%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:47:44 EDT 2022

% Result   : Theorem 4.10s 1.62s
% Output   : Proof 7.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n007.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 10:22:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.58/0.58          ____       _                          
% 0.58/0.58    ___  / __ \_____(_)___  ________  __________
% 0.58/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.58  
% 0.58/0.58  A Theorem Prover for First-Order Logic
% 0.58/0.59  (ePrincess v.1.0)
% 0.58/0.59  
% 0.58/0.59  (c) Philipp Rümmer, 2009-2015
% 0.58/0.59  (c) Peter Backeman, 2014-2015
% 0.58/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59  Bug reports to peter@backeman.se
% 0.58/0.59  
% 0.58/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59  
% 0.58/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.96  Prover 0: Preprocessing ...
% 2.44/1.26  Prover 0: Warning: ignoring some quantifiers
% 2.74/1.29  Prover 0: Constructing countermodel ...
% 4.10/1.62  Prover 0: proved (983ms)
% 4.10/1.62  
% 4.10/1.62  No countermodel exists, formula is valid
% 4.10/1.62  % SZS status Theorem for theBenchmark
% 4.10/1.62  
% 4.10/1.62  Generating proof ... Warning: ignoring some quantifiers
% 6.86/2.21  found it (size 211)
% 6.86/2.21  
% 6.86/2.21  % SZS output start Proof for theBenchmark
% 6.86/2.21  Assumed formulas after preprocessing and simplification: 
% 6.86/2.21  | (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] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) |  ~ empty(v16) |  ~ in(v14, v15)) &  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (powerset(v16) = v17) |  ~ element(v15, v17) |  ~ in(v14, v15) | element(v14, v16)) &  ? [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 |  ~ (powerset(v16) = v15) |  ~ (powerset(v16) = v14)) &  ! [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] : ( ~ (powerset(v15) = v16) |  ~ subset(v14, v15) | element(v14, v16)) &  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (powerset(v15) = v16) |  ~ element(v14, v16) | subset(v14, v15)) &  ! [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] : ( ~ (powerset(v14) = v15) |  ~ empty(v15)) &  ! [v14] :  ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) |  ? [v16] : (element(v16, v15) &  ~ empty(v16))) &  ! [v14] :  ! [v15] : ( ~ (powerset(v14) = v15) |  ? [v16] : (element(v16, v15) & empty(v16))) &  ! [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) &  ? [v14] : subset(v14, v14))
% 6.86/2.25  | 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:
% 6.86/2.25  | (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] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (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 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [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] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_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] : ( ~ (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] : ( ~ (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) &  ? [v0] : subset(v0, v0)
% 6.86/2.27  |
% 6.86/2.27  | Applying alpha-rule on (1) yields:
% 6.86/2.27  | (2)  ~ empty(all_0_4_4)
% 6.86/2.27  | (3)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ relation(v0) |  ~ empty(v1) | empty(v0))
% 6.86/2.27  | (4)  ! [v0] :  ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.86/2.27  | (5) function(all_0_9_9)
% 6.86/2.27  | (6)  ? [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))))
% 6.86/2.27  | (7)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | empty(v1))
% 6.86/2.27  | (8) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8
% 6.86/2.27  | (9)  ? [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)))))
% 6.86/2.27  | (10)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ~ empty(v1))
% 6.86/2.27  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 6.86/2.27  | (12)  ! [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)))))
% 7.30/2.27  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 7.30/2.27  | (14)  ! [v0] :  ! [v1] : ( ~ (relation_dom(v0) = v1) |  ~ empty(v0) | relation(v1))
% 7.30/2.27  | (15)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 7.30/2.27  | (16) relation_dom(all_0_12_12) = all_0_11_11
% 7.30/2.27  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 7.30/2.27  | (18) relation(empty_set)
% 7.30/2.27  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 7.30/2.27  | (20) relation(all_0_12_12)
% 7.30/2.27  | (21)  ? [v0] : subset(v0, v0)
% 7.30/2.27  | (22)  ~ (all_0_6_6 = all_0_7_7)
% 7.30/2.27  | (23) empty(empty_set)
% 7.30/2.27  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 7.30/2.27  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 7.30/2.28  | (26) function(all_0_12_12)
% 7.30/2.28  | (27) apply(all_0_12_12, all_0_13_13) = all_0_10_10
% 7.30/2.28  | (28)  ~ empty(all_0_3_3)
% 7.30/2.28  | (29)  ! [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))))
% 7.30/2.28  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v1, v0) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 7.30/2.28  | (31)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ~ empty(v1))
% 7.30/2.28  | (32) function(all_0_0_0)
% 7.30/2.28  | (33) in(all_0_13_13, all_0_11_11)
% 7.30/2.28  | (34)  ? [v0] :  ? [v1] : element(v1, v0)
% 7.30/2.28  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 7.30/2.28  | (36) relation(all_0_5_5)
% 7.30/2.28  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 7.30/2.28  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 7.30/2.28  | (39) apply(all_0_8_8, all_0_13_13) = all_0_7_7
% 7.30/2.28  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | function(v2))
% 7.30/2.28  | (41) empty(all_0_1_1)
% 7.30/2.28  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 7.30/2.28  | (43)  ! [v0] : ( ~ empty(v0) | function(v0))
% 7.30/2.28  | (44)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 7.30/2.28  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 7.30/2.28  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 7.30/2.28  | (47)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) & empty(v2)))
% 7.30/2.28  | (48) relation_empty_yielding(empty_set)
% 7.30/2.28  | (49)  ! [v0] :  ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 7.30/2.28  | (50)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 7.30/2.28  | (51)  ! [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))))
% 7.30/2.28  | (52)  ! [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))))
% 7.30/2.28  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = empty_set |  ~ (relation_dom(v0) = v1) |  ~ (apply(v0, v2) = v3) |  ~ relation(v0) |  ~ function(v0) | in(v2, v1))
% 7.30/2.28  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) = v0))
% 7.30/2.28  | (55)  ! [v0] : ( ~ empty(v0) | relation(v0))
% 7.30/2.29  | (56) apply(all_0_9_9, all_0_10_10) = all_0_6_6
% 7.30/2.29  | (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)))))
% 7.30/2.29  | (58)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | relation(v2))
% 7.30/2.29  | (59)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) |  ? [v2] : (element(v2, v1) &  ~ empty(v2)))
% 7.30/2.29  | (60) relation(all_0_9_9)
% 7.30/2.29  | (61) relation(all_0_1_1)
% 7.30/2.29  | (62) empty(all_0_2_2)
% 7.30/2.29  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 7.30/2.29  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 7.30/2.29  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ empty(v0) | empty(v2))
% 7.30/2.29  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ empty(v2) |  ~ in(v0, v1))
% 7.30/2.29  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ~ element(v1, v3) |  ~ in(v0, v1) | element(v0, v2))
% 7.30/2.29  | (68) relation(all_0_0_0)
% 7.30/2.29  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ element(v0, v2) | subset(v0, v1))
% 7.30/2.29  | (70)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v1) = v2) |  ~ subset(v0, v1) | element(v0, v2))
% 7.30/2.29  | (71) relation(all_0_3_3)
% 7.30/2.29  | (72)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) | relation(v2))
% 7.30/2.29  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (relation_composition(v0, v1) = v2) |  ~ relation(v1) |  ~ relation(v0) |  ~ function(v1) |  ~ function(v0) | relation(v2))
% 7.30/2.29  | (74) relation_empty_yielding(all_0_5_5)
% 7.30/2.29  |
% 7.30/2.29  | Instantiating (6) with all_5_0_16 yields:
% 7.30/2.29  | (75)  ! [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))))
% 7.40/2.29  |
% 7.40/2.29  | Instantiating (57) with all_7_0_17 yields:
% 7.40/2.29  | (76)  ! [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)))))
% 7.40/2.29  |
% 7.40/2.29  | Instantiating (9) with all_11_0_19 yields:
% 7.40/2.29  | (77)  ! [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_11_0_19) = v6 & ( ~ in(v6, v1) |  ~ in(all_11_0_19, v5) | in(all_11_0_19, v4)) & ( ~ in(all_11_0_19, v4) | (in(v6, v1) & in(all_11_0_19, v5)))))
% 7.40/2.29  |
% 7.40/2.29  | Instantiating formula (52) 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:
% 7.40/2.29  | (78)  ? [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)))
% 7.40/2.29  |
% 7.40/2.29  | Instantiating formula (73) 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:
% 7.40/2.29  | (79) relation(all_0_8_8)
% 7.40/2.29  |
% 7.40/2.29  | Instantiating formula (40) 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:
% 7.40/2.30  | (80) function(all_0_8_8)
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (75) 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:
% 7.40/2.30  | (81)  ? [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)))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (12) 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:
% 7.40/2.30  | (82)  ? [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))))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (76) 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:
% 7.40/2.30  | (83)  ? [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))))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (12) 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:
% 7.40/2.30  | (84)  ? [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))))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (51) 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:
% 7.40/2.30  | (85)  ? [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)))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (84) with all_23_0_20, all_23_1_21, all_23_2_22 yields:
% 7.40/2.30  | (86) relation_composition(all_0_9_9, all_0_12_12) = all_23_2_22 & relation_dom(all_23_2_22) = all_23_1_21 & relation_dom(all_0_9_9) = all_23_0_20 & ( ~ in(all_0_6_6, all_0_11_11) |  ~ in(all_0_10_10, all_23_0_20) | in(all_0_10_10, all_23_1_21)) & ( ~ in(all_0_10_10, all_23_1_21) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_23_0_20)))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (86) yields:
% 7.40/2.30  | (87) relation_dom(all_0_9_9) = all_23_0_20
% 7.40/2.30  | (88)  ~ in(all_0_10_10, all_23_1_21) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_23_0_20))
% 7.40/2.30  | (89) relation_dom(all_23_2_22) = all_23_1_21
% 7.40/2.30  | (90) relation_composition(all_0_9_9, all_0_12_12) = all_23_2_22
% 7.40/2.30  | (91)  ~ in(all_0_6_6, all_0_11_11) |  ~ in(all_0_10_10, all_23_0_20) | in(all_0_10_10, all_23_1_21)
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (82) with all_25_0_23, all_25_1_24, all_25_2_25 yields:
% 7.40/2.30  | (92) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25 & relation_dom(all_25_2_25) = all_25_1_24 & relation_dom(all_0_12_12) = all_25_0_23 & ( ~ in(all_0_10_10, all_0_11_11) |  ~ in(all_0_13_13, all_25_0_23) | in(all_0_13_13, all_25_1_24)) & ( ~ in(all_0_13_13, all_25_1_24) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_25_0_23)))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (92) yields:
% 7.40/2.30  | (93) relation_dom(all_25_2_25) = all_25_1_24
% 7.40/2.30  | (94)  ~ in(all_0_10_10, all_0_11_11) |  ~ in(all_0_13_13, all_25_0_23) | in(all_0_13_13, all_25_1_24)
% 7.40/2.30  | (95) relation_dom(all_0_12_12) = all_25_0_23
% 7.40/2.30  | (96) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25
% 7.40/2.30  | (97)  ~ in(all_0_13_13, all_25_1_24) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_25_0_23))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (81) with all_27_0_26, all_27_1_27, all_27_2_28, all_27_3_29 yields:
% 7.40/2.30  | (98) relation_dom(all_0_8_8) = all_27_3_29 & apply(all_0_8_8, all_5_0_16) = all_27_2_28 & apply(all_0_9_9, all_27_1_27) = all_27_0_26 & apply(all_0_12_12, all_5_0_16) = all_27_1_27 & (all_27_0_26 = all_27_2_28 |  ~ in(all_5_0_16, all_27_3_29))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (98) yields:
% 7.40/2.30  | (99) all_27_0_26 = all_27_2_28 |  ~ in(all_5_0_16, all_27_3_29)
% 7.40/2.30  | (100) apply(all_0_8_8, all_5_0_16) = all_27_2_28
% 7.40/2.30  | (101) apply(all_0_12_12, all_5_0_16) = all_27_1_27
% 7.40/2.30  | (102) apply(all_0_9_9, all_27_1_27) = all_27_0_26
% 7.40/2.30  | (103) relation_dom(all_0_8_8) = all_27_3_29
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (83) with all_29_0_30, all_29_1_31, all_29_2_32 yields:
% 7.40/2.30  | (104) relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32 & relation_dom(all_29_2_32) = all_29_1_31 & apply(all_0_12_12, all_7_0_17) = all_29_0_30 & ( ~ in(all_29_0_30, all_0_11_11) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_29_1_31)) & ( ~ in(all_7_0_17, all_29_1_31) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_0_11_11)))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (104) yields:
% 7.40/2.30  | (105) relation_dom(all_29_2_32) = all_29_1_31
% 7.40/2.30  | (106) relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32
% 7.40/2.30  | (107) apply(all_0_12_12, all_7_0_17) = all_29_0_30
% 7.40/2.30  | (108)  ~ in(all_29_0_30, all_0_11_11) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_29_1_31)
% 7.40/2.30  | (109)  ~ in(all_7_0_17, all_29_1_31) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_0_11_11))
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (85) with all_31_0_33, all_31_1_34, all_31_2_35 yields:
% 7.40/2.30  | (110) relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35 & relation_dom(all_31_2_35) = all_31_1_34 & apply(all_31_2_35, all_0_13_13) = all_31_0_33 & (all_31_0_33 = all_0_6_6 |  ~ in(all_0_13_13, all_31_1_34))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (110) yields:
% 7.40/2.30  | (111) relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35
% 7.40/2.30  | (112) relation_dom(all_31_2_35) = all_31_1_34
% 7.40/2.30  | (113) apply(all_31_2_35, all_0_13_13) = all_31_0_33
% 7.40/2.30  | (114) all_31_0_33 = all_0_6_6 |  ~ in(all_0_13_13, all_31_1_34)
% 7.40/2.30  |
% 7.40/2.30  | Instantiating (78) with all_33_0_36, all_33_1_37, all_33_2_38 yields:
% 7.40/2.30  | (115) relation_dom(all_0_8_8) = all_33_2_38 & apply(all_0_9_9, all_33_1_37) = all_33_0_36 & apply(all_0_12_12, all_0_13_13) = all_33_1_37 & (all_33_0_36 = all_0_7_7 |  ~ in(all_0_13_13, all_33_2_38))
% 7.40/2.30  |
% 7.40/2.30  | Applying alpha-rule on (115) yields:
% 7.40/2.30  | (116) relation_dom(all_0_8_8) = all_33_2_38
% 7.40/2.30  | (117) apply(all_0_9_9, all_33_1_37) = all_33_0_36
% 7.40/2.30  | (118) apply(all_0_12_12, all_0_13_13) = all_33_1_37
% 7.40/2.30  | (119) all_33_0_36 = all_0_7_7 |  ~ in(all_0_13_13, all_33_2_38)
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (54) with all_0_12_12, all_0_9_9, all_31_2_35, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_31_2_35, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 7.40/2.30  | (120) all_31_2_35 = all_0_8_8
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (54) with all_0_12_12, all_0_12_12, all_25_2_25, all_29_2_32 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_29_2_32, relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25, yields:
% 7.40/2.30  | (121) all_29_2_32 = all_25_2_25
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (38) with all_0_8_8, all_27_3_29, all_33_2_38 and discharging atoms relation_dom(all_0_8_8) = all_33_2_38, relation_dom(all_0_8_8) = all_27_3_29, yields:
% 7.40/2.30  | (122) all_33_2_38 = all_27_3_29
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (38) with all_0_12_12, all_25_0_23, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_25_0_23, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 7.40/2.30  | (123) all_25_0_23 = all_0_11_11
% 7.40/2.30  |
% 7.40/2.30  | Instantiating formula (13) with all_0_12_12, all_0_13_13, all_33_1_37, all_0_10_10 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_33_1_37, apply(all_0_12_12, all_0_13_13) = all_0_10_10, yields:
% 7.40/2.31  | (124) all_33_1_37 = all_0_10_10
% 7.40/2.31  |
% 7.40/2.31  | From (120) and (111) follows:
% 7.40/2.31  | (8) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8
% 7.40/2.31  |
% 7.40/2.31  | From (121) and (106) follows:
% 7.40/2.31  | (96) relation_composition(all_0_12_12, all_0_12_12) = all_25_2_25
% 7.40/2.31  |
% 7.40/2.31  | From (120) and (112) follows:
% 7.40/2.31  | (127) relation_dom(all_0_8_8) = all_31_1_34
% 7.40/2.31  |
% 7.40/2.31  | From (122) and (116) follows:
% 7.40/2.31  | (103) relation_dom(all_0_8_8) = all_27_3_29
% 7.40/2.31  |
% 7.40/2.31  | From (123) and (95) follows:
% 7.40/2.31  | (16) relation_dom(all_0_12_12) = all_0_11_11
% 7.40/2.31  |
% 7.40/2.31  | From (120) and (113) follows:
% 7.40/2.31  | (130) apply(all_0_8_8, all_0_13_13) = all_31_0_33
% 7.40/2.31  |
% 7.40/2.31  | From (124) and (117) follows:
% 7.40/2.31  | (131) apply(all_0_9_9, all_0_10_10) = all_33_0_36
% 7.40/2.31  |
% 7.40/2.31  | From (124) and (118) follows:
% 7.40/2.31  | (27) apply(all_0_12_12, all_0_13_13) = all_0_10_10
% 7.40/2.31  |
% 7.40/2.31  | Instantiating formula (38) with all_0_8_8, all_31_1_34, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_31_1_34, relation_dom(all_0_8_8) = all_27_3_29, yields:
% 7.40/2.31  | (133) all_31_1_34 = all_27_3_29
% 7.40/2.31  |
% 7.40/2.31  | Instantiating formula (13) with all_0_8_8, all_0_13_13, all_31_0_33, all_0_7_7 and discharging atoms apply(all_0_8_8, all_0_13_13) = all_31_0_33, apply(all_0_8_8, all_0_13_13) = all_0_7_7, yields:
% 7.40/2.31  | (134) all_31_0_33 = all_0_7_7
% 7.40/2.31  |
% 7.40/2.31  | Instantiating formula (13) with all_0_9_9, all_0_10_10, all_33_0_36, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_33_0_36, apply(all_0_9_9, all_0_10_10) = all_0_6_6, yields:
% 7.40/2.31  | (135) all_33_0_36 = all_0_6_6
% 7.40/2.31  |
% 7.40/2.31  | From (133) and (127) follows:
% 7.40/2.31  | (103) relation_dom(all_0_8_8) = all_27_3_29
% 7.40/2.31  |
% 7.40/2.31  | From (134) and (130) follows:
% 7.40/2.31  | (39) apply(all_0_8_8, all_0_13_13) = all_0_7_7
% 7.40/2.31  |
% 7.40/2.31  | From (135) and (131) follows:
% 7.40/2.31  | (56) apply(all_0_9_9, all_0_10_10) = all_0_6_6
% 7.40/2.31  |
% 7.40/2.31  +-Applying beta-rule and splitting (114), into two cases.
% 7.40/2.31  |-Branch one:
% 7.40/2.31  | (139)  ~ in(all_0_13_13, all_31_1_34)
% 7.40/2.31  |
% 7.40/2.31  	| From (133) and (139) follows:
% 7.40/2.31  	| (140)  ~ in(all_0_13_13, all_27_3_29)
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (77) with all_25_2_25, 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_25_2_25, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.40/2.31  	| (141)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_25_2_25) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_11_0_19) = v2 & ( ~ in(v2, all_0_11_11) |  ~ in(all_11_0_19, v1) | in(all_11_0_19, v0)) & ( ~ in(all_11_0_19, v0) | (in(v2, all_0_11_11) & in(all_11_0_19, v1))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (53) with all_0_6_6, all_0_10_10, all_23_0_20, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), function(all_0_9_9), yields:
% 7.40/2.31  	| (142) all_0_6_6 = empty_set | in(all_0_10_10, all_23_0_20)
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (12) with all_0_10_10, all_0_12_12, all_23_0_20, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, 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:
% 7.40/2.31  	| (143)  ? [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_23_0_20) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, v2))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (77) with all_0_8_8, all_0_12_12, all_23_0_20, 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_23_0_20, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 7.40/2.31  	| (144)  ? [v0] :  ? [v1] :  ? [v2] : (relation_dom(all_0_8_8) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_11_0_19) = v2 & ( ~ in(v2, all_23_0_20) |  ~ in(all_11_0_19, v1) | in(all_11_0_19, v0)) & ( ~ in(all_11_0_19, v0) | (in(v2, all_23_0_20) & in(all_11_0_19, v1))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (76) with all_0_11_11, all_0_12_12, all_23_0_20, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, 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:
% 7.40/2.31  	| (145)  ? [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_23_0_20) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(v2, all_23_0_20) & in(all_7_0_17, all_0_11_11))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (52) with all_27_2_28, 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_27_2_28, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 7.40/2.31  	| (146)  ? [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_27_2_28 |  ~ in(all_5_0_16, v0)))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (12) with all_29_0_30, 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_29_0_30, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.40/2.31  	| (147)  ? [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_29_0_30, all_0_11_11) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, v2))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (12) with all_29_0_30, all_0_12_12, all_23_0_20, all_0_9_9, all_7_0_17 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_12_12, all_7_0_17) = all_29_0_30, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 7.40/2.31  	| (148)  ? [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_29_0_30, all_23_0_20) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, v2))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (12) with all_27_1_27, 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_27_1_27, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.40/2.31  	| (149)  ? [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_1_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_27_1_27, all_0_11_11) & in(all_5_0_16, v2))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (12) with all_27_1_27, all_0_12_12, all_23_0_20, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 7.40/2.31  	| (150)  ? [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_1_27, all_23_0_20) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, v2))))
% 7.40/2.31  	|
% 7.40/2.31  	| Instantiating formula (51) with all_27_0_26, all_27_1_27, all_0_12_12, all_0_9_9, all_5_0_16 and discharging atoms apply(all_0_9_9, all_27_1_27) = all_27_0_26, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields:
% 7.40/2.32  	| (151)  ? [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_27_0_26 |  ~ in(all_5_0_16, v1)))
% 7.40/2.32  	|
% 7.40/2.32  	| Instantiating formula (12) 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:
% 7.40/2.32  	| (152)  ? [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))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_27_2_28, 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_27_2_28, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 7.52/2.32  	| (153)  ? [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_27_2_28, all_0_11_11) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_0_7_7, all_0_8_8, all_27_3_29, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), yields:
% 7.52/2.32  	| (154)  ? [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_27_3_29) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_27_2_28, all_0_8_8, all_27_3_29, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_8_8), function(all_0_8_8), yields:
% 7.52/2.32  	| (155)  ? [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_27_2_28, all_27_3_29) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (53) with all_0_7_7, all_0_13_13, all_27_3_29, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, 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_27_3_29), yields:
% 7.52/2.32  	| (156) all_0_7_7 = empty_set
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_0_10_10, all_0_12_12, all_27_3_29, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, 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:
% 7.52/2.32  	| (157)  ? [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_27_3_29) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_29_0_30, all_0_12_12, all_27_3_29, all_0_8_8, all_7_0_17 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_12_12, all_7_0_17) = all_29_0_30, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 7.52/2.32  	| (158)  ? [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_29_0_30, all_27_3_29) |  ~ in(all_7_0_17, v2) | in(all_7_0_17, v1)) & ( ~ in(all_7_0_17, v1) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_27_1_27, all_0_12_12, all_27_3_29, all_0_8_8, all_5_0_16 and discharging atoms relation_dom(all_0_8_8) = all_27_3_29, apply(all_0_12_12, all_5_0_16) = all_27_1_27, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields:
% 7.52/2.32  	| (159)  ? [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_1_27, all_27_3_29) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_0_7_7, all_0_8_8, all_23_0_20, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, 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:
% 7.52/2.32  	| (160)  ? [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_23_0_20) |  ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating formula (12) with all_27_2_28, all_0_8_8, all_23_0_20, all_0_9_9, all_5_0_16 and discharging atoms relation_dom(all_0_9_9) = all_23_0_20, apply(all_0_8_8, all_5_0_16) = all_27_2_28, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields:
% 7.52/2.32  	| (161)  ? [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_27_2_28, all_23_0_20) |  ~ in(all_5_0_16, v2) | in(all_5_0_16, v1)) & ( ~ in(all_5_0_16, v1) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, v2))))
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating (161) with all_55_0_42, all_55_1_43, all_55_2_44 yields:
% 7.52/2.32  	| (162) relation_composition(all_0_8_8, all_0_9_9) = all_55_2_44 & relation_dom(all_55_2_44) = all_55_1_43 & relation_dom(all_0_8_8) = all_55_0_42 & ( ~ in(all_27_2_28, all_23_0_20) |  ~ in(all_5_0_16, all_55_0_42) | in(all_5_0_16, all_55_1_43)) & ( ~ in(all_5_0_16, all_55_1_43) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, all_55_0_42)))
% 7.52/2.32  	|
% 7.52/2.32  	| Applying alpha-rule on (162) yields:
% 7.52/2.32  	| (163)  ~ in(all_5_0_16, all_55_1_43) | (in(all_27_2_28, all_23_0_20) & in(all_5_0_16, all_55_0_42))
% 7.52/2.32  	| (164) relation_dom(all_55_2_44) = all_55_1_43
% 7.52/2.32  	| (165) relation_dom(all_0_8_8) = all_55_0_42
% 7.52/2.32  	| (166) relation_composition(all_0_8_8, all_0_9_9) = all_55_2_44
% 7.52/2.32  	| (167)  ~ in(all_27_2_28, all_23_0_20) |  ~ in(all_5_0_16, all_55_0_42) | in(all_5_0_16, all_55_1_43)
% 7.52/2.32  	|
% 7.52/2.32  	| Instantiating (159) with all_61_0_52, all_61_1_53, all_61_2_54 yields:
% 7.52/2.32  	| (168) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_54 & relation_dom(all_61_2_54) = all_61_1_53 & relation_dom(all_0_12_12) = all_61_0_52 & ( ~ in(all_27_1_27, all_27_3_29) |  ~ in(all_5_0_16, all_61_0_52) | in(all_5_0_16, all_61_1_53)) & ( ~ in(all_5_0_16, all_61_1_53) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, all_61_0_52)))
% 7.55/2.32  	|
% 7.55/2.32  	| Applying alpha-rule on (168) yields:
% 7.55/2.32  	| (169)  ~ in(all_5_0_16, all_61_1_53) | (in(all_27_1_27, all_27_3_29) & in(all_5_0_16, all_61_0_52))
% 7.55/2.32  	| (170)  ~ in(all_27_1_27, all_27_3_29) |  ~ in(all_5_0_16, all_61_0_52) | in(all_5_0_16, all_61_1_53)
% 7.55/2.32  	| (171) relation_dom(all_0_12_12) = all_61_0_52
% 7.55/2.32  	| (172) relation_composition(all_0_12_12, all_0_8_8) = all_61_2_54
% 7.55/2.32  	| (173) relation_dom(all_61_2_54) = all_61_1_53
% 7.55/2.32  	|
% 7.55/2.32  	| Instantiating (158) with all_63_0_55, all_63_1_56, all_63_2_57 yields:
% 7.55/2.32  	| (174) relation_composition(all_0_12_12, all_0_8_8) = all_63_2_57 & relation_dom(all_63_2_57) = all_63_1_56 & relation_dom(all_0_12_12) = all_63_0_55 & ( ~ in(all_29_0_30, all_27_3_29) |  ~ in(all_7_0_17, all_63_0_55) | in(all_7_0_17, all_63_1_56)) & ( ~ in(all_7_0_17, all_63_1_56) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, all_63_0_55)))
% 7.55/2.32  	|
% 7.55/2.32  	| Applying alpha-rule on (174) yields:
% 7.55/2.32  	| (175)  ~ in(all_7_0_17, all_63_1_56) | (in(all_29_0_30, all_27_3_29) & in(all_7_0_17, all_63_0_55))
% 7.55/2.32  	| (176)  ~ in(all_29_0_30, all_27_3_29) |  ~ in(all_7_0_17, all_63_0_55) | in(all_7_0_17, all_63_1_56)
% 7.55/2.32  	| (177) relation_dom(all_0_12_12) = all_63_0_55
% 7.55/2.32  	| (178) relation_dom(all_63_2_57) = all_63_1_56
% 7.55/2.32  	| (179) relation_composition(all_0_12_12, all_0_8_8) = all_63_2_57
% 7.55/2.32  	|
% 7.55/2.32  	| Instantiating (160) with all_65_0_58, all_65_1_59, all_65_2_60 yields:
% 7.55/2.32  	| (180) relation_composition(all_0_8_8, all_0_9_9) = all_65_2_60 & relation_dom(all_65_2_60) = all_65_1_59 & relation_dom(all_0_8_8) = all_65_0_58 & ( ~ in(all_0_7_7, all_23_0_20) |  ~ in(all_0_13_13, all_65_0_58) | in(all_0_13_13, all_65_1_59)) & ( ~ in(all_0_13_13, all_65_1_59) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, all_65_0_58)))
% 7.55/2.32  	|
% 7.55/2.32  	| Applying alpha-rule on (180) yields:
% 7.55/2.32  	| (181) relation_composition(all_0_8_8, all_0_9_9) = all_65_2_60
% 7.55/2.32  	| (182)  ~ in(all_0_13_13, all_65_1_59) | (in(all_0_7_7, all_23_0_20) & in(all_0_13_13, all_65_0_58))
% 7.55/2.32  	| (183)  ~ in(all_0_7_7, all_23_0_20) |  ~ in(all_0_13_13, all_65_0_58) | in(all_0_13_13, all_65_1_59)
% 7.55/2.32  	| (184) relation_dom(all_65_2_60) = all_65_1_59
% 7.55/2.32  	| (185) relation_dom(all_0_8_8) = all_65_0_58
% 7.55/2.32  	|
% 7.55/2.32  	| Instantiating (149) with all_71_0_67, all_71_1_68, all_71_2_69 yields:
% 7.55/2.32  	| (186) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_69 & relation_dom(all_71_2_69) = all_71_1_68 & relation_dom(all_0_12_12) = all_71_0_67 & ( ~ in(all_27_1_27, all_0_11_11) |  ~ in(all_5_0_16, all_71_0_67) | in(all_5_0_16, all_71_1_68)) & ( ~ in(all_5_0_16, all_71_1_68) | (in(all_27_1_27, all_0_11_11) & in(all_5_0_16, all_71_0_67)))
% 7.55/2.32  	|
% 7.55/2.32  	| Applying alpha-rule on (186) yields:
% 7.55/2.32  	| (187)  ~ in(all_27_1_27, all_0_11_11) |  ~ in(all_5_0_16, all_71_0_67) | in(all_5_0_16, all_71_1_68)
% 7.55/2.32  	| (188) relation_dom(all_71_2_69) = all_71_1_68
% 7.55/2.32  	| (189) relation_dom(all_0_12_12) = all_71_0_67
% 7.55/2.32  	| (190)  ~ in(all_5_0_16, all_71_1_68) | (in(all_27_1_27, all_0_11_11) & in(all_5_0_16, all_71_0_67))
% 7.55/2.33  	| (191) relation_composition(all_0_12_12, all_0_12_12) = all_71_2_69
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (147) with all_73_0_70, all_73_1_71, all_73_2_72 yields:
% 7.55/2.33  	| (192) relation_composition(all_0_12_12, all_0_12_12) = all_73_2_72 & relation_dom(all_73_2_72) = all_73_1_71 & relation_dom(all_0_12_12) = all_73_0_70 & ( ~ in(all_29_0_30, all_0_11_11) |  ~ in(all_7_0_17, all_73_0_70) | in(all_7_0_17, all_73_1_71)) & ( ~ in(all_7_0_17, all_73_1_71) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_73_0_70)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (192) yields:
% 7.55/2.33  	| (193) relation_dom(all_73_2_72) = all_73_1_71
% 7.55/2.33  	| (194)  ~ in(all_7_0_17, all_73_1_71) | (in(all_29_0_30, all_0_11_11) & in(all_7_0_17, all_73_0_70))
% 7.55/2.33  	| (195) relation_dom(all_0_12_12) = all_73_0_70
% 7.55/2.33  	| (196)  ~ in(all_29_0_30, all_0_11_11) |  ~ in(all_7_0_17, all_73_0_70) | in(all_7_0_17, all_73_1_71)
% 7.55/2.33  	| (197) relation_composition(all_0_12_12, all_0_12_12) = all_73_2_72
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (148) with all_75_0_73, all_75_1_74, all_75_2_75 yields:
% 7.55/2.33  	| (198) relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75 & relation_dom(all_75_2_75) = all_75_1_74 & relation_dom(all_0_12_12) = all_75_0_73 & ( ~ in(all_29_0_30, all_23_0_20) |  ~ in(all_7_0_17, all_75_0_73) | in(all_7_0_17, all_75_1_74)) & ( ~ in(all_7_0_17, all_75_1_74) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, all_75_0_73)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (198) yields:
% 7.55/2.33  	| (199) relation_dom(all_0_12_12) = all_75_0_73
% 7.55/2.33  	| (200)  ~ in(all_29_0_30, all_23_0_20) |  ~ in(all_7_0_17, all_75_0_73) | in(all_7_0_17, all_75_1_74)
% 7.55/2.33  	| (201)  ~ in(all_7_0_17, all_75_1_74) | (in(all_29_0_30, all_23_0_20) & in(all_7_0_17, all_75_0_73))
% 7.55/2.33  	| (202) relation_dom(all_75_2_75) = all_75_1_74
% 7.55/2.33  	| (203) relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (146) with all_79_0_79, all_79_1_80, all_79_2_81 yields:
% 7.55/2.33  	| (204) relation_dom(all_0_8_8) = all_79_2_81 & apply(all_0_9_9, all_79_1_80) = all_79_0_79 & apply(all_0_12_12, all_5_0_16) = all_79_1_80 & (all_79_0_79 = all_27_2_28 |  ~ in(all_5_0_16, all_79_2_81))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (204) yields:
% 7.55/2.33  	| (205) relation_dom(all_0_8_8) = all_79_2_81
% 7.55/2.33  	| (206) apply(all_0_9_9, all_79_1_80) = all_79_0_79
% 7.55/2.33  	| (207) apply(all_0_12_12, all_5_0_16) = all_79_1_80
% 7.55/2.33  	| (208) all_79_0_79 = all_27_2_28 |  ~ in(all_5_0_16, all_79_2_81)
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (145) with all_81_0_82, all_81_1_83, all_81_2_84 yields:
% 7.55/2.33  	| (209) relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84 & relation_dom(all_81_2_84) = all_81_1_83 & apply(all_0_12_12, all_7_0_17) = all_81_0_82 & ( ~ in(all_81_0_82, all_23_0_20) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_81_1_83)) & ( ~ in(all_7_0_17, all_81_1_83) | (in(all_81_0_82, all_23_0_20) & in(all_7_0_17, all_0_11_11)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (209) yields:
% 7.55/2.33  	| (210)  ~ in(all_81_0_82, all_23_0_20) |  ~ in(all_7_0_17, all_0_11_11) | in(all_7_0_17, all_81_1_83)
% 7.55/2.33  	| (211) apply(all_0_12_12, all_7_0_17) = all_81_0_82
% 7.55/2.33  	| (212) relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84
% 7.55/2.33  	| (213) relation_dom(all_81_2_84) = all_81_1_83
% 7.55/2.33  	| (214)  ~ in(all_7_0_17, all_81_1_83) | (in(all_81_0_82, all_23_0_20) & in(all_7_0_17, all_0_11_11))
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (157) with all_85_0_88, all_85_1_89, all_85_2_90 yields:
% 7.55/2.33  	| (215) relation_composition(all_0_12_12, all_0_8_8) = all_85_2_90 & relation_dom(all_85_2_90) = all_85_1_89 & relation_dom(all_0_12_12) = all_85_0_88 & ( ~ in(all_0_10_10, all_27_3_29) |  ~ in(all_0_13_13, all_85_0_88) | in(all_0_13_13, all_85_1_89)) & ( ~ in(all_0_13_13, all_85_1_89) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, all_85_0_88)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (215) yields:
% 7.55/2.33  	| (216)  ~ in(all_0_13_13, all_85_1_89) | (in(all_0_10_10, all_27_3_29) & in(all_0_13_13, all_85_0_88))
% 7.55/2.33  	| (217) relation_composition(all_0_12_12, all_0_8_8) = all_85_2_90
% 7.55/2.33  	| (218)  ~ in(all_0_10_10, all_27_3_29) |  ~ in(all_0_13_13, all_85_0_88) | in(all_0_13_13, all_85_1_89)
% 7.55/2.33  	| (219) relation_dom(all_0_12_12) = all_85_0_88
% 7.55/2.33  	| (220) relation_dom(all_85_2_90) = all_85_1_89
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (155) with all_89_0_94, all_89_1_95, all_89_2_96 yields:
% 7.55/2.33  	| (221) relation_composition(all_0_8_8, all_0_8_8) = all_89_2_96 & relation_dom(all_89_2_96) = all_89_1_95 & relation_dom(all_0_8_8) = all_89_0_94 & ( ~ in(all_27_2_28, all_27_3_29) |  ~ in(all_5_0_16, all_89_0_94) | in(all_5_0_16, all_89_1_95)) & ( ~ in(all_5_0_16, all_89_1_95) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, all_89_0_94)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (221) yields:
% 7.55/2.33  	| (222) relation_dom(all_89_2_96) = all_89_1_95
% 7.55/2.33  	| (223) relation_dom(all_0_8_8) = all_89_0_94
% 7.55/2.33  	| (224)  ~ in(all_27_2_28, all_27_3_29) |  ~ in(all_5_0_16, all_89_0_94) | in(all_5_0_16, all_89_1_95)
% 7.55/2.33  	| (225) relation_composition(all_0_8_8, all_0_8_8) = all_89_2_96
% 7.55/2.33  	| (226)  ~ in(all_5_0_16, all_89_1_95) | (in(all_27_2_28, all_27_3_29) & in(all_5_0_16, all_89_0_94))
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (153) with all_91_0_97, all_91_1_98, all_91_2_99 yields:
% 7.55/2.33  	| (227) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_99 & relation_dom(all_91_2_99) = all_91_1_98 & relation_dom(all_0_8_8) = all_91_0_97 & ( ~ in(all_27_2_28, all_0_11_11) |  ~ in(all_5_0_16, all_91_0_97) | in(all_5_0_16, all_91_1_98)) & ( ~ in(all_5_0_16, all_91_1_98) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, all_91_0_97)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (227) yields:
% 7.55/2.33  	| (228) relation_dom(all_0_8_8) = all_91_0_97
% 7.55/2.33  	| (229)  ~ in(all_5_0_16, all_91_1_98) | (in(all_27_2_28, all_0_11_11) & in(all_5_0_16, all_91_0_97))
% 7.55/2.33  	| (230)  ~ in(all_27_2_28, all_0_11_11) |  ~ in(all_5_0_16, all_91_0_97) | in(all_5_0_16, all_91_1_98)
% 7.55/2.33  	| (231) relation_dom(all_91_2_99) = all_91_1_98
% 7.55/2.33  	| (232) relation_composition(all_0_8_8, all_0_12_12) = all_91_2_99
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (152) with all_93_0_100, all_93_1_101, all_93_2_102 yields:
% 7.55/2.33  	| (233) relation_composition(all_0_8_8, all_0_12_12) = all_93_2_102 & relation_dom(all_93_2_102) = all_93_1_101 & relation_dom(all_0_8_8) = all_93_0_100 & ( ~ in(all_0_7_7, all_0_11_11) |  ~ in(all_0_13_13, all_93_0_100) | in(all_0_13_13, all_93_1_101)) & ( ~ in(all_0_13_13, all_93_1_101) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_93_0_100)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (233) yields:
% 7.55/2.33  	| (234)  ~ in(all_0_13_13, all_93_1_101) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_93_0_100))
% 7.55/2.33  	| (235) relation_dom(all_93_2_102) = all_93_1_101
% 7.55/2.33  	| (236)  ~ in(all_0_7_7, all_0_11_11) |  ~ in(all_0_13_13, all_93_0_100) | in(all_0_13_13, all_93_1_101)
% 7.55/2.33  	| (237) relation_dom(all_0_8_8) = all_93_0_100
% 7.55/2.33  	| (238) relation_composition(all_0_8_8, all_0_12_12) = all_93_2_102
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (151) with all_95_0_103, all_95_1_104, all_95_2_105 yields:
% 7.55/2.33  	| (239) relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105 & relation_dom(all_95_2_105) = all_95_1_104 & apply(all_95_2_105, all_5_0_16) = all_95_0_103 & (all_95_0_103 = all_27_0_26 |  ~ in(all_5_0_16, all_95_1_104))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (239) yields:
% 7.55/2.33  	| (240) relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105
% 7.55/2.33  	| (241) relation_dom(all_95_2_105) = all_95_1_104
% 7.55/2.33  	| (242) apply(all_95_2_105, all_5_0_16) = all_95_0_103
% 7.55/2.33  	| (243) all_95_0_103 = all_27_0_26 |  ~ in(all_5_0_16, all_95_1_104)
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (154) with all_97_0_106, all_97_1_107, all_97_2_108 yields:
% 7.55/2.33  	| (244) relation_composition(all_0_8_8, all_0_8_8) = all_97_2_108 & relation_dom(all_97_2_108) = all_97_1_107 & relation_dom(all_0_8_8) = all_97_0_106 & ( ~ in(all_0_7_7, all_27_3_29) |  ~ in(all_0_13_13, all_97_0_106) | in(all_0_13_13, all_97_1_107)) & ( ~ in(all_0_13_13, all_97_1_107) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, all_97_0_106)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (244) yields:
% 7.55/2.33  	| (245)  ~ in(all_0_7_7, all_27_3_29) |  ~ in(all_0_13_13, all_97_0_106) | in(all_0_13_13, all_97_1_107)
% 7.55/2.33  	| (246) relation_dom(all_97_2_108) = all_97_1_107
% 7.55/2.33  	| (247) relation_composition(all_0_8_8, all_0_8_8) = all_97_2_108
% 7.55/2.33  	| (248)  ~ in(all_0_13_13, all_97_1_107) | (in(all_0_7_7, all_27_3_29) & in(all_0_13_13, all_97_0_106))
% 7.55/2.33  	| (249) relation_dom(all_0_8_8) = all_97_0_106
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (141) with all_101_0_112, all_101_1_113, all_101_2_114 yields:
% 7.55/2.33  	| (250) relation_dom(all_25_2_25) = all_101_2_114 & relation_dom(all_0_12_12) = all_101_1_113 & apply(all_0_12_12, all_11_0_19) = all_101_0_112 & ( ~ in(all_101_0_112, all_0_11_11) |  ~ in(all_11_0_19, all_101_1_113) | in(all_11_0_19, all_101_2_114)) & ( ~ in(all_11_0_19, all_101_2_114) | (in(all_101_0_112, all_0_11_11) & in(all_11_0_19, all_101_1_113)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (250) yields:
% 7.55/2.33  	| (251)  ~ in(all_101_0_112, all_0_11_11) |  ~ in(all_11_0_19, all_101_1_113) | in(all_11_0_19, all_101_2_114)
% 7.55/2.33  	| (252)  ~ in(all_11_0_19, all_101_2_114) | (in(all_101_0_112, all_0_11_11) & in(all_11_0_19, all_101_1_113))
% 7.55/2.33  	| (253) relation_dom(all_0_12_12) = all_101_1_113
% 7.55/2.33  	| (254) apply(all_0_12_12, all_11_0_19) = all_101_0_112
% 7.55/2.33  	| (255) relation_dom(all_25_2_25) = all_101_2_114
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (150) with all_103_0_115, all_103_1_116, all_103_2_117 yields:
% 7.55/2.33  	| (256) relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117 & relation_dom(all_103_2_117) = all_103_1_116 & relation_dom(all_0_12_12) = all_103_0_115 & ( ~ in(all_27_1_27, all_23_0_20) |  ~ in(all_5_0_16, all_103_0_115) | in(all_5_0_16, all_103_1_116)) & ( ~ in(all_5_0_16, all_103_1_116) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, all_103_0_115)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (256) yields:
% 7.55/2.33  	| (257)  ~ in(all_5_0_16, all_103_1_116) | (in(all_27_1_27, all_23_0_20) & in(all_5_0_16, all_103_0_115))
% 7.55/2.33  	| (258) relation_dom(all_103_2_117) = all_103_1_116
% 7.55/2.33  	| (259) relation_dom(all_0_12_12) = all_103_0_115
% 7.55/2.33  	| (260)  ~ in(all_27_1_27, all_23_0_20) |  ~ in(all_5_0_16, all_103_0_115) | in(all_5_0_16, all_103_1_116)
% 7.55/2.33  	| (261) relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (144) with all_107_0_121, all_107_1_122, all_107_2_123 yields:
% 7.55/2.33  	| (262) relation_dom(all_0_8_8) = all_107_2_123 & relation_dom(all_0_12_12) = all_107_1_122 & apply(all_0_12_12, all_11_0_19) = all_107_0_121 & ( ~ in(all_107_0_121, all_23_0_20) |  ~ in(all_11_0_19, all_107_1_122) | in(all_11_0_19, all_107_2_123)) & ( ~ in(all_11_0_19, all_107_2_123) | (in(all_107_0_121, all_23_0_20) & in(all_11_0_19, all_107_1_122)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (262) yields:
% 7.55/2.33  	| (263)  ~ in(all_107_0_121, all_23_0_20) |  ~ in(all_11_0_19, all_107_1_122) | in(all_11_0_19, all_107_2_123)
% 7.55/2.33  	| (264) relation_dom(all_0_8_8) = all_107_2_123
% 7.55/2.33  	| (265) apply(all_0_12_12, all_11_0_19) = all_107_0_121
% 7.55/2.33  	| (266)  ~ in(all_11_0_19, all_107_2_123) | (in(all_107_0_121, all_23_0_20) & in(all_11_0_19, all_107_1_122))
% 7.55/2.33  	| (267) relation_dom(all_0_12_12) = all_107_1_122
% 7.55/2.33  	|
% 7.55/2.33  	| Instantiating (143) with all_109_0_124, all_109_1_125, all_109_2_126 yields:
% 7.55/2.33  	| (268) relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126 & relation_dom(all_109_2_126) = all_109_1_125 & relation_dom(all_0_12_12) = all_109_0_124 & ( ~ in(all_0_10_10, all_23_0_20) |  ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125)) & ( ~ in(all_0_13_13, all_109_1_125) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, all_109_0_124)))
% 7.55/2.33  	|
% 7.55/2.33  	| Applying alpha-rule on (268) yields:
% 7.55/2.33  	| (269)  ~ in(all_0_13_13, all_109_1_125) | (in(all_0_10_10, all_23_0_20) & in(all_0_13_13, all_109_0_124))
% 7.55/2.34  	| (270) relation_dom(all_109_2_126) = all_109_1_125
% 7.55/2.34  	| (271)  ~ in(all_0_10_10, all_23_0_20) |  ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125)
% 7.55/2.34  	| (272) relation_dom(all_0_12_12) = all_109_0_124
% 7.55/2.34  	| (273) relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126
% 7.55/2.34  	|
% 7.55/2.34  	| Equations (156) can reduce 22 to:
% 7.55/2.34  	| (274)  ~ (all_0_6_6 = empty_set)
% 7.55/2.34  	|
% 7.55/2.34  	+-Applying beta-rule and splitting (142), into two cases.
% 7.55/2.34  	|-Branch one:
% 7.55/2.34  	| (275) in(all_0_10_10, all_23_0_20)
% 7.55/2.34  	|
% 7.55/2.34  		| Instantiating formula (54) with all_0_12_12, all_0_9_9, all_109_2_126, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields:
% 7.55/2.34  		| (276) all_109_2_126 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (54) with all_0_12_12, all_0_9_9, all_103_2_117, all_109_2_126 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_109_2_126, relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117, yields:
% 7.55/2.34  		| (277) all_109_2_126 = all_103_2_117
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (54) with all_0_12_12, all_0_9_9, all_95_2_105, all_103_2_117 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_103_2_117, relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105, yields:
% 7.55/2.34  		| (278) all_103_2_117 = all_95_2_105
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (54) with all_0_12_12, all_0_9_9, all_81_2_84, all_95_2_105 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_95_2_105, relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84, yields:
% 7.55/2.34  		| (279) all_95_2_105 = all_81_2_84
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (54) with all_0_12_12, all_0_9_9, all_75_2_75, all_81_2_84 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_81_2_84, relation_composition(all_0_12_12, all_0_9_9) = all_75_2_75, yields:
% 7.55/2.34  		| (280) all_81_2_84 = all_75_2_75
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_97_0_106, all_107_2_123 and discharging atoms relation_dom(all_0_8_8) = all_107_2_123, relation_dom(all_0_8_8) = all_97_0_106, yields:
% 7.55/2.34  		| (281) all_107_2_123 = all_97_0_106
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_93_0_100, all_107_2_123 and discharging atoms relation_dom(all_0_8_8) = all_107_2_123, relation_dom(all_0_8_8) = all_93_0_100, yields:
% 7.55/2.34  		| (282) all_107_2_123 = all_93_0_100
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_91_0_97, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_27_3_29, yields:
% 7.55/2.34  		| (283) all_91_0_97 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_89_0_94, all_91_0_97 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_89_0_94, yields:
% 7.55/2.34  		| (284) all_91_0_97 = all_89_0_94
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_79_2_81, all_97_0_106 and discharging atoms relation_dom(all_0_8_8) = all_97_0_106, relation_dom(all_0_8_8) = all_79_2_81, yields:
% 7.55/2.34  		| (285) all_97_0_106 = all_79_2_81
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_79_2_81, all_91_0_97 and discharging atoms relation_dom(all_0_8_8) = all_91_0_97, relation_dom(all_0_8_8) = all_79_2_81, yields:
% 7.55/2.34  		| (286) all_91_0_97 = all_79_2_81
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_65_0_58, all_97_0_106 and discharging atoms relation_dom(all_0_8_8) = all_97_0_106, relation_dom(all_0_8_8) = all_65_0_58, yields:
% 7.55/2.34  		| (287) all_97_0_106 = all_65_0_58
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_8_8, all_55_0_42, all_79_2_81 and discharging atoms relation_dom(all_0_8_8) = all_79_2_81, relation_dom(all_0_8_8) = all_55_0_42, yields:
% 7.55/2.34  		| (288) all_79_2_81 = all_55_0_42
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_101_1_113, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_101_1_113, yields:
% 7.55/2.34  		| (289) all_109_0_124 = all_101_1_113
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_85_0_88, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_85_0_88, yields:
% 7.55/2.34  		| (290) all_109_0_124 = all_85_0_88
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_85_0_88, all_103_0_115 and discharging atoms relation_dom(all_0_12_12) = all_103_0_115, relation_dom(all_0_12_12) = all_85_0_88, yields:
% 7.55/2.34  		| (291) all_103_0_115 = all_85_0_88
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_75_0_73, all_109_0_124 and discharging atoms relation_dom(all_0_12_12) = all_109_0_124, relation_dom(all_0_12_12) = all_75_0_73, yields:
% 7.55/2.34  		| (292) all_109_0_124 = all_75_0_73
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_73_0_70, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_73_0_70, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 7.55/2.34  		| (293) all_73_0_70 = all_0_11_11
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_73_0_70, all_107_1_122 and discharging atoms relation_dom(all_0_12_12) = all_107_1_122, relation_dom(all_0_12_12) = all_73_0_70, yields:
% 7.55/2.34  		| (294) all_107_1_122 = all_73_0_70
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_73_0_70, all_101_1_113 and discharging atoms relation_dom(all_0_12_12) = all_101_1_113, relation_dom(all_0_12_12) = all_73_0_70, yields:
% 7.55/2.34  		| (295) all_101_1_113 = all_73_0_70
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_71_0_67, all_101_1_113 and discharging atoms relation_dom(all_0_12_12) = all_101_1_113, relation_dom(all_0_12_12) = all_71_0_67, yields:
% 7.55/2.34  		| (296) all_101_1_113 = all_71_0_67
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_63_0_55, all_107_1_122 and discharging atoms relation_dom(all_0_12_12) = all_107_1_122, relation_dom(all_0_12_12) = all_63_0_55, yields:
% 7.55/2.34  		| (297) all_107_1_122 = all_63_0_55
% 7.55/2.34  		|
% 7.55/2.34  		| Instantiating formula (38) with all_0_12_12, all_61_0_52, all_103_0_115 and discharging atoms relation_dom(all_0_12_12) = all_103_0_115, relation_dom(all_0_12_12) = all_61_0_52, yields:
% 7.55/2.34  		| (298) all_103_0_115 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (289,292) yields a new equation:
% 7.55/2.34  		| (299) all_101_1_113 = all_75_0_73
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 299 yields:
% 7.55/2.34  		| (300) all_101_1_113 = all_75_0_73
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (290,292) yields a new equation:
% 7.55/2.34  		| (301) all_85_0_88 = all_75_0_73
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 301 yields:
% 7.55/2.34  		| (302) all_85_0_88 = all_75_0_73
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (277,276) yields a new equation:
% 7.55/2.34  		| (303) all_103_2_117 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 303 yields:
% 7.55/2.34  		| (304) all_103_2_117 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (294,297) yields a new equation:
% 7.55/2.34  		| (305) all_73_0_70 = all_63_0_55
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 305 yields:
% 7.55/2.34  		| (306) all_73_0_70 = all_63_0_55
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (281,282) yields a new equation:
% 7.55/2.34  		| (307) all_97_0_106 = all_93_0_100
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 307 yields:
% 7.55/2.34  		| (308) all_97_0_106 = all_93_0_100
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (291,298) yields a new equation:
% 7.55/2.34  		| (309) all_85_0_88 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 309 yields:
% 7.55/2.34  		| (310) all_85_0_88 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (278,304) yields a new equation:
% 7.55/2.34  		| (311) all_95_2_105 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 311 yields:
% 7.55/2.34  		| (312) all_95_2_105 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (300,296) yields a new equation:
% 7.55/2.34  		| (313) all_75_0_73 = all_71_0_67
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 313 yields:
% 7.55/2.34  		| (314) all_75_0_73 = all_71_0_67
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (295,296) yields a new equation:
% 7.55/2.34  		| (315) all_73_0_70 = all_71_0_67
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 315 yields:
% 7.55/2.34  		| (316) all_73_0_70 = all_71_0_67
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (287,308) yields a new equation:
% 7.55/2.34  		| (317) all_93_0_100 = all_65_0_58
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (285,308) yields a new equation:
% 7.55/2.34  		| (318) all_93_0_100 = all_79_2_81
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (279,312) yields a new equation:
% 7.55/2.34  		| (319) all_81_2_84 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 319 yields:
% 7.55/2.34  		| (320) all_81_2_84 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (318,317) yields a new equation:
% 7.55/2.34  		| (321) all_79_2_81 = all_65_0_58
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 321 yields:
% 7.55/2.34  		| (322) all_79_2_81 = all_65_0_58
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (286,284) yields a new equation:
% 7.55/2.34  		| (323) all_89_0_94 = all_79_2_81
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (283,284) yields a new equation:
% 7.55/2.34  		| (324) all_89_0_94 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (323,324) yields a new equation:
% 7.55/2.34  		| (325) all_79_2_81 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 325 yields:
% 7.55/2.34  		| (326) all_79_2_81 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (302,310) yields a new equation:
% 7.55/2.34  		| (327) all_75_0_73 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 327 yields:
% 7.55/2.34  		| (328) all_75_0_73 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (280,320) yields a new equation:
% 7.55/2.34  		| (329) all_75_2_75 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 329 yields:
% 7.55/2.34  		| (330) all_75_2_75 = all_0_8_8
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (288,322) yields a new equation:
% 7.55/2.34  		| (331) all_65_0_58 = all_55_0_42
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (326,322) yields a new equation:
% 7.55/2.34  		| (332) all_65_0_58 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (314,328) yields a new equation:
% 7.55/2.34  		| (333) all_71_0_67 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 333 yields:
% 7.55/2.34  		| (334) all_71_0_67 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (316,306) yields a new equation:
% 7.55/2.34  		| (335) all_71_0_67 = all_63_0_55
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 335 yields:
% 7.55/2.34  		| (336) all_71_0_67 = all_63_0_55
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (293,306) yields a new equation:
% 7.55/2.34  		| (337) all_63_0_55 = all_0_11_11
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (336,334) yields a new equation:
% 7.55/2.34  		| (338) all_63_0_55 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 338 yields:
% 7.55/2.34  		| (339) all_63_0_55 = all_61_0_52
% 7.55/2.34  		|
% 7.55/2.34  		| Combining equations (331,332) yields a new equation:
% 7.55/2.34  		| (340) all_55_0_42 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.34  		| Simplifying 340 yields:
% 7.55/2.34  		| (341) all_55_0_42 = all_27_3_29
% 7.55/2.34  		|
% 7.55/2.35  		| Combining equations (337,339) yields a new equation:
% 7.55/2.35  		| (342) all_61_0_52 = all_0_11_11
% 7.55/2.35  		|
% 7.55/2.35  		| Combining equations (342,328) yields a new equation:
% 7.55/2.35  		| (343) all_75_0_73 = all_0_11_11
% 7.55/2.35  		|
% 7.55/2.35  		| Combining equations (343,292) yields a new equation:
% 7.55/2.35  		| (344) all_109_0_124 = all_0_11_11
% 7.55/2.35  		|
% 7.55/2.35  		| From (276) and (270) follows:
% 7.55/2.35  		| (345) relation_dom(all_0_8_8) = all_109_1_125
% 7.55/2.35  		|
% 7.55/2.35  		| From (304) and (258) follows:
% 7.55/2.35  		| (346) relation_dom(all_0_8_8) = all_103_1_116
% 7.55/2.35  		|
% 7.55/2.35  		| From (312) and (241) follows:
% 7.55/2.35  		| (347) relation_dom(all_0_8_8) = all_95_1_104
% 7.55/2.35  		|
% 7.55/2.35  		| From (320) and (213) follows:
% 7.55/2.35  		| (348) relation_dom(all_0_8_8) = all_81_1_83
% 7.55/2.35  		|
% 7.55/2.35  		| From (330) and (202) follows:
% 7.55/2.35  		| (349) relation_dom(all_0_8_8) = all_75_1_74
% 7.55/2.35  		|
% 7.55/2.35  		| From (341) and (165) follows:
% 7.55/2.35  		| (103) relation_dom(all_0_8_8) = all_27_3_29
% 7.55/2.35  		|
% 7.55/2.35  		+-Applying beta-rule and splitting (271), into two cases.
% 7.55/2.35  		|-Branch one:
% 7.55/2.35  		| (351)  ~ in(all_0_10_10, all_23_0_20)
% 7.55/2.35  		|
% 7.55/2.35  			| Using (275) and (351) yields:
% 7.55/2.35  			| (352) $false
% 7.55/2.35  			|
% 7.55/2.35  			|-The branch is then unsatisfiable
% 7.55/2.35  		|-Branch two:
% 7.55/2.35  		| (275) in(all_0_10_10, all_23_0_20)
% 7.55/2.35  		| (354)  ~ in(all_0_13_13, all_109_0_124) | in(all_0_13_13, all_109_1_125)
% 7.55/2.35  		|
% 7.55/2.35  			+-Applying beta-rule and splitting (354), into two cases.
% 7.55/2.35  			|-Branch one:
% 7.55/2.35  			| (355)  ~ in(all_0_13_13, all_109_0_124)
% 7.55/2.35  			|
% 7.55/2.35  				| From (344) and (355) follows:
% 7.55/2.35  				| (356)  ~ in(all_0_13_13, all_0_11_11)
% 7.55/2.35  				|
% 7.55/2.35  				| Using (33) and (356) yields:
% 7.55/2.35  				| (352) $false
% 7.55/2.35  				|
% 7.55/2.35  				|-The branch is then unsatisfiable
% 7.55/2.35  			|-Branch two:
% 7.55/2.35  			| (358) in(all_0_13_13, all_109_0_124)
% 7.55/2.35  			| (359) in(all_0_13_13, all_109_1_125)
% 7.55/2.35  			|
% 7.55/2.35  				| Instantiating formula (38) with all_0_8_8, all_103_1_116, all_109_1_125 and discharging atoms relation_dom(all_0_8_8) = all_109_1_125, relation_dom(all_0_8_8) = all_103_1_116, yields:
% 7.55/2.35  				| (360) all_109_1_125 = all_103_1_116
% 7.55/2.35  				|
% 7.55/2.35  				| Instantiating formula (38) with all_0_8_8, all_95_1_104, all_27_3_29 and discharging atoms relation_dom(all_0_8_8) = all_95_1_104, relation_dom(all_0_8_8) = all_27_3_29, yields:
% 7.55/2.35  				| (361) all_95_1_104 = all_27_3_29
% 7.55/2.35  				|
% 7.55/2.35  				| Instantiating formula (38) with all_0_8_8, all_81_1_83, all_103_1_116 and discharging atoms relation_dom(all_0_8_8) = all_103_1_116, relation_dom(all_0_8_8) = all_81_1_83, yields:
% 7.55/2.35  				| (362) all_103_1_116 = all_81_1_83
% 7.55/2.35  				|
% 7.55/2.35  				| Instantiating formula (38) with all_0_8_8, all_81_1_83, all_95_1_104 and discharging atoms relation_dom(all_0_8_8) = all_95_1_104, relation_dom(all_0_8_8) = all_81_1_83, yields:
% 7.55/2.35  				| (363) all_95_1_104 = all_81_1_83
% 7.55/2.35  				|
% 7.55/2.35  				| Instantiating formula (38) with all_0_8_8, all_75_1_74, all_109_1_125 and discharging atoms relation_dom(all_0_8_8) = all_109_1_125, relation_dom(all_0_8_8) = all_75_1_74, yields:
% 7.55/2.35  				| (364) all_109_1_125 = all_75_1_74
% 7.55/2.35  				|
% 7.55/2.35  				| Combining equations (360,364) yields a new equation:
% 7.55/2.35  				| (365) all_103_1_116 = all_75_1_74
% 7.55/2.35  				|
% 7.55/2.35  				| Simplifying 365 yields:
% 7.55/2.35  				| (366) all_103_1_116 = all_75_1_74
% 7.55/2.35  				|
% 7.55/2.35  				| Combining equations (362,366) yields a new equation:
% 7.55/2.35  				| (367) all_81_1_83 = all_75_1_74
% 7.55/2.35  				|
% 7.55/2.35  				| Simplifying 367 yields:
% 7.55/2.35  				| (368) all_81_1_83 = all_75_1_74
% 7.55/2.35  				|
% 7.55/2.35  				| Combining equations (363,361) yields a new equation:
% 7.55/2.35  				| (369) all_81_1_83 = all_27_3_29
% 7.55/2.35  				|
% 7.55/2.35  				| Simplifying 369 yields:
% 7.55/2.35  				| (370) all_81_1_83 = all_27_3_29
% 7.55/2.35  				|
% 7.55/2.35  				| Combining equations (370,368) yields a new equation:
% 7.55/2.35  				| (371) all_75_1_74 = all_27_3_29
% 7.55/2.35  				|
% 7.55/2.35  				| Combining equations (371,364) yields a new equation:
% 7.55/2.35  				| (372) all_109_1_125 = all_27_3_29
% 7.55/2.35  				|
% 7.55/2.35  				| From (372) and (359) follows:
% 7.55/2.35  				| (373) in(all_0_13_13, all_27_3_29)
% 7.55/2.35  				|
% 7.55/2.35  				| Using (373) and (140) yields:
% 7.55/2.35  				| (352) $false
% 7.55/2.35  				|
% 7.55/2.35  				|-The branch is then unsatisfiable
% 7.55/2.35  	|-Branch two:
% 7.55/2.35  	| (351)  ~ in(all_0_10_10, all_23_0_20)
% 7.55/2.35  	| (376) all_0_6_6 = empty_set
% 7.55/2.35  	|
% 7.55/2.35  		| Equations (376) can reduce 274 to:
% 7.55/2.35  		| (377) $false
% 7.55/2.35  		|
% 7.55/2.35  		|-The branch is then unsatisfiable
% 7.55/2.35  |-Branch two:
% 7.55/2.35  | (378) in(all_0_13_13, all_31_1_34)
% 7.55/2.35  | (379) all_31_0_33 = all_0_6_6
% 7.55/2.35  |
% 7.55/2.35  	| Combining equations (379,134) yields a new equation:
% 7.55/2.35  	| (380) all_0_6_6 = all_0_7_7
% 7.55/2.35  	|
% 7.55/2.35  	| Simplifying 380 yields:
% 7.55/2.35  	| (381) all_0_6_6 = all_0_7_7
% 7.55/2.35  	|
% 7.55/2.35  	| Equations (381) can reduce 22 to:
% 7.55/2.35  	| (377) $false
% 7.55/2.35  	|
% 7.55/2.35  	|-The branch is then unsatisfiable
% 7.55/2.35  % SZS output end Proof for theBenchmark
% 7.55/2.35  
% 7.55/2.35  1755ms
%------------------------------------------------------------------------------