TSTP Solution File: SET733+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET733+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:42 EDT 2022
% Result : Theorem 19.73s 5.46s
% Output : Proof 29.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET733+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 09:25:57 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.56/0.59 ____ _
% 0.56/0.59 ___ / __ \_____(_)___ ________ __________
% 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.60
% 0.56/0.60 A Theorem Prover for First-Order Logic
% 0.62/0.60 (ePrincess v.1.0)
% 0.62/0.60
% 0.62/0.60 (c) Philipp Rümmer, 2009-2015
% 0.62/0.60 (c) Peter Backeman, 2014-2015
% 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.60 Bug reports to peter@backeman.se
% 0.62/0.60
% 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.60
% 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.98 Prover 0: Preprocessing ...
% 3.23/1.31 Prover 0: Warning: ignoring some quantifiers
% 3.30/1.35 Prover 0: Constructing countermodel ...
% 4.37/1.60 Prover 0: gave up
% 4.37/1.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.57/1.65 Prover 1: Preprocessing ...
% 5.79/1.89 Prover 1: Constructing countermodel ...
% 17.25/4.91 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.48/4.96 Prover 2: Preprocessing ...
% 18.83/5.22 Prover 2: Warning: ignoring some quantifiers
% 18.83/5.24 Prover 2: Constructing countermodel ...
% 19.73/5.46 Prover 2: proved (552ms)
% 19.73/5.46 Prover 1: stopped
% 19.73/5.46
% 19.73/5.46 No countermodel exists, formula is valid
% 19.73/5.46 % SZS status Theorem for theBenchmark
% 19.73/5.46
% 19.73/5.46 Generating proof ... Warning: ignoring some quantifiers
% 28.59/7.49 found it (size 250)
% 28.59/7.49
% 28.59/7.49 % SZS output start Proof for theBenchmark
% 28.59/7.49 Assumed formulas after preprocessing and simplification:
% 28.59/7.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & injective(v0, v2, v3) = v5 & identity(v4, v2) = 0 & compose_function(v1, v0, v2, v3, v2) = v4 & maps(v1, v3, v2) = 0 & maps(v0, v2, v3) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = 0) | ~ (apply(v8, v11, v13) = v15) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (apply(v7, v11, v15) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v15, v12) = v16) | ( ~ (v16 = 0) & member(v15, v9) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (apply(v6, v15, v12) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v11, v15) = v16) | ( ~ (v16 = 0) & member(v15, v9) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (member(v15, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v11, v15) = v16) | ( ~ (v16 = 0) & apply(v6, v15, v12) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v8, v12, v15) = 0) | ~ (apply(v6, v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v15, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v15, v13) = 0) | ~ (apply(v6, v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v12, v15) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v6, v12, v13) = v14) | ~ (member(v15, v10) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v12, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v15, v13) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v7 = v6 | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v7) | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v7, v11, v14) = 0 & apply(v6, v14, v12) = 0 & member(v14, v9) = 0) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v6, v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v8, v12, v14) = 0 & apply(v7, v14, v13) = 0 & member(v14, v10) = 0) | ( ~ (v14 = 0) & member(v13, v11) = v14) | ( ~ (v14 = 0) & member(v12, v9) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v6, v10, v11) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v10, v11) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (member(v12, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & apply(v6, v10, v11) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (member(v14, v11) = 0 & member(v13, v9) = 0 & ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v8, v13, v16) = 0 & apply(v7, v16, v14) = 0 & member(v16, v10) = 0) | (v15 = 0 & apply(v6, v13, v14) = 0)) & (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ! [v20] : ( ~ (apply(v8, v13, v20) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v7, v20, v14) = v21) | ( ~ (v21 = 0) & member(v20, v10) = v21))) & ! [v20] : ( ~ (apply(v7, v20, v14) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v8, v13, v20) = v21) | ( ~ (v21 = 0) & member(v20, v10) = v21))) & ! [v20] : ( ~ (member(v20, v10) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v8, v13, v20) = v21) | ( ~ (v21 = 0) & apply(v7, v20, v14) = v21))))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image3(v6, v7, v8) = v10) | ~ (apply(v6, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v12, v7) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v9, v12) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image3(v6, v7, v8) = v10) | ~ (apply(v6, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image3(v6, v7, v8) = v10) | ~ (member(v12, v7) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v12, v9) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (isomorphism(v12, v11, v10, v9, v8) = v7) | ~ (isomorphism(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (decreasing(v12, v11, v10, v9, v8) = v7) | ~ (decreasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (increasing(v12, v11, v10, v9, v8) = v7) | ~ (increasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (compose_function(v12, v11, v10, v9, v8) = v7) | ~ (compose_function(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_function(v6, v7, v8) = v11) | ~ (apply(v11, v10, v9) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v10, v8) = v13) | ( ~ (v13 = 0) & member(v9, v7) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v6, v9, v10) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v6, v9, v10) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_predicate(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v6, v11, v10) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v6, v11, v10) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_predicate(v6, v7, v8, v9) = 0) | ~ (apply(v6, v11, v10) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v7, v10, v11) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v7, v10, v11) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (apply(v6, v9, v10) = 0) | ? [v12] : (( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (member(v10, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v10) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, 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))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(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(v6, v9, v10) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0 & ((v23 = 0 & apply(v10, v13, v15) = 0) | (v22 = 0 & apply(v8, v12, v14) = 0)) & (( ~ (v23 = 0) & apply(v10, v13, v15) = v23) | ( ~ (v22 = 0) & apply(v8, v12, v14) = v22))) | ( ~ (v12 = 0) & one_to_one(v6, v7, v9) = v12) | ( ~ (v12 = 0) & maps(v6, v7, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v15, v13) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v13, v15) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (apply(v6, v9, v11) = 0) | ? [v12] : (( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v7) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (member(v10, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v10, v11) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v7) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v10, v11) = v12) | ( ~ (v12 = 0) & apply(v6, v9, v11) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image2(v6, v7) = v9) | ~ (apply(v6, v8, v11) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image2(v6, v7) = v9) | ~ (member(v11, v7) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v8, v11) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image2(v6, v7) = v9) | ~ (apply(v6, v11, v8) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image2(v6, v7) = v9) | ~ (member(v11, v7) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v11, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (inverse_predicate(v11, v10, v9, v8) = v7) | ~ (inverse_predicate(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (equal_maps(v11, v10, v9, v8) = v7) | ~ (equal_maps(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (inverse_predicate(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (member(v12, v9) = 0 & member(v11, v8) = 0 & ((v14 = 0 & apply(v6, v12, v11) = 0) | (v13 = 0 & apply(v7, v11, v12) = 0)) & (( ~ (v14 = 0) & apply(v6, v12, v11) = v14) | ( ~ (v13 = 0) & apply(v7, v11, v12) = v13)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_maps(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v6, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v9) = v10) | ~ (member(v6, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ((v11 = 0 & member(v6, v7) = 0) | ( ~ (v11 = 0) & member(v6, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ~ (v11 = 0) & member(v6, v8) = v12 & member(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & member(v6, v8) = v11) | ( ~ (v11 = 0) & member(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sum(v7) = v8) | ~ (member(v10, v7) = 0) | ~ (member(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sum(v7) = v8) | ~ (member(v6, v10) = 0) | ~ (member(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_image3(v10, v9, v8) = v7) | ~ (inverse_image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (image3(v10, v9, v8) = v7) | ~ (image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_function(v10, v9, v8) = v7) | ~ (inverse_function(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (one_to_one(v10, v9, v8) = v7) | ~ (one_to_one(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (surjective(v10, v9, v8) = v7) | ~ (surjective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (injective(v10, v9, v8) = v7) | ~ (injective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (maps(v10, v9, v8) = v7) | ~ (maps(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (apply(v10, v9, v8) = v7) | ~ (apply(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | (one_to_one(v6, v7, v9) = 0 & maps(v6, v7, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v9, v11) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v11, v9) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (one_to_one(v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & surjective(v6, v7, v8) = v10) | ( ~ (v10 = 0) & injective(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (surjective(v6, v7, v8) = v9) | ? [v10] : (member(v10, v8) = 0 & ! [v11] : ( ~ (apply(v6, v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v11] : ( ~ (member(v11, v7) = 0) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v11, v10) = v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (injective(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v11 = v10) & apply(v6, v11, v12) = 0 & apply(v6, v10, v12) = 0 & member(v12, v8) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v6, v7) = 0) | ~ (apply(v6, v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (maps(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v12 = v11) & apply(v6, v10, v12) = 0 & apply(v6, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v7) = 0) | (v11 = 0 & member(v10, v7) = 0 & ! [v18] : ( ~ (apply(v6, v10, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & member(v18, v8) = v19)) & ! [v18] : ( ~ (member(v18, v8) = 0) | ? [v19] : ( ~ (v19 = 0) & apply(v6, v10, v18) = v19))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = 0 & member(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v7, v6) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (power_set(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v6, v7) = 0) | ~ (member(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v6 | v7 = v6 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (inverse_image2(v9, v8) = v7) | ~ (inverse_image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (image2(v9, v8) = v7) | ~ (image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (identity(v9, v8) = v7) | ~ (identity(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unordered_pair(v9, v8) = v7) | ~ (unordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_set(v9, v8) = v7) | ~ (equal_set(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v8, v10) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v10, v8) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v6, v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & injective(v6, v7, v8) = 0) | ( ~ (v10 = 0) & one_to_one(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v6, v7, v8) = 0) | ~ (member(v9, v8) = 0) | ? [v10] : (apply(v6, v10, v9) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (injective(v6, v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & surjective(v6, v7, v8) = 0) | ( ~ (v10 = 0) & one_to_one(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (maps(v6, v7, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v10] : (apply(v6, v9, v10) = 0 & member(v10, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v7) = v8) | ~ (member(v9, v7) = 0) | ~ (member(v6, v8) = 0) | member(v6, v9) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v6, v8) = 0 & member(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ((v10 = 0 & member(v6, v8) = 0) | (v10 = 0 & member(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = 0) | (member(v6, v8) = 0 & member(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (identity(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v6, v9, v9) = v10 & member(v9, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v6) = v7) | ~ (member(v6, v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_set(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & subset(v7, v6) = v9) | ( ~ (v9 = 0) & subset(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & power_set(v7) = v9 & member(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (product(v8) = v7) | ~ (product(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sum(v8) = v7) | ~ (sum(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v7) = v8) | ~ (member(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (power_set(v8) = v7) | ~ (power_set(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (one_to_one(v6, v7, v8) = 0) | (surjective(v6, v7, v8) = 0 & injective(v6, v7, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v6, v7, v8) = 0) | ? [v9] : ((v9 = 0 & one_to_one(v6, v7, v8) = 0) | ( ~ (v9 = 0) & injective(v6, v7, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (injective(v6, v7, v8) = 0) | ? [v9] : ((v9 = 0 & one_to_one(v6, v7, v8) = 0) | ( ~ (v9 = 0) & surjective(v6, v7, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (identity(v6, v7) = 0) | ~ (member(v8, v7) = 0) | apply(v6, v8, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sum(v7) = v8) | ~ (member(v6, v8) = 0) | ? [v9] : (member(v9, v7) = 0 & member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (power_set(v7) = v8) | ~ (member(v6, v8) = 0) | subset(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v7, v6) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & subset(v6, v7) = 0) | ( ~ (v9 = 0) & equal_set(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & subset(v7, v6) = 0) | ( ~ (v9 = 0) & equal_set(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ( ~ (equal_set(v6, v7) = 0) | (subset(v7, v6) = 0 & subset(v6, v7) = 0)) & ! [v6] : ! [v7] : ( ~ (subset(v7, v6) = 0) | ? [v8] : ((v8 = 0 & equal_set(v6, v7) = 0) | ( ~ (v8 = 0) & subset(v6, v7) = v8))) & ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ? [v8] : (power_set(v7) = v8 & member(v6, v8) = 0)) & ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ? [v8] : ((v8 = 0 & equal_set(v6, v7) = 0) | ( ~ (v8 = 0) & subset(v7, v6) = v8))) & ! [v6] : ~ (member(v6, empty_set) = 0) & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : compose_predicate(v11, v10, v9, v8, v7, v6) = v12 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : isomorphism(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : decreasing(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : increasing(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : compose_function(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_predicate(v9, v8, v7, v6) = v10 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : equal_maps(v9, v8, v7, v6) = v10 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : inverse_image3(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : image3(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : inverse_function(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : one_to_one(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : surjective(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : injective(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : maps(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : apply(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : inverse_image2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : image2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : identity(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unordered_pair(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : difference(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : union(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_set(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : subset(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : member(v7, v6) = v8 & ? [v6] : ? [v7] : product(v6) = v7 & ? [v6] : ? [v7] : sum(v6) = v7 & ? [v6] : ? [v7] : singleton(v6) = v7 & ? [v6] : ? [v7] : power_set(v6) = v7)
% 29.23/7.62 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 29.23/7.62 | (1) ~ (all_0_0_0 = 0) & injective(all_0_5_5, all_0_3_3, all_0_2_2) = all_0_0_0 & identity(all_0_1_1, all_0_3_3) = 0 & compose_function(all_0_4_4, all_0_5_5, all_0_3_3, all_0_2_2, all_0_3_3) = all_0_1_1 & maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0 & maps(all_0_5_5, 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
% 29.23/7.67 |
% 29.23/7.67 | Applying alpha-rule on (1) yields:
% 29.23/7.67 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 29.23/7.67 | (3) ! [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)))
% 29.23/7.67 | (4) ! [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)))
% 29.23/7.67 | (5) ! [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)))
% 29.23/7.67 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 29.23/7.67 | (7) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 29.23/7.67 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 29.23/7.67 | (9) ! [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)))
% 29.23/7.67 | (10) ! [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)))
% 29.23/7.67 | (11) ! [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))
% 29.23/7.67 | (12) ! [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)))
% 29.23/7.67 | (13) ! [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)))
% 29.23/7.67 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 29.23/7.67 | (15) ! [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)))
% 29.23/7.67 | (16) ! [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))
% 29.23/7.67 | (17) ! [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)))))
% 29.23/7.67 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 29.23/7.67 | (19) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 29.23/7.67 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 29.23/7.67 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 29.23/7.67 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 29.23/7.67 | (23) ! [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))
% 29.23/7.68 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 29.23/7.68 | (25) ! [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)))
% 29.23/7.68 | (26) ! [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)))
% 29.23/7.68 | (27) ! [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))))
% 29.23/7.68 | (28) ! [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)))
% 29.23/7.68 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 29.23/7.68 | (30) ? [v0] : ? [v1] : power_set(v0) = v1
% 29.23/7.68 | (31) ! [v0] : ~ (member(v0, empty_set) = 0)
% 29.23/7.68 | (32) ! [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))
% 29.23/7.68 | (33) ~ (all_0_0_0 = 0)
% 29.23/7.68 | (34) ! [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))
% 29.23/7.68 | (35) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 29.23/7.68 | (36) ! [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)))
% 29.23/7.68 | (37) ! [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)))
% 29.23/7.68 | (38) ? [v0] : ? [v1] : product(v0) = v1
% 29.23/7.68 | (39) ! [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)))))
% 29.23/7.68 | (40) ! [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)))))
% 29.23/7.68 | (41) ! [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)))
% 29.23/7.68 | (42) ! [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)))
% 29.23/7.68 | (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)))))
% 29.23/7.68 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 29.52/7.68 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 29.52/7.68 | (46) ! [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)))
% 29.52/7.68 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 29.52/7.68 | (48) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 29.52/7.68 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 29.52/7.68 | (50) ! [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)))))
% 29.52/7.68 | (51) ! [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)))
% 29.52/7.69 | (52) ! [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)))
% 29.52/7.69 | (53) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 29.52/7.69 | (54) ! [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)))
% 29.52/7.69 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 29.52/7.69 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 29.52/7.69 | (57) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 29.52/7.69 | (58) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 29.52/7.69 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 29.52/7.69 | (60) ! [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)))
% 29.52/7.69 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 29.52/7.69 | (62) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 29.52/7.69 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 29.52/7.69 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 29.52/7.69 | (65) ! [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)))
% 29.52/7.69 | (66) identity(all_0_1_1, all_0_3_3) = 0
% 29.52/7.69 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 29.52/7.69 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 29.52/7.69 | (69) ! [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)))
% 29.52/7.69 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 29.52/7.69 | (71) ! [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)))
% 29.52/7.69 | (72) ! [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)))
% 29.52/7.69 | (73) ! [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)))
% 29.52/7.69 | (74) ! [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)))
% 29.52/7.69 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 29.52/7.69 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 29.52/7.69 | (77) ! [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)))
% 29.52/7.69 | (78) ! [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)))
% 29.52/7.69 | (79) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 29.52/7.69 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 29.52/7.69 | (81) ! [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)))
% 29.52/7.70 | (82) ! [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))
% 29.52/7.70 | (83) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 29.52/7.70 | (84) ! [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)))))
% 29.52/7.70 | (85) ! [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)))))))
% 29.52/7.70 | (86) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 29.52/7.70 | (87) ! [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)))
% 29.52/7.70 | (88) ! [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)))
% 29.52/7.70 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 29.52/7.70 | (90) ! [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)))
% 29.52/7.70 | (91) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 29.52/7.70 | (92) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 29.52/7.70 | (93) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 29.52/7.70 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 29.52/7.70 | (95) ! [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)))
% 29.52/7.70 | (96) ? [v0] : ? [v1] : singleton(v0) = v1
% 29.52/7.70 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 29.52/7.70 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 29.52/7.70 | (99) ! [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))
% 29.52/7.70 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 29.52/7.70 | (101) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 29.52/7.70 | (102) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 29.52/7.70 | (103) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 29.52/7.70 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 29.52/7.70 | (105) ! [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))
% 29.52/7.70 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 29.52/7.70 | (107) ! [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))
% 29.52/7.70 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 29.52/7.70 | (109) ! [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)))
% 29.52/7.70 | (110) ! [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)))))
% 29.52/7.71 | (111) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 29.52/7.71 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 29.52/7.71 | (113) ! [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)))))
% 29.52/7.71 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 29.52/7.71 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 29.52/7.71 | (116) compose_function(all_0_4_4, all_0_5_5, all_0_3_3, all_0_2_2, all_0_3_3) = all_0_1_1
% 29.52/7.71 | (117) ! [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)))
% 29.52/7.71 | (118) ! [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)))
% 29.52/7.71 | (119) ! [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)))
% 29.52/7.71 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 29.52/7.71 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 29.52/7.71 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 29.52/7.71 | (123) ! [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)))))
% 29.52/7.71 | (124) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 29.52/7.71 | (125) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 29.52/7.71 | (126) ! [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)))))
% 29.52/7.71 | (127) ! [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))
% 29.52/7.71 | (128) ! [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)))))
% 29.52/7.71 | (129) ! [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)))
% 29.52/7.71 | (130) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 29.52/7.71 | (131) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 29.52/7.71 | (132) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 29.52/7.71 | (133) maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0
% 29.52/7.71 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 29.52/7.71 | (135) ! [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)))
% 29.52/7.71 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 29.52/7.72 | (137) ! [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)))))
% 29.52/7.72 | (138) ! [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)))))
% 29.52/7.72 | (139) ! [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))
% 29.52/7.72 | (140) ! [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)))
% 29.52/7.72 | (141) ! [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)))
% 29.52/7.72 | (142) ! [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)))
% 29.52/7.72 | (143) ! [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))))
% 29.52/7.72 | (144) ! [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)))
% 29.52/7.72 | (145) ! [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)))
% 29.52/7.72 | (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(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)))
% 29.52/7.72 | (147) ! [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)))
% 29.52/7.72 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 29.52/7.72 | (149) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 29.52/7.72 | (150) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 29.52/7.72 | (151) ! [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)))))
% 29.52/7.72 | (152) ? [v0] : ? [v1] : sum(v0) = v1
% 29.52/7.72 | (153) ! [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)))
% 29.52/7.72 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 29.52/7.72 | (155) ! [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)))
% 29.52/7.72 | (156) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 29.52/7.72 | (157) injective(all_0_5_5, all_0_3_3, all_0_2_2) = all_0_0_0
% 29.52/7.72 | (158) ! [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)))
% 29.52/7.72 | (159) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 29.52/7.72 | (160) ! [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))
% 29.52/7.72 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 29.52/7.72 | (162) ! [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))
% 29.52/7.73 | (163) ! [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)))
% 29.52/7.73 | (164) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 29.52/7.73 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 29.52/7.73 | (166) ! [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))
% 29.52/7.73 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 29.52/7.73 | (168) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 29.52/7.73 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 29.52/7.73 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 29.52/7.73 | (171) ! [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)))
% 29.52/7.73 | (172) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 29.52/7.73 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 29.52/7.73 | (174) ! [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)))
% 29.52/7.73 | (175) ! [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))
% 29.52/7.73 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 29.52/7.73 | (177) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 29.52/7.73 | (178) ! [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)))
% 29.52/7.73 | (179) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 29.52/7.73 | (180) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 29.52/7.73 | (181) ! [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)))
% 29.52/7.73 | (182) maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 29.52/7.73 | (183) ! [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))
% 29.52/7.73 | (184) ! [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)))
% 29.52/7.73 | (185) ! [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)))
% 29.52/7.73 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 29.52/7.73 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 29.52/7.73 | (188) ! [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)))
% 29.52/7.73 |
% 29.52/7.73 | Instantiating formula (34) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 29.52/7.73 | (189) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_5_5, v1, v2) = 0 & apply(all_0_5_5, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0)
% 29.52/7.73 |
% 29.52/7.73 +-Applying beta-rule and splitting (189), into two cases.
% 29.52/7.73 |-Branch one:
% 29.52/7.73 | (190) all_0_0_0 = 0
% 29.52/7.73 |
% 29.52/7.73 | Equations (190) can reduce 33 to:
% 29.52/7.73 | (191) $false
% 29.52/7.73 |
% 29.52/7.73 |-The branch is then unsatisfiable
% 29.52/7.73 |-Branch two:
% 29.52/7.73 | (33) ~ (all_0_0_0 = 0)
% 29.52/7.73 | (193) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_5_5, v1, v2) = 0 & apply(all_0_5_5, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0)
% 29.52/7.73 |
% 29.52/7.73 | Instantiating (193) with all_69_0_118, all_69_1_119, all_69_2_120 yields:
% 29.52/7.73 | (194) ~ (all_69_1_119 = all_69_2_120) & apply(all_0_5_5, all_69_1_119, all_69_0_118) = 0 & apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0 & member(all_69_0_118, all_0_2_2) = 0 & member(all_69_1_119, all_0_3_3) = 0 & member(all_69_2_120, all_0_3_3) = 0
% 29.52/7.73 |
% 29.52/7.73 | Applying alpha-rule on (194) yields:
% 29.52/7.73 | (195) member(all_69_0_118, all_0_2_2) = 0
% 29.52/7.73 | (196) ~ (all_69_1_119 = all_69_2_120)
% 29.52/7.73 | (197) apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0
% 29.52/7.74 | (198) member(all_69_1_119, all_0_3_3) = 0
% 29.52/7.74 | (199) apply(all_0_5_5, all_69_1_119, all_69_0_118) = 0
% 29.52/7.74 | (200) member(all_69_2_120, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (18) with all_69_0_118, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0, member(all_69_0_118, all_0_2_2) = 0, yields:
% 29.52/7.74 | (201) ? [v0] : (apply(all_0_4_4, all_69_0_118, v0) = 0 & member(v0, all_0_3_3) = 0)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (18) with all_69_1_119, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.74 | (202) ? [v0] : (apply(all_0_5_5, all_69_1_119, v0) = 0 & member(v0, all_0_2_2) = 0)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (94) with all_69_1_119, all_0_3_3, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_3_3) = 0, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.74 | (203) apply(all_0_1_1, all_69_1_119, all_69_1_119) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (155) with all_69_2_120, all_69_1_119, all_69_0_118, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0, member(all_69_0_118, all_0_2_2) = 0, member(all_69_1_119, all_0_3_3) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.74 | (204) all_69_1_119 = all_69_2_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_4_4, all_69_0_118, all_69_1_119) = v0) | ( ~ (v0 = 0) & apply(all_0_4_4, all_69_0_118, all_69_2_120) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (18) with all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.74 | (205) ? [v0] : (apply(all_0_5_5, all_69_2_120, v0) = 0 & member(v0, all_0_2_2) = 0)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (94) with all_69_2_120, all_0_3_3, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_3_3) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.74 | (206) apply(all_0_1_1, all_69_2_120, all_69_2_120) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (202) with all_81_0_121 yields:
% 29.52/7.74 | (207) apply(all_0_5_5, all_69_1_119, all_81_0_121) = 0 & member(all_81_0_121, all_0_2_2) = 0
% 29.52/7.74 |
% 29.52/7.74 | Applying alpha-rule on (207) yields:
% 29.52/7.74 | (208) apply(all_0_5_5, all_69_1_119, all_81_0_121) = 0
% 29.52/7.74 | (209) member(all_81_0_121, all_0_2_2) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (205) with all_83_0_122 yields:
% 29.52/7.74 | (210) apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0 & member(all_83_0_122, all_0_2_2) = 0
% 29.52/7.74 |
% 29.52/7.74 | Applying alpha-rule on (210) yields:
% 29.52/7.74 | (211) apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0
% 29.52/7.74 | (212) member(all_83_0_122, all_0_2_2) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (201) with all_85_0_123 yields:
% 29.52/7.74 | (213) apply(all_0_4_4, all_69_0_118, all_85_0_123) = 0 & member(all_85_0_123, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Applying alpha-rule on (213) yields:
% 29.52/7.74 | (214) apply(all_0_4_4, all_69_0_118, all_85_0_123) = 0
% 29.52/7.74 | (215) member(all_85_0_123, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 +-Applying beta-rule and splitting (204), into two cases.
% 29.52/7.74 |-Branch one:
% 29.52/7.74 | (216) all_69_1_119 = all_69_2_120
% 29.52/7.74 |
% 29.52/7.74 | Equations (216) can reduce 196 to:
% 29.52/7.74 | (191) $false
% 29.52/7.74 |
% 29.52/7.74 |-The branch is then unsatisfiable
% 29.52/7.74 |-Branch two:
% 29.52/7.74 | (196) ~ (all_69_1_119 = all_69_2_120)
% 29.52/7.74 | (219) ? [v0] : (( ~ (v0 = 0) & apply(all_0_4_4, all_69_0_118, all_69_1_119) = v0) | ( ~ (v0 = 0) & apply(all_0_4_4, all_69_0_118, all_69_2_120) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (219) with all_91_0_124 yields:
% 29.52/7.74 | (220) ( ~ (all_91_0_124 = 0) & apply(all_0_4_4, all_69_0_118, all_69_1_119) = all_91_0_124) | ( ~ (all_91_0_124 = 0) & apply(all_0_4_4, all_69_0_118, all_69_2_120) = all_91_0_124)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (28) with all_0_1_1, all_69_1_119, all_69_1_119, all_0_3_3, all_0_2_2, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms compose_function(all_0_4_4, all_0_5_5, all_0_3_3, all_0_2_2, all_0_3_3) = all_0_1_1, apply(all_0_1_1, all_69_1_119, all_69_1_119) = 0, yields:
% 29.52/7.74 | (221) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, v0, all_69_1_119) = 0 & apply(all_0_5_5, all_69_1_119, v0) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_69_1_119, all_0_3_3) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (28) with all_0_1_1, all_69_2_120, all_69_2_120, all_0_3_3, all_0_2_2, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms compose_function(all_0_4_4, all_0_5_5, all_0_3_3, all_0_2_2, all_0_3_3) = all_0_1_1, apply(all_0_1_1, all_69_2_120, all_69_2_120) = 0, yields:
% 29.52/7.74 | (222) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, v0, all_69_2_120) = 0 & apply(all_0_5_5, all_69_2_120, v0) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (37) with all_83_0_122, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.74 | (223) all_83_0_122 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & member(all_83_0_122, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (171) with all_83_0_122, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0, member(all_69_0_118, all_0_2_2) = 0, yields:
% 29.52/7.74 | (224) all_83_0_122 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0) | ( ~ (v0 = 0) & member(all_83_0_122, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (18) with all_83_0_122, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0, member(all_83_0_122, all_0_2_2) = 0, yields:
% 29.52/7.74 | (225) ? [v0] : (apply(all_0_4_4, all_83_0_122, v0) = 0 & member(v0, all_0_3_3) = 0)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (155) with all_83_0_122, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_83_0_122, all_0_2_2) = 0, member(all_69_0_118, all_0_2_2) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.74 | (226) all_83_0_122 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (18) with all_81_0_121, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_2_2, all_0_3_3) = 0, member(all_81_0_121, all_0_2_2) = 0, yields:
% 29.52/7.74 | (227) ? [v0] : (apply(all_0_4_4, all_81_0_121, v0) = 0 & member(v0, all_0_3_3) = 0)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (155) with all_81_0_121, all_69_0_118, all_69_1_119, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_81_0_121, all_0_2_2) = 0, member(all_69_0_118, all_0_2_2) = 0, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.74 | (228) all_81_0_121 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_69_0_118) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (155) with all_81_0_121, all_83_0_122, all_69_1_119, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_83_0_122, all_0_2_2) = 0, member(all_81_0_121, all_0_2_2) = 0, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.74 | (229) all_83_0_122 = all_81_0_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating formula (155) with all_81_0_121, all_83_0_122, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_83_0_122, all_0_2_2) = 0, member(all_81_0_121, all_0_2_2) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.74 | (230) all_83_0_122 = all_81_0_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_81_0_121) = v0))
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (227) with all_102_0_126 yields:
% 29.52/7.74 | (231) apply(all_0_4_4, all_81_0_121, all_102_0_126) = 0 & member(all_102_0_126, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Applying alpha-rule on (231) yields:
% 29.52/7.74 | (232) apply(all_0_4_4, all_81_0_121, all_102_0_126) = 0
% 29.52/7.74 | (233) member(all_102_0_126, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (225) with all_104_0_127 yields:
% 29.52/7.74 | (234) apply(all_0_4_4, all_83_0_122, all_104_0_127) = 0 & member(all_104_0_127, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Applying alpha-rule on (234) yields:
% 29.52/7.74 | (235) apply(all_0_4_4, all_83_0_122, all_104_0_127) = 0
% 29.52/7.74 | (236) member(all_104_0_127, all_0_3_3) = 0
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (222) with all_108_0_129, all_108_1_130, all_108_2_131, all_108_3_132 yields:
% 29.52/7.74 | (237) (all_108_0_129 = 0 & all_108_1_130 = 0 & all_108_2_131 = 0 & apply(all_0_4_4, all_108_3_132, all_69_2_120) = 0 & apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0 & member(all_108_3_132, all_0_2_2) = 0) | ( ~ (all_108_3_132 = 0) & member(all_69_2_120, all_0_3_3) = all_108_3_132)
% 29.52/7.74 |
% 29.52/7.74 | Instantiating (221) with all_109_0_133, all_109_1_134, all_109_2_135, all_109_3_136 yields:
% 29.52/7.74 | (238) (all_109_0_133 = 0 & all_109_1_134 = 0 & all_109_2_135 = 0 & apply(all_0_4_4, all_109_3_136, all_69_1_119) = 0 & apply(all_0_5_5, all_69_1_119, all_109_3_136) = 0 & member(all_109_3_136, all_0_2_2) = 0) | ( ~ (all_109_3_136 = 0) & member(all_69_1_119, all_0_3_3) = all_109_3_136)
% 29.52/7.74 |
% 29.52/7.74 +-Applying beta-rule and splitting (228), into two cases.
% 29.52/7.74 |-Branch one:
% 29.52/7.74 | (239) all_81_0_121 = all_69_0_118
% 29.52/7.74 |
% 29.52/7.74 | From (239) and (208) follows:
% 29.52/7.75 | (199) apply(all_0_5_5, all_69_1_119, all_69_0_118) = 0
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (230), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (241) all_83_0_122 = all_81_0_121
% 29.52/7.75 |
% 29.52/7.75 | Combining equations (239,241) yields a new equation:
% 29.52/7.75 | (242) all_83_0_122 = all_69_0_118
% 29.52/7.75 |
% 29.52/7.75 | From (242) and (211) follows:
% 29.52/7.75 | (197) apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0
% 29.52/7.75 |
% 29.52/7.75 | From (242) and (212) follows:
% 29.52/7.75 | (195) member(all_69_0_118, all_0_2_2) = 0
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (238), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (245) all_109_0_133 = 0 & all_109_1_134 = 0 & all_109_2_135 = 0 & apply(all_0_4_4, all_109_3_136, all_69_1_119) = 0 & apply(all_0_5_5, all_69_1_119, all_109_3_136) = 0 & member(all_109_3_136, all_0_2_2) = 0
% 29.52/7.75 |
% 29.52/7.75 | Applying alpha-rule on (245) yields:
% 29.52/7.75 | (246) all_109_2_135 = 0
% 29.52/7.75 | (247) all_109_1_134 = 0
% 29.52/7.75 | (248) member(all_109_3_136, all_0_2_2) = 0
% 29.52/7.75 | (249) all_109_0_133 = 0
% 29.52/7.75 | (250) apply(all_0_5_5, all_69_1_119, all_109_3_136) = 0
% 29.52/7.75 | (251) apply(all_0_4_4, all_109_3_136, all_69_1_119) = 0
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (237), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (252) all_108_0_129 = 0 & all_108_1_130 = 0 & all_108_2_131 = 0 & apply(all_0_4_4, all_108_3_132, all_69_2_120) = 0 & apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0 & member(all_108_3_132, all_0_2_2) = 0
% 29.52/7.75 |
% 29.52/7.75 | Applying alpha-rule on (252) yields:
% 29.52/7.75 | (253) member(all_108_3_132, all_0_2_2) = 0
% 29.52/7.75 | (254) all_108_2_131 = 0
% 29.52/7.75 | (255) all_108_0_129 = 0
% 29.52/7.75 | (256) all_108_1_130 = 0
% 29.52/7.75 | (257) apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0
% 29.52/7.75 | (258) apply(all_0_4_4, all_108_3_132, all_69_2_120) = 0
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (37) with all_108_3_132, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.75 | (259) all_108_3_132 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (171) with all_108_3_132, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0, member(all_69_0_118, all_0_2_2) = 0, yields:
% 29.52/7.75 | (260) all_108_3_132 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0) | ( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (171) with all_69_0_118, all_109_3_136, all_69_1_119, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_1_119, all_69_0_118) = 0, member(all_109_3_136, all_0_2_2) = 0, yields:
% 29.52/7.75 | (261) all_109_3_136 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_109_3_136) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_1_119, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (171) with all_108_3_132, all_109_3_136, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_69_2_120, all_108_3_132) = 0, member(all_109_3_136, all_0_2_2) = 0, yields:
% 29.52/7.75 | (262) all_109_3_136 = all_108_3_132 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = v0) | ( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_108_3_132, all_69_0_118, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_69_0_118, all_0_2_2) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.75 | (263) all_108_3_132 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_108_3_132) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_108_3_132, all_109_3_136, all_85_0_123, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_109_3_136, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_85_0_123, all_0_3_3) = 0, yields:
% 29.52/7.75 | (264) all_109_3_136 = all_108_3_132 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_85_0_123, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_85_0_123, all_108_3_132) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_108_3_132, all_109_3_136, all_69_2_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_109_3_136, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.75 | (265) all_109_3_136 = all_108_3_132 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_108_3_132) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_109_3_136, all_108_3_132, all_104_0_127, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_109_3_136, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_104_0_127, all_0_3_3) = 0, yields:
% 29.52/7.75 | (266) all_109_3_136 = all_108_3_132 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_104_0_127, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_104_0_127, all_108_3_132) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_69_0_118, all_108_3_132, all_102_0_126, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_102_0_126, all_0_3_3) = 0, member(all_69_0_118, all_0_2_2) = 0, yields:
% 29.52/7.75 | (267) all_108_3_132 = all_69_0_118 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_108_3_132) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_69_0_118) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (155) with all_109_3_136, all_108_3_132, all_102_0_126, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_109_3_136, all_0_2_2) = 0, member(all_108_3_132, all_0_2_2) = 0, member(all_102_0_126, all_0_3_3) = 0, yields:
% 29.52/7.75 | (268) all_109_3_136 = all_108_3_132 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_108_3_132) = v0))
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (261), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (269) all_109_3_136 = all_69_0_118
% 29.52/7.75 |
% 29.52/7.75 | From (269) and (251) follows:
% 29.52/7.75 | (270) apply(all_0_4_4, all_69_0_118, all_69_1_119) = 0
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (260), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.75 |
% 29.52/7.75 | From (271) and (258) follows:
% 29.52/7.75 | (272) apply(all_0_4_4, all_69_0_118, all_69_2_120) = 0
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (220), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (273) ~ (all_91_0_124 = 0) & apply(all_0_4_4, all_69_0_118, all_69_1_119) = all_91_0_124
% 29.52/7.75 |
% 29.52/7.75 | Applying alpha-rule on (273) yields:
% 29.52/7.75 | (274) ~ (all_91_0_124 = 0)
% 29.52/7.75 | (275) apply(all_0_4_4, all_69_0_118, all_69_1_119) = all_91_0_124
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (165) with all_0_4_4, all_69_0_118, all_69_1_119, 0, all_91_0_124 and discharging atoms apply(all_0_4_4, all_69_0_118, all_69_1_119) = all_91_0_124, apply(all_0_4_4, all_69_0_118, all_69_1_119) = 0, yields:
% 29.52/7.75 | (276) all_91_0_124 = 0
% 29.52/7.75 |
% 29.52/7.75 | Equations (276) can reduce 274 to:
% 29.52/7.75 | (191) $false
% 29.52/7.75 |
% 29.52/7.75 |-The branch is then unsatisfiable
% 29.52/7.75 |-Branch two:
% 29.52/7.75 | (278) ~ (all_91_0_124 = 0) & apply(all_0_4_4, all_69_0_118, all_69_2_120) = all_91_0_124
% 29.52/7.75 |
% 29.52/7.75 | Applying alpha-rule on (278) yields:
% 29.52/7.75 | (274) ~ (all_91_0_124 = 0)
% 29.52/7.75 | (280) apply(all_0_4_4, all_69_0_118, all_69_2_120) = all_91_0_124
% 29.52/7.75 |
% 29.52/7.75 | Instantiating formula (165) with all_0_4_4, all_69_0_118, all_69_2_120, 0, all_91_0_124 and discharging atoms apply(all_0_4_4, all_69_0_118, all_69_2_120) = all_91_0_124, apply(all_0_4_4, all_69_0_118, all_69_2_120) = 0, yields:
% 29.52/7.75 | (276) all_91_0_124 = 0
% 29.52/7.75 |
% 29.52/7.75 | Equations (276) can reduce 274 to:
% 29.52/7.75 | (191) $false
% 29.52/7.75 |
% 29.52/7.75 |-The branch is then unsatisfiable
% 29.52/7.75 |-Branch two:
% 29.52/7.75 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.75 | (284) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0) | ( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 | Instantiating (284) with all_160_0_246 yields:
% 29.52/7.75 | (285) ( ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246) | ( ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246) | ( ~ (all_160_0_246 = 0) & member(all_69_2_120, all_0_3_3) = all_160_0_246)
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (259), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.75 |
% 29.52/7.75 | Equations (271) can reduce 283 to:
% 29.52/7.75 | (191) $false
% 29.52/7.75 |
% 29.52/7.75 |-The branch is then unsatisfiable
% 29.52/7.75 |-Branch two:
% 29.52/7.75 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.75 | (289) ? [v0] : (( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.75 |
% 29.52/7.75 +-Applying beta-rule and splitting (266), into two cases.
% 29.52/7.75 |-Branch one:
% 29.52/7.75 | (290) all_109_3_136 = all_108_3_132
% 29.52/7.75 |
% 29.52/7.75 | Combining equations (290,269) yields a new equation:
% 29.52/7.75 | (291) all_108_3_132 = all_69_0_118
% 29.52/7.75 |
% 29.52/7.75 | Simplifying 291 yields:
% 29.52/7.75 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (294) ~ (all_109_3_136 = all_108_3_132)
% 29.52/7.76 | (295) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_104_0_127, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_104_0_127, all_108_3_132) = v0))
% 29.52/7.76 |
% 29.52/7.76 | Equations (269) can reduce 294 to:
% 29.52/7.76 | (296) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 296 yields:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (267), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 | (301) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_108_3_132) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_69_0_118) = v0))
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (265), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (290) all_109_3_136 = all_108_3_132
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (290,269) yields a new equation:
% 29.52/7.76 | (291) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 291 yields:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (294) ~ (all_109_3_136 = all_108_3_132)
% 29.52/7.76 | (307) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_108_3_132) = v0))
% 29.52/7.76 |
% 29.52/7.76 | Equations (269) can reduce 294 to:
% 29.52/7.76 | (296) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 296 yields:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (268), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (290) all_109_3_136 = all_108_3_132
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (290,269) yields a new equation:
% 29.52/7.76 | (291) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 291 yields:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (294) ~ (all_109_3_136 = all_108_3_132)
% 29.52/7.76 | (315) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_102_0_126, all_108_3_132) = v0))
% 29.52/7.76 |
% 29.52/7.76 | Equations (269) can reduce 294 to:
% 29.52/7.76 | (296) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 296 yields:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (263), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 | (321) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_108_3_132) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0))
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (264), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (290) all_109_3_136 = all_108_3_132
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (290,269) yields a new equation:
% 29.52/7.76 | (291) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 291 yields:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (294) ~ (all_109_3_136 = all_108_3_132)
% 29.52/7.76 | (327) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_85_0_123, all_109_3_136) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_85_0_123, all_108_3_132) = v0))
% 29.52/7.76 |
% 29.52/7.76 | Equations (269) can reduce 294 to:
% 29.52/7.76 | (296) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 296 yields:
% 29.52/7.76 | (283) ~ (all_108_3_132 = all_69_0_118)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (262), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (290) all_109_3_136 = all_108_3_132
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (290,269) yields a new equation:
% 29.52/7.76 | (291) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 291 yields:
% 29.52/7.76 | (271) all_108_3_132 = all_69_0_118
% 29.52/7.76 |
% 29.52/7.76 | Equations (271) can reduce 283 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (294) ~ (all_109_3_136 = all_108_3_132)
% 29.52/7.76 | (335) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = v0) | ( ~ (v0 = 0) & member(all_108_3_132, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.76 |
% 29.52/7.76 | Instantiating (335) with all_232_0_379 yields:
% 29.52/7.76 | (336) ( ~ (all_232_0_379 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = all_232_0_379) | ( ~ (all_232_0_379 = 0) & member(all_108_3_132, all_0_2_2) = all_232_0_379) | ( ~ (all_232_0_379 = 0) & member(all_69_2_120, all_0_3_3) = all_232_0_379)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (336), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (337) ( ~ (all_232_0_379 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = all_232_0_379) | ( ~ (all_232_0_379 = 0) & member(all_108_3_132, all_0_2_2) = all_232_0_379)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (337), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (338) ~ (all_232_0_379 = 0) & apply(all_0_5_5, all_69_2_120, all_109_3_136) = all_232_0_379
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (338) yields:
% 29.52/7.76 | (339) ~ (all_232_0_379 = 0)
% 29.52/7.76 | (340) apply(all_0_5_5, all_69_2_120, all_109_3_136) = all_232_0_379
% 29.52/7.76 |
% 29.52/7.76 | From (269) and (340) follows:
% 29.52/7.76 | (341) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_232_0_379
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (285), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (342) ( ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246) | ( ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (342), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (343) ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (343) yields:
% 29.52/7.76 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.76 | (345) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_232_0_379, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_232_0_379, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.76 | (346) all_232_0_379 = 0
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_160_0_246, all_232_0_379 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_232_0_379, apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246, yields:
% 29.52/7.76 | (347) all_232_0_379 = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (347,346) yields a new equation:
% 29.52/7.76 | (348) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Simplifying 348 yields:
% 29.52/7.76 | (349) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Equations (349) can reduce 344 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (351) ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (351) yields:
% 29.52/7.76 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.76 | (353) member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (2) with all_108_3_132, all_0_2_2, all_160_0_246, 0 and discharging atoms member(all_108_3_132, all_0_2_2) = all_160_0_246, member(all_108_3_132, all_0_2_2) = 0, yields:
% 29.52/7.76 | (349) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Equations (349) can reduce 344 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (356) ~ (all_160_0_246 = 0) & member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (356) yields:
% 29.52/7.76 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.76 | (358) member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (2) with all_69_2_120, all_0_3_3, all_160_0_246, 0 and discharging atoms member(all_69_2_120, all_0_3_3) = all_160_0_246, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.76 | (349) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Equations (349) can reduce 344 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (361) ~ (all_232_0_379 = 0) & member(all_108_3_132, all_0_2_2) = all_232_0_379
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (361) yields:
% 29.52/7.76 | (339) ~ (all_232_0_379 = 0)
% 29.52/7.76 | (363) member(all_108_3_132, all_0_2_2) = all_232_0_379
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (285), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (342) ( ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246) | ( ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246)
% 29.52/7.76 |
% 29.52/7.76 +-Applying beta-rule and splitting (342), into two cases.
% 29.52/7.76 |-Branch one:
% 29.52/7.76 | (343) ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (343) yields:
% 29.52/7.76 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.76 | (345) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_160_0_246, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.76 | (349) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Equations (349) can reduce 344 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.76 |-Branch two:
% 29.52/7.76 | (351) ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Applying alpha-rule on (351) yields:
% 29.52/7.76 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.76 | (353) member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (2) with all_108_3_132, all_0_2_2, all_232_0_379, 0 and discharging atoms member(all_108_3_132, all_0_2_2) = all_232_0_379, member(all_108_3_132, all_0_2_2) = 0, yields:
% 29.52/7.76 | (346) all_232_0_379 = 0
% 29.52/7.76 |
% 29.52/7.76 | Instantiating formula (2) with all_108_3_132, all_0_2_2, all_160_0_246, all_232_0_379 and discharging atoms member(all_108_3_132, all_0_2_2) = all_232_0_379, member(all_108_3_132, all_0_2_2) = all_160_0_246, yields:
% 29.52/7.76 | (347) all_232_0_379 = all_160_0_246
% 29.52/7.76 |
% 29.52/7.76 | Combining equations (346,347) yields a new equation:
% 29.52/7.76 | (349) all_160_0_246 = 0
% 29.52/7.76 |
% 29.52/7.76 | Equations (349) can reduce 344 to:
% 29.52/7.76 | (191) $false
% 29.52/7.76 |
% 29.52/7.76 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (356) ~ (all_160_0_246 = 0) & member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (356) yields:
% 29.52/7.77 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.77 | (358) member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_2_120, all_0_3_3, all_160_0_246, 0 and discharging atoms member(all_69_2_120, all_0_3_3) = all_160_0_246, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.77 | (349) all_160_0_246 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (349) can reduce 344 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (382) ~ (all_232_0_379 = 0) & member(all_69_2_120, all_0_3_3) = all_232_0_379
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (382) yields:
% 29.52/7.77 | (339) ~ (all_232_0_379 = 0)
% 29.52/7.77 | (384) member(all_69_2_120, all_0_3_3) = all_232_0_379
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (285), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (342) ( ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246) | ( ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246)
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (342), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (343) ~ (all_160_0_246 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (343) yields:
% 29.52/7.77 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.77 | (345) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_160_0_246, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_160_0_246, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.77 | (349) all_160_0_246 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (349) can reduce 344 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (351) ~ (all_160_0_246 = 0) & member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (351) yields:
% 29.52/7.77 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.77 | (353) member(all_108_3_132, all_0_2_2) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_108_3_132, all_0_2_2, all_160_0_246, 0 and discharging atoms member(all_108_3_132, all_0_2_2) = all_160_0_246, member(all_108_3_132, all_0_2_2) = 0, yields:
% 29.52/7.77 | (349) all_160_0_246 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (349) can reduce 344 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (356) ~ (all_160_0_246 = 0) & member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (356) yields:
% 29.52/7.77 | (344) ~ (all_160_0_246 = 0)
% 29.52/7.77 | (358) member(all_69_2_120, all_0_3_3) = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_2_120, all_0_3_3, all_232_0_379, 0 and discharging atoms member(all_69_2_120, all_0_3_3) = all_232_0_379, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.77 | (346) all_232_0_379 = 0
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_2_120, all_0_3_3, all_160_0_246, all_232_0_379 and discharging atoms member(all_69_2_120, all_0_3_3) = all_232_0_379, member(all_69_2_120, all_0_3_3) = all_160_0_246, yields:
% 29.52/7.77 | (347) all_232_0_379 = all_160_0_246
% 29.52/7.77 |
% 29.52/7.77 | Combining equations (346,347) yields a new equation:
% 29.52/7.77 | (349) all_160_0_246 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (349) can reduce 344 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (403) ~ (all_109_3_136 = all_69_0_118)
% 29.52/7.77 | (404) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_109_3_136) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_1_119, all_0_3_3) = v0))
% 29.52/7.77 |
% 29.52/7.77 | Instantiating (404) with all_156_0_536 yields:
% 29.52/7.77 | (405) ( ~ (all_156_0_536 = 0) & apply(all_0_5_5, all_69_1_119, all_109_3_136) = all_156_0_536) | ( ~ (all_156_0_536 = 0) & member(all_69_0_118, all_0_2_2) = all_156_0_536) | ( ~ (all_156_0_536 = 0) & member(all_69_1_119, all_0_3_3) = all_156_0_536)
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (405), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (406) ( ~ (all_156_0_536 = 0) & apply(all_0_5_5, all_69_1_119, all_109_3_136) = all_156_0_536) | ( ~ (all_156_0_536 = 0) & member(all_69_0_118, all_0_2_2) = all_156_0_536)
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (406), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (407) ~ (all_156_0_536 = 0) & apply(all_0_5_5, all_69_1_119, all_109_3_136) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (407) yields:
% 29.52/7.77 | (408) ~ (all_156_0_536 = 0)
% 29.52/7.77 | (409) apply(all_0_5_5, all_69_1_119, all_109_3_136) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (165) with all_0_5_5, all_69_1_119, all_109_3_136, all_156_0_536, 0 and discharging atoms apply(all_0_5_5, all_69_1_119, all_109_3_136) = all_156_0_536, apply(all_0_5_5, all_69_1_119, all_109_3_136) = 0, yields:
% 29.52/7.77 | (410) all_156_0_536 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (410) can reduce 408 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (412) ~ (all_156_0_536 = 0) & member(all_69_0_118, all_0_2_2) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (412) yields:
% 29.52/7.77 | (408) ~ (all_156_0_536 = 0)
% 29.52/7.77 | (414) member(all_69_0_118, all_0_2_2) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_0_118, all_0_2_2, all_156_0_536, 0 and discharging atoms member(all_69_0_118, all_0_2_2) = all_156_0_536, member(all_69_0_118, all_0_2_2) = 0, yields:
% 29.52/7.77 | (410) all_156_0_536 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (410) can reduce 408 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (417) ~ (all_156_0_536 = 0) & member(all_69_1_119, all_0_3_3) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (417) yields:
% 29.52/7.77 | (408) ~ (all_156_0_536 = 0)
% 29.52/7.77 | (419) member(all_69_1_119, all_0_3_3) = all_156_0_536
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_1_119, all_0_3_3, all_156_0_536, 0 and discharging atoms member(all_69_1_119, all_0_3_3) = all_156_0_536, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.77 | (410) all_156_0_536 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (410) can reduce 408 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (422) ~ (all_108_3_132 = 0) & member(all_69_2_120, all_0_3_3) = all_108_3_132
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (422) yields:
% 29.52/7.77 | (423) ~ (all_108_3_132 = 0)
% 29.52/7.77 | (424) member(all_69_2_120, all_0_3_3) = all_108_3_132
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_2_120, all_0_3_3, all_108_3_132, 0 and discharging atoms member(all_69_2_120, all_0_3_3) = all_108_3_132, member(all_69_2_120, all_0_3_3) = 0, yields:
% 29.52/7.77 | (425) all_108_3_132 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (425) can reduce 423 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (427) ~ (all_109_3_136 = 0) & member(all_69_1_119, all_0_3_3) = all_109_3_136
% 29.52/7.77 |
% 29.52/7.77 | Applying alpha-rule on (427) yields:
% 29.52/7.77 | (428) ~ (all_109_3_136 = 0)
% 29.52/7.77 | (429) member(all_69_1_119, all_0_3_3) = all_109_3_136
% 29.52/7.77 |
% 29.52/7.77 | Instantiating formula (2) with all_69_1_119, all_0_3_3, all_109_3_136, 0 and discharging atoms member(all_69_1_119, all_0_3_3) = all_109_3_136, member(all_69_1_119, all_0_3_3) = 0, yields:
% 29.52/7.77 | (430) all_109_3_136 = 0
% 29.52/7.77 |
% 29.52/7.77 | Equations (430) can reduce 428 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (432) ~ (all_83_0_122 = all_81_0_121)
% 29.52/7.77 | (433) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_81_0_121) = v0))
% 29.52/7.77 |
% 29.52/7.77 | Instantiating (433) with all_118_0_633 yields:
% 29.52/7.77 | (434) ( ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633) | ( ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_81_0_121) = all_118_0_633)
% 29.52/7.77 |
% 29.52/7.77 | Equations (239) can reduce 432 to:
% 29.52/7.77 | (435) ~ (all_83_0_122 = all_69_0_118)
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (229), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (241) all_83_0_122 = all_81_0_121
% 29.52/7.77 |
% 29.52/7.77 | Combining equations (239,241) yields a new equation:
% 29.52/7.77 | (242) all_83_0_122 = all_69_0_118
% 29.52/7.77 |
% 29.52/7.77 | Equations (242) can reduce 435 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (432) ~ (all_83_0_122 = all_81_0_121)
% 29.52/7.77 | (440) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = v0))
% 29.52/7.77 |
% 29.52/7.77 | Equations (239) can reduce 432 to:
% 29.52/7.77 | (435) ~ (all_83_0_122 = all_69_0_118)
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (224), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (242) all_83_0_122 = all_69_0_118
% 29.52/7.77 |
% 29.52/7.77 | Equations (242) can reduce 435 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (435) ~ (all_83_0_122 = all_69_0_118)
% 29.52/7.77 | (445) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0) | ( ~ (v0 = 0) & member(all_83_0_122, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (223), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (242) all_83_0_122 = all_69_0_118
% 29.52/7.77 |
% 29.52/7.77 | Equations (242) can reduce 435 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (435) ~ (all_83_0_122 = all_69_0_118)
% 29.52/7.77 | (449) ? [v0] : (( ~ (v0 = 0) & member(all_83_0_122, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_0_118, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_69_2_120, all_0_3_3) = v0))
% 29.52/7.77 |
% 29.52/7.77 +-Applying beta-rule and splitting (226), into two cases.
% 29.52/7.77 |-Branch one:
% 29.52/7.77 | (242) all_83_0_122 = all_69_0_118
% 29.52/7.77 |
% 29.52/7.77 | Equations (242) can reduce 435 to:
% 29.52/7.77 | (191) $false
% 29.52/7.77 |
% 29.52/7.77 |-The branch is then unsatisfiable
% 29.52/7.77 |-Branch two:
% 29.52/7.77 | (435) ~ (all_83_0_122 = all_69_0_118)
% 29.52/7.77 | (453) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = v0))
% 29.52/7.78 |
% 29.52/7.78 | Instantiating (453) with all_153_0_646 yields:
% 29.52/7.78 | (454) ( ~ (all_153_0_646 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_153_0_646) | ( ~ (all_153_0_646 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_153_0_646)
% 29.52/7.78 |
% 29.52/7.78 +-Applying beta-rule and splitting (454), into two cases.
% 29.52/7.78 |-Branch one:
% 29.52/7.78 | (455) ~ (all_153_0_646 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_153_0_646
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (455) yields:
% 29.52/7.78 | (456) ~ (all_153_0_646 = 0)
% 29.52/7.78 | (457) apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_153_0_646
% 29.52/7.78 |
% 29.52/7.78 +-Applying beta-rule and splitting (434), into two cases.
% 29.52/7.78 |-Branch one:
% 29.52/7.78 | (458) ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (458) yields:
% 29.52/7.78 | (459) ~ (all_118_0_633 = 0)
% 29.52/7.78 | (460) apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_83_0_122, all_153_0_646, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_153_0_646, apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0, yields:
% 29.52/7.78 | (461) all_153_0_646 = 0
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_83_0_122, all_118_0_633, all_153_0_646 and discharging atoms apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_153_0_646, apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633, yields:
% 29.52/7.78 | (462) all_153_0_646 = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Combining equations (461,462) yields a new equation:
% 29.52/7.78 | (463) all_118_0_633 = 0
% 29.52/7.78 |
% 29.52/7.78 | Equations (463) can reduce 459 to:
% 29.52/7.78 | (191) $false
% 29.52/7.78 |
% 29.52/7.78 |-The branch is then unsatisfiable
% 29.52/7.78 |-Branch two:
% 29.52/7.78 | (465) ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_81_0_121) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (465) yields:
% 29.52/7.78 | (459) ~ (all_118_0_633 = 0)
% 29.52/7.78 | (467) apply(all_0_5_5, all_69_2_120, all_81_0_121) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | From (239) and (467) follows:
% 29.52/7.78 | (468) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_118_0_633, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_118_0_633, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.78 | (463) all_118_0_633 = 0
% 29.52/7.78 |
% 29.52/7.78 | Equations (463) can reduce 459 to:
% 29.52/7.78 | (191) $false
% 29.52/7.78 |
% 29.52/7.78 |-The branch is then unsatisfiable
% 29.52/7.78 |-Branch two:
% 29.52/7.78 | (471) ~ (all_153_0_646 = 0) & apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_153_0_646
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (471) yields:
% 29.52/7.78 | (456) ~ (all_153_0_646 = 0)
% 29.52/7.78 | (473) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_153_0_646
% 29.52/7.78 |
% 29.52/7.78 +-Applying beta-rule and splitting (434), into two cases.
% 29.52/7.78 |-Branch one:
% 29.52/7.78 | (458) ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (458) yields:
% 29.52/7.78 | (459) ~ (all_118_0_633 = 0)
% 29.52/7.78 | (460) apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_83_0_122, all_118_0_633, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_83_0_122) = all_118_0_633, apply(all_0_5_5, all_69_2_120, all_83_0_122) = 0, yields:
% 29.52/7.78 | (463) all_118_0_633 = 0
% 29.52/7.78 |
% 29.52/7.78 | Equations (463) can reduce 459 to:
% 29.52/7.78 | (191) $false
% 29.52/7.78 |
% 29.52/7.78 |-The branch is then unsatisfiable
% 29.52/7.78 |-Branch two:
% 29.52/7.78 | (465) ~ (all_118_0_633 = 0) & apply(all_0_5_5, all_69_2_120, all_81_0_121) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (465) yields:
% 29.52/7.78 | (459) ~ (all_118_0_633 = 0)
% 29.52/7.78 | (467) apply(all_0_5_5, all_69_2_120, all_81_0_121) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | From (239) and (467) follows:
% 29.52/7.78 | (468) apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_153_0_646, 0 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_153_0_646, apply(all_0_5_5, all_69_2_120, all_69_0_118) = 0, yields:
% 29.52/7.78 | (461) all_153_0_646 = 0
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_2_120, all_69_0_118, all_118_0_633, all_153_0_646 and discharging atoms apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_153_0_646, apply(all_0_5_5, all_69_2_120, all_69_0_118) = all_118_0_633, yields:
% 29.52/7.78 | (462) all_153_0_646 = all_118_0_633
% 29.52/7.78 |
% 29.52/7.78 | Combining equations (462,461) yields a new equation:
% 29.52/7.78 | (485) all_118_0_633 = 0
% 29.52/7.78 |
% 29.52/7.78 | Simplifying 485 yields:
% 29.52/7.78 | (463) all_118_0_633 = 0
% 29.52/7.78 |
% 29.52/7.78 | Equations (463) can reduce 459 to:
% 29.52/7.78 | (191) $false
% 29.52/7.78 |
% 29.52/7.78 |-The branch is then unsatisfiable
% 29.52/7.78 |-Branch two:
% 29.52/7.78 | (488) ~ (all_81_0_121 = all_69_0_118)
% 29.52/7.78 | (489) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_69_1_119, all_69_0_118) = v0))
% 29.52/7.78 |
% 29.52/7.78 | Instantiating (489) with all_114_0_660 yields:
% 29.52/7.78 | (490) ( ~ (all_114_0_660 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = all_114_0_660) | ( ~ (all_114_0_660 = 0) & apply(all_0_5_5, all_69_1_119, all_69_0_118) = all_114_0_660)
% 29.52/7.78 |
% 29.52/7.78 +-Applying beta-rule and splitting (490), into two cases.
% 29.52/7.78 |-Branch one:
% 29.52/7.78 | (491) ~ (all_114_0_660 = 0) & apply(all_0_5_5, all_69_1_119, all_81_0_121) = all_114_0_660
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (491) yields:
% 29.52/7.78 | (492) ~ (all_114_0_660 = 0)
% 29.52/7.78 | (493) apply(all_0_5_5, all_69_1_119, all_81_0_121) = all_114_0_660
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_1_119, all_81_0_121, all_114_0_660, 0 and discharging atoms apply(all_0_5_5, all_69_1_119, all_81_0_121) = all_114_0_660, apply(all_0_5_5, all_69_1_119, all_81_0_121) = 0, yields:
% 29.52/7.78 | (494) all_114_0_660 = 0
% 29.52/7.78 |
% 29.52/7.78 | Equations (494) can reduce 492 to:
% 29.52/7.78 | (191) $false
% 29.52/7.78 |
% 29.52/7.78 |-The branch is then unsatisfiable
% 29.52/7.78 |-Branch two:
% 29.52/7.78 | (496) ~ (all_114_0_660 = 0) & apply(all_0_5_5, all_69_1_119, all_69_0_118) = all_114_0_660
% 29.52/7.78 |
% 29.52/7.78 | Applying alpha-rule on (496) yields:
% 29.52/7.78 | (492) ~ (all_114_0_660 = 0)
% 29.52/7.78 | (498) apply(all_0_5_5, all_69_1_119, all_69_0_118) = all_114_0_660
% 29.52/7.78 |
% 29.52/7.78 | Instantiating formula (165) with all_0_5_5, all_69_1_119, all_69_0_118, all_114_0_660, 0 and discharging atoms apply(all_0_5_5, all_69_1_119, all_69_0_118) = all_114_0_660, apply(all_0_5_5, all_69_1_119, all_69_0_118) = 0, yields:
% 29.52/7.78 | (494) all_114_0_660 = 0
% 29.52/7.78 |
% 29.94/7.78 | Equations (494) can reduce 492 to:
% 29.94/7.78 | (191) $false
% 29.94/7.78 |
% 29.94/7.78 |-The branch is then unsatisfiable
% 29.94/7.78 % SZS output end Proof for theBenchmark
% 29.94/7.78
% 29.94/7.78 7169ms
%------------------------------------------------------------------------------