_9_9 & one_to_one(all_0_2_2) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_12_12) & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_12_12) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_3_3) & empty(all_0_6_6) & empty(empty_set) &  ~ empty(all_0_4_4) &  ~ empty(all_0_7_7) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v5) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v5)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v5) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5))))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v4) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v4)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v4) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4))))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2)) &  ! [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] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1)) &  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2))) &  ! [v0] :  ! [v1] : ( ~ 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] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ! [v0] : ( ~ empty(v0) | relation(v0)) &  ? [v0] :  ? [v1] : element(v1, v0) &  ? [v0] : subset(v0, v0) & ((in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) &  ~ in(all_0_13_13, all_0_10_10)) | (in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) |  ~ in(all_0_13_13, all_0_9_9))))
% 5.55/1.94  |
% 5.55/1.94  | Applying alpha-rule on (1) yields:
% 5.55/1.94  | (2) empty(all_0_3_3)
% 5.55/1.94  | (3)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 5.55/1.94  | (4) relation_empty_yielding(all_0_5_5)
% 5.55/1.94  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_rng_restriction(v3, v2) = v1) |  ~ (relation_rng_restriction(v3, v2) = v0))
% 5.55/1.94  | (6) relation_dom(all_0_11_11) = all_0_10_10
% 5.55/1.94  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 5.55/1.94  | (8)  ~ empty(all_0_4_4)
% 5.55/1.94  | (9) empty(all_0_1_1)
% 5.55/1.94  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.55/1.94  | (11) function(all_0_2_2)
% 5.55/1.94  | (12) empty(empty_set)
% 5.55/1.94  | (13)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1))
% 5.55/1.94  | (14) relation(all_0_12_12)
% 5.55/1.94  | (15) relation(all_0_3_3)
% 5.55/1.94  | (16)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.55/1.94  | (17) one_to_one(all_0_2_2)
% 5.55/1.94  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) | element(v0, v2))
% 5.55/1.94  | (19)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 5.55/1.94  | (20) relation(all_0_2_2)
% 5.55/1.94  | (21) empty(all_0_6_6)
% 5.55/1.95  | (22)  ~ empty(all_0_7_7)
% 5.55/1.95  | (23) relation(empty_set)
% 5.55/1.95  | (24)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) |  ~ empty(v1))
% 5.55/1.95  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ in(v0, v1) |  ~ element(v1, v3) |  ~ empty(v2))
% 5.55/1.95  | (26) (in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) &  ~ in(all_0_13_13, all_0_10_10)) | (in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) |  ~ in(all_0_13_13, all_0_9_9)))
% 5.55/1.95  | (27)  ! [v0] : ( ~ function(v0) |  ~ relation(v0) |  ~ empty(v0) | one_to_one(v0))
% 5.55/1.95  | (28) relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11
% 5.55/1.95  | (29) relation(all_0_5_5)
% 5.55/1.95  | (30) relation_empty_yielding(empty_set)
% 5.55/1.95  | (31)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 5.55/1.95  | (32) function(all_0_0_0)
% 5.55/1.95  | (33)  ? [v0] : subset(v0, v0)
% 5.55/1.95  | (34) function(all_0_1_1)
% 5.55/1.95  | (35) relation_dom(all_0_12_12) = all_0_9_9
% 5.55/1.95  | (36) apply(all_0_12_12, all_0_13_13) = all_0_8_8
% 5.55/1.95  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | relation(v2))
% 5.55/1.95  | (38)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.55/1.95  | (39) relation(all_0_1_1)
% 5.55/1.95  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v5) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v5)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v5) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5)))))))
% 5.55/1.95  | (41)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 5.55/1.95  | (42) relation(all_0_0_0)
% 5.55/1.95  | (43)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.55/1.95  | (44) function(all_0_12_12)
% 5.55/1.95  | (45)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 5.55/1.95  | (46)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 5.55/1.95  | (47)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.55/1.95  | (48)  ? [v0] :  ? [v1] : element(v1, v0)
% 5.55/1.95  | (49)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ function(v3) |  ~ function(v1) |  ~ relation(v3) |  ~ relation(v1) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v10, v0) |  ~ in(v9, v4) | in(v9, v2)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | apply(v1, v9) = v10) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v10, v0)) &  ! [v9] :  ! [v10] : ( ~ (apply(v3, v9) = v10) |  ~ in(v9, v2) | in(v9, v4)) &  ! [v9] :  ! [v10] : ( ~ (apply(v1, v9) = v10) |  ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) |  ~ in(v6, v4) |  ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4)))))))
% 5.55/1.95  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ relation(v1) | relation(v2))
% 5.55/1.96  | (51)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 5.55/1.96  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 5.55/1.96  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 5.55/1.96  | (54)  ! [v0] : ( ~ empty(v0) | function(v0))
% 5.55/1.96  | (55)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 5.55/1.96  | (56) relation(all_0_4_4)
% 5.55/1.96  | (57)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) |  ~ function(v1) |  ~ relation(v1) | function(v2))
% 5.55/1.96  |
% 5.55/1.96  | Instantiating (49) with all_7_0_18 yields:
% 5.55/1.96  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_dom(v2) = v3) |  ~ (relation_dom(v0) = v1) |  ~ function(v2) |  ~ function(v0) |  ~ relation(v2) |  ~ relation(v0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (relation_rng_restriction(all_7_0_18, v2) = v4 & ( ~ (v4 = v0) | ( ! [v8] :  ! [v9] : ( ~ (apply(v2, v8) = v9) |  ~ in(v9, all_7_0_18) |  ~ in(v8, v3) | in(v8, v1)) &  ! [v8] :  ! [v9] : ( ~ (apply(v2, v8) = v9) |  ~ in(v8, v1) | apply(v0, v8) = v9) &  ! [v8] :  ! [v9] : ( ~ (apply(v2, v8) = v9) |  ~ in(v8, v1) | in(v9, all_7_0_18)) &  ! [v8] :  ! [v9] : ( ~ (apply(v2, v8) = v9) |  ~ in(v8, v1) | in(v8, v3)) &  ! [v8] :  ! [v9] : ( ~ (apply(v0, v8) = v9) |  ~ in(v8, v1) | apply(v2, v8) = v9))) & (v4 = v0 | ( ~ (v7 = v6) & apply(v2, v5) = v7 & apply(v0, v5) = v6 & in(v5, v1)) | (apply(v2, v5) = v6 & ( ~ in(v6, all_7_0_18) |  ~ in(v5, v3) |  ~ in(v5, v1)) & (in(v5, v1) | (in(v6, all_7_0_18) & in(v5, v3)))))))
% 5.55/1.96  |
% 5.55/1.96  | Instantiating formula (40) with all_0_11_11, all_0_12_12, all_0_9_9, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields:
% 5.55/1.96  | (59)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_0_11_11 = all_0_12_12) | ( ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v5, all_0_14_14) |  ~ in(v4, v0) | in(v4, all_0_9_9)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_9_9) | in(v5, all_0_14_14)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_9_9) | in(v4, v0)))) & (all_0_11_11 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_0_14_14) |  ~ in(v1, v0) |  ~ in(v1, all_0_9_9)) & (in(v1, all_0_9_9) | (in(v2, all_0_14_14) & in(v1, v0))))))
% 5.55/1.96  |
% 5.55/1.96  | Instantiating formula (57) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, function(all_0_12_12), relation(all_0_12_12), yields:
% 5.55/1.96  | (60) function(all_0_11_11)
% 5.55/1.96  |
% 5.55/1.96  | Instantiating formula (50) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields:
% 5.55/1.96  | (61) relation(all_0_11_11)
% 5.55/1.96  |
% 5.55/1.96  | Instantiating formula (58) with all_0_9_9, all_0_12_12, all_0_9_9, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields:
% 5.55/1.96  | (62)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_rng_restriction(all_7_0_18, all_0_12_12) = v0 & ( ~ (v0 = all_0_12_12) |  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_9_9) | in(v5, all_7_0_18))) & (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_9_9)) | (apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9) &  ~ in(v2, all_7_0_18))))
% 5.55/1.96  |
% 5.55/1.96  | Instantiating (62) with all_19_0_19, all_19_1_20, all_19_2_21, all_19_3_22 yields:
% 5.55/1.96  | (63) relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22 & ( ~ (all_19_3_22 = all_0_12_12) |  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_7_0_18))) & (all_19_3_22 = 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_9_9)) | (apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9) &  ~ in(all_19_1_20, all_7_0_18)))
% 5.55/1.96  |
% 5.55/1.96  | Applying alpha-rule on (63) yields:
% 5.55/1.96  | (64) relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22
% 5.55/1.96  | (65)  ~ (all_19_3_22 = all_0_12_12) |  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_7_0_18))
% 5.55/1.97  | (66) all_19_3_22 = 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_9_9)) | (apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9) &  ~ in(all_19_1_20, all_7_0_18))
% 5.55/1.97  |
% 5.55/1.97  | Instantiating (59) with all_21_0_23, all_21_1_24, all_21_2_25, all_21_3_26 yields:
% 5.55/1.97  | (67) relation_dom(all_0_12_12) = all_21_3_26 & ( ~ (all_0_11_11 = all_0_12_12) | ( ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_0_14_14) |  ~ in(v0, all_21_3_26) | in(v0, all_0_9_9)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_0_14_14)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v0, all_21_3_26)))) & (all_0_11_11 = all_0_12_12 | ( ~ (all_21_0_23 = all_21_1_24) & apply(all_0_12_12, all_21_2_25) = all_21_0_23 & apply(all_0_12_12, all_21_2_25) = all_21_1_24 & in(all_21_2_25, all_0_9_9)) | (apply(all_0_12_12, all_21_2_25) = all_21_1_24 & ( ~ in(all_21_1_24, all_0_14_14) |  ~ in(all_21_2_25, all_21_3_26) |  ~ in(all_21_2_25, all_0_9_9)) & (in(all_21_2_25, all_0_9_9) | (in(all_21_1_24, all_0_14_14) & in(all_21_2_25, all_21_3_26)))))
% 5.55/1.97  |
% 5.55/1.97  | Applying alpha-rule on (67) yields:
% 5.55/1.97  | (68) relation_dom(all_0_12_12) = all_21_3_26
% 5.55/1.97  | (69)  ~ (all_0_11_11 = all_0_12_12) | ( ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_0_14_14) |  ~ in(v0, all_21_3_26) | in(v0, all_0_9_9)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_0_14_14)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v0, all_21_3_26)))
% 5.55/1.97  | (70) all_0_11_11 = all_0_12_12 | ( ~ (all_21_0_23 = all_21_1_24) & apply(all_0_12_12, all_21_2_25) = all_21_0_23 & apply(all_0_12_12, all_21_2_25) = all_21_1_24 & in(all_21_2_25, all_0_9_9)) | (apply(all_0_12_12, all_21_2_25) = all_21_1_24 & ( ~ in(all_21_1_24, all_0_14_14) |  ~ in(all_21_2_25, all_21_3_26) |  ~ in(all_21_2_25, all_0_9_9)) & (in(all_21_2_25, all_0_9_9) | (in(all_21_1_24, all_0_14_14) & in(all_21_2_25, all_21_3_26))))
% 5.55/1.97  |
% 5.55/1.97  | Instantiating formula (55) with all_0_12_12, all_21_3_26, all_0_9_9 and discharging atoms relation_dom(all_0_12_12) = all_21_3_26, relation_dom(all_0_12_12) = all_0_9_9, yields:
% 5.55/1.97  | (71) all_21_3_26 = all_0_9_9
% 5.55/1.97  |
% 5.55/1.97  | From (71) and (68) follows:
% 5.55/1.97  | (35) relation_dom(all_0_12_12) = all_0_9_9
% 5.55/1.97  |
% 5.55/1.97  | Instantiating formula (40) with all_19_3_22, all_0_12_12, all_0_9_9, all_0_12_12, all_7_0_18 and discharging atoms relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22, relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields:
% 5.55/1.97  | (73)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_19_3_22 = all_0_12_12) | ( ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v5, all_7_0_18) |  ~ in(v4, v0) | in(v4, all_0_9_9)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_9_9) | in(v5, all_7_0_18)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_9_9) | in(v4, v0)))) & (all_19_3_22 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_7_0_18) |  ~ in(v1, v0) |  ~ in(v1, all_0_9_9)) & (in(v1, all_0_9_9) | (in(v2, all_7_0_18) & in(v1, v0))))))
% 5.55/1.97  |
% 5.55/1.97  | Instantiating formula (40) 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_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation_dom(all_0_11_11) = all_0_10_10, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields:
% 5.55/1.97  | (74)  ? [v0] : (relation_dom(all_0_12_12) = v0 &  ! [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(v2, all_0_14_14) |  ~ in(v1, v0) | in(v1, all_0_10_10)) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | apply(all_0_11_11, v1) = v2) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | in(v2, all_0_14_14)) &  ! [v1] :  ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) |  ~ in(v1, all_0_10_10) | in(v1, v0)))
% 5.55/1.97  |
% 5.55/1.97  | Instantiating formula (40) with all_19_3_22, all_0_12_12, all_0_10_10, all_0_11_11, all_7_0_18 and discharging atoms relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22, relation_dom(all_0_11_11) = all_0_10_10, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields:
% 5.55/1.97  | (75)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_19_3_22 = all_0_11_11) | ( ! [v4] :  ! [v5] : ( ~ (apply(all_0_11_11, v4) = v5) |  ~ in(v4, all_0_10_10) | apply(all_0_12_12, v4) = v5) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v5, all_7_0_18) |  ~ in(v4, v0) | in(v4, all_0_10_10)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_10_10) | apply(all_0_11_11, v4) = v5) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_10_10) | in(v5, all_7_0_18)) &  ! [v4] :  ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) |  ~ in(v4, all_0_10_10) | in(v4, v0)))) & (all_19_3_22 = all_0_11_11 | ( ~ (v3 = v2) & apply(all_0_11_11, v1) = v2 & apply(all_0_12_12, v1) = v3 & in(v1, all_0_10_10)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_7_0_18) |  ~ in(v1, v0) |  ~ in(v1, all_0_10_10)) & (in(v1, all_0_10_10) | (in(v2, all_7_0_18) & in(v1, v0))))))
% 5.55/1.98  |
% 5.93/1.98  | Instantiating (73) with all_33_0_27, all_33_1_28, all_33_2_29, all_33_3_30 yields:
% 5.93/1.98  | (76) relation_dom(all_0_12_12) = all_33_3_30 & ( ~ (all_19_3_22 = all_0_12_12) | ( ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_7_0_18) |  ~ in(v0, all_33_3_30) | in(v0, all_0_9_9)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_7_0_18)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v0, all_33_3_30)))) & (all_19_3_22 = all_0_12_12 | ( ~ (all_33_0_27 = all_33_1_28) & apply(all_0_12_12, all_33_2_29) = all_33_0_27 & apply(all_0_12_12, all_33_2_29) = all_33_1_28 & in(all_33_2_29, all_0_9_9)) | (apply(all_0_12_12, all_33_2_29) = all_33_1_28 & ( ~ in(all_33_1_28, all_7_0_18) |  ~ in(all_33_2_29, all_33_3_30) |  ~ in(all_33_2_29, all_0_9_9)) & (in(all_33_2_29, all_0_9_9) | (in(all_33_1_28, all_7_0_18) & in(all_33_2_29, all_33_3_30)))))
% 5.93/1.98  |
% 5.93/1.98  | Applying alpha-rule on (76) yields:
% 5.93/1.98  | (77) relation_dom(all_0_12_12) = all_33_3_30
% 5.93/1.98  | (78)  ~ (all_19_3_22 = all_0_12_12) | ( ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_7_0_18) |  ~ in(v0, all_33_3_30) | in(v0, all_0_9_9)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v1, all_7_0_18)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_9_9) | in(v0, all_33_3_30)))
% 5.93/1.98  | (79) all_19_3_22 = all_0_12_12 | ( ~ (all_33_0_27 = all_33_1_28) & apply(all_0_12_12, all_33_2_29) = all_33_0_27 & apply(all_0_12_12, all_33_2_29) = all_33_1_28 & in(all_33_2_29, all_0_9_9)) | (apply(all_0_12_12, all_33_2_29) = all_33_1_28 & ( ~ in(all_33_1_28, all_7_0_18) |  ~ in(all_33_2_29, all_33_3_30) |  ~ in(all_33_2_29, all_0_9_9)) & (in(all_33_2_29, all_0_9_9) | (in(all_33_1_28, all_7_0_18) & in(all_33_2_29, all_33_3_30))))
% 5.93/1.98  |
% 5.93/1.98  | Instantiating (75) with all_39_0_39, all_39_1_40, all_39_2_41, all_39_3_42 yields:
% 5.93/1.98  | (80) relation_dom(all_0_12_12) = all_39_3_42 & ( ~ (all_19_3_22 = all_0_11_11) | ( ! [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(v1, all_7_0_18) |  ~ in(v0, all_39_3_42) | in(v0, all_0_10_10)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_7_0_18)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_39_3_42)))) & (all_19_3_22 = all_0_11_11 | ( ~ (all_39_0_39 = all_39_1_40) & apply(all_0_11_11, all_39_2_41) = all_39_1_40 & apply(all_0_12_12, all_39_2_41) = all_39_0_39 & in(all_39_2_41, all_0_10_10)) | (apply(all_0_12_12, all_39_2_41) = all_39_1_40 & ( ~ in(all_39_1_40, all_7_0_18) |  ~ in(all_39_2_41, all_39_3_42) |  ~ in(all_39_2_41, all_0_10_10)) & (in(all_39_2_41, all_0_10_10) | (in(all_39_1_40, all_7_0_18) & in(all_39_2_41, all_39_3_42)))))
% 5.93/1.98  |
% 5.93/1.98  | Applying alpha-rule on (80) yields:
% 5.93/1.98  | (81) relation_dom(all_0_12_12) = all_39_3_42
% 5.93/1.98  | (82)  ~ (all_19_3_22 = all_0_11_11) | ( ! [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(v1, all_7_0_18) |  ~ in(v0, all_39_3_42) | in(v0, all_0_10_10)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_7_0_18)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_39_3_42)))
% 5.93/1.99  | (83) all_19_3_22 = all_0_11_11 | ( ~ (all_39_0_39 = all_39_1_40) & apply(all_0_11_11, all_39_2_41) = all_39_1_40 & apply(all_0_12_12, all_39_2_41) = all_39_0_39 & in(all_39_2_41, all_0_10_10)) | (apply(all_0_12_12, all_39_2_41) = all_39_1_40 & ( ~ in(all_39_1_40, all_7_0_18) |  ~ in(all_39_2_41, all_39_3_42) |  ~ in(all_39_2_41, all_0_10_10)) & (in(all_39_2_41, all_0_10_10) | (in(all_39_1_40, all_7_0_18) & in(all_39_2_41, all_39_3_42))))
% 5.93/1.99  |
% 5.93/1.99  | Instantiating (74) with all_43_0_47 yields:
% 5.93/1.99  | (84) relation_dom(all_0_12_12) = all_43_0_47 &  ! [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(v1, all_0_14_14) |  ~ in(v0, all_43_0_47) | in(v0, all_0_10_10)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_0_14_14)) &  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_43_0_47))
% 5.93/1.99  |
% 5.93/1.99  | Applying alpha-rule on (84) yields:
% 5.93/1.99  | (85)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v0, all_43_0_47))
% 5.93/1.99  | (86)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v1, all_0_14_14) |  ~ in(v0, all_43_0_47) | in(v0, all_0_10_10))
% 5.93/1.99  | (87)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | in(v1, all_0_14_14))
% 5.93/1.99  | (88)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 5.93/1.99  | (89) relation_dom(all_0_12_12) = all_43_0_47
% 5.93/1.99  | (90)  ! [v0] :  ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) |  ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1)
% 5.93/1.99  |
% 5.93/1.99  | Instantiating formula (55) with all_0_12_12, all_43_0_47, all_0_9_9 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_0_9_9, yields:
% 5.93/1.99  | (91) all_43_0_47 = all_0_9_9
% 5.93/1.99  |
% 5.93/1.99  | Instantiating formula (55) with all_0_12_12, all_39_3_42, all_43_0_47 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_39_3_42, yields:
% 5.93/1.99  | (92) all_43_0_47 = all_39_3_42
% 5.93/1.99  |
% 5.93/1.99  | Instantiating formula (55) with all_0_12_12, all_33_3_30, all_43_0_47 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_33_3_30, yields:
% 5.93/1.99  | (93) all_43_0_47 = all_33_3_30
% 5.93/1.99  |
% 5.93/1.99  | Combining equations (93,92) yields a new equation:
% 5.93/1.99  | (94) all_39_3_42 = all_33_3_30
% 5.93/1.99  |
% 5.93/1.99  | Combining equations (91,92) yields a new equation:
% 5.93/1.99  | (95) all_39_3_42 = all_0_9_9
% 5.93/1.99  |
% 5.93/1.99  | Combining equations (95,94) yields a new equation:
% 5.93/1.99  | (96) all_33_3_30 = all_0_9_9
% 5.93/1.99  |
% 5.93/1.99  | Combining equations (96,94) yields a new equation:
% 5.93/1.99  | (95) all_39_3_42 = all_0_9_9
% 5.93/1.99  |
% 5.93/1.99  | Combining equations (95,92) yields a new equation:
% 5.93/1.99  | (91) all_43_0_47 = all_0_9_9
% 5.93/1.99  |
% 5.93/1.99  +-Applying beta-rule and splitting (26), into two cases.
% 5.93/1.99  |-Branch one:
% 5.93/1.99  | (99) in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) &  ~ in(all_0_13_13, all_0_10_10)
% 5.93/1.99  |
% 5.93/1.99  	| Applying alpha-rule on (99) yields:
% 5.93/1.99  	| (100) in(all_0_8_8, all_0_14_14)
% 5.93/1.99  	| (101) in(all_0_13_13, all_0_9_9)
% 5.93/1.99  	| (102)  ~ in(all_0_13_13, all_0_10_10)
% 5.93/1.99  	|
% 5.93/1.99  	| Instantiating formula (86) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_8_8, all_0_14_14),  ~ in(all_0_13_13, all_0_10_10), yields:
% 5.93/1.99  	| (103)  ~ in(all_0_13_13, all_43_0_47)
% 5.93/1.99  	|
% 5.93/1.99  	| From (91) and (103) follows:
% 5.93/1.99  	| (104)  ~ in(all_0_13_13, all_0_9_9)
% 5.93/1.99  	|
% 5.93/1.99  	| Using (101) and (104) yields:
% 5.93/1.99  	| (105) $false
% 5.93/1.99  	|
% 5.93/1.99  	|-The branch is then unsatisfiable
% 5.93/1.99  |-Branch two:
% 5.93/1.99  | (106) in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) |  ~ in(all_0_13_13, all_0_9_9))
% 5.93/1.99  |
% 5.93/1.99  	| Applying alpha-rule on (106) yields:
% 5.93/1.99  	| (107) in(all_0_13_13, all_0_10_10)
% 5.93/1.99  	| (108)  ~ in(all_0_8_8, all_0_14_14) |  ~ in(all_0_13_13, all_0_9_9)
% 5.93/1.99  	|
% 5.93/1.99  	| Instantiating formula (87) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_13_13, all_0_10_10), yields:
% 5.93/1.99  	| (100) in(all_0_8_8, all_0_14_14)
% 5.93/1.99  	|
% 5.93/1.99  	| Instantiating formula (85) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_13_13, all_0_10_10), yields:
% 5.93/1.99  	| (110) in(all_0_13_13, all_43_0_47)
% 5.93/1.99  	|
% 5.93/1.99  	| From (91) and (110) follows:
% 5.93/1.99  	| (101) in(all_0_13_13, all_0_9_9)
% 5.93/1.99  	|
% 5.93/1.99  	+-Applying beta-rule and splitting (108), into two cases.
% 5.93/1.99  	|-Branch one:
% 5.93/1.99  	| (112)  ~ in(all_0_8_8, all_0_14_14)
% 5.93/1.99  	|
% 5.93/1.99  		| Using (100) and (112) yields:
% 5.93/1.99  		| (105) $false
% 5.93/1.99  		|
% 5.93/1.99  		|-The branch is then unsatisfiable
% 5.93/1.99  	|-Branch two:
% 5.93/1.99  	| (100) in(all_0_8_8, all_0_14_14)
% 5.93/1.99  	| (104)  ~ in(all_0_13_13, all_0_9_9)
% 5.93/1.99  	|
% 5.93/1.99  		| Using (101) and (104) yields:
% 5.93/1.99  		| (105) $false
% 5.93/1.99  		|
% 5.93/2.00  		|-The branch is then unsatisfiable
% 5.93/2.00  % SZS output end Proof for theBenchmark
% 5.93/2.00  
% 5.93/2.00  1405ms
%------------------------------------------------------------------------------