%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n005.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 00:21:59 EDT 2022

% Result   : Theorem 6.33s 2.04s
% Output   : Proof 14.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.32  % Computer : n005.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 02:10:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.57/0.57          ____       _                          
% 0.57/0.57    ___  / __ \_____(_)___  ________  __________
% 0.57/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.57  
% 0.57/0.57  A Theorem Prover for First-Order Logic
% 0.57/0.57  (ePrincess v.1.0)
% 0.57/0.57  
% 0.57/0.57  (c) Philipp Rümmer, 2009-2015
% 0.57/0.57  (c) Peter Backeman, 2014-2015
% 0.57/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.57  Bug reports to peter@backeman.se
% 0.57/0.57  
% 0.57/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.57  
% 0.57/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/0.93  Prover 0: Preprocessing ...
% 2.52/1.18  Prover 0: Warning: ignoring some quantifiers
% 2.64/1.21  Prover 0: Constructing countermodel ...
% 3.07/1.35  Prover 0: gave up
% 3.07/1.35  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.38/1.39  Prover 1: Preprocessing ...
% 4.15/1.58  Prover 1: Constructing countermodel ...
% 4.88/1.69  Prover 1: gave up
% 4.88/1.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.88/1.72  Prover 2: Preprocessing ...
% 5.47/1.88  Prover 2: Warning: ignoring some quantifiers
% 5.47/1.89  Prover 2: Constructing countermodel ...
% 6.33/2.04  Prover 2: proved (352ms)
% 6.33/2.04  
% 6.33/2.04  No countermodel exists, formula is valid
% 6.33/2.04  % SZS status Theorem for theBenchmark
% 6.33/2.04  
% 6.33/2.04  Generating proof ... Warning: ignoring some quantifiers
% 12.91/3.60  found it (size 314)
% 12.91/3.60  
% 12.91/3.60  % SZS output start Proof for theBenchmark
% 12.91/3.60  Assumed formulas after preprocessing and simplification: 
% 12.91/3.60  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & pre_order(v1, v0) = 0 & equivalence(v2, v0) = v3 &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v7, v8) = 0) |  ~ (apply(v4, v6, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apply(v4, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v6, v8) = v9) |  ~ (apply(v4, v6, v7) = 0) |  ? [v10] : (( ~ (v10 = 0) & apply(v4, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v6, v8) = v9) |  ~ (member(v7, v5) = 0) |  ? [v10] : (( ~ (v10 = 0) & apply(v4, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v4, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equivalence_class(v6, v5, v4) = v8) |  ~ (member(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apply(v4, v6, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v7, v8) = 0) |  ~ (apply(v5, v6, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apply(v5, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v4) = v10) | ( ~ (v10 = 0) & member(v7, v4) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v6, v8) = v9) |  ~ (apply(v5, v6, v7) = 0) |  ? [v10] : (( ~ (v10 = 0) & apply(v5, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v4) = v10) | ( ~ (v10 = 0) & member(v7, v4) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v6, v8) = v9) |  ~ (member(v7, v4) = 0) |  ? [v10] : (( ~ (v10 = 0) & apply(v5, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v5, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v4) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v7, v6) = v8) |  ? [v9] : (( ~ (v9 = 0) & apply(v5, v6, v7) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v6, v4) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (product(v5) = v6) |  ~ (member(v4, v7) = v8) |  ~ (member(v4, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (difference(v6, v5) = v7) |  ~ (member(v4, v7) = v8) |  ? [v9] : ((v9 = 0 & member(v4, v5) = 0) | ( ~ (v9 = 0) & member(v4, v6) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (union(v5, v6) = v7) |  ~ (member(v4, v7) = v8) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) &  ~ (v9 = 0) & member(v4, v6) = v10 & member(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (intersection(v5, v6) = v7) |  ~ (member(v4, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & member(v4, v6) = v9) | ( ~ (v9 = 0) & member(v4, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (partition(v4, v5) = 0) |  ~ (member(v8, v7) = 0) |  ~ (member(v7, v4) = 0) |  ~ (member(v6, v4) = 0) |  ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (partition(v4, v5) = 0) |  ~ (member(v8, v6) = 0) |  ~ (member(v7, v4) = 0) |  ~ (member(v6, v4) = 0) |  ? [v9] : ( ~ (v9 = 0) & member(v8, v7) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = 0 |  ~ (sum(v5) = v6) |  ~ (member(v8, v5) = 0) |  ~ (member(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & member(v4, v8) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = 0 |  ~ (sum(v5) = v6) |  ~ (member(v4, v8) = 0) |  ~ (member(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v5 = v4 |  ~ (equivalence_class(v8, v7, v6) = v5) |  ~ (equivalence_class(v8, v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v5 = v4 |  ~ (apply(v8, v7, v6) = v5) |  ~ (apply(v8, v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v7, v8) = 0) |  ~ (apply(v4, v6, v7) = 0) |  ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & member(v8, v5) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9) | ( ~ (v9 = 0) & member(v6, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v7, v8) = 0) |  ~ (member(v6, v5) = 0) |  ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v6, v7) = v9) | ( ~ (v9 = 0) & member(v8, v5) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v6, v7) = 0) |  ~ (member(v8, v5) = 0) |  ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9) | ( ~ (v9 = 0) & member(v6, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (pre_order(v4, v5) = 0) |  ~ (member(v8, v5) = 0) |  ~ (member(v7, v5) = 0) |  ~ (member(v6, v5) = 0) |  ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v4, v6, v7) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (equivalence_class(v6, v5, v4) = v8) |  ~ (member(v7, v8) = 0) | (apply(v4, v6, v7) = 0 & member(v7, v5) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v7, v8) = 0) |  ~ (apply(v5, v6, v7) = 0) |  ? [v9] : ((v9 = 0 & apply(v5, v6, v8) = 0) | ( ~ (v9 = 0) & member(v8, v4) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v6, v4) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v7, v8) = 0) |  ~ (member(v6, v4) = 0) |  ? [v9] : ((v9 = 0 & apply(v5, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v5, v6, v7) = v9) | ( ~ (v9 = 0) & member(v8, v4) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v6, v7) = 0) |  ~ (member(v8, v4) = 0) |  ? [v9] : ((v9 = 0 & apply(v5, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v5, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v6, v4) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (equivalence(v5, v4) = 0) |  ~ (member(v8, v4) = 0) |  ~ (member(v7, v4) = 0) |  ~ (member(v6, v4) = 0) |  ? [v9] : ((v9 = 0 & apply(v5, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v5, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v5, v6, v7) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (pre_order(v4, v5) = 0) |  ~ (apply(v4, v6, v6) = v7) |  ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v6, v6) = v7) |  ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (partition(v4, v5) = 0) |  ~ (subset(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (product(v5) = v6) |  ~ (member(v4, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = 0 & member(v4, v8) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unordered_pair(v5, v4) = v6) |  ~ (member(v4, v6) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unordered_pair(v4, v5) = v6) |  ~ (member(v4, v6) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (power_set(v5) = v6) |  ~ (member(v4, v6) = v7) |  ? [v8] : ( ~ (v8 = 0) & subset(v4, v5) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subset(v4, v5) = 0) |  ~ (member(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v4 | v5 = v4 |  ~ (unordered_pair(v5, v6) = v7) |  ~ (member(v4, v7) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (pre_order(v7, v6) = v5) |  ~ (pre_order(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (equivalence(v7, v6) = v5) |  ~ (equivalence(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (partition(v7, v6) = v5) |  ~ (partition(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (disjoint(v7, v6) = v5) |  ~ (disjoint(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (unordered_pair(v7, v6) = v5) |  ~ (unordered_pair(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (difference(v7, v6) = v5) |  ~ (difference(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (union(v7, v6) = v5) |  ~ (union(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (intersection(v7, v6) = v5) |  ~ (intersection(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (equal_set(v7, v6) = v5) |  ~ (equal_set(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (subset(v7, v6) = v5) |  ~ (subset(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (member(v7, v6) = v5) |  ~ (member(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (equivalence(v5, v4) = 0) |  ~ (apply(v5, v6, v7) = 0) |  ? [v8] : ((v8 = 0 & apply(v5, v7, v6) = 0) | ( ~ (v8 = 0) & member(v7, v4) = v8) | ( ~ (v8 = 0) & member(v6, v4) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (product(v5) = v6) |  ~ (member(v7, v5) = 0) |  ~ (member(v4, v6) = 0) | member(v4, v7) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (difference(v6, v5) = v7) |  ~ (member(v4, v7) = 0) |  ? [v8] : ( ~ (v8 = 0) & member(v4, v6) = 0 & member(v4, v5) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (union(v5, v6) = v7) |  ~ (member(v4, v7) = 0) |  ? [v8] : ((v8 = 0 & member(v4, v6) = 0) | (v8 = 0 & member(v4, v5) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection(v5, v6) = v7) |  ~ (member(v4, v7) = 0) | (member(v4, v6) = 0 & member(v4, v5) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (pre_order(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 &  ~ (v15 = 0) & apply(v4, v8, v9) = 0 & apply(v4, v7, v9) = v15 & apply(v4, v7, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0) | (v8 = 0 &  ~ (v9 = 0) & apply(v4, v7, v7) = v9 & member(v7, v5) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (equivalence(v5, v4) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 &  ~ (v15 = 0) & apply(v5, v8, v9) = 0 & apply(v5, v7, v9) = v15 & apply(v5, v7, v8) = 0 & member(v9, v4) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v11 = 0 & v10 = 0 & v9 = 0 &  ~ (v12 = 0) & apply(v5, v8, v7) = v12 & apply(v5, v7, v8) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v8 = 0 &  ~ (v9 = 0) & apply(v5, v7, v7) = v9 & member(v7, v4) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (partition(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : ((v13 = 0 & v12 = 0 & v10 = 0 & v9 = 0 &  ~ (v8 = v7) & member(v11, v8) = 0 & member(v11, v7) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v8 = 0 &  ~ (v9 = 0) & subset(v7, v5) = v9 & member(v7, v4) = 0) | (v8 = 0 & member(v7, v5) = 0 &  ! [v14] : ( ~ (member(v14, v4) = 0) |  ? [v15] : ( ~ (v15 = 0) & member(v7, v14) = v15)) &  ! [v14] : ( ~ (member(v7, v14) = 0) |  ? [v15] : ( ~ (v15 = 0) & member(v14, v4) = v15))))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (disjoint(v4, v5) = v6) |  ? [v7] : (member(v7, v5) = 0 & member(v7, v4) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (singleton(v4) = v5) |  ~ (member(v4, v5) = v6)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (equal_set(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & subset(v5, v4) = v7) | ( ~ (v7 = 0) & subset(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subset(v4, v5) = v6) |  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & power_set(v5) = v7 & member(v4, v7) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subset(v4, v5) = v6) |  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (product(v6) = v5) |  ~ (product(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (sum(v6) = v5) |  ~ (sum(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (singleton(v6) = v5) |  ~ (singleton(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (singleton(v5) = v6) |  ~ (member(v4, v6) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (power_set(v6) = v5) |  ~ (power_set(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (pre_order(v4, v5) = 0) |  ~ (member(v6, v5) = 0) | apply(v4, v6, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (equivalence(v5, v4) = 0) |  ~ (member(v6, v4) = 0) | apply(v5, v6, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (apply(v2, v4, v5) = v6) |  ? [v7] :  ? [v8] : (( ~ (v7 = 0) & member(v5, v0) = v7) | ( ~ (v7 = 0) & member(v4, v0) = v7) | (( ~ (v6 = 0) | (v8 = 0 & v7 = 0 & apply(v1, v5, v4) = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v8 = 0) & apply(v1, v5, v4) = v8) | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7))))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (apply(v1, v5, v4) = v6) |  ? [v7] :  ? [v8] : (( ~ (v7 = 0) & member(v5, v0) = v7) | ( ~ (v7 = 0) & member(v4, v0) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v2, v4, v5) = 0) | ( ~ (v8 = 0) & apply(v1, v4, v5) = v8)) & ((v8 = 0 & v6 = 0 & apply(v1, v4, v5) = 0) | ( ~ (v7 = 0) & apply(v2, v4, v5) = v7))))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (apply(v1, v4, v5) = v6) |  ? [v7] :  ? [v8] : (( ~ (v7 = 0) & member(v5, v0) = v7) | ( ~ (v7 = 0) & member(v4, v0) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v2, v4, v5) = 0) | ( ~ (v8 = 0) & apply(v1, v5, v4) = v8)) & ((v8 = 0 & v6 = 0 & apply(v1, v5, v4) = 0) | ( ~ (v7 = 0) & apply(v2, v4, v5) = v7))))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (partition(v4, v5) = 0) |  ~ (member(v6, v5) = 0) |  ? [v7] : (member(v7, v4) = 0 & member(v6, v7) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (partition(v4, v5) = 0) |  ~ (member(v6, v4) = 0) | subset(v6, v5) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (disjoint(v4, v5) = 0) |  ~ (member(v6, v5) = 0) |  ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (disjoint(v4, v5) = 0) |  ~ (member(v6, v4) = 0) |  ? [v7] : ( ~ (v7 = 0) & member(v6, v5) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sum(v5) = v6) |  ~ (member(v4, v6) = 0) |  ? [v7] : (member(v7, v5) = 0 & member(v4, v7) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (power_set(v5) = v6) |  ~ (member(v4, v6) = 0) | subset(v4, v5) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (subset(v5, v4) = v6) |  ? [v7] : ((v7 = 0 & v6 = 0 & subset(v4, v5) = 0) | ( ~ (v7 = 0) & equal_set(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (subset(v4, v5) = v6) |  ? [v7] : ((v7 = 0 & v6 = 0 & subset(v5, v4) = 0) | ( ~ (v7 = 0) & equal_set(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (subset(v4, v5) = 0) |  ~ (member(v6, v4) = 0) | member(v6, v5) = 0) &  ! [v4] :  ! [v5] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) &  ! [v4] :  ! [v5] : ( ~ (subset(v5, v4) = 0) |  ? [v6] : ((v6 = 0 & equal_set(v4, v5) = 0) | ( ~ (v6 = 0) & subset(v4, v5) = v6))) &  ! [v4] :  ! [v5] : ( ~ (subset(v4, v5) = 0) |  ? [v6] : (power_set(v5) = v6 & member(v4, v6) = 0)) &  ! [v4] :  ! [v5] : ( ~ (subset(v4, v5) = 0) |  ? [v6] : ((v6 = 0 & equal_set(v4, v5) = 0) | ( ~ (v6 = 0) & subset(v5, v4) = v6))) &  ! [v4] :  ~ (member(v4, empty_set) = 0) &  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : equivalence_class(v6, v5, v4) = v7 &  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : apply(v6, v5, v4) = v7 &  ? [v4] :  ? [v5] :  ? [v6] : pre_order(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : equivalence(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : partition(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : disjoint(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : unordered_pair(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : difference(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : union(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : intersection(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : equal_set(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : subset(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : member(v5, v4) = v6 &  ? [v4] :  ? [v5] : product(v4) = v5 &  ? [v4] :  ? [v5] : sum(v4) = v5 &  ? [v4] :  ? [v5] : singleton(v4) = v5 &  ? [v4] :  ? [v5] : power_set(v4) = v5)
% 13.34/3.67  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 13.34/3.67  | (1)  ~ (all_0_0_0 = 0) & pre_order(all_0_2_2, all_0_3_3) = 0 & equivalence(all_0_1_1, all_0_3_3) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ~ (apply(v0, v2, v3) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ~ (member(v3, v1) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence_class(v2, v1, v0) = v4) |  ~ (member(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ~ (apply(v1, v2, v3) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ~ (member(v3, v0) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v2) = v4) |  ? [v5] : (( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (product(v1) = v2) |  ~ (member(v0, v3) = v4) |  ~ (member(v0, v2) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (partition(v0, v1) = 0) |  ~ (member(v4, v3) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (partition(v0, v1) = 0) |  ~ (member(v4, v2) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum(v1) = v2) |  ~ (member(v4, v1) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum(v1) = v2) |  ~ (member(v0, v4) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (equivalence_class(v4, v3, v2) = v1) |  ~ (equivalence_class(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (apply(v4, v3, v2) = v1) |  ~ (apply(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (apply(v0, v2, v3) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (member(v2, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v3) = 0) |  ~ (member(v4, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (member(v4, v1) = 0) |  ~ (member(v3, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) |  ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ~ (member(v4, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (member(v4, v0) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (partition(v0, v1) = 0) |  ~ (subset(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (product(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v1) = 0) |  ~ (member(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (pre_order(v3, v2) = v1) |  ~ (pre_order(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equivalence(v3, v2) = v1) |  ~ (equivalence(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (partition(v3, v2) = v1) |  ~ (partition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~ (equal_set(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ? [v4] : ((v4 = 0 & apply(v1, v3, v2) = 0) | ( ~ (v4 = 0) & member(v3, v0) = v4) | ( ~ (v4 = 0) & member(v2, v0) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (product(v1) = v2) |  ~ (member(v3, v1) = 0) |  ~ (member(v0, v2) = 0) | member(v0, v3) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (pre_order(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 &  ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 &  ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equivalence(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 &  ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 &  ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 &  ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (partition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 &  ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 &  ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 &  ! [v10] : ( ~ (member(v10, v0) = 0) |  ? [v11] : ( ~ (v11 = 0) & member(v3, v10) = v11)) &  ! [v10] : ( ~ (member(v3, v10) = 0) |  ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum(v2) = v1) |  ~ (sum(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v1) = v2) |  ~ (member(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (pre_order(v0, v1) = 0) |  ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equivalence(v1, v0) = 0) |  ~ (member(v2, v0) = 0) | apply(v1, v2, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_1_1, v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & apply(all_0_2_2, v1, v0) = 0 & apply(all_0_2_2, v0, v1) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & apply(all_0_2_2, v1, v0) = v4) | ( ~ (v3 = 0) & apply(all_0_2_2, v0, v1) = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_2_2, v1, v0) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_2_2, v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v1, v0) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v1, v0) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (partition(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (partition(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | subset(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (subset(v1, v0) = 0) |  ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) &  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) &  ! [v0] :  ~ (member(v0, empty_set) = 0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : equivalence_class(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : apply(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] : pre_order(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equivalence(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : partition(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : difference(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_set(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2 &  ? [v0] :  ? [v1] : product(v0) = v1 &  ? [v0] :  ? [v1] : sum(v0) = v1 &  ? [v0] :  ? [v1] : singleton(v0) = v1 &  ? [v0] :  ? [v1] : power_set(v0) = v1
% 13.68/3.70  |
% 13.68/3.70  | Applying alpha-rule on (1) yields:
% 13.68/3.70  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 13.68/3.70  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 13.68/3.70  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (equivalence_class(v4, v3, v2) = v1) |  ~ (equivalence_class(v4, v3, v2) = v0))
% 13.68/3.70  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 13.68/3.70  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_1_1, v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v4 = 0 & v3 = 0 & apply(all_0_2_2, v1, v0) = 0 & apply(all_0_2_2, v0, v1) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & apply(all_0_2_2, v1, v0) = v4) | ( ~ (v3 = 0) & apply(all_0_2_2, v0, v1) = v3)))))
% 13.68/3.70  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 13.68/3.70  | (8)  ~ (all_0_0_0 = 0)
% 13.68/3.70  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum(v2) = v1) |  ~ (sum(v2) = v0))
% 13.68/3.70  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0))
% 13.68/3.70  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (product(v1) = v2) |  ~ (member(v0, v3) = v4) |  ~ (member(v0, v2) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 13.68/3.70  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (partition(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0))
% 13.68/3.70  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3))
% 13.68/3.70  | (14)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 13.68/3.71  | (15)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 13.68/3.71  | (16)  ? [v0] :  ? [v1] :  ? [v2] : pre_order(v1, v0) = v2
% 13.68/3.71  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3))
% 13.68/3.71  | (18)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : apply(v2, v1, v0) = v3
% 13.68/3.71  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 13.68/3.71  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum(v1) = v2) |  ~ (member(v0, v4) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 13.68/3.71  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (member(v4, v0) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5)))
% 13.68/3.71  | (22)  ? [v0] :  ? [v1] :  ? [v2] : equivalence(v1, v0) = v2
% 13.68/3.71  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ~ (apply(v1, v2, v3) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6)))
% 13.68/3.71  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (pre_order(v3, v2) = v1) |  ~ (pre_order(v3, v2) = v0))
% 13.68/3.71  | (25)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : equivalence_class(v2, v1, v0) = v3
% 13.68/3.71  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (member(v4, v1) = 0) |  ~ (member(v3, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5)))
% 13.68/3.71  | (27)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 13.68/3.71  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equivalence(v3, v2) = v1) |  ~ (equivalence(v3, v2) = v0))
% 13.68/3.71  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (partition(v3, v2) = v1) |  ~ (partition(v3, v2) = v0))
% 13.68/3.71  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 13.68/3.71  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 13.68/3.71  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equivalence(v1, v0) = 0) |  ~ (member(v2, v0) = 0) | apply(v1, v2, v2) = 0)
% 13.68/3.71  | (33)  ? [v0] :  ? [v1] :  ? [v2] : equal_set(v1, v0) = v2
% 13.68/3.71  | (34)  ? [v0] :  ? [v1] : singleton(v0) = v1
% 13.68/3.71  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 13.68/3.71  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 13.68/3.71  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ? [v4] : ((v4 = 0 & apply(v1, v3, v2) = 0) | ( ~ (v4 = 0) & member(v3, v0) = v4) | ( ~ (v4 = 0) & member(v2, v0) = v4)))
% 13.68/3.71  | (38) equivalence(all_0_1_1, all_0_3_3) = all_0_0_0
% 13.68/3.71  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v3) = 0) |  ~ (member(v4, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5)))
% 13.68/3.71  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (apply(v4, v3, v2) = v1) |  ~ (apply(v4, v3, v2) = v0))
% 13.68/3.71  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 13.68/3.71  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 13.68/3.71  | (43)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 13.68/3.71  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v1) = 0) |  ~ (member(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 13.68/3.71  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (partition(v0, v1) = 0) |  ~ (member(v4, v3) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v2) = v5))
% 13.68/3.72  | (46)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) = v0))
% 13.68/3.72  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (pre_order(v0, v1) = 0) |  ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 13.68/3.72  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5)))
% 13.68/3.72  | (49)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 13.68/3.72  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v0) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5)))
% 13.68/3.72  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence_class(v2, v1, v0) = v4) |  ~ (member(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 13.68/3.72  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (apply(v0, v2, v3) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5)))
% 13.68/3.72  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 13.68/3.72  | (54)  ! [v0] :  ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.68/3.72  | (55)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 13.68/3.72  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3))
% 13.68/3.72  | (57)  ! [v0] :  ~ (member(v0, empty_set) = 0)
% 13.68/3.72  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) |  ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 13.68/3.72  | (59)  ? [v0] :  ? [v1] : sum(v0) = v1
% 13.68/3.72  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~ (equal_set(v3, v2) = v0))
% 13.68/3.72  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ~ (member(v3, v0) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6)))
% 13.68/3.72  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 13.68/3.72  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 13.68/3.72  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ~ (member(v2, v1) = 0) |  ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 13.68/3.72  | (65) pre_order(all_0_2_2, all_0_3_3) = 0
% 13.68/3.72  | (66)  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2
% 13.68/3.72  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (partition(v0, v1) = 0) |  ~ (subset(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 13.68/3.72  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equivalence(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 &  ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 &  ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 &  ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0)))
% 13.68/3.72  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v2, v3) = 0) |  ~ (member(v4, v0) = 0) |  ? [v5] : ((v5 = 0 & apply(v1, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v1, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 13.68/3.72  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (product(v1) = v2) |  ~ (member(v3, v1) = 0) |  ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 13.68/3.72  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 13.68/3.72  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2))
% 13.68/3.72  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_2_2, v1, v0) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v0, v1) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v0, v1) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3)))))
% 13.68/3.73  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (product(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 13.68/3.73  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ~ (apply(v0, v2, v3) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 13.68/3.73  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 13.68/3.73  | (77)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v1) = v2) |  ~ (member(v0, v2) = 0))
% 13.68/3.73  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 13.68/3.73  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 13.68/3.73  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (partition(v0, v1) = 0) |  ~ (member(v4, v2) = 0) |  ~ (member(v3, v0) = 0) |  ~ (member(v2, v0) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5))
% 13.68/3.73  | (81)  ? [v0] :  ? [v1] : product(v0) = v1
% 13.68/3.73  | (82)  ! [v0] :  ! [v1] : ( ~ (subset(v1, v0) = 0) |  ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 13.68/3.73  | (83)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (partition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 &  ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 &  ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 &  ! [v10] : ( ~ (member(v10, v0) = 0) |  ? [v11] : ( ~ (v11 = 0) & member(v3, v10) = v11)) &  ! [v10] : ( ~ (member(v3, v10) = 0) |  ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11)))))
% 13.68/3.73  | (84)  ? [v0] :  ? [v1] : power_set(v0) = v1
% 13.68/3.73  | (85)  ? [v0] :  ? [v1] :  ? [v2] : difference(v1, v0) = v2
% 13.68/3.73  | (86)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 13.68/3.73  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 13.68/3.73  | (88)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 13.68/3.73  | (89)  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2
% 13.68/3.73  | (90)  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2
% 13.68/3.73  | (91)  ? [v0] :  ? [v1] :  ? [v2] : partition(v1, v0) = v2
% 13.68/3.73  | (92)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (pre_order(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 &  ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 &  ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0)))
% 13.68/3.73  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (partition(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | subset(v2, v1) = 0)
% 13.68/3.73  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(all_0_2_2, v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v3 = 0) & member(v1, all_0_3_3) = v3) | ( ~ (v3 = 0) & member(v0, all_0_3_3) = v3) | (( ~ (v2 = 0) | (v3 = 0 & apply(all_0_1_1, v0, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_2_2, v1, v0) = v4)) & ((v4 = 0 & v2 = 0 & apply(all_0_2_2, v1, v0) = 0) | ( ~ (v3 = 0) & apply(all_0_1_1, v0, v1) = v3)))))
% 13.68/3.73  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (pre_order(v0, v1) = 0) |  ~ (apply(v0, v2, v4) = v5) |  ~ (member(v3, v1) = 0) |  ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 13.68/3.73  | (96)  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2
% 13.68/3.73  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v4) = 0) |  ~ (apply(v1, v2, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apply(v1, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v0) = v6) | ( ~ (v6 = 0) & member(v3, v0) = v6) | ( ~ (v6 = 0) & member(v2, v0) = v6)))
% 13.68/3.73  | (98)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum(v1) = v2) |  ~ (member(v4, v1) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 13.68/3.73  | (99)  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2
% 13.68/3.73  | (100)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 13.68/3.73  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equivalence(v1, v0) = 0) |  ~ (apply(v1, v3, v2) = v4) |  ? [v5] : (( ~ (v5 = 0) & apply(v1, v2, v3) = v5) | ( ~ (v5 = 0) & member(v3, v0) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 13.68/3.74  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 13.68/3.74  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 13.68/3.74  | (104)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5)))
% 13.68/3.74  | (105)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 13.68/3.74  |
% 13.68/3.74  | Instantiating formula (68) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equivalence(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 13.68/3.74  | (106) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 &  ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 &  ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v1 = 0 &  ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_3_3) = 0))
% 13.68/3.74  |
% 13.68/3.74  +-Applying beta-rule and splitting (106), into two cases.
% 13.68/3.74  |-Branch one:
% 13.68/3.74  | (107) all_0_0_0 = 0
% 13.68/3.74  |
% 13.68/3.74  	| Equations (107) can reduce 8 to:
% 13.68/3.74  	| (108) $false
% 13.68/3.74  	|
% 13.68/3.74  	|-The branch is then unsatisfiable
% 13.68/3.74  |-Branch two:
% 13.68/3.74  | (8)  ~ (all_0_0_0 = 0)
% 13.68/3.74  | (110)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 &  ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 &  ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v1 = 0 &  ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_3_3) = 0))
% 13.68/3.74  |
% 13.68/3.74  	| Instantiating (110) with all_44_0_53, all_44_1_54, all_44_2_55, all_44_3_56, all_44_4_57, all_44_5_58, all_44_6_59, all_44_7_60, all_44_8_61 yields:
% 13.68/3.74  	| (111) (all_44_1_54 = 0 & all_44_2_55 = 0 & all_44_3_56 = 0 & all_44_4_57 = 0 & all_44_5_58 = 0 &  ~ (all_44_0_53 = 0) & apply(all_0_1_1, all_44_7_60, all_44_6_59) = 0 & apply(all_0_1_1, all_44_8_61, all_44_6_59) = all_44_0_53 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_6_59, all_0_3_3) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0) | (all_44_4_57 = 0 & all_44_5_58 = 0 & all_44_6_59 = 0 &  ~ (all_44_3_56 = 0) & apply(all_0_1_1, all_44_7_60, all_44_8_61) = all_44_3_56 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0) | (all_44_7_60 = 0 &  ~ (all_44_6_59 = 0) & apply(all_0_1_1, all_44_8_61, all_44_8_61) = all_44_6_59 & member(all_44_8_61, all_0_3_3) = 0)
% 13.68/3.74  	|
% 13.68/3.74  	+-Applying beta-rule and splitting (111), into two cases.
% 13.68/3.74  	|-Branch one:
% 13.68/3.74  	| (112) (all_44_1_54 = 0 & all_44_2_55 = 0 & all_44_3_56 = 0 & all_44_4_57 = 0 & all_44_5_58 = 0 &  ~ (all_44_0_53 = 0) & apply(all_0_1_1, all_44_7_60, all_44_6_59) = 0 & apply(all_0_1_1, all_44_8_61, all_44_6_59) = all_44_0_53 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_6_59, all_0_3_3) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0) | (all_44_4_57 = 0 & all_44_5_58 = 0 & all_44_6_59 = 0 &  ~ (all_44_3_56 = 0) & apply(all_0_1_1, all_44_7_60, all_44_8_61) = all_44_3_56 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0)
% 13.68/3.74  	|
% 13.68/3.74  		+-Applying beta-rule and splitting (112), into two cases.
% 13.68/3.74  		|-Branch one:
% 13.68/3.74  		| (113) all_44_1_54 = 0 & all_44_2_55 = 0 & all_44_3_56 = 0 & all_44_4_57 = 0 & all_44_5_58 = 0 &  ~ (all_44_0_53 = 0) & apply(all_0_1_1, all_44_7_60, all_44_6_59) = 0 & apply(all_0_1_1, all_44_8_61, all_44_6_59) = all_44_0_53 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_6_59, all_0_3_3) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0
% 13.68/3.74  		|
% 13.68/3.74  			| Applying alpha-rule on (113) yields:
% 13.68/3.74  			| (114) all_44_4_57 = 0
% 13.68/3.74  			| (115) apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0
% 13.68/3.74  			| (116)  ~ (all_44_0_53 = 0)
% 13.68/3.74  			| (117) apply(all_0_1_1, all_44_7_60, all_44_6_59) = 0
% 13.68/3.74  			| (118) apply(all_0_1_1, all_44_8_61, all_44_6_59) = all_44_0_53
% 13.68/3.74  			| (119) all_44_5_58 = 0
% 13.68/3.74  			| (120) all_44_2_55 = 0
% 13.68/3.74  			| (121) all_44_1_54 = 0
% 13.68/3.74  			| (122) member(all_44_8_61, all_0_3_3) = 0
% 13.68/3.74  			| (123) all_44_3_56 = 0
% 13.68/3.74  			| (124) member(all_44_7_60, all_0_3_3) = 0
% 13.68/3.74  			| (125) member(all_44_6_59, all_0_3_3) = 0
% 13.68/3.74  			|
% 13.68/3.74  			| Instantiating formula (6) with 0, all_44_6_59, all_44_7_60 and discharging atoms apply(all_0_1_1, all_44_7_60, all_44_6_59) = 0, yields:
% 13.68/3.74  			| (126)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0 & apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0) | ( ~ (v0 = 0) & member(all_44_6_59, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_44_7_60, all_0_3_3) = v0))
% 13.68/3.74  			|
% 13.68/3.74  			| Instantiating formula (6) with all_44_0_53, all_44_6_59, all_44_8_61 and discharging atoms apply(all_0_1_1, all_44_8_61, all_44_6_59) = all_44_0_53, yields:
% 13.68/3.74  			| (127)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & member(all_44_6_59, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_44_8_61, all_0_3_3) = v0) | (( ~ (all_44_0_53 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0)) & (all_44_0_53 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = v1) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = v0))))
% 13.68/3.74  			|
% 13.68/3.74  			| Instantiating formula (6) with 0, all_44_7_60, all_44_8_61 and discharging atoms apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0, yields:
% 13.68/3.75  			| (128)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (v0 = 0) & member(all_44_7_60, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_44_8_61, all_0_3_3) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_6_59, all_44_6_59, all_44_6_59, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (129)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (47) with all_44_6_59, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (130) apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_7_60, all_44_6_59, all_44_6_59, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (131)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (47) with all_44_7_60, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (132) apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_6_59, all_44_7_60, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (133)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_6_59) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_6_59, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (134)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_7_60, all_44_6_59, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (135)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_7_60, all_44_7_60, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (136)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_7_60, all_44_8_61, all_44_7_60, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (137)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_7_60, all_44_7_60, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (138)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_7_60, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (139)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_7_60, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (140)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_8_61, all_44_6_59, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_6_59, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (141)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_8_61, all_44_7_60, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (142)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (26) with all_44_8_61, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (143)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating formula (47) with all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 13.68/3.75  			| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (143) with all_58_0_62 yields:
% 13.68/3.75  			| (145) (all_58_0_62 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (all_58_0_62 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_62)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (141) with all_59_0_63 yields:
% 13.68/3.75  			| (146) (all_59_0_63 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (all_59_0_63 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_59_0_63) | ( ~ (all_59_0_63 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_63)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (140) with all_60_0_64 yields:
% 13.68/3.75  			| (147) (all_60_0_64 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_60_0_64 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_64) | ( ~ (all_60_0_64 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_64)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (135) with all_63_0_67 yields:
% 13.68/3.75  			| (148) (all_63_0_67 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (all_63_0_67 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_63_0_67) | ( ~ (all_63_0_67 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_63_0_67)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (142) with all_64_0_68 yields:
% 13.68/3.75  			| (149) (all_64_0_68 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (all_64_0_68 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_64_0_68) | ( ~ (all_64_0_68 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_64_0_68)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (139) with all_65_0_69 yields:
% 13.68/3.75  			| (150) (all_65_0_69 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (all_65_0_69 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_65_0_69) | ( ~ (all_65_0_69 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_65_0_69)
% 13.68/3.75  			|
% 13.68/3.75  			| Instantiating (138) with all_66_0_70 yields:
% 13.68/3.75  			| (151) (all_66_0_70 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_66_0_70 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_66_0_70) | ( ~ (all_66_0_70 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_66_0_70)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (137) with all_67_0_71 yields:
% 13.68/3.76  			| (152) (all_67_0_71 = 0 & apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0) | ( ~ (all_67_0_71 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_67_0_71) | ( ~ (all_67_0_71 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_67_0_71)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (134) with all_68_0_72 yields:
% 13.68/3.76  			| (153) (all_68_0_72 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (all_68_0_72 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_68_0_72) | ( ~ (all_68_0_72 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_68_0_72)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (131) with all_69_0_73 yields:
% 13.68/3.76  			| (154) (all_69_0_73 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0) | ( ~ (all_69_0_73 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_69_0_73) | ( ~ (all_69_0_73 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_69_0_73)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (133) with all_71_0_75 yields:
% 13.68/3.76  			| (155) (all_71_0_75 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (all_71_0_75 = 0) & apply(all_0_2_2, all_44_7_60, all_44_6_59) = all_71_0_75) | ( ~ (all_71_0_75 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_71_0_75)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (136) with all_72_0_76 yields:
% 13.68/3.76  			| (156) (all_72_0_76 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (all_72_0_76 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_72_0_76) | ( ~ (all_72_0_76 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_72_0_76)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (129) with all_78_0_82 yields:
% 13.68/3.76  			| (157) (all_78_0_82 = 0 & apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0) | ( ~ (all_78_0_82 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_78_0_82)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (128) with all_79_0_83, all_79_1_84 yields:
% 13.68/3.76  			| (158) (all_79_0_83 = 0 & all_79_1_84 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_79_1_84 = 0) & member(all_44_7_60, all_0_3_3) = all_79_1_84) | ( ~ (all_79_1_84 = 0) & member(all_44_8_61, all_0_3_3) = all_79_1_84)
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (127) with all_80_0_85, all_80_1_86 yields:
% 13.68/3.76  			| (159) ( ~ (all_80_1_86 = 0) & member(all_44_6_59, all_0_3_3) = all_80_1_86) | ( ~ (all_80_1_86 = 0) & member(all_44_8_61, all_0_3_3) = all_80_1_86) | (( ~ (all_44_0_53 = 0) | (all_80_0_85 = 0 & all_80_1_86 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0)) & (all_44_0_53 = 0 | ( ~ (all_80_0_85 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85) | ( ~ (all_80_1_86 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86)))
% 13.68/3.76  			|
% 13.68/3.76  			| Instantiating (126) with all_81_0_87, all_81_1_88 yields:
% 13.68/3.76  			| (160) (all_81_0_87 = 0 & all_81_1_88 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0 & apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0) | ( ~ (all_81_1_88 = 0) & member(all_44_6_59, all_0_3_3) = all_81_1_88) | ( ~ (all_81_1_88 = 0) & member(all_44_7_60, all_0_3_3) = all_81_1_88)
% 13.68/3.76  			|
% 13.68/3.76  			+-Applying beta-rule and splitting (145), into two cases.
% 13.68/3.76  			|-Branch one:
% 13.68/3.76  			| (161) all_58_0_62 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 13.68/3.76  			|
% 13.68/3.76  				| Applying alpha-rule on (161) yields:
% 13.68/3.76  				| (162) all_58_0_62 = 0
% 13.68/3.76  				| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 13.68/3.76  				|
% 13.68/3.76  				+-Applying beta-rule and splitting (158), into two cases.
% 13.68/3.76  				|-Branch one:
% 13.68/3.76  				| (164) (all_79_0_83 = 0 & all_79_1_84 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_79_1_84 = 0) & member(all_44_7_60, all_0_3_3) = all_79_1_84)
% 13.68/3.76  				|
% 13.68/3.76  					+-Applying beta-rule and splitting (164), into two cases.
% 13.68/3.76  					|-Branch one:
% 13.68/3.76  					| (165) all_79_0_83 = 0 & all_79_1_84 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  					|
% 13.68/3.76  						| Applying alpha-rule on (165) yields:
% 13.68/3.76  						| (166) all_79_0_83 = 0
% 13.68/3.76  						| (167) all_79_1_84 = 0
% 13.68/3.76  						| (168) apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 13.68/3.76  						| (169) apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  						|
% 13.68/3.76  						+-Applying beta-rule and splitting (147), into two cases.
% 13.68/3.76  						|-Branch one:
% 13.68/3.76  						| (170) (all_60_0_64 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_60_0_64 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_64)
% 13.68/3.76  						|
% 13.68/3.76  							+-Applying beta-rule and splitting (170), into two cases.
% 13.68/3.76  							|-Branch one:
% 13.68/3.76  							| (171) all_60_0_64 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  							|
% 13.68/3.76  								| Applying alpha-rule on (171) yields:
% 13.68/3.76  								| (172) all_60_0_64 = 0
% 13.68/3.76  								| (169) apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  								|
% 13.68/3.76  								+-Applying beta-rule and splitting (149), into two cases.
% 13.68/3.76  								|-Branch one:
% 13.68/3.76  								| (174) (all_64_0_68 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (all_64_0_68 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_64_0_68)
% 13.68/3.76  								|
% 13.68/3.76  									+-Applying beta-rule and splitting (174), into two cases.
% 13.68/3.76  									|-Branch one:
% 13.68/3.76  									| (175) all_64_0_68 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 13.68/3.76  									|
% 13.68/3.76  										| Applying alpha-rule on (175) yields:
% 13.68/3.76  										| (176) all_64_0_68 = 0
% 13.68/3.76  										| (168) apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 13.68/3.76  										|
% 13.68/3.76  										+-Applying beta-rule and splitting (151), into two cases.
% 13.68/3.76  										|-Branch one:
% 13.68/3.76  										| (178) (all_66_0_70 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_66_0_70 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_66_0_70)
% 13.68/3.76  										|
% 13.68/3.76  											+-Applying beta-rule and splitting (178), into two cases.
% 13.68/3.76  											|-Branch one:
% 13.68/3.76  											| (179) all_66_0_70 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  											|
% 13.68/3.76  												| Applying alpha-rule on (179) yields:
% 13.68/3.76  												| (180) all_66_0_70 = 0
% 13.68/3.76  												| (169) apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 13.68/3.76  												|
% 13.68/3.76  												+-Applying beta-rule and splitting (156), into two cases.
% 13.68/3.76  												|-Branch one:
% 13.68/3.76  												| (182) (all_72_0_76 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0) | ( ~ (all_72_0_76 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_72_0_76)
% 13.68/3.76  												|
% 13.68/3.76  													+-Applying beta-rule and splitting (182), into two cases.
% 13.68/3.76  													|-Branch one:
% 13.68/3.76  													| (183) all_72_0_76 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 13.68/3.76  													|
% 13.68/3.76  														| Applying alpha-rule on (183) yields:
% 13.68/3.76  														| (184) all_72_0_76 = 0
% 13.68/3.76  														| (168) apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 13.68/3.76  														|
% 13.68/3.76  														+-Applying beta-rule and splitting (150), into two cases.
% 13.68/3.76  														|-Branch one:
% 13.68/3.76  														| (186) (all_65_0_69 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (all_65_0_69 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_65_0_69)
% 13.68/3.76  														|
% 13.68/3.76  															+-Applying beta-rule and splitting (186), into two cases.
% 13.68/3.76  															|-Branch one:
% 13.68/3.76  															| (187) all_65_0_69 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 13.68/3.76  															|
% 13.68/3.76  																| Applying alpha-rule on (187) yields:
% 13.68/3.76  																| (188) all_65_0_69 = 0
% 13.68/3.76  																| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 13.68/3.76  																|
% 13.68/3.76  																+-Applying beta-rule and splitting (157), into two cases.
% 13.68/3.76  																|-Branch one:
% 13.68/3.76  																| (190) all_78_0_82 = 0 & apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0
% 13.68/3.76  																|
% 13.68/3.76  																	| Applying alpha-rule on (190) yields:
% 13.68/3.76  																	| (191) all_78_0_82 = 0
% 13.68/3.76  																	| (130) apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0
% 13.68/3.76  																	|
% 13.68/3.76  																	+-Applying beta-rule and splitting (160), into two cases.
% 13.68/3.76  																	|-Branch one:
% 13.68/3.76  																	| (193) (all_81_0_87 = 0 & all_81_1_88 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0 & apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0) | ( ~ (all_81_1_88 = 0) & member(all_44_6_59, all_0_3_3) = all_81_1_88)
% 13.68/3.76  																	|
% 13.68/3.76  																		+-Applying beta-rule and splitting (193), into two cases.
% 13.68/3.76  																		|-Branch one:
% 13.68/3.76  																		| (194) all_81_0_87 = 0 & all_81_1_88 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0 & apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0
% 13.68/3.76  																		|
% 13.68/3.76  																			| Applying alpha-rule on (194) yields:
% 13.68/3.76  																			| (195) all_81_0_87 = 0
% 13.68/3.76  																			| (196) all_81_1_88 = 0
% 13.68/3.76  																			| (197) apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0
% 13.68/3.76  																			| (198) apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0
% 14.02/3.77  																			|
% 14.02/3.77  																			+-Applying beta-rule and splitting (155), into two cases.
% 14.02/3.77  																			|-Branch one:
% 14.02/3.77  																			| (199) (all_71_0_75 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (all_71_0_75 = 0) & apply(all_0_2_2, all_44_7_60, all_44_6_59) = all_71_0_75)
% 14.02/3.77  																			|
% 14.02/3.77  																				+-Applying beta-rule and splitting (199), into two cases.
% 14.02/3.77  																				|-Branch one:
% 14.02/3.77  																				| (200) all_71_0_75 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0
% 14.02/3.77  																				|
% 14.02/3.77  																					| Applying alpha-rule on (200) yields:
% 14.02/3.77  																					| (201) all_71_0_75 = 0
% 14.02/3.77  																					| (202) apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0
% 14.02/3.77  																					|
% 14.02/3.77  																					+-Applying beta-rule and splitting (153), into two cases.
% 14.02/3.77  																					|-Branch one:
% 14.02/3.77  																					| (203) (all_68_0_72 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0) | ( ~ (all_68_0_72 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_68_0_72)
% 14.02/3.77  																					|
% 14.02/3.77  																						+-Applying beta-rule and splitting (203), into two cases.
% 14.02/3.77  																						|-Branch one:
% 14.02/3.77  																						| (204) all_68_0_72 = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0
% 14.02/3.77  																						|
% 14.02/3.77  																							| Applying alpha-rule on (204) yields:
% 14.02/3.77  																							| (205) all_68_0_72 = 0
% 14.02/3.77  																							| (202) apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0
% 14.02/3.77  																							|
% 14.02/3.77  																							+-Applying beta-rule and splitting (154), into two cases.
% 14.02/3.77  																							|-Branch one:
% 14.02/3.77  																							| (207) (all_69_0_73 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0) | ( ~ (all_69_0_73 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_69_0_73)
% 14.02/3.77  																							|
% 14.02/3.77  																								+-Applying beta-rule and splitting (207), into two cases.
% 14.02/3.77  																								|-Branch one:
% 14.02/3.77  																								| (208) all_69_0_73 = 0 & apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0
% 14.02/3.77  																								|
% 14.02/3.77  																									| Applying alpha-rule on (208) yields:
% 14.02/3.77  																									| (209) all_69_0_73 = 0
% 14.02/3.77  																									| (197) apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0
% 14.02/3.77  																									|
% 14.02/3.77  																									+-Applying beta-rule and splitting (159), into two cases.
% 14.02/3.77  																									|-Branch one:
% 14.02/3.77  																									| (211) ( ~ (all_80_1_86 = 0) & member(all_44_6_59, all_0_3_3) = all_80_1_86) | ( ~ (all_80_1_86 = 0) & member(all_44_8_61, all_0_3_3) = all_80_1_86)
% 14.02/3.77  																									|
% 14.02/3.77  																										+-Applying beta-rule and splitting (211), into two cases.
% 14.02/3.77  																										|-Branch one:
% 14.02/3.77  																										| (212)  ~ (all_80_1_86 = 0) & member(all_44_6_59, all_0_3_3) = all_80_1_86
% 14.02/3.77  																										|
% 14.02/3.77  																											| Applying alpha-rule on (212) yields:
% 14.02/3.77  																											| (213)  ~ (all_80_1_86 = 0)
% 14.02/3.77  																											| (214) member(all_44_6_59, all_0_3_3) = all_80_1_86
% 14.02/3.77  																											|
% 14.02/3.77  																											| Instantiating formula (19) with all_44_6_59, all_0_3_3, all_80_1_86, 0 and discharging atoms member(all_44_6_59, all_0_3_3) = all_80_1_86, member(all_44_6_59, all_0_3_3) = 0, yields:
% 14.02/3.77  																											| (215) all_80_1_86 = 0
% 14.02/3.77  																											|
% 14.02/3.77  																											| Equations (215) can reduce 213 to:
% 14.02/3.77  																											| (108) $false
% 14.02/3.77  																											|
% 14.02/3.77  																											|-The branch is then unsatisfiable
% 14.02/3.77  																										|-Branch two:
% 14.02/3.77  																										| (217)  ~ (all_80_1_86 = 0) & member(all_44_8_61, all_0_3_3) = all_80_1_86
% 14.02/3.77  																										|
% 14.02/3.77  																											| Applying alpha-rule on (217) yields:
% 14.02/3.77  																											| (213)  ~ (all_80_1_86 = 0)
% 14.02/3.77  																											| (219) member(all_44_8_61, all_0_3_3) = all_80_1_86
% 14.02/3.77  																											|
% 14.02/3.77  																											| Instantiating formula (19) with all_44_8_61, all_0_3_3, all_80_1_86, 0 and discharging atoms member(all_44_8_61, all_0_3_3) = all_80_1_86, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.77  																											| (215) all_80_1_86 = 0
% 14.02/3.77  																											|
% 14.02/3.77  																											| Equations (215) can reduce 213 to:
% 14.02/3.77  																											| (108) $false
% 14.02/3.77  																											|
% 14.02/3.77  																											|-The branch is then unsatisfiable
% 14.02/3.77  																									|-Branch two:
% 14.02/3.77  																									| (222) ( ~ (all_44_0_53 = 0) | (all_80_0_85 = 0 & all_80_1_86 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0)) & (all_44_0_53 = 0 | ( ~ (all_80_0_85 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85) | ( ~ (all_80_1_86 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86))
% 14.02/3.77  																									|
% 14.02/3.77  																										| Applying alpha-rule on (222) yields:
% 14.02/3.77  																										| (223)  ~ (all_44_0_53 = 0) | (all_80_0_85 = 0 & all_80_1_86 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0)
% 14.02/3.77  																										| (224) all_44_0_53 = 0 | ( ~ (all_80_0_85 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85) | ( ~ (all_80_1_86 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86)
% 14.02/3.77  																										|
% 14.02/3.77  																										+-Applying beta-rule and splitting (148), into two cases.
% 14.02/3.77  																										|-Branch one:
% 14.02/3.77  																										| (225) (all_63_0_67 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (all_63_0_67 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_63_0_67)
% 14.02/3.77  																										|
% 14.02/3.77  																											+-Applying beta-rule and splitting (225), into two cases.
% 14.02/3.77  																											|-Branch one:
% 14.02/3.77  																											| (226) all_63_0_67 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0
% 14.02/3.77  																											|
% 14.02/3.77  																												| Applying alpha-rule on (226) yields:
% 14.02/3.77  																												| (227) all_63_0_67 = 0
% 14.02/3.77  																												| (228) apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0
% 14.02/3.77  																												|
% 14.02/3.77  																												+-Applying beta-rule and splitting (146), into two cases.
% 14.02/3.77  																												|-Branch one:
% 14.02/3.77  																												| (229) (all_59_0_63 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0) | ( ~ (all_59_0_63 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_59_0_63)
% 14.02/3.77  																												|
% 14.02/3.77  																													+-Applying beta-rule and splitting (229), into two cases.
% 14.02/3.77  																													|-Branch one:
% 14.02/3.77  																													| (230) all_59_0_63 = 0 & apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0
% 14.02/3.77  																													|
% 14.02/3.77  																														| Applying alpha-rule on (230) yields:
% 14.02/3.77  																														| (231) all_59_0_63 = 0
% 14.02/3.77  																														| (228) apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0
% 14.02/3.77  																														|
% 14.02/3.77  																														+-Applying beta-rule and splitting (224), into two cases.
% 14.02/3.77  																														|-Branch one:
% 14.02/3.77  																														| (233) all_44_0_53 = 0
% 14.02/3.77  																														|
% 14.02/3.77  																															| Equations (233) can reduce 116 to:
% 14.02/3.77  																															| (108) $false
% 14.02/3.77  																															|
% 14.02/3.77  																															|-The branch is then unsatisfiable
% 14.02/3.77  																														|-Branch two:
% 14.02/3.77  																														| (116)  ~ (all_44_0_53 = 0)
% 14.02/3.77  																														| (236) ( ~ (all_80_0_85 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85) | ( ~ (all_80_1_86 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86)
% 14.02/3.77  																														|
% 14.02/3.77  																															+-Applying beta-rule and splitting (236), into two cases.
% 14.02/3.77  																															|-Branch one:
% 14.02/3.77  																															| (237)  ~ (all_80_0_85 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85
% 14.02/3.77  																															|
% 14.02/3.77  																																| Applying alpha-rule on (237) yields:
% 14.02/3.77  																																| (238)  ~ (all_80_0_85 = 0)
% 14.02/3.77  																																| (239) apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85
% 14.02/3.77  																																|
% 14.02/3.77  																																| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_8_61, 0, all_80_0_85 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_80_0_85, apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0, yields:
% 14.02/3.77  																																| (240) all_80_0_85 = 0
% 14.02/3.77  																																|
% 14.02/3.77  																																| Equations (240) can reduce 238 to:
% 14.02/3.77  																																| (108) $false
% 14.02/3.77  																																|
% 14.02/3.77  																																|-The branch is then unsatisfiable
% 14.02/3.77  																															|-Branch two:
% 14.02/3.77  																															| (242)  ~ (all_80_1_86 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86
% 14.02/3.77  																															|
% 14.02/3.77  																																| Applying alpha-rule on (242) yields:
% 14.02/3.77  																																| (213)  ~ (all_80_1_86 = 0)
% 14.02/3.77  																																| (244) apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86
% 14.02/3.77  																																|
% 14.02/3.77  																																| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_6_59, 0, all_80_1_86 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_80_1_86, apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0, yields:
% 14.02/3.77  																																| (215) all_80_1_86 = 0
% 14.02/3.77  																																|
% 14.02/3.77  																																| Equations (215) can reduce 213 to:
% 14.02/3.77  																																| (108) $false
% 14.02/3.77  																																|
% 14.02/3.77  																																|-The branch is then unsatisfiable
% 14.02/3.77  																													|-Branch two:
% 14.02/3.77  																													| (247)  ~ (all_59_0_63 = 0) & apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_59_0_63
% 14.02/3.77  																													|
% 14.02/3.77  																														| Applying alpha-rule on (247) yields:
% 14.02/3.77  																														| (248)  ~ (all_59_0_63 = 0)
% 14.02/3.77  																														| (249) apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_59_0_63
% 14.02/3.77  																														|
% 14.02/3.77  																														| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_8_61, 0, all_59_0_63 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_8_61) = all_59_0_63, apply(all_0_2_2, all_44_6_59, all_44_8_61) = 0, yields:
% 14.02/3.77  																														| (231) all_59_0_63 = 0
% 14.02/3.77  																														|
% 14.02/3.77  																														| Equations (231) can reduce 248 to:
% 14.02/3.77  																														| (108) $false
% 14.02/3.77  																														|
% 14.02/3.77  																														|-The branch is then unsatisfiable
% 14.02/3.77  																												|-Branch two:
% 14.02/3.77  																												| (252)  ~ (all_59_0_63 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_63
% 14.02/3.77  																												|
% 14.02/3.77  																													| Applying alpha-rule on (252) yields:
% 14.02/3.77  																													| (248)  ~ (all_59_0_63 = 0)
% 14.02/3.77  																													| (254) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_63
% 14.02/3.77  																													|
% 14.02/3.77  																													| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_59_0_63 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_63, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.77  																													| (231) all_59_0_63 = 0
% 14.02/3.77  																													|
% 14.02/3.77  																													| Equations (231) can reduce 248 to:
% 14.02/3.77  																													| (108) $false
% 14.02/3.77  																													|
% 14.02/3.77  																													|-The branch is then unsatisfiable
% 14.02/3.77  																											|-Branch two:
% 14.02/3.77  																											| (257)  ~ (all_63_0_67 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_63_0_67
% 14.02/3.77  																											|
% 14.02/3.77  																												| Applying alpha-rule on (257) yields:
% 14.02/3.77  																												| (258)  ~ (all_63_0_67 = 0)
% 14.02/3.77  																												| (259) apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_63_0_67
% 14.02/3.77  																												|
% 14.02/3.77  																												| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_7_60, 0, all_63_0_67 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_63_0_67, apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0, yields:
% 14.02/3.77  																												| (227) all_63_0_67 = 0
% 14.02/3.77  																												|
% 14.02/3.77  																												| Equations (227) can reduce 258 to:
% 14.02/3.77  																												| (108) $false
% 14.02/3.77  																												|
% 14.02/3.77  																												|-The branch is then unsatisfiable
% 14.02/3.77  																										|-Branch two:
% 14.02/3.77  																										| (262)  ~ (all_63_0_67 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_63_0_67
% 14.02/3.77  																										|
% 14.02/3.77  																											| Applying alpha-rule on (262) yields:
% 14.02/3.77  																											| (258)  ~ (all_63_0_67 = 0)
% 14.02/3.77  																											| (264) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_63_0_67
% 14.02/3.77  																											|
% 14.02/3.77  																											| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_63_0_67 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_63_0_67, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.77  																											| (227) all_63_0_67 = 0
% 14.02/3.77  																											|
% 14.02/3.77  																											| Equations (227) can reduce 258 to:
% 14.02/3.77  																											| (108) $false
% 14.02/3.77  																											|
% 14.02/3.77  																											|-The branch is then unsatisfiable
% 14.02/3.77  																								|-Branch two:
% 14.02/3.77  																								| (267)  ~ (all_69_0_73 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_69_0_73
% 14.02/3.77  																								|
% 14.02/3.77  																									| Applying alpha-rule on (267) yields:
% 14.02/3.77  																									| (268)  ~ (all_69_0_73 = 0)
% 14.02/3.77  																									| (269) apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_69_0_73
% 14.02/3.77  																									|
% 14.02/3.77  																									| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_6_59, 0, all_69_0_73 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_69_0_73, apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0, yields:
% 14.02/3.78  																									| (209) all_69_0_73 = 0
% 14.02/3.78  																									|
% 14.02/3.78  																									| Equations (209) can reduce 268 to:
% 14.02/3.78  																									| (108) $false
% 14.02/3.78  																									|
% 14.02/3.78  																									|-The branch is then unsatisfiable
% 14.02/3.78  																							|-Branch two:
% 14.02/3.78  																							| (272)  ~ (all_69_0_73 = 0) & apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_69_0_73
% 14.02/3.78  																							|
% 14.02/3.78  																								| Applying alpha-rule on (272) yields:
% 14.02/3.78  																								| (268)  ~ (all_69_0_73 = 0)
% 14.02/3.78  																								| (274) apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_69_0_73
% 14.02/3.78  																								|
% 14.02/3.78  																								| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_7_60, 0, all_69_0_73 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_7_60) = all_69_0_73, apply(all_0_2_2, all_44_6_59, all_44_7_60) = 0, yields:
% 14.02/3.78  																								| (209) all_69_0_73 = 0
% 14.02/3.78  																								|
% 14.02/3.78  																								| Equations (209) can reduce 268 to:
% 14.02/3.78  																								| (108) $false
% 14.02/3.78  																								|
% 14.02/3.78  																								|-The branch is then unsatisfiable
% 14.02/3.78  																						|-Branch two:
% 14.02/3.78  																						| (277)  ~ (all_68_0_72 = 0) & apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_68_0_72
% 14.02/3.78  																						|
% 14.02/3.78  																							| Applying alpha-rule on (277) yields:
% 14.02/3.78  																							| (278)  ~ (all_68_0_72 = 0)
% 14.02/3.78  																							| (279) apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_68_0_72
% 14.02/3.78  																							|
% 14.02/3.78  																							| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_6_59, 0, all_68_0_72 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_6_59) = all_68_0_72, apply(all_0_2_2, all_44_8_61, all_44_6_59) = 0, yields:
% 14.02/3.78  																							| (205) all_68_0_72 = 0
% 14.02/3.78  																							|
% 14.02/3.78  																							| Equations (205) can reduce 278 to:
% 14.02/3.78  																							| (108) $false
% 14.02/3.78  																							|
% 14.02/3.78  																							|-The branch is then unsatisfiable
% 14.02/3.78  																					|-Branch two:
% 14.02/3.78  																					| (282)  ~ (all_68_0_72 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_68_0_72
% 14.02/3.78  																					|
% 14.02/3.78  																						| Applying alpha-rule on (282) yields:
% 14.02/3.78  																						| (278)  ~ (all_68_0_72 = 0)
% 14.02/3.78  																						| (284) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_68_0_72
% 14.02/3.78  																						|
% 14.02/3.78  																						| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_68_0_72 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_68_0_72, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.78  																						| (205) all_68_0_72 = 0
% 14.02/3.78  																						|
% 14.02/3.78  																						| Equations (205) can reduce 278 to:
% 14.02/3.78  																						| (108) $false
% 14.02/3.78  																						|
% 14.02/3.78  																						|-The branch is then unsatisfiable
% 14.02/3.78  																				|-Branch two:
% 14.02/3.78  																				| (287)  ~ (all_71_0_75 = 0) & apply(all_0_2_2, all_44_7_60, all_44_6_59) = all_71_0_75
% 14.02/3.78  																				|
% 14.02/3.78  																					| Applying alpha-rule on (287) yields:
% 14.02/3.78  																					| (288)  ~ (all_71_0_75 = 0)
% 14.02/3.78  																					| (289) apply(all_0_2_2, all_44_7_60, all_44_6_59) = all_71_0_75
% 14.02/3.78  																					|
% 14.02/3.78  																					| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_6_59, 0, all_71_0_75 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_6_59) = all_71_0_75, apply(all_0_2_2, all_44_7_60, all_44_6_59) = 0, yields:
% 14.02/3.78  																					| (201) all_71_0_75 = 0
% 14.02/3.78  																					|
% 14.02/3.78  																					| Equations (201) can reduce 288 to:
% 14.02/3.78  																					| (108) $false
% 14.02/3.78  																					|
% 14.02/3.78  																					|-The branch is then unsatisfiable
% 14.02/3.78  																			|-Branch two:
% 14.02/3.78  																			| (292)  ~ (all_71_0_75 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_71_0_75
% 14.02/3.78  																			|
% 14.02/3.78  																				| Applying alpha-rule on (292) yields:
% 14.02/3.78  																				| (288)  ~ (all_71_0_75 = 0)
% 14.02/3.78  																				| (294) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_71_0_75
% 14.02/3.78  																				|
% 14.02/3.78  																				| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_71_0_75 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_71_0_75, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.78  																				| (201) all_71_0_75 = 0
% 14.02/3.78  																				|
% 14.02/3.78  																				| Equations (201) can reduce 288 to:
% 14.02/3.78  																				| (108) $false
% 14.02/3.78  																				|
% 14.02/3.78  																				|-The branch is then unsatisfiable
% 14.02/3.78  																		|-Branch two:
% 14.02/3.78  																		| (297)  ~ (all_81_1_88 = 0) & member(all_44_6_59, all_0_3_3) = all_81_1_88
% 14.02/3.78  																		|
% 14.02/3.78  																			| Applying alpha-rule on (297) yields:
% 14.02/3.78  																			| (298)  ~ (all_81_1_88 = 0)
% 14.02/3.78  																			| (299) member(all_44_6_59, all_0_3_3) = all_81_1_88
% 14.02/3.78  																			|
% 14.02/3.78  																			| Instantiating formula (19) with all_44_6_59, all_0_3_3, all_81_1_88, 0 and discharging atoms member(all_44_6_59, all_0_3_3) = all_81_1_88, member(all_44_6_59, all_0_3_3) = 0, yields:
% 14.02/3.78  																			| (196) all_81_1_88 = 0
% 14.02/3.78  																			|
% 14.02/3.78  																			| Equations (196) can reduce 298 to:
% 14.02/3.78  																			| (108) $false
% 14.02/3.78  																			|
% 14.02/3.78  																			|-The branch is then unsatisfiable
% 14.02/3.78  																	|-Branch two:
% 14.02/3.78  																	| (302)  ~ (all_81_1_88 = 0) & member(all_44_7_60, all_0_3_3) = all_81_1_88
% 14.02/3.78  																	|
% 14.02/3.78  																		| Applying alpha-rule on (302) yields:
% 14.02/3.78  																		| (298)  ~ (all_81_1_88 = 0)
% 14.02/3.78  																		| (304) member(all_44_7_60, all_0_3_3) = all_81_1_88
% 14.02/3.78  																		|
% 14.02/3.78  																		| Instantiating formula (19) with all_44_7_60, all_0_3_3, all_81_1_88, 0 and discharging atoms member(all_44_7_60, all_0_3_3) = all_81_1_88, member(all_44_7_60, all_0_3_3) = 0, yields:
% 14.02/3.78  																		| (196) all_81_1_88 = 0
% 14.02/3.78  																		|
% 14.02/3.78  																		| Equations (196) can reduce 298 to:
% 14.02/3.78  																		| (108) $false
% 14.02/3.78  																		|
% 14.02/3.78  																		|-The branch is then unsatisfiable
% 14.02/3.78  																|-Branch two:
% 14.02/3.78  																| (307)  ~ (all_78_0_82 = 0) & apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_78_0_82
% 14.02/3.78  																|
% 14.02/3.78  																	| Applying alpha-rule on (307) yields:
% 14.02/3.78  																	| (308)  ~ (all_78_0_82 = 0)
% 14.02/3.78  																	| (309) apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_78_0_82
% 14.02/3.78  																	|
% 14.02/3.78  																	| Instantiating formula (40) with all_0_2_2, all_44_6_59, all_44_6_59, 0, all_78_0_82 and discharging atoms apply(all_0_2_2, all_44_6_59, all_44_6_59) = all_78_0_82, apply(all_0_2_2, all_44_6_59, all_44_6_59) = 0, yields:
% 14.02/3.78  																	| (191) all_78_0_82 = 0
% 14.02/3.78  																	|
% 14.02/3.78  																	| Equations (191) can reduce 308 to:
% 14.02/3.78  																	| (108) $false
% 14.02/3.78  																	|
% 14.02/3.78  																	|-The branch is then unsatisfiable
% 14.02/3.78  															|-Branch two:
% 14.02/3.78  															| (312)  ~ (all_65_0_69 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_65_0_69
% 14.02/3.78  															|
% 14.02/3.78  																| Applying alpha-rule on (312) yields:
% 14.02/3.78  																| (313)  ~ (all_65_0_69 = 0)
% 14.02/3.78  																| (314) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_65_0_69
% 14.02/3.78  																|
% 14.02/3.78  																| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_65_0_69 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_65_0_69, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.78  																| (188) all_65_0_69 = 0
% 14.02/3.78  																|
% 14.02/3.78  																| Equations (188) can reduce 313 to:
% 14.02/3.78  																| (108) $false
% 14.02/3.78  																|
% 14.02/3.78  																|-The branch is then unsatisfiable
% 14.02/3.78  														|-Branch two:
% 14.02/3.78  														| (317)  ~ (all_65_0_69 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_65_0_69
% 14.02/3.78  														|
% 14.02/3.78  															| Applying alpha-rule on (317) yields:
% 14.02/3.78  															| (313)  ~ (all_65_0_69 = 0)
% 14.02/3.78  															| (319) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_65_0_69
% 14.02/3.78  															|
% 14.02/3.78  															| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_65_0_69 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_65_0_69, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.78  															| (188) all_65_0_69 = 0
% 14.02/3.78  															|
% 14.02/3.78  															| Equations (188) can reduce 313 to:
% 14.02/3.78  															| (108) $false
% 14.02/3.78  															|
% 14.02/3.78  															|-The branch is then unsatisfiable
% 14.02/3.78  													|-Branch two:
% 14.02/3.78  													| (322)  ~ (all_72_0_76 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_72_0_76
% 14.02/3.78  													|
% 14.02/3.78  														| Applying alpha-rule on (322) yields:
% 14.02/3.78  														| (323)  ~ (all_72_0_76 = 0)
% 14.02/3.78  														| (324) apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_72_0_76
% 14.02/3.78  														|
% 14.02/3.78  														+-Applying beta-rule and splitting (152), into two cases.
% 14.02/3.78  														|-Branch one:
% 14.02/3.78  														| (325) (all_67_0_71 = 0 & apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0) | ( ~ (all_67_0_71 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_67_0_71)
% 14.02/3.78  														|
% 14.02/3.78  															+-Applying beta-rule and splitting (325), into two cases.
% 14.02/3.78  															|-Branch one:
% 14.02/3.78  															| (326) all_67_0_71 = 0 & apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0
% 14.02/3.78  															|
% 14.02/3.78  																| Applying alpha-rule on (326) yields:
% 14.02/3.78  																| (327) all_67_0_71 = 0
% 14.02/3.78  																| (132) apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0
% 14.02/3.78  																|
% 14.02/3.78  																| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_7_60, 0, all_72_0_76 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_72_0_76, apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0, yields:
% 14.02/3.78  																| (184) all_72_0_76 = 0
% 14.02/3.78  																|
% 14.02/3.78  																| Equations (184) can reduce 323 to:
% 14.02/3.78  																| (108) $false
% 14.02/3.78  																|
% 14.02/3.78  																|-The branch is then unsatisfiable
% 14.02/3.78  															|-Branch two:
% 14.02/3.78  															| (331)  ~ (all_67_0_71 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_67_0_71
% 14.02/3.78  															|
% 14.02/3.78  																| Applying alpha-rule on (331) yields:
% 14.02/3.78  																| (332)  ~ (all_67_0_71 = 0)
% 14.02/3.78  																| (333) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_67_0_71
% 14.02/3.78  																|
% 14.02/3.78  																| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_67_0_71 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_67_0_71, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.78  																| (327) all_67_0_71 = 0
% 14.02/3.78  																|
% 14.02/3.78  																| Equations (327) can reduce 332 to:
% 14.02/3.78  																| (108) $false
% 14.02/3.78  																|
% 14.02/3.78  																|-The branch is then unsatisfiable
% 14.02/3.78  														|-Branch two:
% 14.02/3.78  														| (336)  ~ (all_67_0_71 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_67_0_71
% 14.02/3.78  														|
% 14.02/3.78  															| Applying alpha-rule on (336) yields:
% 14.02/3.78  															| (332)  ~ (all_67_0_71 = 0)
% 14.02/3.78  															| (338) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_67_0_71
% 14.02/3.78  															|
% 14.02/3.78  															| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_67_0_71 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_67_0_71, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.78  															| (327) all_67_0_71 = 0
% 14.02/3.79  															|
% 14.02/3.79  															| Equations (327) can reduce 332 to:
% 14.02/3.79  															| (108) $false
% 14.02/3.79  															|
% 14.02/3.79  															|-The branch is then unsatisfiable
% 14.02/3.79  												|-Branch two:
% 14.02/3.79  												| (341)  ~ (all_72_0_76 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_72_0_76
% 14.02/3.79  												|
% 14.02/3.79  													| Applying alpha-rule on (341) yields:
% 14.02/3.79  													| (323)  ~ (all_72_0_76 = 0)
% 14.02/3.79  													| (343) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_72_0_76
% 14.02/3.79  													|
% 14.02/3.79  													| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_72_0_76 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_72_0_76, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.79  													| (184) all_72_0_76 = 0
% 14.02/3.79  													|
% 14.02/3.79  													| Equations (184) can reduce 323 to:
% 14.02/3.79  													| (108) $false
% 14.02/3.79  													|
% 14.02/3.79  													|-The branch is then unsatisfiable
% 14.02/3.79  											|-Branch two:
% 14.02/3.79  											| (346)  ~ (all_66_0_70 = 0) & apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_66_0_70
% 14.02/3.79  											|
% 14.02/3.79  												| Applying alpha-rule on (346) yields:
% 14.02/3.79  												| (347)  ~ (all_66_0_70 = 0)
% 14.02/3.79  												| (348) apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_66_0_70
% 14.02/3.79  												|
% 14.02/3.79  												| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_7_60, 0, all_66_0_70 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_7_60) = all_66_0_70, apply(all_0_2_2, all_44_7_60, all_44_7_60) = 0, yields:
% 14.02/3.79  												| (180) all_66_0_70 = 0
% 14.02/3.79  												|
% 14.02/3.79  												| Equations (180) can reduce 347 to:
% 14.02/3.79  												| (108) $false
% 14.02/3.79  												|
% 14.02/3.79  												|-The branch is then unsatisfiable
% 14.02/3.79  										|-Branch two:
% 14.02/3.79  										| (351)  ~ (all_66_0_70 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_66_0_70
% 14.02/3.79  										|
% 14.02/3.79  											| Applying alpha-rule on (351) yields:
% 14.02/3.79  											| (347)  ~ (all_66_0_70 = 0)
% 14.02/3.79  											| (353) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_66_0_70
% 14.02/3.79  											|
% 14.02/3.79  											| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_66_0_70 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_66_0_70, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.79  											| (180) all_66_0_70 = 0
% 14.02/3.79  											|
% 14.02/3.79  											| Equations (180) can reduce 347 to:
% 14.02/3.79  											| (108) $false
% 14.02/3.79  											|
% 14.02/3.79  											|-The branch is then unsatisfiable
% 14.02/3.79  									|-Branch two:
% 14.02/3.79  									| (356)  ~ (all_64_0_68 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_64_0_68
% 14.02/3.79  									|
% 14.02/3.79  										| Applying alpha-rule on (356) yields:
% 14.02/3.79  										| (357)  ~ (all_64_0_68 = 0)
% 14.02/3.79  										| (358) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_64_0_68
% 14.02/3.79  										|
% 14.02/3.79  										| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_64_0_68 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_64_0_68, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.79  										| (176) all_64_0_68 = 0
% 14.02/3.79  										|
% 14.02/3.79  										| Equations (176) can reduce 357 to:
% 14.02/3.79  										| (108) $false
% 14.02/3.79  										|
% 14.02/3.79  										|-The branch is then unsatisfiable
% 14.02/3.79  								|-Branch two:
% 14.02/3.79  								| (361)  ~ (all_64_0_68 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_64_0_68
% 14.02/3.79  								|
% 14.02/3.79  									| Applying alpha-rule on (361) yields:
% 14.02/3.79  									| (357)  ~ (all_64_0_68 = 0)
% 14.02/3.79  									| (363) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_64_0_68
% 14.02/3.79  									|
% 14.02/3.79  									| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_64_0_68 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_64_0_68, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.79  									| (176) all_64_0_68 = 0
% 14.02/3.79  									|
% 14.02/3.79  									| Equations (176) can reduce 357 to:
% 14.02/3.79  									| (108) $false
% 14.02/3.79  									|
% 14.02/3.79  									|-The branch is then unsatisfiable
% 14.02/3.79  							|-Branch two:
% 14.02/3.79  							| (366)  ~ (all_60_0_64 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_64
% 14.02/3.79  							|
% 14.02/3.79  								| Applying alpha-rule on (366) yields:
% 14.02/3.79  								| (367)  ~ (all_60_0_64 = 0)
% 14.02/3.79  								| (368) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_64
% 14.02/3.79  								|
% 14.02/3.79  								| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_60_0_64 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_64, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.79  								| (172) all_60_0_64 = 0
% 14.02/3.79  								|
% 14.02/3.79  								| Equations (172) can reduce 367 to:
% 14.02/3.79  								| (108) $false
% 14.02/3.79  								|
% 14.02/3.79  								|-The branch is then unsatisfiable
% 14.02/3.79  						|-Branch two:
% 14.02/3.79  						| (371)  ~ (all_60_0_64 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_64
% 14.02/3.79  						|
% 14.02/3.79  							| Applying alpha-rule on (371) yields:
% 14.02/3.79  							| (367)  ~ (all_60_0_64 = 0)
% 14.02/3.79  							| (373) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_64
% 14.02/3.79  							|
% 14.02/3.79  							| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_60_0_64 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_64, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.79  							| (172) all_60_0_64 = 0
% 14.02/3.79  							|
% 14.02/3.79  							| Equations (172) can reduce 367 to:
% 14.02/3.79  							| (108) $false
% 14.02/3.79  							|
% 14.02/3.79  							|-The branch is then unsatisfiable
% 14.02/3.79  					|-Branch two:
% 14.02/3.79  					| (376)  ~ (all_79_1_84 = 0) & member(all_44_7_60, all_0_3_3) = all_79_1_84
% 14.02/3.79  					|
% 14.02/3.79  						| Applying alpha-rule on (376) yields:
% 14.02/3.79  						| (377)  ~ (all_79_1_84 = 0)
% 14.02/3.79  						| (378) member(all_44_7_60, all_0_3_3) = all_79_1_84
% 14.02/3.79  						|
% 14.02/3.79  						| Instantiating formula (19) with all_44_7_60, all_0_3_3, all_79_1_84, 0 and discharging atoms member(all_44_7_60, all_0_3_3) = all_79_1_84, member(all_44_7_60, all_0_3_3) = 0, yields:
% 14.02/3.79  						| (167) all_79_1_84 = 0
% 14.02/3.79  						|
% 14.02/3.79  						| Equations (167) can reduce 377 to:
% 14.02/3.79  						| (108) $false
% 14.02/3.79  						|
% 14.02/3.79  						|-The branch is then unsatisfiable
% 14.02/3.79  				|-Branch two:
% 14.02/3.79  				| (381)  ~ (all_79_1_84 = 0) & member(all_44_8_61, all_0_3_3) = all_79_1_84
% 14.02/3.79  				|
% 14.02/3.79  					| Applying alpha-rule on (381) yields:
% 14.02/3.79  					| (377)  ~ (all_79_1_84 = 0)
% 14.02/3.79  					| (383) member(all_44_8_61, all_0_3_3) = all_79_1_84
% 14.02/3.79  					|
% 14.02/3.79  					| Instantiating formula (19) with all_44_8_61, all_0_3_3, all_79_1_84, 0 and discharging atoms member(all_44_8_61, all_0_3_3) = all_79_1_84, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.79  					| (167) all_79_1_84 = 0
% 14.02/3.79  					|
% 14.02/3.79  					| Equations (167) can reduce 377 to:
% 14.02/3.79  					| (108) $false
% 14.02/3.79  					|
% 14.02/3.79  					|-The branch is then unsatisfiable
% 14.02/3.79  			|-Branch two:
% 14.02/3.79  			| (386)  ~ (all_58_0_62 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_62
% 14.02/3.79  			|
% 14.02/3.79  				| Applying alpha-rule on (386) yields:
% 14.02/3.79  				| (387)  ~ (all_58_0_62 = 0)
% 14.02/3.79  				| (388) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_62
% 14.02/3.79  				|
% 14.02/3.79  				| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_58_0_62 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_62, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.79  				| (162) all_58_0_62 = 0
% 14.02/3.79  				|
% 14.02/3.79  				| Equations (162) can reduce 387 to:
% 14.02/3.79  				| (108) $false
% 14.02/3.79  				|
% 14.02/3.79  				|-The branch is then unsatisfiable
% 14.02/3.79  		|-Branch two:
% 14.02/3.79  		| (391) all_44_4_57 = 0 & all_44_5_58 = 0 & all_44_6_59 = 0 &  ~ (all_44_3_56 = 0) & apply(all_0_1_1, all_44_7_60, all_44_8_61) = all_44_3_56 & apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0 & member(all_44_7_60, all_0_3_3) = 0 & member(all_44_8_61, all_0_3_3) = 0
% 14.02/3.79  		|
% 14.02/3.79  			| Applying alpha-rule on (391) yields:
% 14.02/3.79  			| (114) all_44_4_57 = 0
% 14.02/3.79  			| (115) apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0
% 14.02/3.79  			| (394) apply(all_0_1_1, all_44_7_60, all_44_8_61) = all_44_3_56
% 14.02/3.79  			| (119) all_44_5_58 = 0
% 14.02/3.79  			| (122) member(all_44_8_61, all_0_3_3) = 0
% 14.02/3.79  			| (397)  ~ (all_44_3_56 = 0)
% 14.02/3.79  			| (398) all_44_6_59 = 0
% 14.02/3.79  			| (124) member(all_44_7_60, all_0_3_3) = 0
% 14.02/3.79  			|
% 14.02/3.79  			| Instantiating formula (6) with all_44_3_56, all_44_8_61, all_44_7_60 and discharging atoms apply(all_0_1_1, all_44_7_60, all_44_8_61) = all_44_3_56, yields:
% 14.02/3.79  			| (400)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & member(all_44_7_60, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_44_8_61, all_0_3_3) = v0) | (( ~ (all_44_3_56 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0)) & (all_44_3_56 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v1) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = v0))))
% 14.02/3.79  			|
% 14.02/3.79  			| Instantiating formula (6) with 0, all_44_7_60, all_44_8_61 and discharging atoms apply(all_0_1_1, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.80  			| (128)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (v0 = 0) & member(all_44_7_60, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_44_8_61, all_0_3_3) = v0))
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating formula (26) with all_44_7_60, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_7_60, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.80  			| (140)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating formula (26) with all_44_8_61, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.80  			| (143)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating formula (47) with all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.80  			| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating (143) with all_58_0_95 yields:
% 14.02/3.80  			| (405) (all_58_0_95 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (all_58_0_95 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_95)
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating (140) with all_60_0_97 yields:
% 14.02/3.80  			| (406) (all_60_0_97 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_60_0_97 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_97) | ( ~ (all_60_0_97 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_97)
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating (128) with all_61_0_98, all_61_1_99 yields:
% 14.02/3.80  			| (407) (all_61_0_98 = 0 & all_61_1_99 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_61_1_99 = 0) & member(all_44_7_60, all_0_3_3) = all_61_1_99) | ( ~ (all_61_1_99 = 0) & member(all_44_8_61, all_0_3_3) = all_61_1_99)
% 14.02/3.80  			|
% 14.02/3.80  			| Instantiating (400) with all_62_0_100, all_62_1_101 yields:
% 14.02/3.80  			| (408) ( ~ (all_62_1_101 = 0) & member(all_44_7_60, all_0_3_3) = all_62_1_101) | ( ~ (all_62_1_101 = 0) & member(all_44_8_61, all_0_3_3) = all_62_1_101) | (( ~ (all_44_3_56 = 0) | (all_62_0_100 = 0 & all_62_1_101 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0)) & (all_44_3_56 = 0 | ( ~ (all_62_0_100 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100) | ( ~ (all_62_1_101 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101)))
% 14.02/3.80  			|
% 14.02/3.80  			+-Applying beta-rule and splitting (405), into two cases.
% 14.02/3.80  			|-Branch one:
% 14.02/3.80  			| (409) all_58_0_95 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.80  			|
% 14.02/3.80  				| Applying alpha-rule on (409) yields:
% 14.02/3.80  				| (410) all_58_0_95 = 0
% 14.02/3.80  				| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.80  				|
% 14.02/3.80  				+-Applying beta-rule and splitting (407), into two cases.
% 14.02/3.80  				|-Branch one:
% 14.02/3.80  				| (412) (all_61_0_98 = 0 & all_61_1_99 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_61_1_99 = 0) & member(all_44_7_60, all_0_3_3) = all_61_1_99)
% 14.02/3.80  				|
% 14.02/3.80  					+-Applying beta-rule and splitting (412), into two cases.
% 14.02/3.80  					|-Branch one:
% 14.02/3.80  					| (413) all_61_0_98 = 0 & all_61_1_99 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 14.02/3.80  					|
% 14.02/3.80  						| Applying alpha-rule on (413) yields:
% 14.02/3.80  						| (414) all_61_0_98 = 0
% 14.02/3.80  						| (415) all_61_1_99 = 0
% 14.02/3.80  						| (168) apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0
% 14.02/3.80  						| (169) apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 14.02/3.80  						|
% 14.02/3.80  						+-Applying beta-rule and splitting (406), into two cases.
% 14.02/3.80  						|-Branch one:
% 14.02/3.80  						| (418) (all_60_0_97 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0) | ( ~ (all_60_0_97 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_97)
% 14.02/3.80  						|
% 14.02/3.80  							+-Applying beta-rule and splitting (418), into two cases.
% 14.02/3.80  							|-Branch one:
% 14.02/3.80  							| (419) all_60_0_97 = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 14.02/3.80  							|
% 14.02/3.80  								| Applying alpha-rule on (419) yields:
% 14.02/3.80  								| (420) all_60_0_97 = 0
% 14.02/3.80  								| (169) apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0
% 14.02/3.80  								|
% 14.02/3.80  								+-Applying beta-rule and splitting (408), into two cases.
% 14.02/3.80  								|-Branch one:
% 14.02/3.80  								| (422) ( ~ (all_62_1_101 = 0) & member(all_44_7_60, all_0_3_3) = all_62_1_101) | ( ~ (all_62_1_101 = 0) & member(all_44_8_61, all_0_3_3) = all_62_1_101)
% 14.02/3.80  								|
% 14.02/3.80  									+-Applying beta-rule and splitting (422), into two cases.
% 14.02/3.80  									|-Branch one:
% 14.02/3.80  									| (423)  ~ (all_62_1_101 = 0) & member(all_44_7_60, all_0_3_3) = all_62_1_101
% 14.02/3.80  									|
% 14.02/3.80  										| Applying alpha-rule on (423) yields:
% 14.02/3.80  										| (424)  ~ (all_62_1_101 = 0)
% 14.02/3.80  										| (425) member(all_44_7_60, all_0_3_3) = all_62_1_101
% 14.02/3.80  										|
% 14.02/3.80  										| Instantiating formula (19) with all_44_7_60, all_0_3_3, all_62_1_101, 0 and discharging atoms member(all_44_7_60, all_0_3_3) = all_62_1_101, member(all_44_7_60, all_0_3_3) = 0, yields:
% 14.02/3.80  										| (426) all_62_1_101 = 0
% 14.02/3.80  										|
% 14.02/3.80  										| Equations (426) can reduce 424 to:
% 14.02/3.80  										| (108) $false
% 14.02/3.80  										|
% 14.02/3.80  										|-The branch is then unsatisfiable
% 14.02/3.80  									|-Branch two:
% 14.02/3.80  									| (428)  ~ (all_62_1_101 = 0) & member(all_44_8_61, all_0_3_3) = all_62_1_101
% 14.02/3.80  									|
% 14.02/3.80  										| Applying alpha-rule on (428) yields:
% 14.02/3.80  										| (424)  ~ (all_62_1_101 = 0)
% 14.02/3.80  										| (430) member(all_44_8_61, all_0_3_3) = all_62_1_101
% 14.02/3.80  										|
% 14.02/3.80  										| Instantiating formula (19) with all_44_8_61, all_0_3_3, all_62_1_101, 0 and discharging atoms member(all_44_8_61, all_0_3_3) = all_62_1_101, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.80  										| (426) all_62_1_101 = 0
% 14.02/3.80  										|
% 14.02/3.80  										| Equations (426) can reduce 424 to:
% 14.02/3.80  										| (108) $false
% 14.02/3.80  										|
% 14.02/3.80  										|-The branch is then unsatisfiable
% 14.02/3.80  								|-Branch two:
% 14.02/3.80  								| (433) ( ~ (all_44_3_56 = 0) | (all_62_0_100 = 0 & all_62_1_101 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0)) & (all_44_3_56 = 0 | ( ~ (all_62_0_100 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100) | ( ~ (all_62_1_101 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101))
% 14.02/3.80  								|
% 14.02/3.80  									| Applying alpha-rule on (433) yields:
% 14.02/3.80  									| (434)  ~ (all_44_3_56 = 0) | (all_62_0_100 = 0 & all_62_1_101 = 0 & apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0 & apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0)
% 14.02/3.80  									| (435) all_44_3_56 = 0 | ( ~ (all_62_0_100 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100) | ( ~ (all_62_1_101 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101)
% 14.02/3.80  									|
% 14.02/3.80  									+-Applying beta-rule and splitting (435), into two cases.
% 14.02/3.80  									|-Branch one:
% 14.02/3.80  									| (123) all_44_3_56 = 0
% 14.02/3.80  									|
% 14.02/3.80  										| Equations (123) can reduce 397 to:
% 14.02/3.80  										| (108) $false
% 14.02/3.80  										|
% 14.02/3.80  										|-The branch is then unsatisfiable
% 14.02/3.80  									|-Branch two:
% 14.02/3.80  									| (397)  ~ (all_44_3_56 = 0)
% 14.02/3.80  									| (439) ( ~ (all_62_0_100 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100) | ( ~ (all_62_1_101 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101)
% 14.02/3.80  									|
% 14.02/3.80  										+-Applying beta-rule and splitting (439), into two cases.
% 14.02/3.80  										|-Branch one:
% 14.02/3.80  										| (440)  ~ (all_62_0_100 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100
% 14.02/3.80  										|
% 14.02/3.80  											| Applying alpha-rule on (440) yields:
% 14.02/3.80  											| (441)  ~ (all_62_0_100 = 0)
% 14.02/3.80  											| (442) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100
% 14.02/3.80  											|
% 14.02/3.80  											| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_62_0_100 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_62_0_100, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.80  											| (443) all_62_0_100 = 0
% 14.02/3.80  											|
% 14.02/3.80  											| Equations (443) can reduce 441 to:
% 14.02/3.80  											| (108) $false
% 14.02/3.80  											|
% 14.02/3.80  											|-The branch is then unsatisfiable
% 14.02/3.80  										|-Branch two:
% 14.02/3.80  										| (445)  ~ (all_62_1_101 = 0) & apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101
% 14.02/3.80  										|
% 14.02/3.80  											| Applying alpha-rule on (445) yields:
% 14.02/3.80  											| (424)  ~ (all_62_1_101 = 0)
% 14.02/3.80  											| (447) apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101
% 14.02/3.80  											|
% 14.02/3.81  											| Instantiating formula (40) with all_0_2_2, all_44_7_60, all_44_8_61, 0, all_62_1_101 and discharging atoms apply(all_0_2_2, all_44_7_60, all_44_8_61) = all_62_1_101, apply(all_0_2_2, all_44_7_60, all_44_8_61) = 0, yields:
% 14.02/3.81  											| (426) all_62_1_101 = 0
% 14.02/3.81  											|
% 14.02/3.81  											| Equations (426) can reduce 424 to:
% 14.02/3.81  											| (108) $false
% 14.02/3.81  											|
% 14.02/3.81  											|-The branch is then unsatisfiable
% 14.02/3.81  							|-Branch two:
% 14.02/3.81  							| (450)  ~ (all_60_0_97 = 0) & apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_97
% 14.02/3.81  							|
% 14.02/3.81  								| Applying alpha-rule on (450) yields:
% 14.02/3.81  								| (451)  ~ (all_60_0_97 = 0)
% 14.02/3.81  								| (452) apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_97
% 14.02/3.81  								|
% 14.02/3.81  								| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_7_60, 0, all_60_0_97 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_7_60) = all_60_0_97, apply(all_0_2_2, all_44_8_61, all_44_7_60) = 0, yields:
% 14.02/3.81  								| (420) all_60_0_97 = 0
% 14.02/3.81  								|
% 14.02/3.81  								| Equations (420) can reduce 451 to:
% 14.02/3.81  								| (108) $false
% 14.02/3.81  								|
% 14.02/3.81  								|-The branch is then unsatisfiable
% 14.02/3.81  						|-Branch two:
% 14.02/3.81  						| (455)  ~ (all_60_0_97 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_97
% 14.02/3.81  						|
% 14.02/3.81  							| Applying alpha-rule on (455) yields:
% 14.02/3.81  							| (451)  ~ (all_60_0_97 = 0)
% 14.02/3.81  							| (457) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_97
% 14.02/3.81  							|
% 14.02/3.81  							| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_60_0_97 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_60_0_97, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.81  							| (420) all_60_0_97 = 0
% 14.02/3.81  							|
% 14.02/3.81  							| Equations (420) can reduce 451 to:
% 14.02/3.81  							| (108) $false
% 14.02/3.81  							|
% 14.02/3.81  							|-The branch is then unsatisfiable
% 14.02/3.81  					|-Branch two:
% 14.02/3.81  					| (460)  ~ (all_61_1_99 = 0) & member(all_44_7_60, all_0_3_3) = all_61_1_99
% 14.02/3.81  					|
% 14.02/3.81  						| Applying alpha-rule on (460) yields:
% 14.02/3.81  						| (461)  ~ (all_61_1_99 = 0)
% 14.02/3.81  						| (462) member(all_44_7_60, all_0_3_3) = all_61_1_99
% 14.02/3.81  						|
% 14.02/3.81  						| Instantiating formula (19) with all_44_7_60, all_0_3_3, all_61_1_99, 0 and discharging atoms member(all_44_7_60, all_0_3_3) = all_61_1_99, member(all_44_7_60, all_0_3_3) = 0, yields:
% 14.02/3.81  						| (415) all_61_1_99 = 0
% 14.02/3.81  						|
% 14.02/3.81  						| Equations (415) can reduce 461 to:
% 14.02/3.81  						| (108) $false
% 14.02/3.81  						|
% 14.02/3.81  						|-The branch is then unsatisfiable
% 14.02/3.81  				|-Branch two:
% 14.02/3.81  				| (465)  ~ (all_61_1_99 = 0) & member(all_44_8_61, all_0_3_3) = all_61_1_99
% 14.02/3.81  				|
% 14.02/3.81  					| Applying alpha-rule on (465) yields:
% 14.02/3.81  					| (461)  ~ (all_61_1_99 = 0)
% 14.02/3.81  					| (467) member(all_44_8_61, all_0_3_3) = all_61_1_99
% 14.02/3.81  					|
% 14.02/3.81  					| Instantiating formula (19) with all_44_8_61, all_0_3_3, all_61_1_99, 0 and discharging atoms member(all_44_8_61, all_0_3_3) = all_61_1_99, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.81  					| (415) all_61_1_99 = 0
% 14.02/3.81  					|
% 14.02/3.81  					| Equations (415) can reduce 461 to:
% 14.02/3.81  					| (108) $false
% 14.02/3.81  					|
% 14.02/3.81  					|-The branch is then unsatisfiable
% 14.02/3.81  			|-Branch two:
% 14.02/3.81  			| (470)  ~ (all_58_0_95 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_95
% 14.02/3.81  			|
% 14.02/3.81  				| Applying alpha-rule on (470) yields:
% 14.02/3.81  				| (471)  ~ (all_58_0_95 = 0)
% 14.02/3.81  				| (472) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_95
% 14.02/3.81  				|
% 14.02/3.81  				| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_58_0_95 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_95, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.81  				| (410) all_58_0_95 = 0
% 14.02/3.81  				|
% 14.02/3.81  				| Equations (410) can reduce 471 to:
% 14.02/3.81  				| (108) $false
% 14.02/3.81  				|
% 14.02/3.81  				|-The branch is then unsatisfiable
% 14.02/3.81  	|-Branch two:
% 14.02/3.81  	| (475) all_44_7_60 = 0 &  ~ (all_44_6_59 = 0) & apply(all_0_1_1, all_44_8_61, all_44_8_61) = all_44_6_59 & member(all_44_8_61, all_0_3_3) = 0
% 14.02/3.81  	|
% 14.02/3.81  		| Applying alpha-rule on (475) yields:
% 14.02/3.81  		| (476) all_44_7_60 = 0
% 14.02/3.81  		| (477)  ~ (all_44_6_59 = 0)
% 14.02/3.81  		| (478) apply(all_0_1_1, all_44_8_61, all_44_8_61) = all_44_6_59
% 14.02/3.81  		| (122) member(all_44_8_61, all_0_3_3) = 0
% 14.02/3.81  		|
% 14.02/3.81  		| Instantiating formula (6) with all_44_6_59, all_44_8_61, all_44_8_61 and discharging atoms apply(all_0_1_1, all_44_8_61, all_44_8_61) = all_44_6_59, yields:
% 14.02/3.81  		| (480)  ? [v0] :  ? [v1] : (( ~ (v0 = 0) & member(all_44_8_61, all_0_3_3) = v0) | (( ~ (all_44_6_59 = 0) | (v1 = 0 & v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0)) & (all_44_6_59 = 0 | ( ~ (v1 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v1) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))))
% 14.02/3.81  		|
% 14.02/3.81  		| Instantiating formula (26) with all_44_8_61, all_44_8_61, all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.81  		| (143)  ? [v0] : ((v0 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = v0))
% 14.02/3.81  		|
% 14.02/3.81  		| Instantiating formula (47) with all_44_8_61, all_0_3_3, all_0_2_2 and discharging atoms pre_order(all_0_2_2, all_0_3_3) = 0, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.81  		| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.81  		|
% 14.02/3.81  		| Instantiating (143) with all_58_0_107 yields:
% 14.02/3.81  		| (483) (all_58_0_107 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0) | ( ~ (all_58_0_107 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_107)
% 14.02/3.81  		|
% 14.02/3.81  		| Instantiating (480) with all_59_0_108, all_59_1_109 yields:
% 14.02/3.81  		| (484) ( ~ (all_59_1_109 = 0) & member(all_44_8_61, all_0_3_3) = all_59_1_109) | (( ~ (all_44_6_59 = 0) | (all_59_0_108 = 0 & all_59_1_109 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0)) & (all_44_6_59 = 0 | ( ~ (all_59_0_108 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108) | ( ~ (all_59_1_109 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109)))
% 14.02/3.81  		|
% 14.02/3.81  		+-Applying beta-rule and splitting (483), into two cases.
% 14.02/3.81  		|-Branch one:
% 14.02/3.81  		| (485) all_58_0_107 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.81  		|
% 14.02/3.81  			| Applying alpha-rule on (485) yields:
% 14.02/3.81  			| (486) all_58_0_107 = 0
% 14.02/3.81  			| (144) apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0
% 14.02/3.81  			|
% 14.02/3.81  			+-Applying beta-rule and splitting (484), into two cases.
% 14.02/3.81  			|-Branch one:
% 14.02/3.81  			| (488)  ~ (all_59_1_109 = 0) & member(all_44_8_61, all_0_3_3) = all_59_1_109
% 14.02/3.81  			|
% 14.02/3.81  				| Applying alpha-rule on (488) yields:
% 14.02/3.81  				| (489)  ~ (all_59_1_109 = 0)
% 14.02/3.81  				| (490) member(all_44_8_61, all_0_3_3) = all_59_1_109
% 14.02/3.81  				|
% 14.02/3.81  				| Instantiating formula (19) with all_44_8_61, all_0_3_3, all_59_1_109, 0 and discharging atoms member(all_44_8_61, all_0_3_3) = all_59_1_109, member(all_44_8_61, all_0_3_3) = 0, yields:
% 14.02/3.81  				| (491) all_59_1_109 = 0
% 14.02/3.81  				|
% 14.02/3.81  				| Equations (491) can reduce 489 to:
% 14.02/3.81  				| (108) $false
% 14.02/3.81  				|
% 14.02/3.81  				|-The branch is then unsatisfiable
% 14.02/3.81  			|-Branch two:
% 14.02/3.81  			| (493) ( ~ (all_44_6_59 = 0) | (all_59_0_108 = 0 & all_59_1_109 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0)) & (all_44_6_59 = 0 | ( ~ (all_59_0_108 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108) | ( ~ (all_59_1_109 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109))
% 14.02/3.81  			|
% 14.02/3.81  				| Applying alpha-rule on (493) yields:
% 14.02/3.81  				| (494)  ~ (all_44_6_59 = 0) | (all_59_0_108 = 0 & all_59_1_109 = 0 & apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0)
% 14.02/3.81  				| (495) all_44_6_59 = 0 | ( ~ (all_59_0_108 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108) | ( ~ (all_59_1_109 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109)
% 14.02/3.81  				|
% 14.02/3.81  				+-Applying beta-rule and splitting (495), into two cases.
% 14.02/3.81  				|-Branch one:
% 14.02/3.81  				| (398) all_44_6_59 = 0
% 14.02/3.81  				|
% 14.02/3.81  					| Equations (398) can reduce 477 to:
% 14.02/3.81  					| (108) $false
% 14.02/3.81  					|
% 14.02/3.81  					|-The branch is then unsatisfiable
% 14.02/3.81  				|-Branch two:
% 14.02/3.81  				| (477)  ~ (all_44_6_59 = 0)
% 14.02/3.82  				| (499) ( ~ (all_59_0_108 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108) | ( ~ (all_59_1_109 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109)
% 14.02/3.82  				|
% 14.02/3.82  					+-Applying beta-rule and splitting (499), into two cases.
% 14.02/3.82  					|-Branch one:
% 14.02/3.82  					| (500)  ~ (all_59_0_108 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108
% 14.02/3.82  					|
% 14.02/3.82  						| Applying alpha-rule on (500) yields:
% 14.02/3.82  						| (501)  ~ (all_59_0_108 = 0)
% 14.02/3.82  						| (502) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108
% 14.02/3.82  						|
% 14.02/3.82  						| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_59_0_108 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_0_108, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.82  						| (503) all_59_0_108 = 0
% 14.02/3.82  						|
% 14.02/3.82  						| Equations (503) can reduce 501 to:
% 14.02/3.82  						| (108) $false
% 14.02/3.82  						|
% 14.02/3.82  						|-The branch is then unsatisfiable
% 14.02/3.82  					|-Branch two:
% 14.02/3.82  					| (505)  ~ (all_59_1_109 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109
% 14.02/3.82  					|
% 14.02/3.82  						| Applying alpha-rule on (505) yields:
% 14.02/3.82  						| (489)  ~ (all_59_1_109 = 0)
% 14.02/3.82  						| (507) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109
% 14.02/3.82  						|
% 14.02/3.82  						| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_59_1_109 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_59_1_109, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.82  						| (491) all_59_1_109 = 0
% 14.02/3.82  						|
% 14.02/3.82  						| Equations (491) can reduce 489 to:
% 14.02/3.82  						| (108) $false
% 14.02/3.82  						|
% 14.02/3.82  						|-The branch is then unsatisfiable
% 14.02/3.82  		|-Branch two:
% 14.02/3.82  		| (510)  ~ (all_58_0_107 = 0) & apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_107
% 14.02/3.82  		|
% 14.02/3.82  			| Applying alpha-rule on (510) yields:
% 14.02/3.82  			| (511)  ~ (all_58_0_107 = 0)
% 14.02/3.82  			| (512) apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_107
% 14.02/3.82  			|
% 14.02/3.82  			| Instantiating formula (40) with all_0_2_2, all_44_8_61, all_44_8_61, 0, all_58_0_107 and discharging atoms apply(all_0_2_2, all_44_8_61, all_44_8_61) = all_58_0_107, apply(all_0_2_2, all_44_8_61, all_44_8_61) = 0, yields:
% 14.02/3.82  			| (486) all_58_0_107 = 0
% 14.02/3.82  			|
% 14.02/3.82  			| Equations (486) can reduce 511 to:
% 14.02/3.82  			| (108) $false
% 14.02/3.82  			|
% 14.02/3.82  			|-The branch is then unsatisfiable
% 14.02/3.82  % SZS output end Proof for theBenchmark
% 14.02/3.82  
% 14.02/3.82  3241ms
%------------------------------------------------------------------------------