%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET716+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n018.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 00:21:35 EDT 2022

% Result   : Theorem 6.30s 1.98s
% Output   : Proof 8.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET716+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 00:48:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.58/0.58          ____       _                          
% 0.58/0.58    ___  / __ \_____(_)___  ________  __________
% 0.58/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.58  
% 0.58/0.58  A Theorem Prover for First-Order Logic
% 0.58/0.58  (ePrincess v.1.0)
% 0.58/0.58  
% 0.58/0.58  (c) Philipp Rümmer, 2009-2015
% 0.58/0.58  (c) Peter Backeman, 2014-2015
% 0.58/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.58  Bug reports to peter@backeman.se
% 0.58/0.58  
% 0.58/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.58  
% 0.58/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/0.96  Prover 0: Preprocessing ...
% 3.03/1.29  Prover 0: Warning: ignoring some quantifiers
% 3.29/1.32  Prover 0: Constructing countermodel ...
% 4.28/1.60  Prover 0: gave up
% 4.28/1.60  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.63/1.65  Prover 1: Preprocessing ...
% 5.59/1.88  Prover 1: Constructing countermodel ...
% 6.30/1.98  Prover 1: proved (382ms)
% 6.30/1.98  
% 6.30/1.98  No countermodel exists, formula is valid
% 6.30/1.98  % SZS status Theorem for theBenchmark
% 6.30/1.98  
% 6.30/1.98  Generating proof ... found it (size 95)
% 8.09/2.45  
% 8.09/2.45  % SZS output start Proof for theBenchmark
% 8.09/2.45  Assumed formulas after preprocessing and simplification: 
% 8.09/2.45  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & injective(v5, v2, v4) = v6 & injective(v1, v3, v4) = 0 & injective(v0, v2, v3) = 0 & compose_function(v1, v0, v2, v3, v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v15 = 0 |  ~ (compose_function(v7, v8, v9, v10, v11) = v14) |  ~ (apply(v14, v12, v13) = v15) |  ~ (apply(v7, v16, v13) = 0) |  ? [v17] :  ? [v18] : ((apply(v8, v12, v16) = v18 & member(v16, v10) = v17 & ( ~ (v18 = 0) |  ~ (v17 = 0))) | (member(v13, v11) = v18 & member(v12, v9) = v17 & ( ~ (v18 = 0) |  ~ (v17 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v15 = 0 |  ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) |  ~ (apply(v8, v16, v14) = 0) |  ~ (apply(v7, v13, v14) = v15) |  ? [v17] :  ? [v18] : ((apply(v9, v13, v16) = v18 & member(v16, v11) = v17 & ( ~ (v18 = 0) |  ~ (v17 = 0))) | (member(v14, v12) = v18 & member(v13, v10) = v17 & ( ~ (v18 = 0) |  ~ (v17 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) |  ~ (apply(v7, v14, v15) = 0) |  ~ (apply(v7, v12, v13) = 0) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : (apply(v11, v13, v15) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v19 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) | (( ~ (v21 = 0) | v20 = 0) & ( ~ (v20 = 0) | v21 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) |  ~ (apply(v7, v14, v15) = 0) |  ~ (apply(v7, v12, v13) = 0) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : (apply(v11, v15, v13) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v20 = 0) |  ~ (v19 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) | v21 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) |  ~ (apply(v7, v14, v15) = 0) |  ~ (apply(v7, v12, v13) = 0) |  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : (apply(v11, v13, v15) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v20 = 0) |  ~ (v19 = 0) |  ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0) | v21 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v8 = v7 |  ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v8) |  ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (compose_function(v7, v8, v9, v10, v11) = v14) |  ~ (apply(v14, v12, v13) = 0) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v8, v12, v15) = 0 & apply(v7, v15, v13) = 0 & member(v15, v10) = 0) | (member(v13, v11) = v16 & member(v12, v9) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) |  ~ (apply(v7, v13, v14) = 0) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v9, v13, v15) = 0 & apply(v8, v15, v14) = 0 & member(v15, v11) = 0) | (member(v14, v12) = v16 & member(v13, v10) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (equal_maps(v7, v8, v9, v10) = 0) |  ~ (apply(v8, v11, v13) = 0) |  ~ (apply(v7, v11, v12) = 0) |  ? [v14] :  ? [v15] :  ? [v16] : (member(v13, v10) = v16 & member(v12, v10) = v15 & member(v11, v9) = v14 & ( ~ (v16 = 0) |  ~ (v15 = 0) |  ~ (v14 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] : (apply(v7, v14, v15) = v16 & member(v15, v12) = 0 & member(v14, v10) = 0 & ( ~ (v16 = 0) |  ! [v21] : ( ~ (apply(v8, v21, v15) = 0) |  ? [v22] :  ? [v23] : (apply(v9, v14, v21) = v23 & member(v21, v11) = v22 & ( ~ (v23 = 0) |  ~ (v22 = 0))))) & (v16 = 0 | (v20 = 0 & v19 = 0 & v18 = 0 & apply(v9, v14, v17) = 0 & apply(v8, v17, v15) = 0 & member(v17, v11) = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v12 = 0 |  ~ (inverse_image3(v7, v8, v9) = v11) |  ~ (apply(v7, v10, v13) = 0) |  ~ (member(v10, v11) = v12) |  ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v12 = 0 |  ~ (image3(v7, v8, v9) = v11) |  ~ (apply(v7, v13, v10) = 0) |  ~ (member(v10, v11) = v12) |  ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v8 = v7 |  ~ (isomorphism(v13, v12, v11, v10, v9) = v8) |  ~ (isomorphism(v13, v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v8 = v7 |  ~ (decreasing(v13, v12, v11, v10, v9) = v8) |  ~ (decreasing(v13, v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v8 = v7 |  ~ (increasing(v13, v12, v11, v10, v9) = v8) |  ~ (increasing(v13, v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v8 = v7 |  ~ (compose_function(v13, v12, v11, v10, v9) = v8) |  ~ (compose_function(v13, v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (inverse_function(v7, v8, v9) = v12) |  ~ (apply(v12, v11, v10) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (apply(v7, v10, v11) = v16 & member(v11, v9) = v15 & member(v10, v8) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0) | (( ~ (v16 = 0) | v13 = 0) & ( ~ (v13 = 0) | v16 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) |  ~ (apply(v7, v12, v11) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (apply(v8, v11, v12) = v16 & member(v12, v10) = v15 & member(v11, v9) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0) | (( ~ (v16 = 0) | v13 = 0) & ( ~ (v13 = 0) | v16 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (maps(v7, v8, v9) = 0) |  ~ (apply(v7, v10, v12) = 0) |  ~ (apply(v7, v10, v11) = 0) |  ? [v13] :  ? [v14] :  ? [v15] : (member(v12, v9) = v15 & member(v11, v9) = v14 & member(v10, v8) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (isomorphism(v7, v8, v9, v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & apply(v11, v14, v16) = v24 & apply(v9, v13, v15) = v23 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0 & ( ~ (v24 = 0) |  ~ (v23 = 0)) & (v24 = 0 | v23 = 0)) | (one_to_one(v7, v8, v10) = v14 & maps(v7, v8, v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (decreasing(v7, v8, v9, v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : ( ~ (v17 = 0) & apply(v11, v16, v14) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (increasing(v7, v8, v9, v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : ( ~ (v17 = 0) & apply(v11, v14, v16) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (injective(v7, v8, v9) = 0) |  ~ (apply(v7, v11, v12) = 0) |  ~ (apply(v7, v10, v12) = 0) |  ? [v13] :  ? [v14] :  ? [v15] : (member(v12, v9) = v15 & member(v11, v8) = v14 & member(v10, v8) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = 0 |  ~ (inverse_image2(v7, v8) = v10) |  ~ (apply(v7, v9, v12) = 0) |  ~ (member(v9, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = 0 |  ~ (image2(v7, v8) = v10) |  ~ (apply(v7, v12, v9) = 0) |  ~ (member(v9, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v8 = v7 |  ~ (inverse_predicate(v12, v11, v10, v9) = v8) |  ~ (inverse_predicate(v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v8 = v7 |  ~ (equal_maps(v12, v11, v10, v9) = v8) |  ~ (equal_maps(v12, v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (inverse_predicate(v7, v8, v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (apply(v8, v12, v13) = v14 & apply(v7, v13, v12) = v15 & member(v13, v10) = 0 & member(v12, v9) = 0 & ( ~ (v15 = 0) |  ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (equal_maps(v7, v8, v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v7, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (product(v8) = v9) |  ~ (member(v7, v10) = v11) |  ~ (member(v7, v9) = 0) |  ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (difference(v9, v8) = v10) |  ~ (member(v7, v10) = v11) |  ? [v12] :  ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (union(v8, v9) = v10) |  ~ (member(v7, v10) = v11) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) &  ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (intersection(v8, v9) = v10) |  ~ (member(v7, v10) = v11) |  ? [v12] :  ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v10 = 0 |  ~ (sum(v8) = v9) |  ~ (member(v7, v11) = 0) |  ~ (member(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (inverse_image3(v11, v10, v9) = v8) |  ~ (inverse_image3(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (image3(v11, v10, v9) = v8) |  ~ (image3(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (inverse_function(v11, v10, v9) = v8) |  ~ (inverse_function(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (one_to_one(v11, v10, v9) = v8) |  ~ (one_to_one(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (surjective(v11, v10, v9) = v8) |  ~ (surjective(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (injective(v11, v10, v9) = v8) |  ~ (injective(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (maps(v11, v10, v9) = v8) |  ~ (maps(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v8 = v7 |  ~ (apply(v11, v10, v9) = v8) |  ~ (apply(v11, v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | (one_to_one(v7, v8, v10) = 0 & maps(v7, v8, v10) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) |  ~ (member(v10, v11) = 0) | member(v10, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) |  ~ (member(v10, v11) = 0) |  ? [v12] : (apply(v7, v10, v12) = 0 & member(v12, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (image3(v7, v8, v9) = v11) |  ~ (member(v10, v11) = 0) | member(v10, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (image3(v7, v8, v9) = v11) |  ~ (member(v10, v11) = 0) |  ? [v12] : (apply(v7, v12, v10) = 0 & member(v12, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (surjective(v7, v8, v9) = v10) |  ? [v11] : (member(v11, v9) = 0 &  ! [v12] : ( ~ (apply(v7, v12, v11) = 0) |  ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (injective(v7, v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : ( ~ (v12 = v11) & apply(v7, v12, v13) = 0 & apply(v7, v11, v13) = 0 & member(v13, v9) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (identity(v7, v8) = 0) |  ~ (apply(v7, v9, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (maps(v7, v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 &  ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v7, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0) | (v12 = 0 & member(v11, v8) = 0 &  ! [v19] : ( ~ (apply(v7, v11, v19) = 0) |  ? [v20] : ( ~ (v20 = 0) & member(v19, v9) = v20))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (product(v8) = v9) |  ~ (member(v7, v9) = v10) |  ? [v11] :  ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unordered_pair(v8, v7) = v9) |  ~ (member(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unordered_pair(v7, v8) = v9) |  ~ (member(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (power_set(v8) = v9) |  ~ (member(v7, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v7 | v8 = v7 |  ~ (unordered_pair(v8, v9) = v10) |  ~ (member(v7, v10) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (inverse_image2(v10, v9) = v8) |  ~ (inverse_image2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (image2(v10, v9) = v8) |  ~ (image2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (identity(v10, v9) = v8) |  ~ (identity(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unordered_pair(v10, v9) = v8) |  ~ (unordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (difference(v10, v9) = v8) |  ~ (difference(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (union(v10, v9) = v8) |  ~ (union(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (intersection(v10, v9) = v8) |  ~ (intersection(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (equal_set(v10, v9) = v8) |  ~ (equal_set(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (subset(v10, v9) = v8) |  ~ (subset(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (member(v10, v9) = v8) |  ~ (member(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (inverse_image2(v7, v8) = v10) |  ~ (member(v9, v10) = 0) |  ? [v11] : (apply(v7, v9, v11) = 0 & member(v11, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (image2(v7, v8) = v10) |  ~ (member(v9, v10) = 0) |  ? [v11] : (apply(v7, v11, v9) = 0 & member(v11, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (surjective(v7, v8, v9) = v10) |  ? [v11] :  ? [v12] : (one_to_one(v7, v8, v9) = v11 & injective(v7, v8, v9) = v12 & ( ~ (v11 = 0) | (v12 = 0 & v10 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (surjective(v7, v8, v9) = 0) |  ~ (member(v10, v9) = 0) |  ? [v11] : (apply(v7, v11, v10) = 0 & member(v11, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (maps(v7, v8, v9) = 0) |  ~ (member(v10, v8) = 0) |  ? [v11] : (apply(v7, v10, v11) = 0 & member(v11, v9) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (difference(v9, v8) = v10) |  ~ (member(v7, v10) = 0) |  ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v8, v9) = v10) |  ~ (member(v7, v10) = 0) |  ? [v11] :  ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection(v8, v9) = v10) |  ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (identity(v7, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & apply(v7, v10, v10) = v11 & member(v10, v8) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (singleton(v7) = v8) |  ~ (member(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equal_set(v7, v8) = v9) |  ? [v10] :  ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v7, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (product(v9) = v8) |  ~ (product(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (sum(v9) = v8) |  ~ (sum(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (singleton(v9) = v8) |  ~ (singleton(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (singleton(v8) = v9) |  ~ (member(v7, v9) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (power_set(v9) = v8) |  ~ (power_set(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (surjective(v7, v8, v9) = 0) |  ? [v10] :  ? [v11] : (one_to_one(v7, v8, v9) = v11 & injective(v7, v8, v9) = v10 & ( ~ (v10 = 0) | v11 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (sum(v8) = v9) |  ~ (member(v7, v9) = 0) |  ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (power_set(v8) = v9) |  ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (subset(v7, v8) = 0) |  ~ (member(v9, v7) = 0) | member(v9, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) &  ! [v7] :  ~ (member(v7, empty_set) = 0))
% 8.63/2.51  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 8.63/2.51  | (1)  ~ (all_0_0_0 = 0) & injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0 & injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0 & compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (compose_function(v0, v1, v2, v3, v4) = v7) |  ~ (apply(v7, v5, v6) = v8) |  ~ (apply(v0, v9, v6) = 0) |  ? [v10] :  ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) |  ~ (apply(v1, v9, v7) = 0) |  ~ (apply(v0, v6, v7) = v8) |  ? [v10] :  ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) |  ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | v14 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) |  ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | v14 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v1 = v0 |  ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) |  ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) |  ~ (apply(v7, v5, v6) = 0) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) |  ~ (apply(v0, v6, v7) = 0) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (equal_maps(v0, v1, v2, v3) = 0) |  ~ (apply(v1, v4, v6) = 0) |  ~ (apply(v0, v4, v5) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) |  ! [v14] : ( ~ (apply(v1, v14, v8) = 0) |  ? [v15] :  ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (apply(v0, v3, v6) = 0) |  ~ (member(v3, v4) = v5) |  ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (image3(v0, v1, v2) = v4) |  ~ (apply(v0, v6, v3) = 0) |  ~ (member(v3, v4) = v5) |  ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (isomorphism(v6, v5, v4, v3, v2) = v1) |  ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (decreasing(v6, v5, v4, v3, v2) = v1) |  ~ (decreasing(v6, v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (increasing(v6, v5, v4, v3, v2) = v1) |  ~ (increasing(v6, v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (compose_function(v6, v5, v4, v3, v2) = v1) |  ~ (compose_function(v6, v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) |  ~ (apply(v5, v4, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) |  ~ (apply(v0, v5, v4) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (maps(v0, v1, v2) = 0) |  ~ (apply(v0, v3, v5) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (isomorphism(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ( ~ (v17 = 0) |  ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (decreasing(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (increasing(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (injective(v0, v1, v2) = 0) |  ~ (apply(v0, v4, v5) = 0) |  ~ (apply(v0, v3, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = 0 |  ~ (inverse_image2(v0, v1) = v3) |  ~ (apply(v0, v2, v5) = 0) |  ~ (member(v2, v3) = v4) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = 0 |  ~ (image2(v0, v1) = v3) |  ~ (apply(v0, v5, v2) = 0) |  ~ (member(v2, v3) = v4) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (inverse_predicate(v5, v4, v3, v2) = v1) |  ~ (inverse_predicate(v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (equal_maps(v5, v4, v3, v2) = v1) |  ~ (equal_maps(v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (inverse_predicate(v0, v1, v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) |  ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equal_maps(v0, v1, v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0)) &  ! [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] :  ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [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] :  ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [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 |  ~ (inverse_image3(v4, v3, v2) = v1) |  ~ (inverse_image3(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (image3(v4, v3, v2) = v1) |  ~ (image3(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (inverse_function(v4, v3, v2) = v1) |  ~ (inverse_function(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (one_to_one(v4, v3, v2) = v1) |  ~ (one_to_one(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (surjective(v4, v3, v2) = v1) |  ~ (surjective(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (injective(v4, v3, v2) = v1) |  ~ (injective(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (maps(v4, v3, v2) = v1) |  ~ (maps(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] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) | member(v3, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) |  ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) | member(v3, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) |  ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (surjective(v0, v1, v2) = v3) |  ? [v4] : (member(v4, v2) = 0 &  ! [v5] : ( ~ (apply(v0, v5, v4) = 0) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (injective(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (identity(v0, v1) = 0) |  ~ (apply(v0, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (maps(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 &  ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 &  ! [v12] : ( ~ (apply(v0, v4, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13))))) &  ! [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] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (inverse_image2(v3, v2) = v1) |  ~ (inverse_image2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (image2(v3, v2) = v1) |  ~ (image2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (identity(v3, v2) = v1) |  ~ (identity(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] : ( ~ (inverse_image2(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (image2(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) |  ~ (member(v3, v2) = 0) |  ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (maps(v0, v1, v2) = 0) |  ~ (member(v3, v1) = 0) |  ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 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] :  ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 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 |  ~ (identity(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] :  ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [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] : ( ~ (surjective(v0, v1, v2) = 0) |  ? [v3] :  ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) &  ! [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(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] :  ~ (member(v0, empty_set) = 0)
% 8.82/2.53  |
% 8.82/2.53  | Applying alpha-rule on (1) yields:
% 8.82/2.53  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 8.82/2.53  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (apply(v0, v3, v6) = 0) |  ~ (member(v3, v4) = v5) |  ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 8.82/2.53  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 8.82/2.53  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (identity(v0, v1) = 0) |  ~ (apply(v0, v2, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 8.82/2.53  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) |  ~ (apply(v5, v4, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 8.82/2.53  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) |  ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0))
% 8.82/2.53  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) |  ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | v14 = 0)))
% 8.82/2.53  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (maps(v0, v1, v2) = 0) |  ~ (member(v3, v1) = 0) |  ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 8.82/2.53  | (10) injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0
% 8.82/2.53  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~ (equal_set(v3, v2) = v0))
% 8.82/2.53  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.82/2.54  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2))
% 8.82/2.54  | (14)  ! [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))
% 8.82/2.54  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 8.82/2.54  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3))
% 8.82/2.54  | (17)  ! [v0] :  ~ (member(v0, empty_set) = 0)
% 8.82/2.54  | (18)  ! [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))
% 8.82/2.54  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (injective(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0))
% 8.82/2.54  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) |  ! [v14] : ( ~ (apply(v1, v14, v8) = 0) |  ? [v15] :  ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0))))
% 8.82/2.54  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (image3(v0, v1, v2) = v4) |  ~ (apply(v0, v6, v3) = 0) |  ~ (member(v3, v4) = v5) |  ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 8.82/2.54  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (surjective(v0, v1, v2) = v3) |  ? [v4] : (member(v4, v2) = 0 &  ! [v5] : ( ~ (apply(v0, v5, v4) = 0) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))))
% 8.82/2.54  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) = v0))
% 8.82/2.54  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (equal_maps(v0, v1, v2, v3) = 0) |  ~ (apply(v1, v4, v6) = 0) |  ~ (apply(v0, v4, v5) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) |  ~ (v8 = 0) |  ~ (v7 = 0))))
% 8.82/2.54  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (inverse_image2(v3, v2) = v1) |  ~ (inverse_image2(v3, v2) = v0))
% 8.82/2.54  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.82/2.54  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 8.82/2.54  | (28) injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 8.82/2.54  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (one_to_one(v4, v3, v2) = v1) |  ~ (one_to_one(v4, v3, v2) = v0))
% 8.82/2.54  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (inverse_function(v4, v3, v2) = v1) |  ~ (inverse_function(v4, v3, v2) = v0))
% 8.82/2.54  | (31) compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 8.82/2.54  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) |  ~ (apply(v1, v9, v7) = 0) |  ~ (apply(v0, v6, v7) = v8) |  ? [v10] :  ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)))))
% 8.82/2.54  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] :  ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 8.82/2.54  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 8.82/2.54  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 8.82/2.54  | (36) maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 8.82/2.54  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 8.82/2.54  | (38)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 8.82/2.54  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (increasing(v6, v5, v4, v3, v2) = v1) |  ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 8.82/2.54  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (maps(v4, v3, v2) = v1) |  ~ (maps(v4, v3, v2) = v0))
% 8.82/2.54  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 8.82/2.54  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) |  ~ (member(v3, v2) = 0) |  ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 8.82/2.54  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) |  ~ (apply(v7, v5, v6) = 0) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0)))))
% 8.82/2.54  | (44)  ! [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))
% 8.82/2.55  | (45)  ! [v0] :  ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.82/2.55  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (maps(v0, v1, v2) = 0) |  ~ (apply(v0, v3, v5) = 0) |  ~ (apply(v0, v3, v4) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0))))
% 8.82/2.55  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) |  ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 8.82/2.55  | (48)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (identity(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 8.82/2.55  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (inverse_image3(v4, v3, v2) = v1) |  ~ (inverse_image3(v4, v3, v2) = v0))
% 8.82/2.55  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 8.82/2.55  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (injective(v4, v3, v2) = v1) |  ~ (injective(v4, v3, v2) = v0))
% 8.82/2.55  | (52)  ~ (all_0_0_0 = 0)
% 8.82/2.55  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 8.82/2.55  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equal_maps(v0, v1, v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0))
% 8.82/2.55  | (55)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v1) = v2) |  ~ (member(v0, v2) = 0))
% 8.82/2.55  | (56)  ! [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))
% 8.82/2.55  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (image2(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 8.82/2.55  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (isomorphism(v6, v5, v4, v3, v2) = v1) |  ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 8.82/2.55  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 8.82/2.55  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 8.82/2.55  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (identity(v3, v2) = v1) |  ~ (identity(v3, v2) = v0))
% 8.82/2.55  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.82/2.55  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (decreasing(v6, v5, v4, v3, v2) = v1) |  ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 8.82/2.55  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) |  ? [v3] :  ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 8.82/2.55  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (surjective(v4, v3, v2) = v1) |  ~ (surjective(v4, v3, v2) = v0))
% 8.82/2.55  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (inverse_predicate(v5, v4, v3, v2) = v1) |  ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 8.82/2.55  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = 0 |  ~ (image2(v0, v1) = v3) |  ~ (apply(v0, v5, v2) = 0) |  ~ (member(v2, v3) = v4) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 8.82/2.55  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) |  ~ (apply(v0, v5, v4) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 8.82/2.55  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (inverse_predicate(v0, v1, v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) |  ~ (v7 = 0)) & (v8 = 0 | v7 = 0)))
% 8.82/2.55  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (injective(v0, v1, v2) = 0) |  ~ (apply(v0, v4, v5) = 0) |  ~ (apply(v0, v3, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) |  ~ (v6 = 0))))
% 8.82/2.55  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) |  ~ (apply(v0, v6, v7) = 0) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0)))))
% 8.82/2.55  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (equal_maps(v5, v4, v3, v2) = v1) |  ~ (equal_maps(v5, v4, v3, v2) = v0))
% 8.82/2.55  | (73)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 8.82/2.55  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] :  ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.82/2.55  | (75) injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 8.82/2.55  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0)))))
% 8.82/2.55  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = 0 |  ~ (inverse_image2(v0, v1) = v3) |  ~ (apply(v0, v2, v5) = 0) |  ~ (member(v2, v3) = v4) |  ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 8.82/2.56  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v1 = v0 |  ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) |  ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0))
% 8.82/2.56  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (apply(v4, v3, v2) = v1) |  ~ (apply(v4, v3, v2) = v0))
% 8.82/2.56  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v1 = v0 |  ~ (compose_function(v6, v5, v4, v3, v2) = v1) |  ~ (compose_function(v6, v5, v4, v3, v2) = v0))
% 8.82/2.56  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (image2(v3, v2) = v1) |  ~ (image2(v3, v2) = v0))
% 8.82/2.56  | (82)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum(v2) = v1) |  ~ (sum(v2) = v0))
% 8.82/2.56  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (image3(v0, v1, v2) = v4) |  ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 8.82/2.56  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 8.82/2.56  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (isomorphism(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ( ~ (v17 = 0) |  ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0)))))
% 8.82/2.56  | (86)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0))
% 8.82/2.56  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (image3(v4, v3, v2) = v1) |  ~ (image3(v4, v3, v2) = v0))
% 8.82/2.56  | (88)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (maps(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 &  ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 &  ! [v12] : ( ~ (apply(v0, v4, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13)))))
% 8.82/2.56  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (increasing(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 8.82/2.56  | (90)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 8.82/2.56  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (compose_function(v0, v1, v2, v3, v4) = v7) |  ~ (apply(v7, v5, v6) = v8) |  ~ (apply(v0, v9, v6) = 0) |  ? [v10] :  ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)))))
% 8.82/2.56  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
% 8.82/2.56  | (93) maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 8.82/2.56  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (decreasing(v0, v1, v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 8.82/2.56  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 8.82/2.56  | (96)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3))
% 8.82/2.56  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) |  ~ (apply(v0, v7, v8) = 0) |  ~ (apply(v0, v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) |  ~ (v12 = 0) |  ~ (v11 = 0) |  ~ (v10 = 0) |  ~ (v9 = 0) | v14 = 0)))
% 8.82/2.56  |
% 8.82/2.56  | Instantiating formula (19) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.82/2.56  | (98) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v1 = v0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 8.82/2.56  |
% 8.82/2.56  +-Applying beta-rule and splitting (98), into two cases.
% 8.82/2.56  |-Branch one:
% 8.82/2.56  | (99) all_0_0_0 = 0
% 8.82/2.56  |
% 8.82/2.56  	| Equations (99) can reduce 52 to:
% 8.82/2.56  	| (100) $false
% 8.82/2.56  	|
% 8.82/2.57  	|-The branch is then unsatisfiable
% 8.82/2.57  |-Branch two:
% 8.82/2.57  | (52)  ~ (all_0_0_0 = 0)
% 8.82/2.57  | (102)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v1 = v0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 8.82/2.57  |
% 8.82/2.57  	| Instantiating (102) with all_10_0_7, all_10_1_8, all_10_2_9 yields:
% 8.82/2.57  	| (103)  ~ (all_10_1_8 = all_10_2_9) & apply(all_0_1_1, all_10_1_8, all_10_0_7) = 0 & apply(all_0_1_1, all_10_2_9, all_10_0_7) = 0 & member(all_10_0_7, all_0_2_2) = 0 & member(all_10_1_8, all_0_4_4) = 0 & member(all_10_2_9, all_0_4_4) = 0
% 8.82/2.57  	|
% 8.82/2.57  	| Applying alpha-rule on (103) yields:
% 8.82/2.57  	| (104) member(all_10_1_8, all_0_4_4) = 0
% 8.82/2.57  	| (105) apply(all_0_1_1, all_10_2_9, all_10_0_7) = 0
% 8.82/2.57  	| (106) member(all_10_2_9, all_0_4_4) = 0
% 8.82/2.57  	| (107)  ~ (all_10_1_8 = all_10_2_9)
% 8.82/2.57  	| (108) member(all_10_0_7, all_0_2_2) = 0
% 8.82/2.57  	| (109) apply(all_0_1_1, all_10_1_8, all_10_0_7) = 0
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating formula (43) with all_0_1_1, all_10_0_7, all_10_1_8, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_10_1_8, all_10_0_7) = 0, yields:
% 8.82/2.57  	| (110)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_10_0_7) = 0 & apply(all_0_6_6, all_10_1_8, v0) = 0 & member(v0, all_0_3_3) = 0) | (member(all_10_0_7, all_0_2_2) = v1 & member(all_10_1_8, all_0_4_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating formula (43) with all_0_1_1, all_10_0_7, all_10_2_9, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_10_2_9, all_10_0_7) = 0, yields:
% 8.82/2.57  	| (111)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_10_0_7) = 0 & apply(all_0_6_6, all_10_2_9, v0) = 0 & member(v0, all_0_3_3) = 0) | (member(all_10_0_7, all_0_2_2) = v1 & member(all_10_2_9, all_0_4_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0))))
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating formula (9) with all_10_2_9, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_10_2_9, all_0_4_4) = 0, yields:
% 8.82/2.57  	| (112)  ? [v0] : (apply(all_0_6_6, all_10_2_9, v0) = 0 & member(v0, all_0_3_3) = 0)
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating (112) with all_25_0_10 yields:
% 8.82/2.57  	| (113) apply(all_0_6_6, all_10_2_9, all_25_0_10) = 0 & member(all_25_0_10, all_0_3_3) = 0
% 8.82/2.57  	|
% 8.82/2.57  	| Applying alpha-rule on (113) yields:
% 8.82/2.57  	| (114) apply(all_0_6_6, all_10_2_9, all_25_0_10) = 0
% 8.82/2.57  	| (115) member(all_25_0_10, all_0_3_3) = 0
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating (111) with all_27_0_11, all_27_1_12, all_27_2_13, all_27_3_14 yields:
% 8.82/2.57  	| (116) (all_27_0_11 = 0 & all_27_1_12 = 0 & all_27_2_13 = 0 & apply(all_0_5_5, all_27_3_14, all_10_0_7) = 0 & apply(all_0_6_6, all_10_2_9, all_27_3_14) = 0 & member(all_27_3_14, all_0_3_3) = 0) | (member(all_10_0_7, all_0_2_2) = all_27_2_13 & member(all_10_2_9, all_0_4_4) = all_27_3_14 & ( ~ (all_27_2_13 = 0) |  ~ (all_27_3_14 = 0)))
% 8.82/2.57  	|
% 8.82/2.57  	| Instantiating (110) with all_28_0_15, all_28_1_16, all_28_2_17, all_28_3_18 yields:
% 8.82/2.57  	| (117) (all_28_0_15 = 0 & all_28_1_16 = 0 & all_28_2_17 = 0 & apply(all_0_5_5, all_28_3_18, all_10_0_7) = 0 & apply(all_0_6_6, all_10_1_8, all_28_3_18) = 0 & member(all_28_3_18, all_0_3_3) = 0) | (member(all_10_0_7, all_0_2_2) = all_28_2_17 & member(all_10_1_8, all_0_4_4) = all_28_3_18 & ( ~ (all_28_2_17 = 0) |  ~ (all_28_3_18 = 0)))
% 8.82/2.57  	|
% 8.82/2.57  	+-Applying beta-rule and splitting (117), into two cases.
% 8.82/2.57  	|-Branch one:
% 8.82/2.57  	| (118) all_28_0_15 = 0 & all_28_1_16 = 0 & all_28_2_17 = 0 & apply(all_0_5_5, all_28_3_18, all_10_0_7) = 0 & apply(all_0_6_6, all_10_1_8, all_28_3_18) = 0 & member(all_28_3_18, all_0_3_3) = 0
% 8.82/2.57  	|
% 8.82/2.57  		| Applying alpha-rule on (118) yields:
% 8.82/2.57  		| (119) all_28_2_17 = 0
% 8.82/2.57  		| (120) all_28_1_16 = 0
% 8.82/2.57  		| (121) all_28_0_15 = 0
% 8.82/2.57  		| (122) member(all_28_3_18, all_0_3_3) = 0
% 8.82/2.57  		| (123) apply(all_0_5_5, all_28_3_18, all_10_0_7) = 0
% 8.82/2.57  		| (124) apply(all_0_6_6, all_10_1_8, all_28_3_18) = 0
% 8.82/2.57  		|
% 8.82/2.57  		+-Applying beta-rule and splitting (116), into two cases.
% 8.82/2.57  		|-Branch one:
% 8.82/2.57  		| (125) all_27_0_11 = 0 & all_27_1_12 = 0 & all_27_2_13 = 0 & apply(all_0_5_5, all_27_3_14, all_10_0_7) = 0 & apply(all_0_6_6, all_10_2_9, all_27_3_14) = 0 & member(all_27_3_14, all_0_3_3) = 0
% 8.82/2.57  		|
% 8.82/2.57  			| Applying alpha-rule on (125) yields:
% 8.82/2.57  			| (126) apply(all_0_6_6, all_10_2_9, all_27_3_14) = 0
% 8.82/2.57  			| (127) all_27_2_13 = 0
% 8.82/2.57  			| (128) member(all_27_3_14, all_0_3_3) = 0
% 8.82/2.57  			| (129) all_27_1_12 = 0
% 8.82/2.57  			| (130) apply(all_0_5_5, all_27_3_14, all_10_0_7) = 0
% 8.82/2.57  			| (131) all_27_0_11 = 0
% 8.82/2.57  			|
% 8.82/2.57  			| Instantiating formula (70) with all_10_0_7, all_28_3_18, all_27_3_14, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_28_3_18, all_10_0_7) = 0, apply(all_0_5_5, all_27_3_14, all_10_0_7) = 0, yields:
% 8.82/2.57  			| (132) all_28_3_18 = all_27_3_14 |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_28_3_18, all_0_3_3) = v1 & member(all_27_3_14, all_0_3_3) = v0 & member(all_10_0_7, all_0_2_2) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.57  			|
% 8.82/2.57  			| Instantiating formula (70) with all_27_3_14, all_10_2_9, all_10_1_8, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_10_2_9, all_27_3_14) = 0, yields:
% 8.82/2.57  			| (133) all_10_1_8 = all_10_2_9 |  ~ (apply(all_0_6_6, all_10_1_8, all_27_3_14) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_27_3_14, all_0_3_3) = v2 & member(all_10_1_8, all_0_4_4) = v0 & member(all_10_2_9, all_0_4_4) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.57  			|
% 8.82/2.57  			| Instantiating formula (46) with all_27_3_14, all_25_0_10, all_10_2_9, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_10_2_9, all_27_3_14) = 0, apply(all_0_6_6, all_10_2_9, all_25_0_10) = 0, yields:
% 8.82/2.57  			| (134) all_27_3_14 = all_25_0_10 |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_27_3_14, all_0_3_3) = v2 & member(all_25_0_10, all_0_3_3) = v1 & member(all_10_2_9, all_0_4_4) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.57  			|
% 8.82/2.57  			| Instantiating formula (70) with all_25_0_10, all_10_1_8, all_10_2_9, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_10_2_9, all_25_0_10) = 0, yields:
% 8.82/2.57  			| (135) all_10_1_8 = all_10_2_9 |  ~ (apply(all_0_6_6, all_10_1_8, all_25_0_10) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_25_0_10, all_0_3_3) = v2 & member(all_10_1_8, all_0_4_4) = v1 & member(all_10_2_9, all_0_4_4) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.57  			|
% 8.82/2.57  			+-Applying beta-rule and splitting (134), into two cases.
% 8.82/2.57  			|-Branch one:
% 8.82/2.57  			| (136) all_27_3_14 = all_25_0_10
% 8.82/2.57  			|
% 8.82/2.57  				| From (136) and (128) follows:
% 8.82/2.57  				| (115) member(all_25_0_10, all_0_3_3) = 0
% 8.82/2.58  				|
% 8.82/2.58  				+-Applying beta-rule and splitting (135), into two cases.
% 8.82/2.58  				|-Branch one:
% 8.82/2.58  				| (138)  ~ (apply(all_0_6_6, all_10_1_8, all_25_0_10) = 0)
% 8.82/2.58  				|
% 8.82/2.58  					+-Applying beta-rule and splitting (132), into two cases.
% 8.82/2.58  					|-Branch one:
% 8.82/2.58  					| (139) all_28_3_18 = all_27_3_14
% 8.82/2.58  					|
% 8.82/2.58  						| Combining equations (136,139) yields a new equation:
% 8.82/2.58  						| (140) all_28_3_18 = all_25_0_10
% 8.82/2.58  						|
% 8.82/2.58  						| From (140) and (124) follows:
% 8.82/2.58  						| (141) apply(all_0_6_6, all_10_1_8, all_25_0_10) = 0
% 8.82/2.58  						|
% 8.82/2.58  						| Using (141) and (138) yields:
% 8.82/2.58  						| (142) $false
% 8.82/2.58  						|
% 8.82/2.58  						|-The branch is then unsatisfiable
% 8.82/2.58  					|-Branch two:
% 8.82/2.58  					| (143)  ~ (all_28_3_18 = all_27_3_14)
% 8.82/2.58  					| (144)  ? [v0] :  ? [v1] :  ? [v2] : (member(all_28_3_18, all_0_3_3) = v1 & member(all_27_3_14, all_0_3_3) = v0 & member(all_10_0_7, all_0_2_2) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.58  					|
% 8.82/2.58  						| Instantiating (144) with all_72_0_24, all_72_1_25, all_72_2_26 yields:
% 8.82/2.58  						| (145) member(all_28_3_18, all_0_3_3) = all_72_1_25 & member(all_27_3_14, all_0_3_3) = all_72_2_26 & member(all_10_0_7, all_0_2_2) = all_72_0_24 & ( ~ (all_72_0_24 = 0) |  ~ (all_72_1_25 = 0) |  ~ (all_72_2_26 = 0))
% 8.82/2.58  						|
% 8.82/2.58  						| Applying alpha-rule on (145) yields:
% 8.82/2.58  						| (146) member(all_28_3_18, all_0_3_3) = all_72_1_25
% 8.82/2.58  						| (147) member(all_27_3_14, all_0_3_3) = all_72_2_26
% 8.82/2.58  						| (148) member(all_10_0_7, all_0_2_2) = all_72_0_24
% 8.82/2.58  						| (149)  ~ (all_72_0_24 = 0) |  ~ (all_72_1_25 = 0) |  ~ (all_72_2_26 = 0)
% 8.82/2.58  						|
% 8.82/2.58  						| From (136) and (147) follows:
% 8.82/2.58  						| (150) member(all_25_0_10, all_0_3_3) = all_72_2_26
% 8.82/2.58  						|
% 8.82/2.58  						| Instantiating formula (2) with all_28_3_18, all_0_3_3, all_72_1_25, 0 and discharging atoms member(all_28_3_18, all_0_3_3) = all_72_1_25, member(all_28_3_18, all_0_3_3) = 0, yields:
% 8.82/2.58  						| (151) all_72_1_25 = 0
% 8.82/2.58  						|
% 8.82/2.58  						| Instantiating formula (2) with all_25_0_10, all_0_3_3, all_72_2_26, 0 and discharging atoms member(all_25_0_10, all_0_3_3) = all_72_2_26, member(all_25_0_10, all_0_3_3) = 0, yields:
% 8.82/2.58  						| (152) all_72_2_26 = 0
% 8.82/2.58  						|
% 8.82/2.58  						| Instantiating formula (2) with all_10_0_7, all_0_2_2, all_72_0_24, 0 and discharging atoms member(all_10_0_7, all_0_2_2) = all_72_0_24, member(all_10_0_7, all_0_2_2) = 0, yields:
% 8.82/2.58  						| (153) all_72_0_24 = 0
% 8.82/2.58  						|
% 8.82/2.58  						+-Applying beta-rule and splitting (149), into two cases.
% 8.82/2.58  						|-Branch one:
% 8.82/2.58  						| (154)  ~ (all_72_0_24 = 0)
% 8.82/2.58  						|
% 8.82/2.58  							| Equations (153) can reduce 154 to:
% 8.82/2.58  							| (100) $false
% 8.82/2.58  							|
% 8.82/2.58  							|-The branch is then unsatisfiable
% 8.82/2.58  						|-Branch two:
% 8.82/2.58  						| (153) all_72_0_24 = 0
% 8.82/2.58  						| (157)  ~ (all_72_1_25 = 0) |  ~ (all_72_2_26 = 0)
% 8.82/2.58  						|
% 8.82/2.58  							+-Applying beta-rule and splitting (157), into two cases.
% 8.82/2.58  							|-Branch one:
% 8.82/2.58  							| (158)  ~ (all_72_1_25 = 0)
% 8.82/2.58  							|
% 8.82/2.58  								| Equations (151) can reduce 158 to:
% 8.82/2.58  								| (100) $false
% 8.82/2.58  								|
% 8.82/2.58  								|-The branch is then unsatisfiable
% 8.82/2.58  							|-Branch two:
% 8.82/2.58  							| (151) all_72_1_25 = 0
% 8.82/2.58  							| (161)  ~ (all_72_2_26 = 0)
% 8.82/2.58  							|
% 8.82/2.58  								| Equations (152) can reduce 161 to:
% 8.82/2.58  								| (100) $false
% 8.82/2.58  								|
% 8.82/2.58  								|-The branch is then unsatisfiable
% 8.82/2.58  				|-Branch two:
% 8.82/2.58  				| (141) apply(all_0_6_6, all_10_1_8, all_25_0_10) = 0
% 8.82/2.58  				| (164) all_10_1_8 = all_10_2_9 |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_25_0_10, all_0_3_3) = v2 & member(all_10_1_8, all_0_4_4) = v1 & member(all_10_2_9, all_0_4_4) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.58  				|
% 8.82/2.58  					+-Applying beta-rule and splitting (133), into two cases.
% 8.82/2.58  					|-Branch one:
% 8.82/2.58  					| (165)  ~ (apply(all_0_6_6, all_10_1_8, all_27_3_14) = 0)
% 8.82/2.58  					|
% 8.82/2.58  						| From (136) and (165) follows:
% 8.82/2.58  						| (138)  ~ (apply(all_0_6_6, all_10_1_8, all_25_0_10) = 0)
% 8.82/2.58  						|
% 8.82/2.58  						| Using (141) and (138) yields:
% 8.82/2.58  						| (142) $false
% 8.82/2.58  						|
% 8.82/2.58  						|-The branch is then unsatisfiable
% 8.82/2.58  					|-Branch two:
% 8.82/2.58  					| (168) apply(all_0_6_6, all_10_1_8, all_27_3_14) = 0
% 8.82/2.58  					| (169) all_10_1_8 = all_10_2_9 |  ? [v0] :  ? [v1] :  ? [v2] : (member(all_27_3_14, all_0_3_3) = v2 & member(all_10_1_8, all_0_4_4) = v0 & member(all_10_2_9, all_0_4_4) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.58  					|
% 8.82/2.58  						+-Applying beta-rule and splitting (169), into two cases.
% 8.82/2.58  						|-Branch one:
% 8.82/2.58  						| (170) all_10_1_8 = all_10_2_9
% 8.82/2.58  						|
% 8.82/2.58  							| Equations (170) can reduce 107 to:
% 8.82/2.58  							| (100) $false
% 8.82/2.58  							|
% 8.82/2.58  							|-The branch is then unsatisfiable
% 8.82/2.58  						|-Branch two:
% 8.82/2.58  						| (107)  ~ (all_10_1_8 = all_10_2_9)
% 8.82/2.58  						| (173)  ? [v0] :  ? [v1] :  ? [v2] : (member(all_27_3_14, all_0_3_3) = v2 & member(all_10_1_8, all_0_4_4) = v0 & member(all_10_2_9, all_0_4_4) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.58  						|
% 8.82/2.58  							| Instantiating (173) with all_76_0_30, all_76_1_31, all_76_2_32 yields:
% 8.82/2.58  							| (174) member(all_27_3_14, all_0_3_3) = all_76_0_30 & member(all_10_1_8, all_0_4_4) = all_76_2_32 & member(all_10_2_9, all_0_4_4) = all_76_1_31 & ( ~ (all_76_0_30 = 0) |  ~ (all_76_1_31 = 0) |  ~ (all_76_2_32 = 0))
% 8.82/2.58  							|
% 8.82/2.58  							| Applying alpha-rule on (174) yields:
% 8.82/2.58  							| (175) member(all_27_3_14, all_0_3_3) = all_76_0_30
% 8.82/2.58  							| (176) member(all_10_1_8, all_0_4_4) = all_76_2_32
% 8.82/2.58  							| (177) member(all_10_2_9, all_0_4_4) = all_76_1_31
% 8.82/2.58  							| (178)  ~ (all_76_0_30 = 0) |  ~ (all_76_1_31 = 0) |  ~ (all_76_2_32 = 0)
% 8.82/2.58  							|
% 8.82/2.58  							| From (136) and (175) follows:
% 8.82/2.58  							| (179) member(all_25_0_10, all_0_3_3) = all_76_0_30
% 8.82/2.58  							|
% 8.82/2.58  							| Instantiating formula (2) with all_25_0_10, all_0_3_3, all_76_0_30, 0 and discharging atoms member(all_25_0_10, all_0_3_3) = all_76_0_30, member(all_25_0_10, all_0_3_3) = 0, yields:
% 8.82/2.58  							| (180) all_76_0_30 = 0
% 8.82/2.58  							|
% 8.82/2.58  							| Instantiating formula (2) with all_10_1_8, all_0_4_4, all_76_2_32, 0 and discharging atoms member(all_10_1_8, all_0_4_4) = all_76_2_32, member(all_10_1_8, all_0_4_4) = 0, yields:
% 8.82/2.58  							| (181) all_76_2_32 = 0
% 8.82/2.58  							|
% 8.82/2.58  							| Instantiating formula (2) with all_10_2_9, all_0_4_4, all_76_1_31, 0 and discharging atoms member(all_10_2_9, all_0_4_4) = all_76_1_31, member(all_10_2_9, all_0_4_4) = 0, yields:
% 8.82/2.59  							| (182) all_76_1_31 = 0
% 8.82/2.59  							|
% 8.82/2.59  							+-Applying beta-rule and splitting (178), into two cases.
% 8.82/2.59  							|-Branch one:
% 8.82/2.59  							| (183)  ~ (all_76_0_30 = 0)
% 8.82/2.59  							|
% 8.82/2.59  								| Equations (180) can reduce 183 to:
% 8.82/2.59  								| (100) $false
% 8.82/2.59  								|
% 8.82/2.59  								|-The branch is then unsatisfiable
% 8.82/2.59  							|-Branch two:
% 8.82/2.59  							| (180) all_76_0_30 = 0
% 8.82/2.59  							| (186)  ~ (all_76_1_31 = 0) |  ~ (all_76_2_32 = 0)
% 8.82/2.59  							|
% 8.82/2.59  								+-Applying beta-rule and splitting (186), into two cases.
% 8.82/2.59  								|-Branch one:
% 8.82/2.59  								| (187)  ~ (all_76_1_31 = 0)
% 8.82/2.59  								|
% 8.82/2.59  									| Equations (182) can reduce 187 to:
% 8.82/2.59  									| (100) $false
% 8.82/2.59  									|
% 8.82/2.59  									|-The branch is then unsatisfiable
% 8.82/2.59  								|-Branch two:
% 8.82/2.59  								| (182) all_76_1_31 = 0
% 8.82/2.59  								| (190)  ~ (all_76_2_32 = 0)
% 8.82/2.59  								|
% 8.82/2.59  									| Equations (181) can reduce 190 to:
% 8.82/2.59  									| (100) $false
% 8.82/2.59  									|
% 8.82/2.59  									|-The branch is then unsatisfiable
% 8.82/2.59  			|-Branch two:
% 8.82/2.59  			| (192)  ~ (all_27_3_14 = all_25_0_10)
% 8.82/2.59  			| (193)  ? [v0] :  ? [v1] :  ? [v2] : (member(all_27_3_14, all_0_3_3) = v2 & member(all_25_0_10, all_0_3_3) = v1 & member(all_10_2_9, all_0_4_4) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0)))
% 8.82/2.59  			|
% 8.82/2.59  				| Instantiating (193) with all_64_0_36, all_64_1_37, all_64_2_38 yields:
% 8.82/2.59  				| (194) member(all_27_3_14, all_0_3_3) = all_64_0_36 & member(all_25_0_10, all_0_3_3) = all_64_1_37 & member(all_10_2_9, all_0_4_4) = all_64_2_38 & ( ~ (all_64_0_36 = 0) |  ~ (all_64_1_37 = 0) |  ~ (all_64_2_38 = 0))
% 8.82/2.59  				|
% 8.82/2.59  				| Applying alpha-rule on (194) yields:
% 8.82/2.59  				| (195) member(all_27_3_14, all_0_3_3) = all_64_0_36
% 8.82/2.59  				| (196) member(all_25_0_10, all_0_3_3) = all_64_1_37
% 8.82/2.59  				| (197) member(all_10_2_9, all_0_4_4) = all_64_2_38
% 8.82/2.59  				| (198)  ~ (all_64_0_36 = 0) |  ~ (all_64_1_37 = 0) |  ~ (all_64_2_38 = 0)
% 8.82/2.59  				|
% 8.82/2.59  				| Instantiating formula (2) with all_27_3_14, all_0_3_3, all_64_0_36, 0 and discharging atoms member(all_27_3_14, all_0_3_3) = all_64_0_36, member(all_27_3_14, all_0_3_3) = 0, yields:
% 8.82/2.59  				| (199) all_64_0_36 = 0
% 8.82/2.59  				|
% 8.82/2.59  				| Instantiating formula (2) with all_25_0_10, all_0_3_3, all_64_1_37, 0 and discharging atoms member(all_25_0_10, all_0_3_3) = all_64_1_37, member(all_25_0_10, all_0_3_3) = 0, yields:
% 8.82/2.59  				| (200) all_64_1_37 = 0
% 8.82/2.59  				|
% 8.82/2.59  				| Instantiating formula (2) with all_10_2_9, all_0_4_4, all_64_2_38, 0 and discharging atoms member(all_10_2_9, all_0_4_4) = all_64_2_38, member(all_10_2_9, all_0_4_4) = 0, yields:
% 8.82/2.59  				| (201) all_64_2_38 = 0
% 8.82/2.59  				|
% 8.82/2.59  				+-Applying beta-rule and splitting (198), into two cases.
% 8.82/2.59  				|-Branch one:
% 8.82/2.59  				| (202)  ~ (all_64_0_36 = 0)
% 8.82/2.59  				|
% 8.82/2.59  					| Equations (199) can reduce 202 to:
% 8.82/2.59  					| (100) $false
% 8.82/2.59  					|
% 8.82/2.59  					|-The branch is then unsatisfiable
% 8.82/2.59  				|-Branch two:
% 8.82/2.59  				| (199) all_64_0_36 = 0
% 8.82/2.59  				| (205)  ~ (all_64_1_37 = 0) |  ~ (all_64_2_38 = 0)
% 8.82/2.59  				|
% 8.82/2.59  					+-Applying beta-rule and splitting (205), into two cases.
% 8.82/2.59  					|-Branch one:
% 8.82/2.59  					| (206)  ~ (all_64_1_37 = 0)
% 8.82/2.59  					|
% 8.82/2.59  						| Equations (200) can reduce 206 to:
% 8.82/2.59  						| (100) $false
% 8.82/2.59  						|
% 8.82/2.59  						|-The branch is then unsatisfiable
% 8.82/2.59  					|-Branch two:
% 8.82/2.59  					| (200) all_64_1_37 = 0
% 8.82/2.59  					| (209)  ~ (all_64_2_38 = 0)
% 8.82/2.59  					|
% 8.82/2.59  						| Equations (201) can reduce 209 to:
% 8.82/2.59  						| (100) $false
% 8.82/2.59  						|
% 8.82/2.59  						|-The branch is then unsatisfiable
% 8.82/2.59  		|-Branch two:
% 8.82/2.59  		| (211) member(all_10_0_7, all_0_2_2) = all_27_2_13 & member(all_10_2_9, all_0_4_4) = all_27_3_14 & ( ~ (all_27_2_13 = 0) |  ~ (all_27_3_14 = 0))
% 8.82/2.59  		|
% 8.82/2.59  			| Applying alpha-rule on (211) yields:
% 8.82/2.59  			| (212) member(all_10_0_7, all_0_2_2) = all_27_2_13
% 8.82/2.59  			| (213) member(all_10_2_9, all_0_4_4) = all_27_3_14
% 8.82/2.59  			| (214)  ~ (all_27_2_13 = 0) |  ~ (all_27_3_14 = 0)
% 8.82/2.59  			|
% 8.82/2.59  			| Instantiating formula (2) with all_10_0_7, all_0_2_2, all_27_2_13, 0 and discharging atoms member(all_10_0_7, all_0_2_2) = all_27_2_13, member(all_10_0_7, all_0_2_2) = 0, yields:
% 8.82/2.59  			| (127) all_27_2_13 = 0
% 8.82/2.59  			|
% 8.82/2.59  			| Instantiating formula (2) with all_10_2_9, all_0_4_4, all_27_3_14, 0 and discharging atoms member(all_10_2_9, all_0_4_4) = all_27_3_14, member(all_10_2_9, all_0_4_4) = 0, yields:
% 8.82/2.59  			| (216) all_27_3_14 = 0
% 8.82/2.59  			|
% 8.82/2.59  			+-Applying beta-rule and splitting (214), into two cases.
% 8.82/2.59  			|-Branch one:
% 8.82/2.59  			| (217)  ~ (all_27_2_13 = 0)
% 8.82/2.59  			|
% 8.82/2.59  				| Equations (127) can reduce 217 to:
% 8.82/2.59  				| (100) $false
% 8.82/2.59  				|
% 8.82/2.59  				|-The branch is then unsatisfiable
% 8.82/2.59  			|-Branch two:
% 8.82/2.59  			| (127) all_27_2_13 = 0
% 8.82/2.59  			| (220)  ~ (all_27_3_14 = 0)
% 8.82/2.59  			|
% 8.82/2.59  				| Equations (216) can reduce 220 to:
% 8.82/2.59  				| (100) $false
% 8.82/2.59  				|
% 8.82/2.59  				|-The branch is then unsatisfiable
% 8.82/2.59  	|-Branch two:
% 8.82/2.59  	| (222) member(all_10_0_7, all_0_2_2) = all_28_2_17 & member(all_10_1_8, all_0_4_4) = all_28_3_18 & ( ~ (all_28_2_17 = 0) |  ~ (all_28_3_18 = 0))
% 8.82/2.59  	|
% 8.82/2.59  		| Applying alpha-rule on (222) yields:
% 8.82/2.59  		| (223) member(all_10_0_7, all_0_2_2) = all_28_2_17
% 8.82/2.59  		| (224) member(all_10_1_8, all_0_4_4) = all_28_3_18
% 8.82/2.59  		| (225)  ~ (all_28_2_17 = 0) |  ~ (all_28_3_18 = 0)
% 8.82/2.59  		|
% 8.82/2.59  		| Instantiating formula (2) with all_10_0_7, all_0_2_2, all_28_2_17, 0 and discharging atoms member(all_10_0_7, all_0_2_2) = all_28_2_17, member(all_10_0_7, all_0_2_2) = 0, yields:
% 8.82/2.59  		| (119) all_28_2_17 = 0
% 8.82/2.59  		|
% 8.82/2.59  		| Instantiating formula (2) with all_10_1_8, all_0_4_4, all_28_3_18, 0 and discharging atoms member(all_10_1_8, all_0_4_4) = all_28_3_18, member(all_10_1_8, all_0_4_4) = 0, yields:
% 8.82/2.59  		| (227) all_28_3_18 = 0
% 8.82/2.59  		|
% 8.82/2.59  		+-Applying beta-rule and splitting (225), into two cases.
% 8.82/2.59  		|-Branch one:
% 8.82/2.60  		| (228)  ~ (all_28_2_17 = 0)
% 8.82/2.60  		|
% 8.82/2.60  			| Equations (119) can reduce 228 to:
% 8.82/2.60  			| (100) $false
% 8.82/2.60  			|
% 8.82/2.60  			|-The branch is then unsatisfiable
% 8.82/2.60  		|-Branch two:
% 8.82/2.60  		| (119) all_28_2_17 = 0
% 8.82/2.60  		| (231)  ~ (all_28_3_18 = 0)
% 8.82/2.60  		|
% 8.82/2.60  			| Equations (227) can reduce 231 to:
% 8.82/2.60  			| (100) $false
% 8.82/2.60  			|
% 8.82/2.60  			|-The branch is then unsatisfiable
% 8.82/2.60  % SZS output end Proof for theBenchmark
% 8.82/2.60  
% 8.82/2.60  2009ms
%------------------------------------------------------------------------------