%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU215+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 08:47:43 EDT 2022

% Result   : Theorem 4.20s 1.88s
% Output   : Proof 9.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU215+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n020.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 : Mon Jun 20 07:45:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/1.04  Prover 0: Preprocessing ...
% 2.58/1.39  Prover 0: Warning: ignoring some quantifiers
% 2.58/1.42  Prover 0: Constructing countermodel ...
% 4.20/1.88  Prover 0: proved (1234ms)
% 4.20/1.88  
% 4.20/1.88  No countermodel exists, formula is valid
% 4.20/1.88  % SZS status Theorem for theBenchmark
% 4.20/1.88  
% 4.20/1.88  Generating proof ... Warning: ignoring some quantifiers
% 8.24/2.79  found it (size 211)
% 8.24/2.79  
% 8.24/2.79  % SZS output start Proof for theBenchmark
% 8.24/2.79  Assumed formulas after preprocessing and simplification: 
% 8.24/2.79  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : ( ~ (v7 = v6) & relation_composition(v1, v4) = v5 & relation_dom(v1) = v2 & apply(v5, v0) = v6 & apply(v4, v3) = v7 & apply(v1, v0) = v3 & relation_empty_yielding(v8) & relation_empty_yielding(empty_set) & relation(v13) & relation(v12) & relation(v10) & relation(v8) & relation(v4) & relation(v1) & relation(empty_set) & function(v13) & function(v4) & function(v1) & empty(v12) & empty(v11) & empty(empty_set) & in(v0, v2) &  ~ empty(v10) &  ~ empty(v9) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (relation_composition(v16, v15) = v17) |  ~ (apply(v17, v14) = v18) |  ~ relation(v16) |  ~ relation(v15) |  ~ function(v16) |  ~ function(v15) |  ? [v19] :  ? [v20] :  ? [v21] : (relation_dom(v17) = v19 & apply(v16, v14) = v20 & apply(v15, v20) = v21 & (v21 = v18 |  ~ in(v14, v19)))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (singleton(v14) = v17) |  ~ (unordered_pair(v16, v17) = v18) |  ~ (unordered_pair(v14, v15) = v16) | ordered_pair(v14, v15) = v18) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (relation_dom(v15) = v16) |  ~ (apply(v17, v14) = v18) |  ~ relation(v17) |  ~ relation(v15) |  ~ function(v17) |  ~ function(v15) |  ? [v19] :  ? [v20] :  ? [v21] : (relation_composition(v17, v15) = v19 & relation_dom(v19) = v20 & relation_dom(v17) = v21 & ( ~ in(v18, v16) |  ~ in(v14, v21) | in(v14, v20)) & ( ~ in(v14, v20) | (in(v18, v16) & in(v14, v21))))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (relation_dom(v14) = v15) |  ~ (ordered_pair(v16, v17) = v18) |  ~ relation(v14) |  ~ function(v14) |  ~ in(v16, v15) |  ? [v19] : (apply(v14, v16) = v19 & ( ~ (v19 = v17) | in(v18, v14)) & (v19 = v17 |  ~ in(v18, v14)))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (apply(v16, v14) = v17) |  ~ (apply(v15, v17) = v18) |  ~ relation(v16) |  ~ relation(v15) |  ~ function(v16) |  ~ function(v15) |  ? [v19] :  ? [v20] :  ? [v21] : (relation_composition(v16, v15) = v19 & relation_dom(v19) = v20 & apply(v19, v14) = v21 & (v21 = v18 |  ~ in(v14, v20)))) &  ? [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (relation_composition(v17, v15) = v18) |  ~ (relation_dom(v15) = v16) |  ~ relation(v17) |  ~ relation(v15) |  ~ function(v17) |  ~ function(v15) |  ? [v19] :  ? [v20] :  ? [v21] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & apply(v17, v14) = v21 & ( ~ in(v21, v16) |  ~ in(v14, v20) | in(v14, v19)) & ( ~ in(v14, v19) | (in(v21, v16) & in(v14, v20))))) &  ? [v14] :  ! [v15] :  ! [v16] :  ! [v17] :  ! [v18] : ( ~ (relation_dom(v17) = v18) |  ~ (relation_dom(v15) = v16) |  ~ relation(v17) |  ~ relation(v15) |  ~ function(v17) |  ~ function(v15) |  ? [v19] :  ? [v20] :  ? [v21] : (relation_composition(v17, v15) = v19 & relation_dom(v19) = v20 & apply(v17, v14) = v21 & ( ~ in(v21, v16) |  ~ in(v14, v18) | in(v14, v20)) & ( ~ in(v14, v20) | (in(v21, v16) & in(v14, v18))))) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v17 = empty_set |  ~ (relation_dom(v14) = v15) |  ~ (apply(v14, v16) = v17) |  ~ relation(v14) |  ~ function(v14) | in(v16, v15)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (relation_composition(v17, v16) = v15) |  ~ (relation_composition(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (ordered_pair(v17, v16) = v15) |  ~ (ordered_pair(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (apply(v17, v16) = v15) |  ~ (apply(v17, v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = v14 |  ~ (unordered_pair(v17, v16) = v15) |  ~ (unordered_pair(v17, v16) = v14)) &  ? [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (relation_composition(v16, v15) = v17) |  ~ relation(v16) |  ~ relation(v15) |  ~ function(v16) |  ~ function(v15) |  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : (relation_dom(v17) = v18 & apply(v17, v14) = v19 & apply(v16, v14) = v20 & apply(v15, v20) = v21 & (v21 = v19 |  ~ in(v14, v18)))) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (singleton(v16) = v15) |  ~ (singleton(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : (v15 = v14 |  ~ (relation_dom(v16) = v15) |  ~ (relation_dom(v16) = v14)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v15, v14) = v16) |  ~ relation(v15) |  ~ empty(v14) | relation(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v15, v14) = v16) |  ~ relation(v15) |  ~ empty(v14) | empty(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v14, v15) = v16) |  ~ relation(v15) |  ~ relation(v14) |  ~ function(v15) |  ~ function(v14) | relation(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v14, v15) = v16) |  ~ relation(v15) |  ~ relation(v14) |  ~ function(v15) |  ~ function(v14) | function(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v14, v15) = v16) |  ~ relation(v15) |  ~ relation(v14) | relation(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v14, v15) = v16) |  ~ relation(v15) |  ~ empty(v14) | relation(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (relation_composition(v14, v15) = v16) |  ~ relation(v15) |  ~ empty(v14) | empty(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) |  ~ empty(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) |  ? [v17] :  ? [v18] : (singleton(v14) = v18 & unordered_pair(v17, v18) = v16 & unordered_pair(v14, v15) = v17)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v15, v14) = v16) | unordered_pair(v14, v15) = v16) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) |  ~ empty(v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | unordered_pair(v15, v14) = v16) &  ! [v14] :  ! [v15] : (v15 = v14 |  ~ empty(v15) |  ~ empty(v14)) &  ! [v14] :  ! [v15] : ( ~ (singleton(v14) = v15) |  ~ empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ relation(v14) |  ~ empty(v15) | empty(v14)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ empty(v14) | relation(v15)) &  ! [v14] :  ! [v15] : ( ~ (relation_dom(v14) = v15) |  ~ empty(v14) | empty(v15)) &  ! [v14] :  ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ empty(v15) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ in(v15, v14) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) &  ! [v14] : (v14 = empty_set |  ~ empty(v14)) &  ! [v14] : ( ~ empty(v14) | relation(v14)) &  ! [v14] : ( ~ empty(v14) | function(v14)) &  ? [v14] :  ? [v15] : element(v15, v14))
% 8.65/2.85  | 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 yields:
% 8.65/2.85  | (1)  ~ (all_0_6_6 = all_0_7_7) & relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 & relation_dom(all_0_12_12) = all_0_11_11 & apply(all_0_8_8, all_0_13_13) = all_0_7_7 & apply(all_0_9_9, all_0_10_10) = all_0_6_6 & apply(all_0_12_12, all_0_13_13) = all_0_10_10 & 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_3_3) & relation(all_0_5_5) & relation(all_0_9_9) & relation(all_0_12_12) & relation(empty_set) & function(all_0_0_0) & function(all_0_9_9) & function(all_0_12_12) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & in(all_0_13_13, all_0_11_11) &  ~ empty(all_0_3_3) &  ~ empty(all_0_4_4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_composition(v2, v1) = v3) |  ~ (apply(v3, v0) = v4) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 |  ~ in(v0, v5)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v1) = v2) |  ~ (apply(v3, v0) = v4) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) |  ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v3) = v4) |  ~ relation(v0) |  ~ function(v0) |  ~ in(v2, v1) |  ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 |  ~ in(v4, v0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apply(v2, v0) = v3) |  ~ (apply(v1, v3) = v4) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 |  ~ in(v0, v6)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_composition(v3, v1) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) |  ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) |  ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = empty_set |  ~ (relation_dom(v0) = v1) |  ~ (apply(v0, v2) = v3) |  ~ relation(v0) |  ~ function(v0) | in(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_composition(v2, v1) = v3) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 |  ~ in(v0, v4)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(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] : ( ~ empty(v0) | relation(v0)) &  ! [v0] : ( ~ empty(v0) | function(v0)) &  ? [v0] :  ? [v1] : element(v1, v0)
% 8.65/2.87  |
% 8.65/2.87  | Applying alpha-rule on (1) yields:
% 8.65/2.87  | (2)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 8.65/2.87  | (3)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_composition(v2, v1) = v3) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 |  ~ in(v0, v4))))
% 8.65/2.88  | (4) empty(all_0_2_2)
% 8.65/2.88  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 8.65/2.88  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v0) = v1) |  ~ (ordered_pair(v2, v3) = v4) |  ~ relation(v0) |  ~ function(v0) |  ~ in(v2, v1) |  ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 |  ~ in(v4, v0))))
% 8.65/2.88  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 8.65/2.88  | (8)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 8.65/2.88  | (9) in(all_0_13_13, all_0_11_11)
% 8.65/2.88  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 8.65/2.88  | (11)  ~ empty(all_0_3_3)
% 8.65/2.88  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 8.65/2.88  | (13)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 8.65/2.88  | (14) relation(all_0_9_9)
% 8.65/2.88  | (15)  ! [v0] : ( ~ empty(v0) | function(v0))
% 8.65/2.88  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 8.65/2.88  | (17)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 8.65/2.88  | (18)  ~ empty(all_0_4_4)
% 8.65/2.88  | (19)  ~ (all_0_6_6 = all_0_7_7)
% 8.65/2.88  | (20) relation(all_0_1_1)
% 8.65/2.88  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 8.65/2.88  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 8.65/2.88  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apply(v2, v0) = v3) |  ~ (apply(v1, v3) = v4) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 |  ~ in(v0, v6))))
% 8.65/2.88  | (24)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 8.65/2.88  | (25) function(all_0_12_12)
% 8.65/2.88  | (26) relation_empty_yielding(all_0_5_5)
% 8.65/2.88  | (27)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 8.65/2.89  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 8.65/2.89  | (29) relation(all_0_3_3)
% 8.65/2.89  | (30) relation(all_0_12_12)
% 8.65/2.89  | (31) relation(all_0_0_0)
% 8.65/2.89  | (32)  ? [v0] :  ? [v1] : element(v1, v0)
% 8.65/2.89  | (33) relation_empty_yielding(empty_set)
% 8.65/2.89  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 8.65/2.89  | (35) relation(all_0_5_5)
% 8.65/2.89  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 8.65/2.89  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 8.65/2.89  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 8.65/2.89  | (39) empty(empty_set)
% 8.65/2.89  | (40) function(all_0_0_0)
% 8.65/2.89  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_composition(v2, v1) = v3) |  ~ (apply(v3, v0) = v4) |  ~ relation(v2) |  ~ relation(v1) |  ~ function(v2) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 |  ~ in(v0, v5))))
% 8.65/2.89  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) = v0))
% 8.65/2.89  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2))
% 8.65/2.89  | (44)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 8.65/2.89  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2))
% 8.65/2.89  | (46) apply(all_0_8_8, all_0_13_13) = all_0_7_7
% 8.65/2.89  | (47) empty(all_0_1_1)
% 8.65/2.89  | (48)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_composition(v3, v1) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) |  ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6)))))
% 9.06/2.89  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 9.06/2.90  | (50) relation(empty_set)
% 9.06/2.90  | (51) relation_dom(all_0_12_12) = all_0_11_11
% 9.06/2.90  | (52)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 9.06/2.90  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v1) = v2) |  ~ (apply(v3, v0) = v4) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) |  ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7)))))
% 9.06/2.90  | (54)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 9.06/2.90  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = empty_set |  ~ (relation_dom(v0) = v1) |  ~ (apply(v0, v2) = v3) |  ~ relation(v0) |  ~ function(v0) | in(v2, v1))
% 9.06/2.90  | (56) function(all_0_9_9)
% 9.06/2.90  | (57)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (relation_dom(v3) = v4) |  ~ (relation_dom(v1) = v2) |  ~ relation(v3) |  ~ relation(v1) |  ~ function(v3) |  ~ function(v1) |  ? [v5] :  ? [v6] :  ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) |  ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4)))))
% 9.06/2.90  | (58) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8
% 9.06/2.90  | (59)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 9.06/2.90  | (60) apply(all_0_12_12, all_0_13_13) = all_0_10_10
% 9.06/2.90  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 9.06/2.90  | (62)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 9.06/2.90  | (63) apply(all_0_9_9, all_0_10_10) = all_0_6_6
% 9.06/2.90  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 9.06/2.90  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 9.06/2.90  |
% 9.06/2.90  | Instantiating (3) with all_5_0_16 yields:
% 9.06/2.90  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (relation_dom(v2) = v3 & apply(v2, all_5_0_16) = v4 & apply(v1, all_5_0_16) = v5 & apply(v0, v5) = v6 & (v6 = v4 |  ~ in(all_5_0_16, v3))))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating (57) with all_7_0_17 yields:
% 9.06/2.91  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_dom(v2) = v3) |  ~ (relation_dom(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ~ function(v2) |  ~ function(v0) |  ? [v4] :  ? [v5] :  ? [v6] : (relation_composition(v2, v0) = v4 & relation_dom(v4) = v5 & apply(v2, all_7_0_17) = v6 & ( ~ in(v6, v1) |  ~ in(all_7_0_17, v3) | in(all_7_0_17, v5)) & ( ~ in(all_7_0_17, v5) | (in(v6, v1) & in(all_7_0_17, v3)))))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating (48) with all_9_0_18 yields:
% 9.06/2.91  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (relation_composition(v2, v0) = v3) |  ~ (relation_dom(v0) = v1) |  ~ relation(v2) |  ~ relation(v0) |  ~ function(v2) |  ~ function(v0) |  ? [v4] :  ? [v5] :  ? [v6] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & apply(v2, all_9_0_18) = v6 & ( ~ in(v6, v1) |  ~ in(all_9_0_18, v5) | in(all_9_0_18, v4)) & ( ~ in(all_9_0_18, v4) | (in(v6, v1) & in(all_9_0_18, v5)))))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (41) with all_0_7_7, all_0_8_8, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.91  | (69)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_0_13_13) = v1 & (v2 = all_0_7_7 |  ~ in(all_0_13_13, v0)))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (43) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.91  | (70) relation(all_0_8_8)
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (45) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.91  | (71) function(all_0_8_8)
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (66) with all_0_8_8, all_0_12_12, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.91  | (72)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (relation_dom(all_0_8_8) = v0 & apply(all_0_8_8, all_5_0_16) = v1 & apply(all_0_9_9, v2) = v3 & apply(all_0_12_12, all_5_0_16) = v2 & (v3 = v1 |  ~ in(all_5_0_16, v0)))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (53) with all_0_10_10, all_0_12_12, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_12_12), function(all_0_12_12), yields:
% 9.06/2.91  | (73)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_0_11_11) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, v2))))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (67) with all_0_11_11, all_0_12_12, 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:
% 9.06/2.91  | (74)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & apply(all_0_12_12, all_7_0_17) = v2 & ( ~ in(v2, all_0_11_11) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(v2, all_0_11_11) & in(all_7_0_17, all_0_11_11))))
% 9.06/2.91  |
% 9.06/2.91  | Instantiating formula (53) with all_0_6_6, all_0_9_9, all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.91  | (75)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_9_9, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_9_9) = v2 & ( ~ in(all_0_6_6, all_0_11_11) |  ~ in(all_0_10_10, v2) | in(all_0_10_10, v1)) & ( ~ in(all_0_10_10, v1) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, v2))))
% 9.06/2.92  |
% 9.06/2.92  | Instantiating formula (23) with all_0_6_6, all_0_10_10, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_6_6, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.92  | (76)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_0_13_13) = v2 & (v2 = all_0_6_6 |  ~ in(all_0_13_13, v1)))
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (75) with all_21_0_19, all_21_1_20, all_21_2_21 yields:
% 9.06/2.92  | (77) relation_composition(all_0_9_9, all_0_12_12) = all_21_2_21 & relation_dom(all_21_2_21) = all_21_1_20 & relation_dom(all_0_9_9) = all_21_0_19 & ( ~ in(all_0_6_6, all_0_11_11) |  ~ in(all_0_10_10, all_21_0_19) | in(all_0_10_10, all_21_1_20)) & ( ~ in(all_0_10_10, all_21_1_20) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_21_0_19)))
% 9.06/2.92  |
% 9.06/2.92  | Applying alpha-rule on (77) yields:
% 9.06/2.92  | (78) relation_dom(all_21_2_21) = all_21_1_20
% 9.06/2.92  | (79) relation_dom(all_0_9_9) = all_21_0_19
% 9.06/2.92  | (80) relation_composition(all_0_9_9, all_0_12_12) = all_21_2_21
% 9.06/2.92  | (81)  ~ in(all_0_6_6, all_0_11_11) |  ~ in(all_0_10_10, all_21_0_19) | in(all_0_10_10, all_21_1_20)
% 9.06/2.92  | (82)  ~ in(all_0_10_10, all_21_1_20) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_21_0_19))
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (73) with all_23_0_22, all_23_1_23, all_23_2_24 yields:
% 9.06/2.92  | (83) relation_composition(all_0_12_12, all_0_12_12) = all_23_2_24 & relation_dom(all_23_2_24) = all_23_1_23 & relation_dom(all_0_12_12) = all_23_0_22 & ( ~ in(all_0_10_10, all_0_11_11) |  ~ in(all_0_13_13, all_23_0_22) | in(all_0_13_13, all_23_1_23)) & ( ~ in(all_0_13_13, all_23_1_23) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_23_0_22)))
% 9.06/2.92  |
% 9.06/2.92  | Applying alpha-rule on (83) yields:
% 9.06/2.92  | (84)  ~ in(all_0_13_13, all_23_1_23) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_23_0_22))
% 9.06/2.92  | (85) relation_dom(all_23_2_24) = all_23_1_23
% 9.06/2.92  | (86) relation_composition(all_0_12_12, all_0_12_12) = all_23_2_24
% 9.06/2.92  | (87)  ~ in(all_0_10_10, all_0_11_11) |  ~ in(all_0_13_13, all_23_0_22) | in(all_0_13_13, all_23_1_23)
% 9.06/2.92  | (88) relation_dom(all_0_12_12) = all_23_0_22
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (72) with all_25_0_25, all_25_1_26, all_25_2_27, all_25_3_28 yields:
% 9.06/2.92  | (89) relation_dom(all_0_8_8) = all_25_3_28 & apply(all_0_8_8, all_5_0_16) = all_25_2_27 & apply(all_0_9_9, all_25_1_26) = all_25_0_25 & apply(all_0_12_12, all_5_0_16) = all_25_1_26 & (all_25_0_25 = all_25_2_27 |  ~ in(all_5_0_16, all_25_3_28))
% 9.06/2.92  |
% 9.06/2.92  | Applying alpha-rule on (89) yields:
% 9.06/2.92  | (90) all_25_0_25 = all_25_2_27 |  ~ in(all_5_0_16, all_25_3_28)
% 9.06/2.92  | (91) apply(all_0_9_9, all_25_1_26) = all_25_0_25
% 9.06/2.92  | (92) relation_dom(all_0_8_8) = all_25_3_28
% 9.06/2.92  | (93) apply(all_0_12_12, all_5_0_16) = all_25_1_26
% 9.06/2.92  | (94) apply(all_0_8_8, all_5_0_16) = all_25_2_27
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (74) with all_27_0_29, all_27_1_30, all_27_2_31 yields:
% 9.06/2.92  | (95) relation_composition(all_0_12_12, all_0_12_12) = all_27_2_31 & relation_dom(all_27_2_31) = all_27_1_30 & apply(all_0_12_12, all_7_0_17) = all_27_0_29 & ( ~ in(all_27_0_29, all_0_11_11) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_27_1_30)) & ( ~ in(all_7_0_17, all_27_1_30) | (in(all_27_0_29, all_0_11_11) & in(all_7_0_17, all_0_11_11)))
% 9.06/2.92  |
% 9.06/2.92  | Applying alpha-rule on (95) yields:
% 9.06/2.92  | (96) apply(all_0_12_12, all_7_0_17) = all_27_0_29
% 9.06/2.92  | (97)  ~ in(all_27_0_29, all_0_11_11) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_27_1_30)
% 9.06/2.92  | (98) relation_composition(all_0_12_12, all_0_12_12) = all_27_2_31
% 9.06/2.92  | (99) relation_dom(all_27_2_31) = all_27_1_30
% 9.06/2.92  | (100)  ~ in(all_7_0_17, all_27_1_30) | (in(all_27_0_29, all_0_11_11) & in(all_7_0_17, all_0_11_11))
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (76) with all_29_0_32, all_29_1_33, all_29_2_34 yields:
% 9.06/2.92  | (101) relation_composition(all_0_12_12, all_0_9_9) = all_29_2_34 & relation_dom(all_29_2_34) = all_29_1_33 & apply(all_29_2_34, all_0_13_13) = all_29_0_32 & (all_29_0_32 = all_0_6_6 |  ~ in(all_0_13_13, all_29_1_33))
% 9.06/2.92  |
% 9.06/2.92  | Applying alpha-rule on (101) yields:
% 9.06/2.92  | (102) relation_composition(all_0_12_12, all_0_9_9) = all_29_2_34
% 9.06/2.92  | (103) relation_dom(all_29_2_34) = all_29_1_33
% 9.06/2.92  | (104) apply(all_29_2_34, all_0_13_13) = all_29_0_32
% 9.06/2.92  | (105) all_29_0_32 = all_0_6_6 |  ~ in(all_0_13_13, all_29_1_33)
% 9.06/2.92  |
% 9.06/2.92  | Instantiating (69) with all_31_0_35, all_31_1_36, all_31_2_37 yields:
% 9.06/2.92  | (106) relation_dom(all_0_8_8) = all_31_2_37 & apply(all_0_9_9, all_31_1_36) = all_31_0_35 & apply(all_0_12_12, all_0_13_13) = all_31_1_36 & (all_31_0_35 = all_0_7_7 |  ~ in(all_0_13_13, all_31_2_37))
% 9.06/2.93  |
% 9.06/2.93  | Applying alpha-rule on (106) yields:
% 9.06/2.93  | (107) relation_dom(all_0_8_8) = all_31_2_37
% 9.06/2.93  | (108) apply(all_0_9_9, all_31_1_36) = all_31_0_35
% 9.06/2.93  | (109) apply(all_0_12_12, all_0_13_13) = all_31_1_36
% 9.06/2.93  | (110) all_31_0_35 = all_0_7_7 |  ~ in(all_0_13_13, all_31_2_37)
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (42) with all_0_12_12, all_0_9_9, all_29_2_34, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_29_2_34, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 9.06/2.93  | (111) all_29_2_34 = all_0_8_8
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (42) with all_0_12_12, all_0_12_12, all_23_2_24, all_27_2_31 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_27_2_31, relation_composition(all_0_12_12, all_0_12_12) = all_23_2_24, yields:
% 9.06/2.93  | (112) all_27_2_31 = all_23_2_24
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (38) with all_0_8_8, all_25_3_28, all_31_2_37 and discharging atoms relation_dom(all_0_8_8) = all_31_2_37, relation_dom(all_0_8_8) = all_25_3_28, yields:
% 9.06/2.93  | (113) all_31_2_37 = all_25_3_28
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (38) with all_0_12_12, all_23_0_22, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_23_0_22, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 9.06/2.93  | (114) all_23_0_22 = all_0_11_11
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (65) with all_0_12_12, all_0_13_13, all_31_1_36, all_0_10_10 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_31_1_36, apply(all_0_12_12, all_0_13_13) = all_0_10_10, yields:
% 9.06/2.93  | (115) all_31_1_36 = all_0_10_10
% 9.06/2.93  |
% 9.06/2.93  | From (111) and (102) follows:
% 9.06/2.93  | (58) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8
% 9.06/2.93  |
% 9.06/2.93  | From (112) and (98) follows:
% 9.06/2.93  | (86) relation_composition(all_0_12_12, all_0_12_12) = all_23_2_24
% 9.06/2.93  |
% 9.06/2.93  | From (111) and (103) follows:
% 9.06/2.93  | (118) relation_dom(all_0_8_8) = all_29_1_33
% 9.06/2.93  |
% 9.06/2.93  | From (113) and (107) follows:
% 9.06/2.93  | (92) relation_dom(all_0_8_8) = all_25_3_28
% 9.06/2.93  |
% 9.06/2.93  | From (114) and (88) follows:
% 9.06/2.93  | (51) relation_dom(all_0_12_12) = all_0_11_11
% 9.06/2.93  |
% 9.06/2.93  | From (111) and (104) follows:
% 9.06/2.93  | (121) apply(all_0_8_8, all_0_13_13) = all_29_0_32
% 9.06/2.93  |
% 9.06/2.93  | From (115) and (108) follows:
% 9.06/2.93  | (122) apply(all_0_9_9, all_0_10_10) = all_31_0_35
% 9.06/2.93  |
% 9.06/2.93  | From (115) and (109) follows:
% 9.06/2.93  | (60) apply(all_0_12_12, all_0_13_13) = all_0_10_10
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (38) with all_0_8_8, all_29_1_33, all_25_3_28 and discharging atoms relation_dom(all_0_8_8) = all_29_1_33, relation_dom(all_0_8_8) = all_25_3_28, yields:
% 9.06/2.93  | (124) all_29_1_33 = all_25_3_28
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (65) with all_0_8_8, all_0_13_13, all_29_0_32, all_0_7_7 and discharging atoms apply(all_0_8_8, all_0_13_13) = all_29_0_32, apply(all_0_8_8, all_0_13_13) = all_0_7_7, yields:
% 9.06/2.93  | (125) all_29_0_32 = all_0_7_7
% 9.06/2.93  |
% 9.06/2.93  | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_31_0_35, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_31_0_35, apply(all_0_9_9, all_0_10_10) = all_0_6_6, yields:
% 9.06/2.93  | (126) all_31_0_35 = all_0_6_6
% 9.06/2.93  |
% 9.06/2.93  | From (124) and (118) follows:
% 9.06/2.93  | (92) relation_dom(all_0_8_8) = all_25_3_28
% 9.06/2.93  |
% 9.06/2.93  | From (125) and (121) follows:
% 9.06/2.93  | (46) apply(all_0_8_8, all_0_13_13) = all_0_7_7
% 9.06/2.93  |
% 9.06/2.93  | From (126) and (122) follows:
% 9.06/2.93  | (63) apply(all_0_9_9, all_0_10_10) = all_0_6_6
% 9.06/2.93  |
% 9.06/2.93  +-Applying beta-rule and splitting (105), into two cases.
% 9.06/2.93  |-Branch one:
% 9.06/2.93  | (130)  ~ in(all_0_13_13, all_29_1_33)
% 9.06/2.93  |
% 9.06/2.93  	| From (124) and (130) follows:
% 9.06/2.93  	| (131)  ~ in(all_0_13_13, all_25_3_28)
% 9.06/2.93  	|
% 9.06/2.93  	| Instantiating formula (68) with all_23_2_24, all_0_12_12, all_0_11_11, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_23_2_24, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 9.06/2.93  	| (132)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_23_2_24) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_9_0_18) = v2 & ( ~ in(v2, all_0_11_11) |  ~ in(all_9_0_18, v1) | in(all_9_0_18, v0)) & ( ~ in(all_9_0_18, v0) | (in(v2, all_0_11_11) & in(all_9_0_18, v1))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (55) with all_0_6_6, all_0_10_10, all_21_0_19, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), function(all_0_9_9), yields:
% 9.06/2.94  	| (133) all_0_6_6 = empty_set | in(all_0_10_10, all_21_0_19)
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (53) with all_0_10_10, all_0_12_12, all_21_0_19, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (134)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_21_0_19) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_21_0_19) & in(all_0_13_13, v2))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (68) with all_0_8_8, all_0_12_12, all_21_0_19, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation_dom(all_0_9_9) = all_21_0_19, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (135)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_0_8_8) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_9_0_18) = v2 & ( ~ in(v2, all_21_0_19) |  ~ in(all_9_0_18, v1) | in(all_9_0_18, v0)) & ( ~ in(all_9_0_18, v0) | (in(v2, all_21_0_19) & in(all_9_0_18, v1))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (67) with all_0_11_11, all_0_12_12, all_21_0_19, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (136)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(all_0_12_12, all_7_0_17) = v2 & ( ~ in(v2, all_21_0_19) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(v2, all_21_0_19) & in(all_7_0_17, all_0_11_11))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (41) with all_25_2_27, all_0_8_8, all_0_12_12, all_0_9_9, all_5_0_16 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_5_0_16) = all_25_2_27, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (137)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_5_0_16) = v1 & (v2 = all_25_2_27 |  ~ in(all_5_0_16, v0)))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (53) with all_27_0_29, all_0_12_12, all_0_11_11, all_0_12_12, all_7_0_17 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_7_0_17) = all_27_0_29, relation(all_0_12_12), function(all_0_12_12), yields:
% 9.06/2.94  	| (138)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_0_29, all_0_11_11) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_27_0_29, all_0_11_11) & in(all_7_0_17, v2))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (53) with all_27_0_29, all_0_12_12, all_21_0_19, all_0_9_9, all_7_0_17 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_12_12, all_7_0_17) = all_27_0_29, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (139)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_0_29, all_21_0_19) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_27_0_29, all_21_0_19) & in(all_7_0_17, v2))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (53) with all_25_1_26, all_0_12_12, all_0_11_11, all_0_12_12, all_5_0_16 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_5_0_16) = all_25_1_26, relation(all_0_12_12), function(all_0_12_12), yields:
% 9.06/2.94  	| (140)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_25_1_26, all_0_11_11) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_1_26, all_0_11_11) & in(all_5_0_16, v2))))
% 9.06/2.94  	|
% 9.06/2.94  	| Instantiating formula (53) with all_25_1_26, all_0_12_12, all_21_0_19, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_12_12, all_5_0_16) = all_25_1_26, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.94  	| (141)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_25_1_26, all_21_0_19) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_1_26, all_21_0_19) & in(all_5_0_16, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (23) with all_25_0_25, all_25_1_26, all_0_12_12, all_0_9_9, all_5_0_16 and discharging atoms apply(all_0_9_9, all_25_1_26) = all_25_0_25, apply(all_0_12_12, all_5_0_16) = all_25_1_26, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 9.06/2.95  	| (142)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_5_0_16) = v2 & (v2 = all_25_0_25 |  ~ in(all_5_0_16, v1)))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_0_7_7, all_0_8_8, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 9.06/2.95  	| (143)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_0_11_11) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_25_2_27, all_0_8_8, all_0_11_11, all_0_12_12, all_5_0_16 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_5_0_16) = all_25_2_27, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 9.06/2.95  	| (144)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_25_2_27, all_0_11_11) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_2_27, all_0_11_11) & in(all_5_0_16, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_0_7_7, all_0_8_8, all_25_3_28, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), yields:
% 9.06/2.95  	| (145)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_25_3_28) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_25_3_28) & in(all_0_13_13, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_25_2_27, all_0_8_8, all_25_3_28, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_8_8, all_5_0_16) = all_25_2_27, relation(all_0_8_8), function(all_0_8_8), yields:
% 9.06/2.95  	| (146)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_25_2_27, all_25_3_28) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_2_27, all_25_3_28) & in(all_5_0_16, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (55) with all_0_7_7, all_0_13_13, all_25_3_28, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8),  ~ in(all_0_13_13, all_25_3_28), yields:
% 9.06/2.95  	| (147) all_0_7_7 = empty_set
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_0_10_10, all_0_12_12, all_25_3_28, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 9.06/2.95  	| (148)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_25_3_28) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_25_3_28) & in(all_0_13_13, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_27_0_29, all_0_12_12, all_25_3_28, all_0_8_8, all_7_0_17 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_12_12, all_7_0_17) = all_27_0_29, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 9.06/2.95  	| (149)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_27_0_29, all_25_3_28) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_27_0_29, all_25_3_28) & in(all_7_0_17, v2))))
% 9.06/2.95  	|
% 9.06/2.95  	| Instantiating formula (53) with all_25_1_26, all_0_12_12, all_25_3_28, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_25_3_28, apply(all_0_12_12, all_5_0_16) = all_25_1_26, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 9.06/2.95  	| (150)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_25_1_26, all_25_3_28) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_1_26, all_25_3_28) & in(all_5_0_16, v2))))
% 9.06/2.95  	|
% 9.06/2.96  	| Instantiating formula (53) with all_0_7_7, all_0_8_8, all_21_0_19, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields:
% 9.06/2.96  	| (151)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_21_0_19) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_21_0_19) & in(all_0_13_13, v2))))
% 9.06/2.96  	|
% 9.06/2.96  	| Instantiating formula (53) with all_25_2_27, all_0_8_8, all_21_0_19, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_21_0_19, apply(all_0_8_8, all_5_0_16) = all_25_2_27, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields:
% 9.06/2.96  	| (152)  ? [v0] :  ? [v1] :  ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_25_2_27, all_21_0_19) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_25_2_27, all_21_0_19) & in(all_5_0_16, v2))))
% 9.06/2.96  	|
% 9.06/2.96  	| Instantiating (152) with all_53_0_41, all_53_1_42, all_53_2_43 yields:
% 9.06/2.96  	| (153) relation_composition(all_0_8_8, all_0_9_9) = all_53_2_43 & relation_dom(all_53_2_43) = all_53_1_42 & relation_dom(all_0_8_8) = all_53_0_41 & ( ~ in(all_25_2_27, all_21_0_19) |  ~ in(all_5_0_16, all_53_0_41) | in(all_5_0_16, all_53_1_42)) & ( ~ in(all_5_0_16, all_53_1_42) | (in(all_25_2_27, all_21_0_19) & in(all_5_0_16, all_53_0_41)))
% 9.06/2.96  	|
% 9.06/2.96  	| Applying alpha-rule on (153) yields:
% 9.06/2.96  	| (154) relation_composition(all_0_8_8, all_0_9_9) = all_53_2_43
% 9.06/2.96  	| (155) relation_dom(all_0_8_8) = all_53_0_41
% 9.06/2.96  	| (156)  ~ in(all_5_0_16, all_53_1_42) | (in(all_25_2_27, all_21_0_19) & in(all_5_0_16, all_53_0_41))
% 9.06/2.96  	| (157) relation_dom(all_53_2_43) = all_53_1_42
% 9.06/2.96  	| (158)  ~ in(all_25_2_27, all_21_0_19) |  ~ in(all_5_0_16, all_53_0_41) | in(all_5_0_16, all_53_1_42)
% 9.06/2.96  	|
% 9.06/2.96  	| Instantiating (150) with all_59_0_51, all_59_1_52, all_59_2_53 yields:
% 9.06/2.96  	| (159) relation_composition(all_0_12_12, all_0_8_8) = all_59_2_53 & relation_dom(all_59_2_53) = all_59_1_52 & relation_dom(all_0_12_12) = all_59_0_51 & ( ~ in(all_25_1_26, all_25_3_28) |  ~ in(all_5_0_16, all_59_0_51) | in(all_5_0_16, all_59_1_52)) & ( ~ in(all_5_0_16, all_59_1_52) | (in(all_25_1_26, all_25_3_28) & in(all_5_0_16, all_59_0_51)))
% 9.06/2.96  	|
% 9.06/2.96  	| Applying alpha-rule on (159) yields:
% 9.06/2.96  	| (160) relation_dom(all_0_12_12) = all_59_0_51
% 9.06/2.96  	| (161)  ~ in(all_25_1_26, all_25_3_28) |  ~ in(all_5_0_16, all_59_0_51) | in(all_5_0_16, all_59_1_52)
% 9.06/2.96  	| (162) relation_composition(all_0_12_12, all_0_8_8) = all_59_2_53
% 9.06/2.96  	| (163)  ~ in(all_5_0_16, all_59_1_52) | (in(all_25_1_26, all_25_3_28) & in(all_5_0_16, all_59_0_51))
% 9.06/2.96  	| (164) relation_dom(all_59_2_53) = all_59_1_52
% 9.06/2.96  	|
% 9.06/2.96  	| Instantiating (149) with all_61_0_54, all_61_1_55, all_61_2_56 yields:
% 9.06/2.96  	| (165) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_56 & relation_dom(all_61_2_56) = all_61_1_55 & relation_dom(all_0_12_12) = all_61_0_54 & ( ~ in(all_27_0_29, all_25_3_28) |  ~ in(all_7_0_17, all_61_0_54) | in(all_7_0_17, all_61_1_55)) & ( ~ in(all_7_0_17, all_61_1_55) | (in(all_27_0_29, all_25_3_28) & in(all_7_0_17, all_61_0_54)))
% 9.06/2.96  	|
% 9.06/2.96  	| Applying alpha-rule on (165) yields:
% 9.06/2.96  	| (166)  ~ in(all_27_0_29, all_25_3_28) |  ~ in(all_7_0_17, all_61_0_54) | in(all_7_0_17, all_61_1_55)
% 9.06/2.96  	| (167)  ~ in(all_7_0_17, all_61_1_55) | (in(all_27_0_29, all_25_3_28) & in(all_7_0_17, all_61_0_54))
% 9.06/2.96  	| (168) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_56
% 9.06/2.96  	| (169) relation_dom(all_0_12_12) = all_61_0_54
% 9.06/2.96  	| (170) relation_dom(all_61_2_56) = all_61_1_55
% 9.06/2.96  	|
% 9.06/2.96  	| Instantiating (151) with all_63_0_57, all_63_1_58, all_63_2_59 yields:
% 9.06/2.96  	| (171) relation_composition(all_0_8_8, all_0_9_9) = all_63_2_59 & relation_dom(all_63_2_59) = all_63_1_58 & relation_dom(all_0_8_8) = all_63_0_57 & ( ~ in(all_0_7_7, all_21_0_19) |  ~ in(all_0_13_13, all_63_0_57) | in(all_0_13_13, all_63_1_58)) & ( ~ in(all_0_13_13, all_63_1_58) | (in(all_0_7_7, all_21_0_19) & in(all_0_13_13, all_63_0_57)))
% 9.06/2.96  	|
% 9.06/2.96  	| Applying alpha-rule on (171) yields:
% 9.06/2.96  	| (172) relation_dom(all_63_2_59) = all_63_1_58
% 9.06/2.96  	| (173) relation_dom(all_0_8_8) = all_63_0_57
% 9.06/2.96  	| (174) relation_composition(all_0_8_8, all_0_9_9) = all_63_2_59
% 9.06/2.96  	| (175)  ~ in(all_0_7_7, all_21_0_19) |  ~ in(all_0_13_13, all_63_0_57) | in(all_0_13_13, all_63_1_58)
% 9.06/2.97  	| (176)  ~ in(all_0_13_13, all_63_1_58) | (in(all_0_7_7, all_21_0_19) & in(all_0_13_13, all_63_0_57))
% 9.06/2.97  	|
% 9.06/2.97  	| Instantiating (140) with all_69_0_66, all_69_1_67, all_69_2_68 yields:
% 9.06/2.97  	| (177) relation_composition(all_0_12_12, all_0_12_12) = all_69_2_68 & relation_dom(all_69_2_68) = all_69_1_67 & relation_dom(all_0_12_12) = all_69_0_66 & ( ~ in(all_25_1_26, all_0_11_11) |  ~ in(all_5_0_16, all_69_0_66) | in(all_5_0_16, all_69_1_67)) & ( ~ in(all_5_0_16, all_69_1_67) | (in(all_25_1_26, all_0_11_11) & in(all_5_0_16, all_69_0_66)))
% 9.06/2.97  	|
% 9.06/2.97  	| Applying alpha-rule on (177) yields:
% 9.06/2.97  	| (178)  ~ in(all_5_0_16, all_69_1_67) | (in(all_25_1_26, all_0_11_11) & in(all_5_0_16, all_69_0_66))
% 9.06/2.97  	| (179) relation_composition(all_0_12_12, all_0_12_12) = all_69_2_68
% 9.06/2.97  	| (180)  ~ in(all_25_1_26, all_0_11_11) |  ~ in(all_5_0_16, all_69_0_66) | in(all_5_0_16, all_69_1_67)
% 9.06/2.97  	| (181) relation_dom(all_0_12_12) = all_69_0_66
% 9.06/2.97  	| (182) relation_dom(all_69_2_68) = all_69_1_67
% 9.06/2.97  	|
% 9.06/2.97  	| Instantiating (138) with all_71_0_69, all_71_1_70, all_71_2_71 yields:
% 9.06/2.97  	| (183) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_71 & relation_dom(all_71_2_71) = all_71_1_70 & relation_dom(all_0_12_12) = all_71_0_69 & ( ~ in(all_27_0_29, all_0_11_11) |  ~ in(all_7_0_17, all_71_0_69) | in(all_7_0_17, all_71_1_70)) & ( ~ in(all_7_0_17, all_71_1_70) | (in(all_27_0_29, all_0_11_11) & in(all_7_0_17, all_71_0_69)))
% 9.06/2.97  	|
% 9.06/2.97  	| Applying alpha-rule on (183) yields:
% 9.06/2.97  	| (184)  ~ in(all_27_0_29, all_0_11_11) |  ~ in(all_7_0_17, all_71_0_69) | in(all_7_0_17, all_71_1_70)
% 9.06/2.97  	| (185) relation_dom(all_0_12_12) = all_71_0_69
% 9.06/2.97  	| (186)  ~ in(all_7_0_17, all_71_1_70) | (in(all_27_0_29, all_0_11_11) & in(all_7_0_17, all_71_0_69))
% 9.06/2.97  	| (187) relation_dom(all_71_2_71) = all_71_1_70
% 9.06/2.97  	| (188) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_71
% 9.06/2.97  	|
% 9.06/2.97  	| Instantiating (139) with all_73_0_72, all_73_1_73, all_73_2_74 yields:
% 9.06/2.97  	| (189) relation_composition(all_0_12_12, all_0_9_9) = all_73_2_74 & relation_dom(all_73_2_74) = all_73_1_73 & relation_dom(all_0_12_12) = all_73_0_72 & ( ~ in(all_27_0_29, all_21_0_19) |  ~ in(all_7_0_17, all_73_0_72) | in(all_7_0_17, all_73_1_73)) & ( ~ in(all_7_0_17, all_73_1_73) | (in(all_27_0_29, all_21_0_19) & in(all_7_0_17, all_73_0_72)))
% 9.06/2.97  	|
% 9.06/2.97  	| Applying alpha-rule on (189) yields:
% 9.06/2.97  	| (190)  ~ in(all_27_0_29, all_21_0_19) |  ~ in(all_7_0_17, all_73_0_72) | in(all_7_0_17, all_73_1_73)
% 9.06/2.97  	| (191)  ~ in(all_7_0_17, all_73_1_73) | (in(all_27_0_29, all_21_0_19) & in(all_7_0_17, all_73_0_72))
% 9.06/2.97  	| (192) relation_composition(all_0_12_12, all_0_9_9) = all_73_2_74
% 9.06/2.97  	| (193) relation_dom(all_0_12_12) = all_73_0_72
% 9.06/2.97  	| (194) relation_dom(all_73_2_74) = all_73_1_73
% 9.06/2.97  	|
% 9.06/2.97  	| Instantiating (137) with all_77_0_78, all_77_1_79, all_77_2_80 yields:
% 9.06/2.97  	| (195) relation_dom(all_0_8_8) = all_77_2_80 & apply(all_0_9_9, all_77_1_79) = all_77_0_78 & apply(all_0_12_12, all_5_0_16) = all_77_1_79 & (all_77_0_78 = all_25_2_27 |  ~ in(all_5_0_16, all_77_2_80))
% 9.06/2.97  	|
% 9.06/2.97  	| Applying alpha-rule on (195) yields:
% 9.06/2.97  	| (196) relation_dom(all_0_8_8) = all_77_2_80
% 9.06/2.97  	| (197) apply(all_0_9_9, all_77_1_79) = all_77_0_78
% 9.06/2.97  	| (198) apply(all_0_12_12, all_5_0_16) = all_77_1_79
% 9.06/2.97  	| (199) all_77_0_78 = all_25_2_27 |  ~ in(all_5_0_16, all_77_2_80)
% 9.06/2.97  	|
% 9.06/2.97  	| Instantiating (136) with all_79_0_81, all_79_1_82, all_79_2_83 yields:
% 9.06/2.97  	| (200) relation_composition(all_0_12_12, all_0_9_9) = all_79_2_83 & relation_dom(all_79_2_83) = all_79_1_82 & apply(all_0_12_12, all_7_0_17) = all_79_0_81 & ( ~ in(all_79_0_81, all_21_0_19) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_79_1_82)) & ( ~ in(all_7_0_17, all_79_1_82) | (in(all_79_0_81, all_21_0_19) & in(all_7_0_17, all_0_11_11)))
% 9.06/2.97  	|
% 9.06/2.97  	| Applying alpha-rule on (200) yields:
% 9.06/2.97  	| (201) relation_dom(all_79_2_83) = all_79_1_82
% 9.06/2.97  	| (202) relation_composition(all_0_12_12, all_0_9_9) = all_79_2_83
% 9.06/2.97  	| (203) apply(all_0_12_12, all_7_0_17) = all_79_0_81
% 9.06/2.97  	| (204)  ~ in(all_79_0_81, all_21_0_19) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_79_1_82)
% 9.06/2.98  	| (205)  ~ in(all_7_0_17, all_79_1_82) | (in(all_79_0_81, all_21_0_19) & in(all_7_0_17, all_0_11_11))
% 9.06/2.98  	|
% 9.06/2.98  	| Instantiating (148) with all_83_0_87, all_83_1_88, all_83_2_89 yields:
% 9.06/2.98  	| (206) relation_composition(all_0_12_12, all_0_8_8) = all_83_2_89 & relation_dom(all_83_2_89) = all_83_1_88 & relation_dom(all_0_12_12) = all_83_0_87 & ( ~ in(all_0_10_10, all_25_3_28) |  ~ in(all_0_13_13, all_83_0_87) | in(all_0_13_13, all_83_1_88)) & ( ~ in(all_0_13_13, all_83_1_88) | (in(all_0_10_10, all_25_3_28) & in(all_0_13_13, all_83_0_87)))
% 9.06/2.98  	|
% 9.06/2.98  	| Applying alpha-rule on (206) yields:
% 9.06/2.98  	| (207) relation_dom(all_83_2_89) = all_83_1_88
% 9.06/2.98  	| (208)  ~ in(all_0_13_13, all_83_1_88) | (in(all_0_10_10, all_25_3_28) & in(all_0_13_13, all_83_0_87))
% 9.06/2.98  	| (209) relation_composition(all_0_12_12, all_0_8_8) = all_83_2_89
% 9.06/2.98  	| (210)  ~ in(all_0_10_10, all_25_3_28) |  ~ in(all_0_13_13, all_83_0_87) | in(all_0_13_13, all_83_1_88)
% 9.06/2.98  	| (211) relation_dom(all_0_12_12) = all_83_0_87
% 9.06/2.98  	|
% 9.06/2.98  	| Instantiating (146) with all_87_0_93, all_87_1_94, all_87_2_95 yields:
% 9.06/2.98  	| (212) relation_composition(all_0_8_8, all_0_8_8) = all_87_2_95 & relation_dom(all_87_2_95) = all_87_1_94 & relation_dom(all_0_8_8) = all_87_0_93 & ( ~ in(all_25_2_27, all_25_3_28) |  ~ in(all_5_0_16, all_87_0_93) | in(all_5_0_16, all_87_1_94)) & ( ~ in(all_5_0_16, all_87_1_94) | (in(all_25_2_27, all_25_3_28) & in(all_5_0_16, all_87_0_93)))
% 9.06/2.98  	|
% 9.06/2.98  	| Applying alpha-rule on (212) yields:
% 9.06/2.98  	| (213) relation_composition(all_0_8_8, all_0_8_8) = all_87_2_95
% 9.06/2.98  	| (214)  ~ in(all_25_2_27, all_25_3_28) |  ~ in(all_5_0_16, all_87_0_93) | in(all_5_0_16, all_87_1_94)
% 9.06/2.98  	| (215)  ~ in(all_5_0_16, all_87_1_94) | (in(all_25_2_27, all_25_3_28) & in(all_5_0_16, all_87_0_93))
% 9.06/2.98  	| (216) relation_dom(all_87_2_95) = all_87_1_94
% 9.06/2.98  	| (217) relation_dom(all_0_8_8) = all_87_0_93
% 9.06/2.98  	|
% 9.06/2.98  	| Instantiating (144) with all_89_0_96, all_89_1_97, all_89_2_98 yields:
% 9.06/2.98  	| (218) relation_composition(all_0_8_8, all_0_12_12) = all_89_2_98 & relation_dom(all_89_2_98) = all_89_1_97 & relation_dom(all_0_8_8) = all_89_0_96 & ( ~ in(all_25_2_27, all_0_11_11) |  ~ in(all_5_0_16, all_89_0_96) | in(all_5_0_16, all_89_1_97)) & ( ~ in(all_5_0_16, all_89_1_97) | (in(all_25_2_27, all_0_11_11) & in(all_5_0_16, all_89_0_96)))
% 9.06/2.98  	|
% 9.06/2.98  	| Applying alpha-rule on (218) yields:
% 9.06/2.98  	| (219)  ~ in(all_5_0_16, all_89_1_97) | (in(all_25_2_27, all_0_11_11) & in(all_5_0_16, all_89_0_96))
% 9.06/2.98  	| (220) relation_composition(all_0_8_8, all_0_12_12) = all_89_2_98
% 9.06/2.98  	| (221) relation_dom(all_89_2_98) = all_89_1_97
% 9.06/2.98  	| (222) relation_dom(all_0_8_8) = all_89_0_96
% 9.06/2.98  	| (223)  ~ in(all_25_2_27, all_0_11_11) |  ~ in(all_5_0_16, all_89_0_96) | in(all_5_0_16, all_89_1_97)
% 9.06/2.98  	|
% 9.06/2.98  	| Instantiating (143) with all_91_0_99, all_91_1_100, all_91_2_101 yields:
% 9.06/2.98  	| (224) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_101 & relation_dom(all_91_2_101) = all_91_1_100 & relation_dom(all_0_8_8) = all_91_0_99 & ( ~ in(all_0_7_7, all_0_11_11) |  ~ in(all_0_13_13, all_91_0_99) | in(all_0_13_13, all_91_1_100)) & ( ~ in(all_0_13_13, all_91_1_100) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_91_0_99)))
% 9.06/2.98  	|
% 9.06/2.98  	| Applying alpha-rule on (224) yields:
% 9.06/2.98  	| (225) relation_dom(all_91_2_101) = all_91_1_100
% 9.06/2.98  	| (226) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_101
% 9.06/2.98  	| (227)  ~ in(all_0_7_7, all_0_11_11) |  ~ in(all_0_13_13, all_91_0_99) | in(all_0_13_13, all_91_1_100)
% 9.06/2.98  	| (228)  ~ in(all_0_13_13, all_91_1_100) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_91_0_99))
% 9.06/2.98  	| (229) relation_dom(all_0_8_8) = all_91_0_99
% 9.06/2.98  	|
% 9.06/2.98  	| Instantiating (142) with all_93_0_102, all_93_1_103, all_93_2_104 yields:
% 9.06/2.98  	| (230) relation_composition(all_0_12_12, all_0_9_9) = all_93_2_104 & relation_dom(all_93_2_104) = all_93_1_103 & apply(all_93_2_104, all_5_0_16) = all_93_0_102 & (all_93_0_102 = all_25_0_25 |  ~ in(all_5_0_16, all_93_1_103))
% 9.06/2.98  	|
% 9.06/2.98  	| Applying alpha-rule on (230) yields:
% 9.06/2.98  	| (231) relation_composition(all_0_12_12, all_0_9_9) = all_93_2_104
% 9.06/2.99  	| (232) relation_dom(all_93_2_104) = all_93_1_103
% 9.06/2.99  	| (233) apply(all_93_2_104, all_5_0_16) = all_93_0_102
% 9.06/2.99  	| (234) all_93_0_102 = all_25_0_25 |  ~ in(all_5_0_16, all_93_1_103)
% 9.06/2.99  	|
% 9.06/2.99  	| Instantiating (145) with all_95_0_105, all_95_1_106, all_95_2_107 yields:
% 9.06/2.99  	| (235) relation_composition(all_0_8_8, all_0_8_8) = all_95_2_107 & relation_dom(all_95_2_107) = all_95_1_106 & relation_dom(all_0_8_8) = all_95_0_105 & ( ~ in(all_0_7_7, all_25_3_28) |  ~ in(all_0_13_13, all_95_0_105) | in(all_0_13_13, all_95_1_106)) & ( ~ in(all_0_13_13, all_95_1_106) | (in(all_0_7_7, all_25_3_28) & in(all_0_13_13, all_95_0_105)))
% 9.06/2.99  	|
% 9.06/2.99  	| Applying alpha-rule on (235) yields:
% 9.06/2.99  	| (236)  ~ in(all_0_7_7, all_25_3_28) |  ~ in(all_0_13_13, all_95_0_105) | in(all_0_13_13, all_95_1_106)
% 9.06/2.99  	| (237) relation_dom(all_95_2_107) = all_95_1_106
% 9.06/2.99  	| (238) relation_dom(all_0_8_8) = all_95_0_105
% 9.06/2.99  	| (239) relation_composition(all_0_8_8, all_0_8_8) = all_95_2_107
% 9.06/2.99  	| (240)  ~ in(all_0_13_13, all_95_1_106) | (in(all_0_7_7, all_25_3_28) & in(all_0_13_13, all_95_0_105))
% 9.06/2.99  	|
% 9.06/2.99  	| Instantiating (132) with all_99_0_111, all_99_1_112, all_99_2_113 yields:
% 9.06/2.99  	| (241) relation_dom(all_23_2_24) = all_99_2_113 & relation_dom(all_0_12_12) = all_99_1_112 & apply(all_0_12_12, all_9_0_18) = all_99_0_111 & ( ~ in(all_99_0_111, all_0_11_11) |  ~ in(all_9_0_18, all_99_1_112) | in(all_9_0_18, all_99_2_113)) & ( ~ in(all_9_0_18, all_99_2_113) | (in(all_99_0_111, all_0_11_11) & in(all_9_0_18, all_99_1_112)))
% 9.06/2.99  	|
% 9.06/2.99  	| Applying alpha-rule on (241) yields:
% 9.06/2.99  	| (242) relation_dom(all_23_2_24) = all_99_2_113
% 9.06/2.99  	| (243) apply(all_0_12_12, all_9_0_18) = all_99_0_111
% 9.06/2.99  	| (244)  ~ in(all_9_0_18, all_99_2_113) | (in(all_99_0_111, all_0_11_11) & in(all_9_0_18, all_99_1_112))
% 9.06/2.99  	| (245)  ~ in(all_99_0_111, all_0_11_11) |  ~ in(all_9_0_18, all_99_1_112) | in(all_9_0_18, all_99_2_113)
% 9.06/2.99  	| (246) relation_dom(all_0_12_12) = all_99_1_112
% 9.06/2.99  	|
% 9.06/2.99  	| Instantiating (141) with all_101_0_114, all_101_1_115, all_101_2_116 yields:
% 9.06/2.99  	| (247) relation_composition(all_0_12_12, all_0_9_9) = all_101_2_116 & relation_dom(all_101_2_116) = all_101_1_115 & relation_dom(all_0_12_12) = all_101_0_114 & ( ~ in(all_25_1_26, all_21_0_19) |  ~ in(all_5_0_16, all_101_0_114) | in(all_5_0_16, all_101_1_115)) & ( ~ in(all_5_0_16, all_101_1_115) | (in(all_25_1_26, all_21_0_19) & in(all_5_0_16, all_101_0_114)))
% 9.06/2.99  	|
% 9.06/2.99  	| Applying alpha-rule on (247) yields:
% 9.06/2.99  	| (248) relation_composition(all_0_12_12, all_0_9_9) = all_101_2_116
% 9.06/2.99  	| (249)  ~ in(all_5_0_16, all_101_1_115) | (in(all_25_1_26, all_21_0_19) & in(all_5_0_16, all_101_0_114))
% 9.06/2.99  	| (250)  ~ in(all_25_1_26, all_21_0_19) |  ~ in(all_5_0_16, all_101_0_114) | in(all_5_0_16, all_101_1_115)
% 9.06/2.99  	| (251) relation_dom(all_101_2_116) = all_101_1_115
% 9.56/2.99  	| (252) relation_dom(all_0_12_12) = all_101_0_114
% 9.56/2.99  	|
% 9.56/2.99  	| Instantiating (135) with all_105_0_120, all_105_1_121, all_105_2_122 yields:
% 9.56/2.99  	| (253) relation_dom(all_0_8_8) = all_105_2_122 & relation_dom(all_0_12_12) = all_105_1_121 & apply(all_0_12_12, all_9_0_18) = all_105_0_120 & ( ~ in(all_105_0_120, all_21_0_19) |  ~ in(all_9_0_18, all_105_1_121) | in(all_9_0_18, all_105_2_122)) & ( ~ in(all_9_0_18, all_105_2_122) | (in(all_105_0_120, all_21_0_19) & in(all_9_0_18, all_105_1_121)))
% 9.56/2.99  	|
% 9.56/2.99  	| Applying alpha-rule on (253) yields:
% 9.56/2.99  	| (254) relation_dom(all_0_8_8) = all_105_2_122
% 9.56/2.99  	| (255) relation_dom(all_0_12_12) = all_105_1_121
% 9.56/2.99  	| (256)  ~ in(all_105_0_120, all_21_0_19) |  ~ in(all_9_0_18, all_105_1_121) | in(all_9_0_18, all_105_2_122)
% 9.56/2.99  	| (257) apply(all_0_12_12, all_9_0_18) = all_105_0_120
% 9.56/2.99  	| (258)  ~ in(all_9_0_18, all_105_2_122) | (in(all_105_0_120, all_21_0_19) & in(all_9_0_18, all_105_1_121))
% 9.56/2.99  	|
% 9.56/2.99  	| Instantiating (134) with all_107_0_123, all_107_1_124, all_107_2_125 yields:
% 9.56/3.00  	| (259) relation_composition(all_0_12_12, all_0_9_9) = all_107_2_125 & relation_dom(all_107_2_125) = all_107_1_124 & relation_dom(all_0_12_12) = all_107_0_123 & ( ~ in(all_0_10_10, all_21_0_19) |  ~ in(all_0_13_13, all_107_0_123) | in(all_0_13_13, all_107_1_124)) & ( ~ in(all_0_13_13, all_107_1_124) | (in(all_0_10_10, all_21_0_19) & in(all_0_13_13, all_107_0_123)))
% 9.58/3.00  	|
% 9.58/3.00  	| Applying alpha-rule on (259) yields:
% 9.58/3.00  	| (260)  ~ in(all_0_10_10, all_21_0_19) |  ~ in(all_0_13_13, all_107_0_123) | in(all_0_13_13, all_107_1_124)
% 9.58/3.00  	| (261) relation_dom(all_107_2_125) = all_107_1_124
% 9.58/3.00  	| (262)  ~ in(all_0_13_13, all_107_1_124) | (in(all_0_10_10, all_21_0_19) & in(all_0_13_13, all_107_0_123))
% 9.58/3.00  	| (263) relation_composition(all_0_12_12, all_0_9_9) = all_107_2_125
% 9.58/3.00  	| (264) relation_dom(all_0_12_12) = all_107_0_123
% 9.58/3.00  	|
% 9.58/3.00  	| Equations (147) can reduce 19 to:
% 9.58/3.00  	| (265)  ~ (all_0_6_6 = empty_set)
% 9.58/3.00  	|
% 9.58/3.00  	+-Applying beta-rule and splitting (133), into two cases.
% 9.58/3.00  	|-Branch one:
% 9.58/3.00  	| (266) in(all_0_10_10, all_21_0_19)
% 9.58/3.00  	|
% 9.58/3.00  		| Instantiating formula (42) with all_0_12_12, all_0_9_9, all_107_2_125, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_107_2_125, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 9.58/3.00  		| (267) all_107_2_125 = all_0_8_8
% 9.58/3.00  		|
% 9.58/3.00  		| Instantiating formula (42) with all_0_12_12, all_0_9_9, all_101_2_116, all_107_2_125 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_107_2_125, relation_composition(all_0_12_12, all_0_9_9) = all_101_2_116, yields:
% 9.58/3.00  		| (268) all_107_2_125 = all_101_2_116
% 9.58/3.00  		|
% 9.58/3.00  		| Instantiating formula (42) with all_0_12_12, all_0_9_9, all_93_2_104, all_101_2_116 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_101_2_116, relation_composition(all_0_12_12, all_0_9_9) = all_93_2_104, yields:
% 9.58/3.00  		| (269) all_101_2_116 = all_93_2_104
% 9.58/3.00  		|
% 9.60/3.00  		| Instantiating formula (42) with all_0_12_12, all_0_9_9, all_79_2_83, all_93_2_104 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_93_2_104, relation_composition(all_0_12_12, all_0_9_9) = all_79_2_83, yields:
% 9.60/3.00  		| (270) all_93_2_104 = all_79_2_83
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (42) with all_0_12_12, all_0_9_9, all_73_2_74, all_79_2_83 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_79_2_83, relation_composition(all_0_12_12, all_0_9_9) = all_73_2_74, yields:
% 9.60/3.00  		| (271) all_79_2_83 = all_73_2_74
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_95_0_105, all_105_2_122 and discharging atoms relation_dom(all_0_8_8) = all_105_2_122, relation_dom(all_0_8_8) = all_95_0_105, yields:
% 9.60/3.00  		| (272) all_105_2_122 = all_95_0_105
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_91_0_99, all_105_2_122 and discharging atoms relation_dom(all_0_8_8) = all_105_2_122, relation_dom(all_0_8_8) = all_91_0_99, yields:
% 9.60/3.00  		| (273) all_105_2_122 = all_91_0_99
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_89_0_96, all_25_3_28 and discharging atoms relation_dom(all_0_8_8) = all_89_0_96, relation_dom(all_0_8_8) = all_25_3_28, yields:
% 9.60/3.00  		| (274) all_89_0_96 = all_25_3_28
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_87_0_93, all_89_0_96 and discharging atoms relation_dom(all_0_8_8) = all_89_0_96, relation_dom(all_0_8_8) = all_87_0_93, yields:
% 9.60/3.00  		| (275) all_89_0_96 = all_87_0_93
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_77_2_80, all_95_0_105 and discharging atoms relation_dom(all_0_8_8) = all_95_0_105, relation_dom(all_0_8_8) = all_77_2_80, yields:
% 9.60/3.00  		| (276) all_95_0_105 = all_77_2_80
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_77_2_80, all_89_0_96 and discharging atoms relation_dom(all_0_8_8) = all_89_0_96, relation_dom(all_0_8_8) = all_77_2_80, yields:
% 9.60/3.00  		| (277) all_89_0_96 = all_77_2_80
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_63_0_57, all_95_0_105 and discharging atoms relation_dom(all_0_8_8) = all_95_0_105, relation_dom(all_0_8_8) = all_63_0_57, yields:
% 9.60/3.00  		| (278) all_95_0_105 = all_63_0_57
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_8_8, all_53_0_41, all_77_2_80 and discharging atoms relation_dom(all_0_8_8) = all_77_2_80, relation_dom(all_0_8_8) = all_53_0_41, yields:
% 9.60/3.00  		| (279) all_77_2_80 = all_53_0_41
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_12_12, all_99_1_112, all_107_0_123 and discharging atoms relation_dom(all_0_12_12) = all_107_0_123, relation_dom(all_0_12_12) = all_99_1_112, yields:
% 9.60/3.00  		| (280) all_107_0_123 = all_99_1_112
% 9.60/3.00  		|
% 9.60/3.00  		| Instantiating formula (38) with all_0_12_12, all_83_0_87, all_107_0_123 and discharging atoms relation_dom(all_0_12_12) = all_107_0_123, relation_dom(all_0_12_12) = all_83_0_87, yields:
% 9.60/3.01  		| (281) all_107_0_123 = all_83_0_87
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_83_0_87, all_101_0_114 and discharging atoms relation_dom(all_0_12_12) = all_101_0_114, relation_dom(all_0_12_12) = all_83_0_87, yields:
% 9.60/3.01  		| (282) all_101_0_114 = all_83_0_87
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_73_0_72, all_107_0_123 and discharging atoms relation_dom(all_0_12_12) = all_107_0_123, relation_dom(all_0_12_12) = all_73_0_72, yields:
% 9.60/3.01  		| (283) all_107_0_123 = all_73_0_72
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_71_0_69, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_71_0_69, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 9.60/3.01  		| (284) all_71_0_69 = all_0_11_11
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_71_0_69, all_105_1_121 and discharging atoms relation_dom(all_0_12_12) = all_105_1_121, relation_dom(all_0_12_12) = all_71_0_69, yields:
% 9.60/3.01  		| (285) all_105_1_121 = all_71_0_69
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_71_0_69, all_99_1_112 and discharging atoms relation_dom(all_0_12_12) = all_99_1_112, relation_dom(all_0_12_12) = all_71_0_69, yields:
% 9.60/3.01  		| (286) all_99_1_112 = all_71_0_69
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_69_0_66, all_99_1_112 and discharging atoms relation_dom(all_0_12_12) = all_99_1_112, relation_dom(all_0_12_12) = all_69_0_66, yields:
% 9.60/3.01  		| (287) all_99_1_112 = all_69_0_66
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_61_0_54, all_105_1_121 and discharging atoms relation_dom(all_0_12_12) = all_105_1_121, relation_dom(all_0_12_12) = all_61_0_54, yields:
% 9.60/3.01  		| (288) all_105_1_121 = all_61_0_54
% 9.60/3.01  		|
% 9.60/3.01  		| Instantiating formula (38) with all_0_12_12, all_59_0_51, all_101_0_114 and discharging atoms relation_dom(all_0_12_12) = all_101_0_114, relation_dom(all_0_12_12) = all_59_0_51, yields:
% 9.60/3.01  		| (289) all_101_0_114 = all_59_0_51
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (280,283) yields a new equation:
% 9.60/3.01  		| (290) all_99_1_112 = all_73_0_72
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 290 yields:
% 9.60/3.01  		| (291) all_99_1_112 = all_73_0_72
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (281,283) yields a new equation:
% 9.60/3.01  		| (292) all_83_0_87 = all_73_0_72
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 292 yields:
% 9.60/3.01  		| (293) all_83_0_87 = all_73_0_72
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (268,267) yields a new equation:
% 9.60/3.01  		| (294) all_101_2_116 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 294 yields:
% 9.60/3.01  		| (295) all_101_2_116 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (285,288) yields a new equation:
% 9.60/3.01  		| (296) all_71_0_69 = all_61_0_54
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 296 yields:
% 9.60/3.01  		| (297) all_71_0_69 = all_61_0_54
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (272,273) yields a new equation:
% 9.60/3.01  		| (298) all_95_0_105 = all_91_0_99
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 298 yields:
% 9.60/3.01  		| (299) all_95_0_105 = all_91_0_99
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (282,289) yields a new equation:
% 9.60/3.01  		| (300) all_83_0_87 = all_59_0_51
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 300 yields:
% 9.60/3.01  		| (301) all_83_0_87 = all_59_0_51
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (269,295) yields a new equation:
% 9.60/3.01  		| (302) all_93_2_104 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 302 yields:
% 9.60/3.01  		| (303) all_93_2_104 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (291,287) yields a new equation:
% 9.60/3.01  		| (304) all_73_0_72 = all_69_0_66
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 304 yields:
% 9.60/3.01  		| (305) all_73_0_72 = all_69_0_66
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (286,287) yields a new equation:
% 9.60/3.01  		| (306) all_71_0_69 = all_69_0_66
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 306 yields:
% 9.60/3.01  		| (307) all_71_0_69 = all_69_0_66
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (278,299) yields a new equation:
% 9.60/3.01  		| (308) all_91_0_99 = all_63_0_57
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (276,299) yields a new equation:
% 9.60/3.01  		| (309) all_91_0_99 = all_77_2_80
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (270,303) yields a new equation:
% 9.60/3.01  		| (310) all_79_2_83 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 310 yields:
% 9.60/3.01  		| (311) all_79_2_83 = all_0_8_8
% 9.60/3.01  		|
% 9.60/3.01  		| Combining equations (309,308) yields a new equation:
% 9.60/3.01  		| (312) all_77_2_80 = all_63_0_57
% 9.60/3.01  		|
% 9.60/3.01  		| Simplifying 312 yields:
% 9.60/3.01  		| (313) all_77_2_80 = all_63_0_57
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (277,275) yields a new equation:
% 9.60/3.02  		| (314) all_87_0_93 = all_77_2_80
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (274,275) yields a new equation:
% 9.60/3.02  		| (315) all_87_0_93 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (314,315) yields a new equation:
% 9.60/3.02  		| (316) all_77_2_80 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 316 yields:
% 9.60/3.02  		| (317) all_77_2_80 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (293,301) yields a new equation:
% 9.60/3.02  		| (318) all_73_0_72 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 318 yields:
% 9.60/3.02  		| (319) all_73_0_72 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (271,311) yields a new equation:
% 9.60/3.02  		| (320) all_73_2_74 = all_0_8_8
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 320 yields:
% 9.60/3.02  		| (321) all_73_2_74 = all_0_8_8
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (279,313) yields a new equation:
% 9.60/3.02  		| (322) all_63_0_57 = all_53_0_41
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (317,313) yields a new equation:
% 9.60/3.02  		| (323) all_63_0_57 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (305,319) yields a new equation:
% 9.60/3.02  		| (324) all_69_0_66 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 324 yields:
% 9.60/3.02  		| (325) all_69_0_66 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (307,297) yields a new equation:
% 9.60/3.02  		| (326) all_69_0_66 = all_61_0_54
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 326 yields:
% 9.60/3.02  		| (327) all_69_0_66 = all_61_0_54
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (284,297) yields a new equation:
% 9.60/3.02  		| (328) all_61_0_54 = all_0_11_11
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (327,325) yields a new equation:
% 9.60/3.02  		| (329) all_61_0_54 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 329 yields:
% 9.60/3.02  		| (330) all_61_0_54 = all_59_0_51
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (322,323) yields a new equation:
% 9.60/3.02  		| (331) all_53_0_41 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Simplifying 331 yields:
% 9.60/3.02  		| (332) all_53_0_41 = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (328,330) yields a new equation:
% 9.60/3.02  		| (333) all_59_0_51 = all_0_11_11
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (333,319) yields a new equation:
% 9.60/3.02  		| (334) all_73_0_72 = all_0_11_11
% 9.60/3.02  		|
% 9.60/3.02  		| Combining equations (334,283) yields a new equation:
% 9.60/3.02  		| (335) all_107_0_123 = all_0_11_11
% 9.60/3.02  		|
% 9.60/3.02  		| From (267) and (261) follows:
% 9.60/3.02  		| (336) relation_dom(all_0_8_8) = all_107_1_124
% 9.60/3.02  		|
% 9.60/3.02  		| From (295) and (251) follows:
% 9.60/3.02  		| (337) relation_dom(all_0_8_8) = all_101_1_115
% 9.60/3.02  		|
% 9.60/3.02  		| From (303) and (232) follows:
% 9.60/3.02  		| (338) relation_dom(all_0_8_8) = all_93_1_103
% 9.60/3.02  		|
% 9.60/3.02  		| From (311) and (201) follows:
% 9.60/3.02  		| (339) relation_dom(all_0_8_8) = all_79_1_82
% 9.60/3.02  		|
% 9.60/3.02  		| From (321) and (194) follows:
% 9.60/3.02  		| (340) relation_dom(all_0_8_8) = all_73_1_73
% 9.60/3.02  		|
% 9.60/3.02  		| From (332) and (155) follows:
% 9.60/3.02  		| (92) relation_dom(all_0_8_8) = all_25_3_28
% 9.60/3.02  		|
% 9.60/3.02  		+-Applying beta-rule and splitting (260), into two cases.
% 9.60/3.02  		|-Branch one:
% 9.60/3.02  		| (342)  ~ in(all_0_10_10, all_21_0_19)
% 9.60/3.02  		|
% 9.60/3.02  			| Using (266) and (342) yields:
% 9.60/3.02  			| (343) $false
% 9.60/3.02  			|
% 9.60/3.02  			|-The branch is then unsatisfiable
% 9.60/3.02  		|-Branch two:
% 9.60/3.02  		| (266) in(all_0_10_10, all_21_0_19)
% 9.60/3.02  		| (345)  ~ in(all_0_13_13, all_107_0_123) | in(all_0_13_13, all_107_1_124)
% 9.60/3.02  		|
% 9.60/3.02  			+-Applying beta-rule and splitting (345), into two cases.
% 9.60/3.02  			|-Branch one:
% 9.60/3.02  			| (346)  ~ in(all_0_13_13, all_107_0_123)
% 9.60/3.02  			|
% 9.60/3.02  				| From (335) and (346) follows:
% 9.60/3.03  				| (347)  ~ in(all_0_13_13, all_0_11_11)
% 9.60/3.03  				|
% 9.60/3.03  				| Using (9) and (347) yields:
% 9.60/3.03  				| (343) $false
% 9.60/3.03  				|
% 9.60/3.03  				|-The branch is then unsatisfiable
% 9.60/3.03  			|-Branch two:
% 9.60/3.03  			| (349) in(all_0_13_13, all_107_0_123)
% 9.60/3.03  			| (350) in(all_0_13_13, all_107_1_124)
% 9.60/3.03  			|
% 9.60/3.03  				| Instantiating formula (38) with all_0_8_8, all_101_1_115, all_107_1_124 and discharging atoms relation_dom(all_0_8_8) = all_107_1_124, relation_dom(all_0_8_8) = all_101_1_115, yields:
% 9.60/3.03  				| (351) all_107_1_124 = all_101_1_115
% 9.60/3.03  				|
% 9.60/3.03  				| Instantiating formula (38) with all_0_8_8, all_93_1_103, all_25_3_28 and discharging atoms relation_dom(all_0_8_8) = all_93_1_103, relation_dom(all_0_8_8) = all_25_3_28, yields:
% 9.60/3.03  				| (352) all_93_1_103 = all_25_3_28
% 9.60/3.03  				|
% 9.60/3.03  				| Instantiating formula (38) with all_0_8_8, all_79_1_82, all_101_1_115 and discharging atoms relation_dom(all_0_8_8) = all_101_1_115, relation_dom(all_0_8_8) = all_79_1_82, yields:
% 9.60/3.03  				| (353) all_101_1_115 = all_79_1_82
% 9.60/3.03  				|
% 9.60/3.03  				| Instantiating formula (38) with all_0_8_8, all_79_1_82, all_93_1_103 and discharging atoms relation_dom(all_0_8_8) = all_93_1_103, relation_dom(all_0_8_8) = all_79_1_82, yields:
% 9.60/3.03  				| (354) all_93_1_103 = all_79_1_82
% 9.60/3.03  				|
% 9.60/3.03  				| Instantiating formula (38) with all_0_8_8, all_73_1_73, all_107_1_124 and discharging atoms relation_dom(all_0_8_8) = all_107_1_124, relation_dom(all_0_8_8) = all_73_1_73, yields:
% 9.60/3.03  				| (355) all_107_1_124 = all_73_1_73
% 9.60/3.03  				|
% 9.60/3.03  				| Combining equations (351,355) yields a new equation:
% 9.60/3.03  				| (356) all_101_1_115 = all_73_1_73
% 9.60/3.03  				|
% 9.60/3.03  				| Simplifying 356 yields:
% 9.60/3.03  				| (357) all_101_1_115 = all_73_1_73
% 9.60/3.03  				|
% 9.60/3.03  				| Combining equations (353,357) yields a new equation:
% 9.60/3.03  				| (358) all_79_1_82 = all_73_1_73
% 9.60/3.03  				|
% 9.60/3.03  				| Simplifying 358 yields:
% 9.60/3.03  				| (359) all_79_1_82 = all_73_1_73
% 9.60/3.03  				|
% 9.60/3.03  				| Combining equations (354,352) yields a new equation:
% 9.60/3.03  				| (360) all_79_1_82 = all_25_3_28
% 9.60/3.03  				|
% 9.60/3.03  				| Simplifying 360 yields:
% 9.60/3.03  				| (361) all_79_1_82 = all_25_3_28
% 9.60/3.03  				|
% 9.60/3.03  				| Combining equations (361,359) yields a new equation:
% 9.60/3.03  				| (362) all_73_1_73 = all_25_3_28
% 9.60/3.03  				|
% 9.60/3.03  				| Combining equations (362,355) yields a new equation:
% 9.60/3.03  				| (363) all_107_1_124 = all_25_3_28
% 9.60/3.03  				|
% 9.60/3.03  				| From (363) and (350) follows:
% 9.60/3.03  				| (364) in(all_0_13_13, all_25_3_28)
% 9.60/3.03  				|
% 9.60/3.03  				| Using (364) and (131) yields:
% 9.60/3.03  				| (343) $false
% 9.60/3.03  				|
% 9.60/3.03  				|-The branch is then unsatisfiable
% 9.60/3.03  	|-Branch two:
% 9.60/3.03  	| (342)  ~ in(all_0_10_10, all_21_0_19)
% 9.60/3.03  	| (367) all_0_6_6 = empty_set
% 9.60/3.03  	|
% 9.60/3.03  		| Equations (367) can reduce 265 to:
% 9.60/3.03  		| (368) $false
% 9.60/3.03  		|
% 9.60/3.03  		|-The branch is then unsatisfiable
% 9.60/3.03  |-Branch two:
% 9.60/3.03  | (369) in(all_0_13_13, all_29_1_33)
% 9.60/3.03  | (370) all_29_0_32 = all_0_6_6
% 9.60/3.03  |
% 9.60/3.03  	| Combining equations (370,125) yields a new equation:
% 9.60/3.03  	| (371) all_0_6_6 = all_0_7_7
% 9.60/3.03  	|
% 9.60/3.03  	| Simplifying 371 yields:
% 9.60/3.03  	| (372) all_0_6_6 = all_0_7_7
% 9.60/3.03  	|
% 9.60/3.03  	| Equations (372) can reduce 19 to:
% 9.60/3.03  	| (368) $false
% 9.60/3.03  	|
% 9.60/3.03  	|-The branch is then unsatisfiable
% 9.60/3.03  % SZS output end Proof for theBenchmark
% 9.60/3.03  
% 9.60/3.03  2436ms
%------------------------------------------------------------------------------