TSTP Solution File: SET712+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET712+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 00:21:34 EDT 2022
% Result : Theorem 8.72s 2.60s
% Output : Proof 12.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET712+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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 : Sun Jul 10 18:50:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/0.96 Prover 0: Preprocessing ...
% 3.26/1.30 Prover 0: Warning: ignoring some quantifiers
% 3.26/1.34 Prover 0: Constructing countermodel ...
% 4.24/1.57 Prover 0: gave up
% 4.24/1.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.62/1.62 Prover 1: Preprocessing ...
% 5.58/1.87 Prover 1: Constructing countermodel ...
% 6.34/2.01 Prover 1: gave up
% 6.34/2.01 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.34/2.05 Prover 2: Preprocessing ...
% 7.73/2.35 Prover 2: Warning: ignoring some quantifiers
% 7.73/2.37 Prover 2: Constructing countermodel ...
% 8.72/2.59 Prover 2: proved (584ms)
% 8.72/2.60
% 8.72/2.60 No countermodel exists, formula is valid
% 8.72/2.60 % SZS status Theorem for theBenchmark
% 8.72/2.60
% 8.72/2.60 Generating proof ... Warning: ignoring some quantifiers
% 11.90/3.27 found it (size 78)
% 11.90/3.27
% 11.90/3.27 % SZS output start Proof for theBenchmark
% 11.90/3.27 Assumed formulas after preprocessing and simplification:
% 11.90/3.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & inverse_function(v0, v1, v2) = v3 & one_to_one(v0, v1, v2) = 0 & maps(v3, v2, v1) = v4 & maps(v0, v1, v2) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v7, v10, v12) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = 0) | ~ (apply(v7, v10, v12) = v14) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v13, v11) = v14) | ~ (apply(v7, v10, v12) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v13, v11) = v14) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v13, v11) = v14) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v12, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v13, v11) = v14) | ~ (member(v12, v6) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v7, v10, v12) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v12, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (member(v12, v6) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v10, v12) = v15) | ( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = v13) | ~ (apply(v6, v10, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v14, v11) = v15) | ( ~ (v15 = 0) & member(v14, v8) = v15) | ( ~ (v15 = 0) & member(v11, v9) = v15) | ( ~ (v15 = 0) & member(v10, v7) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = v13) | ~ (apply(v5, v14, v11) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v6, v10, v14) = v15) | ( ~ (v15 = 0) & member(v14, v8) = v15) | ( ~ (v15 = 0) & member(v11, v9) = v15) | ( ~ (v15 = 0) & member(v10, v7) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = v13) | ~ (member(v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v6, v10, v14) = v15) | ( ~ (v15 = 0) & apply(v5, v14, v11) = v15) | ( ~ (v15 = 0) & member(v11, v9) = v15) | ( ~ (v15 = 0) & member(v10, v7) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v7, v11, v14) = 0) | ~ (apply(v5, v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & apply(v6, v14, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v14, v12) = 0) | ~ (apply(v5, v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v11, v14) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v5, v11, v12) = v13) | ~ (member(v14, v9) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v7, v11, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v14, v12) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v7, v10, v12) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v7, v10, v12) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v12, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v7, v10, v12) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v7, v10, v12) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v9, v11, v13) = v14) | ~ (member(v12, v6) = 0) | ~ (member(v10, v6) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v7, v10, v12) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v7, v10, v12) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = v14) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v13, v8) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v9, v11, v13) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = v14) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v11, v8) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v9, v11, v13) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = v14) | ~ (member(v13, v8) = 0) | ~ (member(v11, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v5, v12, v13) = v15) | ( ~ (v15 = 0) & apply(v5, v10, v11) = v15) | ( ~ (v15 = 0) & member(v12, v6) = v15) | ( ~ (v15 = 0) & member(v10, v6) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v9, v11, v13) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14) | (((v15 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14)) & ((v14 = 0 & apply(v7, v10, v12) = 0) | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | (((v15 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14)) & ((v14 = 0 & apply(v7, v10, v12) = 0) | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14) | (((v15 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14)) & ((v14 = 0 & apply(v7, v10, v12) = 0) | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | (((v15 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14)) & ((v14 = 0 & apply(v7, v10, v12) = 0) | ( ~ (v15 = 0) & apply(v9, v11, v13) = v15))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v11, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v13, v11) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v11, v8) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14) | ( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v12, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v10, v11) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14) | ( ~ (v14 = 0) & member(v10, v6) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (member(v13, v8) = 0) | ~ (member(v12, v6) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v6) = 0) | ? [v14] : ((v14 = 0 & apply(v9, v11, v13) = 0) | ( ~ (v14 = 0) & apply(v7, v10, v12) = v14) | ( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v5, v10, v11) = v14))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v6 = v5 | ~ (compose_predicate(v12, v11, v10, v9, v8, v7) = v6) | ~ (compose_predicate(v12, v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & apply(v6, v10, v13) = 0 & apply(v5, v13, v11) = 0 & member(v13, v8) = 0) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v7) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v5, v11, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & apply(v7, v11, v13) = 0 & apply(v6, v13, v12) = 0 & member(v13, v9) = 0) | ( ~ (v13 = 0) & member(v12, v10) = v13) | ( ~ (v13 = 0) & member(v11, v8) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (equal_maps(v5, v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (apply(v5, v9, v10) = 0) | ? [v12] : (( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (equal_maps(v5, v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (member(v10, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v5, v9, v10) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (equal_maps(v5, v6, v7, v8) = 0) | ~ (apply(v5, v9, v10) = 0) | ~ (member(v11, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (equal_maps(v5, v6, v7, v8) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & apply(v5, v9, v10) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (member(v13, v10) = 0 & member(v12, v8) = 0 & ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v7, v12, v15) = 0 & apply(v6, v15, v13) = 0 & member(v15, v9) = 0) | (v14 = 0 & apply(v5, v12, v13) = 0)) & (( ~ (v14 = 0) & apply(v5, v12, v13) = v14) | ( ! [v19] : ( ~ (apply(v7, v12, v19) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v6, v19, v13) = v20) | ( ~ (v20 = 0) & member(v19, v9) = v20))) & ! [v19] : ( ~ (apply(v6, v19, v13) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v7, v12, v19) = v20) | ( ~ (v20 = 0) & member(v19, v9) = v20))) & ! [v19] : ( ~ (member(v19, v9) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v7, v12, v19) = v20) | ( ~ (v20 = 0) & apply(v6, v19, v13) = v20))))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image3(v5, v6, v7) = v9) | ~ (apply(v5, v8, v11) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & member(v11, v6) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image3(v5, v6, v7) = v9) | ~ (member(v11, v6) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & apply(v5, v8, v11) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image3(v5, v6, v7) = v9) | ~ (apply(v5, v11, v8) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & member(v11, v6) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image3(v5, v6, v7) = v9) | ~ (member(v11, v6) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & apply(v5, v11, v8) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (isomorphism(v11, v10, v9, v8, v7) = v6) | ~ (isomorphism(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (decreasing(v11, v10, v9, v8, v7) = v6) | ~ (decreasing(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (increasing(v11, v10, v9, v8, v7) = v6) | ~ (increasing(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (compose_function(v11, v10, v9, v8, v7) = v6) | ~ (compose_function(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_function(v5, v6, v7) = v10) | ~ (apply(v10, v9, v8) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v9, v7) = v12) | ( ~ (v12 = 0) & member(v8, v6) = v12) | (( ~ (v11 = 0) | (v12 = 0 & apply(v5, v8, v9) = 0)) & (v11 = 0 | ( ~ (v12 = 0) & apply(v5, v8, v9) = v12))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_predicate(v5, v6, v7, v8) = 0) | ~ (apply(v6, v9, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12) | (( ~ (v11 = 0) | (v12 = 0 & apply(v5, v10, v9) = 0)) & (v11 = 0 | ( ~ (v12 = 0) & apply(v5, v10, v9) = v12))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_predicate(v5, v6, v7, v8) = 0) | ~ (apply(v5, v10, v9) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12) | (( ~ (v11 = 0) | (v12 = 0 & apply(v6, v9, v10) = 0)) & (v11 = 0 | ( ~ (v12 = 0) & apply(v6, v9, v10) = v12))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (maps(v5, v6, v7) = 0) | ~ (apply(v5, v8, v10) = 0) | ~ (apply(v5, v8, v9) = 0) | ? [v11] : (( ~ (v11 = 0) & member(v10, v7) = v11) | ( ~ (v11 = 0) & member(v9, v7) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (maps(v5, v6, v7) = 0) | ~ (apply(v5, v8, v10) = 0) | ~ (member(v9, v7) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v9) = v11) | ( ~ (v11 = 0) & member(v10, v7) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (maps(v5, v6, v7) = 0) | ~ (apply(v5, v8, v9) = 0) | ~ (member(v10, v7) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v10) = v11) | ( ~ (v11 = 0) & member(v9, v7) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (maps(v5, v6, v7) = 0) | ~ (member(v10, v7) = 0) | ~ (member(v9, v7) = 0) | ~ (member(v8, v6) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v10) = v11) | ( ~ (v11 = 0) & apply(v5, v8, v9) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (isomorphism(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0 & ((v22 = 0 & apply(v9, v12, v14) = 0) | (v21 = 0 & apply(v7, v11, v13) = 0)) & (( ~ (v22 = 0) & apply(v9, v12, v14) = v22) | ( ~ (v21 = 0) & apply(v7, v11, v13) = v21))) | ( ~ (v11 = 0) & one_to_one(v5, v6, v8) = v11) | ( ~ (v11 = 0) & maps(v5, v6, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v9, v14, v12) = v15 & apply(v7, v11, v13) = 0 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v9, v12, v14) = v15 & apply(v7, v11, v13) = 0 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (injective(v5, v6, v7) = 0) | ~ (apply(v5, v9, v10) = 0) | ~ (apply(v5, v8, v10) = 0) | ? [v11] : (( ~ (v11 = 0) & member(v10, v7) = v11) | ( ~ (v11 = 0) & member(v9, v6) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (injective(v5, v6, v7) = 0) | ~ (apply(v5, v9, v10) = 0) | ~ (member(v8, v6) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v8, v10) = v11) | ( ~ (v11 = 0) & member(v10, v7) = v11) | ( ~ (v11 = 0) & member(v9, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (injective(v5, v6, v7) = 0) | ~ (apply(v5, v8, v10) = 0) | ~ (member(v9, v6) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v9, v10) = v11) | ( ~ (v11 = 0) & member(v10, v7) = v11) | ( ~ (v11 = 0) & member(v8, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (injective(v5, v6, v7) = 0) | ~ (member(v10, v7) = 0) | ~ (member(v9, v6) = 0) | ~ (member(v8, v6) = 0) | ? [v11] : (( ~ (v11 = 0) & apply(v5, v9, v10) = v11) | ( ~ (v11 = 0) & apply(v5, v8, v10) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (inverse_image2(v5, v6) = v8) | ~ (apply(v5, v7, v10) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (inverse_image2(v5, v6) = v8) | ~ (member(v10, v6) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apply(v5, v7, v10) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (image2(v5, v6) = v8) | ~ (apply(v5, v10, v7) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (image2(v5, v6) = v8) | ~ (member(v10, v6) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apply(v5, v10, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (inverse_predicate(v10, v9, v8, v7) = v6) | ~ (inverse_predicate(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (equal_maps(v10, v9, v8, v7) = v6) | ~ (equal_maps(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (inverse_predicate(v5, v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (member(v11, v8) = 0 & member(v10, v7) = 0 & ((v13 = 0 & apply(v5, v11, v10) = 0) | (v12 = 0 & apply(v6, v10, v11) = 0)) & (( ~ (v13 = 0) & apply(v5, v11, v10) = v13) | ( ~ (v12 = 0) & apply(v6, v10, v11) = v12)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_maps(v5, v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & apply(v6, v10, v12) = 0 & apply(v5, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ((v10 = 0 & member(v5, v6) = 0) | ( ~ (v10 = 0) & member(v5, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & member(v5, v7) = v10) | ( ~ (v10 = 0) & member(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v9, v6) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (inverse_image3(v9, v8, v7) = v6) | ~ (inverse_image3(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (image3(v9, v8, v7) = v6) | ~ (image3(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (inverse_function(v9, v8, v7) = v6) | ~ (inverse_function(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (one_to_one(v9, v8, v7) = v6) | ~ (one_to_one(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (surjective(v9, v8, v7) = v6) | ~ (surjective(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (injective(v9, v8, v7) = v6) | ~ (injective(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (maps(v9, v8, v7) = v6) | ~ (maps(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (apply(v9, v8, v7) = v6) | ~ (apply(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | (one_to_one(v5, v6, v8) = 0 & maps(v5, v6, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | member(v8, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v5, v8, v10) = 0 & member(v10, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | member(v8, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v5, v10, v8) = 0 & member(v10, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (one_to_one(v5, v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & surjective(v5, v6, v7) = v9) | ( ~ (v9 = 0) & injective(v5, v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (surjective(v5, v6, v7) = v8) | ? [v9] : (member(v9, v7) = 0 & ! [v10] : ( ~ (apply(v5, v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)) & ! [v10] : ( ~ (member(v10, v6) = 0) | ? [v11] : ( ~ (v11 = 0) & apply(v5, v10, v9) = v11)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (injective(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v10 = v9) & apply(v5, v10, v11) = 0 & apply(v5, v9, v11) = 0 & member(v11, v7) = 0 & member(v10, v6) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (identity(v5, v6) = 0) | ~ (apply(v5, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (maps(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v11 = v10) & apply(v5, v9, v11) = 0 & apply(v5, v9, v10) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0 & member(v9, v6) = 0) | (v10 = 0 & member(v9, v6) = 0 & ! [v17] : ( ~ (apply(v5, v9, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & member(v17, v7) = v18)) & ! [v17] : ( ~ (member(v17, v7) = 0) | ? [v18] : ( ~ (v18 = 0) & apply(v5, v9, v17) = v18))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v5, v6) = 0) | ~ (member(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (inverse_image2(v8, v7) = v6) | ~ (inverse_image2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (image2(v8, v7) = v6) | ~ (image2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (identity(v8, v7) = v6) | ~ (identity(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (inverse_image2(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : (apply(v5, v7, v9) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (image2(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : (apply(v5, v9, v7) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v5, v6, v7) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & injective(v5, v6, v7) = 0) | ( ~ (v9 = 0) & one_to_one(v5, v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v5, v6, v7) = 0) | ~ (member(v8, v7) = 0) | ? [v9] : (apply(v5, v9, v8) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (injective(v5, v6, v7) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & surjective(v5, v6, v7) = 0) | ( ~ (v9 = 0) & one_to_one(v5, v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (maps(v5, v6, v7) = 0) | ~ (member(v8, v6) = 0) | ? [v9] : (apply(v5, v8, v9) = 0 & member(v9, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (product(v6) = v7) | ~ (member(v8, v6) = 0) | ~ (member(v5, v7) = 0) | member(v5, v8) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ((v9 = 0 & member(v5, v7) = 0) | (v9 = 0 & member(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (identity(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v5, v8, v8) = v9 & member(v8, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & subset(v6, v5) = v8) | ( ~ (v8 = 0) & subset(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & power_set(v6) = v8 & member(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (one_to_one(v5, v6, v7) = 0) | (surjective(v5, v6, v7) = 0 & injective(v5, v6, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (surjective(v5, v6, v7) = 0) | ? [v8] : ((v8 = 0 & one_to_one(v5, v6, v7) = 0) | ( ~ (v8 = 0) & injective(v5, v6, v7) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (injective(v5, v6, v7) = 0) | ? [v8] : ((v8 = 0 & one_to_one(v5, v6, v7) = 0) | ( ~ (v8 = 0) & surjective(v5, v6, v7) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (identity(v5, v6) = 0) | ~ (member(v7, v6) = 0) | apply(v5, v7, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v6, v5) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v5, v6) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & subset(v6, v5) = 0) | ( ~ (v8 = 0) & equal_set(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v6, v5) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v5, v6) = v7))) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : (power_set(v6) = v7 & member(v5, v7) = 0)) & ! [v5] : ! [v6] : ( ~ (subset(v5, v6) = 0) | ? [v7] : ((v7 = 0 & equal_set(v5, v6) = 0) | ( ~ (v7 = 0) & subset(v6, v5) = v7))) & ! [v5] : ~ (member(v5, empty_set) = 0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : compose_predicate(v10, v9, v8, v7, v6, v5) = v11 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : isomorphism(v9, v8, v7, v6, v5) = v10 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : decreasing(v9, v8, v7, v6, v5) = v10 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : increasing(v9, v8, v7, v6, v5) = v10 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : compose_function(v9, v8, v7, v6, v5) = v10 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : inverse_predicate(v8, v7, v6, v5) = v9 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : equal_maps(v8, v7, v6, v5) = v9 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : inverse_image3(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : image3(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : inverse_function(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : one_to_one(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : surjective(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : injective(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : maps(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : apply(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : inverse_image2(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : image2(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : identity(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unordered_pair(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : difference(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : union(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equal_set(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : subset(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : member(v6, v5) = v7 & ? [v5] : ? [v6] : product(v5) = v6 & ? [v5] : ? [v6] : sum(v5) = v6 & ? [v5] : ? [v6] : singleton(v5) = v6 & ? [v5] : ? [v6] : power_set(v5) = v6)
% 12.44/3.38 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 12.44/3.38 | (1) ~ (all_0_0_0 = 0) & inverse_function(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & one_to_one(all_0_4_4, all_0_3_3, all_0_2_2) = 0 & maps(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0 & maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [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(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [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] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [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) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [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] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [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] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [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] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [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] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [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) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8))) & ! [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) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8))) & ! [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] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7))) & ! [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] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15))))))) & ! [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 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = 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] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = 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] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6))) & ! [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(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 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6))) & ! [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] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6))) & ! [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 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = 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] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = 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] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7)))) & ! [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] : ((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 = 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 | ~ (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 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4))) & ! [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)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = 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)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = 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] : (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 | ~ (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] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [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] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [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] : ( ~ (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 | ~ (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] : (( ~ (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] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 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(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] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : identity(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
% 12.65/3.42 |
% 12.65/3.42 | Applying alpha-rule on (1) yields:
% 12.65/3.42 | (2) ! [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)))
% 12.65/3.42 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 12.65/3.42 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 12.65/3.42 | (5) maps(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0
% 12.65/3.42 | (6) ! [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(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 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6)))
% 12.65/3.42 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 12.65/3.42 | (8) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 12.65/3.42 | (9) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 12.65/3.42 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 12.65/3.42 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 12.65/3.42 | (12) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 12.65/3.42 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 12.65/3.43 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.65/3.43 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 12.65/3.43 | (16) ! [v0] : ~ (member(v0, empty_set) = 0)
% 12.65/3.43 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6)))
% 12.65/3.43 | (18) ! [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] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 12.65/3.43 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 12.65/3.43 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.65/3.43 | (21) ! [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)))
% 12.65/3.43 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.65/3.43 | (23) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 12.65/3.43 | (24) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 12.65/3.43 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 12.65/3.43 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 12.65/3.43 | (27) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 12.65/3.43 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 12.65/3.43 | (29) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 12.65/3.43 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9)))
% 12.65/3.43 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7)))))
% 12.65/3.43 | (32) ! [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))
% 12.65/3.43 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3)))
% 12.65/3.43 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3)))
% 12.65/3.43 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 12.65/3.43 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.65/3.43 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 12.65/3.43 | (38) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 12.65/3.43 | (39) ! [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))
% 12.65/3.43 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = v6))
% 12.65/3.43 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 12.65/3.43 | (42) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 12.65/3.43 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.65/3.43 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 12.65/3.43 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 12.65/3.43 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 12.65/3.44 | (47) maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.65/3.44 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 12.65/3.44 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 12.65/3.44 | (50) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 12.65/3.44 | (51) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 12.65/3.44 | (52) ! [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))
% 12.65/3.44 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.65/3.44 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 12.65/3.44 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 12.65/3.44 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6)))
% 12.65/3.44 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.65/3.44 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 12.65/3.44 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 12.65/3.44 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 12.65/3.44 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 12.65/3.44 | (62) one_to_one(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.65/3.44 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.65/3.44 | (64) ! [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] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.65/3.44 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 12.65/3.44 | (66) ? [v0] : ? [v1] : sum(v0) = v1
% 12.65/3.44 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 12.65/3.44 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9)))
% 12.65/3.44 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.65/3.44 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 12.65/3.44 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9)))
% 12.65/3.44 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4)))
% 12.65/3.44 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.65/3.44 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 12.65/3.44 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 12.65/3.44 | (76) ~ (all_0_0_0 = 0)
% 12.65/3.44 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 12.65/3.44 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 12.65/3.44 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 12.65/3.44 | (80) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 12.65/3.45 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 12.65/3.45 | (82) ! [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))
% 12.65/3.45 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 12.65/3.45 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 12.65/3.45 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 12.65/3.45 | (86) ! [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)))
% 12.65/3.45 | (87) ! [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)))
% 12.65/3.45 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 12.65/3.45 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 12.65/3.45 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.65/3.45 | (91) ? [v0] : ? [v1] : product(v0) = v1
% 12.65/3.45 | (92) ! [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)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = v13)))))
% 12.65/3.45 | (93) ! [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))
% 12.65/3.45 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 12.65/3.45 | (95) ! [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] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 12.65/3.45 | (96) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 12.65/3.45 | (97) ! [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))
% 12.65/3.45 | (98) ! [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)))
% 12.65/3.45 | (99) ! [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))
% 12.65/3.45 | (100) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 12.65/3.45 | (101) ! [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))
% 12.65/3.45 | (102) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 12.65/3.45 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 12.65/3.45 | (104) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 12.65/3.45 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 12.65/3.45 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 12.65/3.45 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7))))
% 12.65/3.45 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 12.65/3.45 | (109) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 12.65/3.45 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 12.65/3.45 | (111) ! [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))
% 12.65/3.45 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9)))
% 12.65/3.45 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.65/3.45 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.65/3.46 | (115) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 12.65/3.46 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 12.65/3.46 | (117) ! [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] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.85/3.46 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 12.85/3.46 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 12.85/3.46 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 12.85/3.46 | (121) ? [v0] : ? [v1] : singleton(v0) = v1
% 12.85/3.46 | (122) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 12.85/3.46 | (123) ! [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))
% 12.85/3.46 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 12.85/3.46 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.46 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 12.85/3.46 | (127) ! [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))
% 12.85/3.46 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.85/3.46 | (129) ! [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] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.46 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7)))
% 12.85/3.46 | (131) inverse_function(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 12.85/3.46 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.46 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 12.85/3.46 | (134) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 12.85/3.46 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4)))
% 12.85/3.46 | (136) ! [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)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = v6))))
% 12.85/3.46 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 12.85/3.46 | (138) ! [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) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8)))
% 12.85/3.46 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 12.85/3.46 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 12.85/3.46 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 12.85/3.46 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 12.85/3.46 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 12.85/3.46 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 12.85/3.46 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6)))
% 12.85/3.46 | (146) ! [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(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 12.85/3.47 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7)))))
% 12.85/3.47 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 12.85/3.47 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4)))
% 12.85/3.47 | (150) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 12.85/3.47 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.47 | (152) ! [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) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 12.85/3.47 | (153) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 12.85/3.47 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 12.85/3.47 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 12.85/3.47 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7)))))
% 12.85/3.47 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.85/3.47 | (158) ? [v0] : ? [v1] : power_set(v0) = v1
% 12.85/3.47 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 12.85/3.47 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 12.85/3.47 | (161) ! [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))
% 12.85/3.47 | (162) ! [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] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.47 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 12.85/3.47 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 12.85/3.47 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 12.85/3.47 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 12.85/3.47 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.85/3.47 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.85/3.47 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 12.85/3.47 | (170) ! [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))
% 12.85/3.47 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.85/3.47 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 12.85/3.47 | (173) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 12.85/3.47 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 12.85/3.47 | (175) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 12.85/3.47 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 12.85/3.47 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 12.85/3.48 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 12.85/3.48 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 12.85/3.48 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 12.85/3.48 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.85/3.48 | (182) ! [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] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15)))))))
% 12.85/3.48 | (183) ! [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))
% 12.85/3.48 | (184) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 12.85/3.48 | (185) ! [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) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8)))
% 12.85/3.48 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = v6))
% 12.85/3.48 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 12.85/3.48 |
% 12.85/3.48 | Instantiating formula (19) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms one_to_one(all_0_4_4, all_0_3_3, all_0_2_2) = 0, yields:
% 12.85/3.48 | (188) surjective(all_0_4_4, all_0_3_3, all_0_2_2) = 0 & injective(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.85/3.48 |
% 12.85/3.48 | Applying alpha-rule on (188) yields:
% 12.85/3.48 | (189) surjective(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.85/3.48 | (190) injective(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.85/3.48 |
% 12.85/3.48 | Instantiating formula (92) with all_0_0_0, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms maps(all_0_1_1, all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 12.85/3.48 | (191) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & 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_2_2) = 0) | (v1 = 0 & member(v0, all_0_2_2) = 0 & ! [v8] : ( ~ (apply(all_0_1_1, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_3_3) = v9)) & ! [v8] : ( ~ (member(v8, all_0_3_3) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_1_1, v0, v8) = v9))))
% 12.85/3.48 |
% 12.85/3.48 +-Applying beta-rule and splitting (191), into two cases.
% 12.85/3.48 |-Branch one:
% 12.85/3.48 | (192) all_0_0_0 = 0
% 12.85/3.48 |
% 12.85/3.48 | Equations (192) can reduce 76 to:
% 12.85/3.48 | (193) $false
% 12.85/3.48 |
% 12.85/3.48 |-The branch is then unsatisfiable
% 12.85/3.48 |-Branch two:
% 12.85/3.48 | (76) ~ (all_0_0_0 = 0)
% 12.85/3.48 | (195) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & 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_2_2) = 0) | (v1 = 0 & member(v0, all_0_2_2) = 0 & ! [v8] : ( ~ (apply(all_0_1_1, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_3_3) = v9)) & ! [v8] : ( ~ (member(v8, all_0_3_3) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_1_1, v0, v8) = v9))))
% 12.85/3.48 |
% 12.85/3.48 | Instantiating (195) with all_71_0_116, all_71_1_117, all_71_2_118, all_71_3_119, all_71_4_120, all_71_5_121, all_71_6_122, all_71_7_123 yields:
% 12.85/3.48 | (196) (all_71_0_116 = 0 & all_71_1_117 = 0 & all_71_2_118 = 0 & all_71_3_119 = 0 & all_71_4_120 = 0 & ~ (all_71_5_121 = all_71_6_122) & apply(all_0_1_1, all_71_7_123, all_71_5_121) = 0 & apply(all_0_1_1, all_71_7_123, all_71_6_122) = 0 & member(all_71_5_121, all_0_3_3) = 0 & member(all_71_6_122, all_0_3_3) = 0 & member(all_71_7_123, all_0_2_2) = 0) | (all_71_6_122 = 0 & member(all_71_7_123, all_0_2_2) = 0 & ! [v0] : ( ~ (apply(all_0_1_1, all_71_7_123, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1)) & ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_71_7_123, v0) = v1)))
% 12.85/3.48 |
% 12.85/3.48 +-Applying beta-rule and splitting (196), into two cases.
% 12.85/3.48 |-Branch one:
% 12.85/3.48 | (197) all_71_0_116 = 0 & all_71_1_117 = 0 & all_71_2_118 = 0 & all_71_3_119 = 0 & all_71_4_120 = 0 & ~ (all_71_5_121 = all_71_6_122) & apply(all_0_1_1, all_71_7_123, all_71_5_121) = 0 & apply(all_0_1_1, all_71_7_123, all_71_6_122) = 0 & member(all_71_5_121, all_0_3_3) = 0 & member(all_71_6_122, all_0_3_3) = 0 & member(all_71_7_123, all_0_2_2) = 0
% 12.85/3.48 |
% 12.85/3.48 | Applying alpha-rule on (197) yields:
% 12.85/3.48 | (198) all_71_1_117 = 0
% 12.85/3.48 | (199) member(all_71_5_121, all_0_3_3) = 0
% 12.85/3.48 | (200) member(all_71_7_123, all_0_2_2) = 0
% 12.85/3.48 | (201) ~ (all_71_5_121 = all_71_6_122)
% 12.85/3.48 | (202) all_71_4_120 = 0
% 12.85/3.48 | (203) apply(all_0_1_1, all_71_7_123, all_71_6_122) = 0
% 12.85/3.48 | (204) all_71_0_116 = 0
% 12.85/3.48 | (205) member(all_71_6_122, all_0_3_3) = 0
% 12.85/3.49 | (206) all_71_2_118 = 0
% 12.85/3.49 | (207) all_71_3_119 = 0
% 12.85/3.49 | (208) apply(all_0_1_1, all_71_7_123, all_71_5_121) = 0
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (156) with 0, all_0_1_1, all_71_7_123, all_71_5_121, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms inverse_function(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_71_7_123, all_71_5_121) = 0, yields:
% 12.85/3.49 | (209) ? [v0] : ((v0 = 0 & apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0) | ( ~ (v0 = 0) & member(all_71_5_121, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_71_7_123, all_0_2_2) = v0))
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (156) with 0, all_0_1_1, all_71_7_123, all_71_6_122, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms inverse_function(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_71_7_123, all_71_6_122) = 0, yields:
% 12.85/3.49 | (210) ? [v0] : ((v0 = 0 & apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0) | ( ~ (v0 = 0) & member(all_71_6_122, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_71_7_123, all_0_2_2) = v0))
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (56) with all_71_7_123, all_71_5_121, all_71_6_122, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms injective(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_71_5_121, all_0_3_3) = 0, member(all_71_6_122, all_0_3_3) = 0, member(all_71_7_123, all_0_2_2) = 0, yields:
% 12.85/3.49 | (211) all_71_5_121 = all_71_6_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_4_4, all_71_5_121, all_71_7_123) = v0) | ( ~ (v0 = 0) & apply(all_0_4_4, all_71_6_122, all_71_7_123) = v0))
% 12.85/3.49 |
% 12.85/3.49 | Instantiating (210) with all_88_0_126 yields:
% 12.85/3.49 | (212) (all_88_0_126 = 0 & apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0) | ( ~ (all_88_0_126 = 0) & member(all_71_6_122, all_0_3_3) = all_88_0_126) | ( ~ (all_88_0_126 = 0) & member(all_71_7_123, all_0_2_2) = all_88_0_126)
% 12.85/3.49 |
% 12.85/3.49 | Instantiating (209) with all_89_0_127 yields:
% 12.85/3.49 | (213) (all_89_0_127 = 0 & apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0) | ( ~ (all_89_0_127 = 0) & member(all_71_5_121, all_0_3_3) = all_89_0_127) | ( ~ (all_89_0_127 = 0) & member(all_71_7_123, all_0_2_2) = all_89_0_127)
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (212), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (214) (all_88_0_126 = 0 & apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0) | ( ~ (all_88_0_126 = 0) & member(all_71_6_122, all_0_3_3) = all_88_0_126)
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (214), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (215) all_88_0_126 = 0 & apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (215) yields:
% 12.85/3.49 | (216) all_88_0_126 = 0
% 12.85/3.49 | (217) apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (211), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (218) all_71_5_121 = all_71_6_122
% 12.85/3.49 |
% 12.85/3.49 | Equations (218) can reduce 201 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (201) ~ (all_71_5_121 = all_71_6_122)
% 12.85/3.49 | (221) ? [v0] : (( ~ (v0 = 0) & apply(all_0_4_4, all_71_5_121, all_71_7_123) = v0) | ( ~ (v0 = 0) & apply(all_0_4_4, all_71_6_122, all_71_7_123) = v0))
% 12.85/3.49 |
% 12.85/3.49 | Instantiating (221) with all_99_0_129 yields:
% 12.85/3.49 | (222) ( ~ (all_99_0_129 = 0) & apply(all_0_4_4, all_71_5_121, all_71_7_123) = all_99_0_129) | ( ~ (all_99_0_129 = 0) & apply(all_0_4_4, all_71_6_122, all_71_7_123) = all_99_0_129)
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (213), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (223) (all_89_0_127 = 0 & apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0) | ( ~ (all_89_0_127 = 0) & member(all_71_5_121, all_0_3_3) = all_89_0_127)
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (223), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (224) all_89_0_127 = 0 & apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (224) yields:
% 12.85/3.49 | (225) all_89_0_127 = 0
% 12.85/3.49 | (226) apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0
% 12.85/3.49 |
% 12.85/3.49 +-Applying beta-rule and splitting (222), into two cases.
% 12.85/3.49 |-Branch one:
% 12.85/3.49 | (227) ~ (all_99_0_129 = 0) & apply(all_0_4_4, all_71_5_121, all_71_7_123) = all_99_0_129
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (227) yields:
% 12.85/3.49 | (228) ~ (all_99_0_129 = 0)
% 12.85/3.49 | (229) apply(all_0_4_4, all_71_5_121, all_71_7_123) = all_99_0_129
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (54) with all_0_4_4, all_71_5_121, all_71_7_123, 0, all_99_0_129 and discharging atoms apply(all_0_4_4, all_71_5_121, all_71_7_123) = all_99_0_129, apply(all_0_4_4, all_71_5_121, all_71_7_123) = 0, yields:
% 12.85/3.49 | (230) all_99_0_129 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (230) can reduce 228 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (232) ~ (all_99_0_129 = 0) & apply(all_0_4_4, all_71_6_122, all_71_7_123) = all_99_0_129
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (232) yields:
% 12.85/3.49 | (228) ~ (all_99_0_129 = 0)
% 12.85/3.49 | (234) apply(all_0_4_4, all_71_6_122, all_71_7_123) = all_99_0_129
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (54) with all_0_4_4, all_71_6_122, all_71_7_123, 0, all_99_0_129 and discharging atoms apply(all_0_4_4, all_71_6_122, all_71_7_123) = all_99_0_129, apply(all_0_4_4, all_71_6_122, all_71_7_123) = 0, yields:
% 12.85/3.49 | (230) all_99_0_129 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (230) can reduce 228 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (237) ~ (all_89_0_127 = 0) & member(all_71_5_121, all_0_3_3) = all_89_0_127
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (237) yields:
% 12.85/3.49 | (238) ~ (all_89_0_127 = 0)
% 12.85/3.49 | (239) member(all_71_5_121, all_0_3_3) = all_89_0_127
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (148) with all_71_5_121, all_0_3_3, all_89_0_127, 0 and discharging atoms member(all_71_5_121, all_0_3_3) = all_89_0_127, member(all_71_5_121, all_0_3_3) = 0, yields:
% 12.85/3.49 | (225) all_89_0_127 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (225) can reduce 238 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (242) ~ (all_89_0_127 = 0) & member(all_71_7_123, all_0_2_2) = all_89_0_127
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (242) yields:
% 12.85/3.49 | (238) ~ (all_89_0_127 = 0)
% 12.85/3.49 | (244) member(all_71_7_123, all_0_2_2) = all_89_0_127
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (148) with all_71_7_123, all_0_2_2, all_89_0_127, 0 and discharging atoms member(all_71_7_123, all_0_2_2) = all_89_0_127, member(all_71_7_123, all_0_2_2) = 0, yields:
% 12.85/3.49 | (225) all_89_0_127 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (225) can reduce 238 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (247) ~ (all_88_0_126 = 0) & member(all_71_6_122, all_0_3_3) = all_88_0_126
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (247) yields:
% 12.85/3.49 | (248) ~ (all_88_0_126 = 0)
% 12.85/3.49 | (249) member(all_71_6_122, all_0_3_3) = all_88_0_126
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (148) with all_71_6_122, all_0_3_3, all_88_0_126, 0 and discharging atoms member(all_71_6_122, all_0_3_3) = all_88_0_126, member(all_71_6_122, all_0_3_3) = 0, yields:
% 12.85/3.49 | (216) all_88_0_126 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (216) can reduce 248 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (252) ~ (all_88_0_126 = 0) & member(all_71_7_123, all_0_2_2) = all_88_0_126
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (252) yields:
% 12.85/3.49 | (248) ~ (all_88_0_126 = 0)
% 12.85/3.49 | (254) member(all_71_7_123, all_0_2_2) = all_88_0_126
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (148) with all_71_7_123, all_0_2_2, all_88_0_126, 0 and discharging atoms member(all_71_7_123, all_0_2_2) = all_88_0_126, member(all_71_7_123, all_0_2_2) = 0, yields:
% 12.85/3.49 | (216) all_88_0_126 = 0
% 12.85/3.49 |
% 12.85/3.49 | Equations (216) can reduce 248 to:
% 12.85/3.49 | (193) $false
% 12.85/3.49 |
% 12.85/3.49 |-The branch is then unsatisfiable
% 12.85/3.49 |-Branch two:
% 12.85/3.49 | (257) all_71_6_122 = 0 & member(all_71_7_123, all_0_2_2) = 0 & ! [v0] : ( ~ (apply(all_0_1_1, all_71_7_123, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1)) & ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_71_7_123, v0) = v1))
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (257) yields:
% 12.85/3.49 | (258) all_71_6_122 = 0
% 12.85/3.49 | (200) member(all_71_7_123, all_0_2_2) = 0
% 12.85/3.49 | (260) ! [v0] : ( ~ (apply(all_0_1_1, all_71_7_123, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1))
% 12.85/3.49 | (261) ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_71_7_123, v0) = v1))
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (58) with all_71_7_123, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms surjective(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_71_7_123, all_0_2_2) = 0, yields:
% 12.85/3.49 | (262) ? [v0] : (apply(all_0_4_4, v0, all_71_7_123) = 0 & member(v0, all_0_3_3) = 0)
% 12.85/3.49 |
% 12.85/3.49 | Instantiating (262) with all_85_0_132 yields:
% 12.85/3.49 | (263) apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0 & member(all_85_0_132, all_0_3_3) = 0
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (263) yields:
% 12.85/3.49 | (264) apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0
% 12.85/3.49 | (265) member(all_85_0_132, all_0_3_3) = 0
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (261) with all_85_0_132 and discharging atoms member(all_85_0_132, all_0_3_3) = 0, yields:
% 12.85/3.49 | (266) ? [v0] : ( ~ (v0 = 0) & apply(all_0_1_1, all_71_7_123, all_85_0_132) = v0)
% 12.85/3.49 |
% 12.85/3.49 | Instantiating (266) with all_92_0_133 yields:
% 12.85/3.49 | (267) ~ (all_92_0_133 = 0) & apply(all_0_1_1, all_71_7_123, all_85_0_132) = all_92_0_133
% 12.85/3.49 |
% 12.85/3.49 | Applying alpha-rule on (267) yields:
% 12.85/3.49 | (268) ~ (all_92_0_133 = 0)
% 12.85/3.49 | (269) apply(all_0_1_1, all_71_7_123, all_85_0_132) = all_92_0_133
% 12.85/3.49 |
% 12.85/3.49 | Instantiating formula (156) with all_92_0_133, all_0_1_1, all_71_7_123, all_85_0_132, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms inverse_function(all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_71_7_123, all_85_0_132) = all_92_0_133, yields:
% 12.85/3.49 | (270) ? [v0] : (( ~ (v0 = 0) & member(all_85_0_132, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_71_7_123, all_0_2_2) = v0) | (( ~ (all_92_0_133 = 0) | (v0 = 0 & apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0)) & (all_92_0_133 = 0 | ( ~ (v0 = 0) & apply(all_0_4_4, all_85_0_132, all_71_7_123) = v0))))
% 12.85/3.49 |
% 12.85/3.50 | Instantiating (270) with all_103_0_136 yields:
% 12.85/3.50 | (271) ( ~ (all_103_0_136 = 0) & member(all_85_0_132, all_0_3_3) = all_103_0_136) | ( ~ (all_103_0_136 = 0) & member(all_71_7_123, all_0_2_2) = all_103_0_136) | (( ~ (all_92_0_133 = 0) | (all_103_0_136 = 0 & apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0)) & (all_92_0_133 = 0 | ( ~ (all_103_0_136 = 0) & apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136)))
% 12.85/3.50 |
% 12.85/3.50 +-Applying beta-rule and splitting (271), into two cases.
% 12.85/3.50 |-Branch one:
% 12.85/3.50 | (272) ( ~ (all_103_0_136 = 0) & member(all_85_0_132, all_0_3_3) = all_103_0_136) | ( ~ (all_103_0_136 = 0) & member(all_71_7_123, all_0_2_2) = all_103_0_136)
% 12.85/3.50 |
% 12.85/3.50 +-Applying beta-rule and splitting (272), into two cases.
% 12.85/3.50 |-Branch one:
% 12.85/3.50 | (273) ~ (all_103_0_136 = 0) & member(all_85_0_132, all_0_3_3) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Applying alpha-rule on (273) yields:
% 12.85/3.50 | (274) ~ (all_103_0_136 = 0)
% 12.85/3.50 | (275) member(all_85_0_132, all_0_3_3) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Instantiating formula (148) with all_85_0_132, all_0_3_3, all_103_0_136, 0 and discharging atoms member(all_85_0_132, all_0_3_3) = all_103_0_136, member(all_85_0_132, all_0_3_3) = 0, yields:
% 12.85/3.50 | (276) all_103_0_136 = 0
% 12.85/3.50 |
% 12.85/3.50 | Equations (276) can reduce 274 to:
% 12.85/3.50 | (193) $false
% 12.85/3.50 |
% 12.85/3.50 |-The branch is then unsatisfiable
% 12.85/3.50 |-Branch two:
% 12.85/3.50 | (278) ~ (all_103_0_136 = 0) & member(all_71_7_123, all_0_2_2) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Applying alpha-rule on (278) yields:
% 12.85/3.50 | (274) ~ (all_103_0_136 = 0)
% 12.85/3.50 | (280) member(all_71_7_123, all_0_2_2) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Instantiating formula (148) with all_71_7_123, all_0_2_2, all_103_0_136, 0 and discharging atoms member(all_71_7_123, all_0_2_2) = all_103_0_136, member(all_71_7_123, all_0_2_2) = 0, yields:
% 12.85/3.50 | (276) all_103_0_136 = 0
% 12.85/3.50 |
% 12.85/3.50 | Equations (276) can reduce 274 to:
% 12.85/3.50 | (193) $false
% 12.85/3.50 |
% 12.85/3.50 |-The branch is then unsatisfiable
% 12.85/3.50 |-Branch two:
% 12.85/3.50 | (283) ( ~ (all_92_0_133 = 0) | (all_103_0_136 = 0 & apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0)) & (all_92_0_133 = 0 | ( ~ (all_103_0_136 = 0) & apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136))
% 12.85/3.50 |
% 12.85/3.50 | Applying alpha-rule on (283) yields:
% 12.85/3.50 | (284) ~ (all_92_0_133 = 0) | (all_103_0_136 = 0 & apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0)
% 12.85/3.50 | (285) all_92_0_133 = 0 | ( ~ (all_103_0_136 = 0) & apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136)
% 12.85/3.50 |
% 12.85/3.50 +-Applying beta-rule and splitting (285), into two cases.
% 12.85/3.50 |-Branch one:
% 12.85/3.50 | (286) all_92_0_133 = 0
% 12.85/3.50 |
% 12.85/3.50 | Equations (286) can reduce 268 to:
% 12.85/3.50 | (193) $false
% 12.85/3.50 |
% 12.85/3.50 |-The branch is then unsatisfiable
% 12.85/3.50 |-Branch two:
% 12.85/3.50 | (268) ~ (all_92_0_133 = 0)
% 12.85/3.50 | (289) ~ (all_103_0_136 = 0) & apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Applying alpha-rule on (289) yields:
% 12.85/3.50 | (274) ~ (all_103_0_136 = 0)
% 12.85/3.50 | (291) apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136
% 12.85/3.50 |
% 12.85/3.50 | Instantiating formula (54) with all_0_4_4, all_85_0_132, all_71_7_123, all_103_0_136, 0 and discharging atoms apply(all_0_4_4, all_85_0_132, all_71_7_123) = all_103_0_136, apply(all_0_4_4, all_85_0_132, all_71_7_123) = 0, yields:
% 12.85/3.50 | (276) all_103_0_136 = 0
% 12.85/3.50 |
% 12.85/3.50 | Equations (276) can reduce 274 to:
% 12.85/3.50 | (193) $false
% 12.85/3.50 |
% 12.85/3.50 |-The branch is then unsatisfiable
% 12.85/3.50 % SZS output end Proof for theBenchmark
% 12.85/3.50
% 12.85/3.50 2914ms
%------------------------------------------------------------------------------