TSTP Solution File: SET709+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET709+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:32 EDT 2022
% Result : Theorem 9.38s 2.79s
% Output : Proof 14.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET709+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 02:00:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.60 ____ _
% 0.57/0.60 ___ / __ \_____(_)___ ________ __________
% 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic
% 0.57/0.60 (ePrincess v.1.0)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2015
% 0.57/0.60 (c) Peter Backeman, 2014-2015
% 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.60 Bug reports to peter@backeman.se
% 0.57/0.60
% 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.09/1.03 Prover 0: Preprocessing ...
% 3.29/1.38 Prover 0: Warning: ignoring some quantifiers
% 3.57/1.41 Prover 0: Constructing countermodel ...
% 4.52/1.69 Prover 0: gave up
% 4.52/1.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.87/1.75 Prover 1: Preprocessing ...
% 5.90/1.98 Prover 1: Constructing countermodel ...
% 6.84/2.20 Prover 1: gave up
% 6.84/2.20 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.28/2.23 Prover 2: Preprocessing ...
% 8.51/2.53 Prover 2: Warning: ignoring some quantifiers
% 8.51/2.55 Prover 2: Constructing countermodel ...
% 9.38/2.79 Prover 2: proved (591ms)
% 9.38/2.79
% 9.38/2.79 No countermodel exists, formula is valid
% 9.38/2.79 % SZS status Theorem for theBenchmark
% 9.38/2.79
% 9.38/2.79 Generating proof ... Warning: ignoring some quantifiers
% 13.37/3.67 found it (size 179)
% 13.37/3.67
% 13.37/3.67 % SZS output start Proof for theBenchmark
% 13.37/3.67 Assumed formulas after preprocessing and simplification:
% 13.37/3.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & compose_function(v1, v0, v2, v3, v4) = v5 & maps(v5, v2, v4) = v6 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = 0) | ~ (apply(v9, v12, v14) = v16) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (apply(v8, v12, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v16, v13) = v17) | ( ~ (v17 = 0) & member(v16, v10) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (apply(v7, v16, v13) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v12, v16) = v17) | ( ~ (v17 = 0) & member(v16, v10) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (member(v16, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v12, v16) = v17) | ( ~ (v17 = 0) & apply(v7, v16, v13) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v9, v13, v16) = 0) | ~ (apply(v7, v13, v14) = v15) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v16, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v16, v14) = 0) | ~ (apply(v7, v13, v14) = v15) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v13, v16) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v7, v13, v14) = v15) | ~ (member(v16, v11) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v13, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v16, v14) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v8 = v7 | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v8) | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v8, v12, v15) = 0 & apply(v7, v15, v13) = 0 & member(v15, v10) = 0) | ( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v7, v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v9, v13, v15) = 0 & apply(v8, v15, v14) = 0 & member(v15, v11) = 0) | ( ~ (v15 = 0) & member(v14, v12) = v15) | ( ~ (v15 = 0) & member(v13, v10) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v7, v11, v12) = 0) | ? [v14] : (( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v12, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v11, v12) = v14) | ( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (member(v13, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & apply(v7, v11, v12) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (member(v15, v12) = 0 & member(v14, v10) = 0 & ((v20 = 0 & v19 = 0 & v18 = 0 & apply(v9, v14, v17) = 0 & apply(v8, v17, v15) = 0 & member(v17, v11) = 0) | (v16 = 0 & apply(v7, v14, v15) = 0)) & (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ! [v21] : ( ~ (apply(v9, v14, v21) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v8, v21, v15) = v22) | ( ~ (v22 = 0) & member(v21, v11) = v22))) & ! [v21] : ( ~ (apply(v8, v21, v15) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v9, v14, v21) = v22) | ( ~ (v22 = 0) & member(v21, v11) = v22))) & ! [v21] : ( ~ (member(v21, v11) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v9, v14, v21) = v22) | ( ~ (v22 = 0) & apply(v8, v21, v15) = v22))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image3(v7, v8, v9) = v11) | ~ (apply(v7, v10, v13) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v13, v8) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v10, v13) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image3(v7, v8, v9) = v11) | ~ (apply(v7, v13, v10) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image3(v7, v8, v9) = v11) | ~ (member(v13, v8) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v13, v10) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (isomorphism(v13, v12, v11, v10, v9) = v8) | ~ (isomorphism(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (decreasing(v13, v12, v11, v10, v9) = v8) | ~ (decreasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (increasing(v13, v12, v11, v10, v9) = v8) | ~ (increasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (compose_function(v13, v12, v11, v10, v9) = v8) | ~ (compose_function(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_function(v7, v8, v9) = v12) | ~ (apply(v12, v11, v10) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v11, v9) = v14) | ( ~ (v14 = 0) & member(v10, v8) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v7, v10, v11) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v7, v10, v11) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v7, v12, v11) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v7, v12, v11) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) | ~ (apply(v7, v12, v11) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v8, v11, v12) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v8, v11, v12) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v7, v10, v11) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v11) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, 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))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(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(v7, v10, v11) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0 & ((v24 = 0 & apply(v11, v14, v16) = 0) | (v23 = 0 & apply(v9, v13, v15) = 0)) & (( ~ (v24 = 0) & apply(v11, v14, v16) = v24) | ( ~ (v23 = 0) & apply(v9, v13, v15) = v23))) | ( ~ (v13 = 0) & one_to_one(v7, v8, v10) = v13) | ( ~ (v13 = 0) & maps(v7, v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v16, v14) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v14, v16) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (apply(v7, v10, v12) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v8) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v11, v12) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v11, v12) = v13) | ( ~ (v13 = 0) & apply(v7, v10, v12) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image2(v7, v8) = v10) | ~ (apply(v7, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image2(v7, v8) = v10) | ~ (member(v12, v8) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v9, v12) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image2(v7, v8) = v10) | ~ (apply(v7, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image2(v7, v8) = v10) | ~ (member(v12, v8) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v12, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (inverse_predicate(v12, v11, v10, v9) = v8) | ~ (inverse_predicate(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (equal_maps(v12, v11, v10, v9) = v8) | ~ (equal_maps(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (inverse_predicate(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (member(v13, v10) = 0 & member(v12, v9) = 0 & ((v15 = 0 & apply(v7, v13, v12) = 0) | (v14 = 0 & apply(v8, v12, v13) = 0)) & (( ~ (v15 = 0) & apply(v7, v13, v12) = v15) | ( ~ (v14 = 0) & apply(v8, v12, v13) = v14)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equal_maps(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v7, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ((v12 = 0 & member(v7, v8) = 0) | ( ~ (v12 = 0) & member(v7, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v7, v9) = v12) | ( ~ (v12 = 0) & member(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v11, v8) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_image3(v11, v10, v9) = v8) | ~ (inverse_image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (image3(v11, v10, v9) = v8) | ~ (image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_function(v11, v10, v9) = v8) | ~ (inverse_function(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (one_to_one(v11, v10, v9) = v8) | ~ (one_to_one(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (surjective(v11, v10, v9) = v8) | ~ (surjective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (injective(v11, v10, v9) = v8) | ~ (injective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (maps(v11, v10, v9) = v8) | ~ (maps(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (apply(v11, v10, v9) = v8) | ~ (apply(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | (one_to_one(v7, v8, v10) = 0 & maps(v7, v8, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v10, v12) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v12, v10) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (one_to_one(v7, v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & surjective(v7, v8, v9) = v11) | ( ~ (v11 = 0) & injective(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (surjective(v7, v8, v9) = v10) | ? [v11] : (member(v11, v9) = 0 & ! [v12] : ( ~ (apply(v7, v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v12] : ( ~ (member(v12, v8) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v12, v11) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (injective(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v12 = v11) & apply(v7, v12, v13) = 0 & apply(v7, v11, v13) = 0 & member(v13, v9) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (identity(v7, v8) = 0) | ~ (apply(v7, v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (maps(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v7, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0) | (v12 = 0 & member(v11, v8) = 0 & ! [v19] : ( ~ (apply(v7, v11, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & member(v19, v9) = v20)) & ! [v19] : ( ~ (member(v19, v9) = 0) | ? [v20] : ( ~ (v20 = 0) & apply(v7, v11, v19) = v20))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (member(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (inverse_image2(v10, v9) = v8) | ~ (inverse_image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (image2(v10, v9) = v8) | ~ (image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (identity(v10, v9) = v8) | ~ (identity(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v9, v11) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v11, v9) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & injective(v7, v8, v9) = 0) | ( ~ (v11 = 0) & one_to_one(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = 0) | ~ (member(v10, v9) = 0) | ? [v11] : (apply(v7, v11, v10) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (injective(v7, v8, v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & surjective(v7, v8, v9) = 0) | ( ~ (v11 = 0) & one_to_one(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (maps(v7, v8, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v11] : (apply(v7, v10, v11) = 0 & member(v11, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (product(v8) = v9) | ~ (member(v10, v8) = 0) | ~ (member(v7, v9) = 0) | member(v7, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ((v11 = 0 & member(v7, v9) = 0) | (v11 = 0 & member(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & apply(v7, v10, v10) = v11 & member(v10, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & subset(v8, v7) = v10) | ( ~ (v10 = 0) & subset(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & power_set(v8) = v10 & member(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (one_to_one(v7, v8, v9) = 0) | (surjective(v7, v8, v9) = 0 & injective(v7, v8, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v7, v8, v9) = 0) | ? [v10] : ((v10 = 0 & one_to_one(v7, v8, v9) = 0) | ( ~ (v10 = 0) & injective(v7, v8, v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (injective(v7, v8, v9) = 0) | ? [v10] : ((v10 = 0 & one_to_one(v7, v8, v9) = 0) | ( ~ (v10 = 0) & surjective(v7, v8, v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (identity(v7, v8) = 0) | ~ (member(v9, v8) = 0) | apply(v7, v9, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v7, v8) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v8, v7) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v8, v7) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (power_set(v8) = v9 & member(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v8, v7) = v9))) & ! [v7] : ~ (member(v7, empty_set) = 0) & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : compose_predicate(v12, v11, v10, v9, v8, v7) = v13 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : isomorphism(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : decreasing(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : increasing(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : compose_function(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : inverse_predicate(v10, v9, v8, v7) = v11 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : equal_maps(v10, v9, v8, v7) = v11 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_image3(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : image3(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_function(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : one_to_one(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : surjective(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : injective(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : maps(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : apply(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : inverse_image2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : image2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : identity(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : difference(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : union(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_set(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : member(v8, v7) = v9 & ? [v7] : ? [v8] : product(v7) = v8 & ? [v7] : ? [v8] : sum(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : ? [v8] : power_set(v7) = v8)
% 13.77/3.77 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 13.77/3.77 | (1) ~ (all_0_0_0 = 0) & compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & maps(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0 & maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (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
% 14.20/3.82 |
% 14.20/3.82 | Applying alpha-rule on (1) yields:
% 14.20/3.82 | (2) ? [v0] : ? [v1] : singleton(v0) = v1
% 14.20/3.82 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 14.20/3.82 | (4) ! [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)))
% 14.20/3.82 | (5) ! [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)))
% 14.20/3.82 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 14.20/3.82 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 14.20/3.82 | (8) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 14.20/3.82 | (9) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 14.20/3.82 | (10) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 14.20/3.82 | (11) ! [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)))
% 14.20/3.82 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 14.20/3.82 | (13) ! [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)))))
% 14.20/3.82 | (14) ! [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)))
% 14.20/3.82 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 14.20/3.82 | (16) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 14.20/3.82 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 14.20/3.82 | (18) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 14.20/3.82 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 14.20/3.82 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 14.20/3.82 | (21) ! [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))
% 14.20/3.82 | (22) maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 14.20/3.82 | (23) ! [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)))
% 14.20/3.82 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 14.20/3.82 | (25) ! [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)))
% 14.20/3.82 | (26) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 14.20/3.82 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 14.20/3.82 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 14.20/3.82 | (29) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 14.20/3.82 | (30) ! [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)))))
% 14.20/3.82 | (31) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 14.20/3.82 | (32) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 14.20/3.82 | (33) ! [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)))
% 14.20/3.82 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 14.20/3.82 | (35) ! [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)))
% 14.20/3.82 | (36) ! [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)))))
% 14.20/3.83 | (37) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 14.20/3.83 | (38) ! [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)))
% 14.20/3.83 | (39) ! [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)))
% 14.20/3.83 | (40) ! [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))
% 14.20/3.83 | (41) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 14.20/3.83 | (42) ! [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)))))
% 14.20/3.83 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 14.20/3.83 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 14.20/3.83 | (45) ! [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))
% 14.20/3.83 | (46) ! [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))))
% 14.20/3.83 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 14.20/3.83 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 14.20/3.83 | (49) ! [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))
% 14.20/3.83 | (50) ! [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)))
% 14.20/3.83 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 14.20/3.83 | (52) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 14.20/3.83 | (53) ! [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)))
% 14.20/3.83 | (54) maps(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0
% 14.20/3.83 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 14.20/3.83 | (56) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 14.20/3.83 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 14.20/3.83 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 14.20/3.83 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 14.20/3.83 | (60) ! [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)))
% 14.20/3.83 | (61) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 14.20/3.83 | (62) ! [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))
% 14.20/3.83 | (63) ! [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)))
% 14.20/3.83 | (64) ! [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)))
% 14.20/3.83 | (65) ! [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)))
% 14.20/3.83 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 14.20/3.83 | (67) ! [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)))
% 14.20/3.83 | (68) ! [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))
% 14.20/3.84 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 14.20/3.84 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 14.20/3.84 | (71) ~ (all_0_0_0 = 0)
% 14.20/3.84 | (72) ? [v0] : ? [v1] : sum(v0) = v1
% 14.20/3.84 | (73) ! [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)))
% 14.20/3.84 | (74) ? [v0] : ? [v1] : power_set(v0) = v1
% 14.20/3.84 | (75) ! [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)))
% 14.20/3.84 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 14.20/3.84 | (77) ! [v0] : ~ (member(v0, empty_set) = 0)
% 14.20/3.84 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 14.20/3.84 | (79) ! [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)))
% 14.20/3.84 | (80) ! [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)))
% 14.20/3.84 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 14.20/3.84 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 14.20/3.84 | (83) ! [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))
% 14.20/3.84 | (84) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 14.20/3.84 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 14.20/3.84 | (86) ! [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)))
% 14.20/3.84 | (87) ! [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)))
% 14.20/3.84 | (88) ! [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)))))
% 14.20/3.84 | (89) ! [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)))
% 14.20/3.84 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 14.20/3.84 | (91) ! [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)))
% 14.20/3.84 | (92) ! [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))
% 14.20/3.84 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 14.20/3.84 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 14.20/3.84 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 14.20/3.84 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 14.20/3.84 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 14.20/3.84 | (98) ! [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)))
% 14.20/3.84 | (99) ! [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)))
% 14.20/3.84 | (100) ! [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)))
% 14.20/3.84 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 14.20/3.84 | (102) ! [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)))
% 14.20/3.84 | (103) ! [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)))))
% 14.20/3.85 | (104) maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 14.20/3.85 | (105) ! [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)))))
% 14.20/3.85 | (106) ! [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)))
% 14.20/3.85 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 14.20/3.85 | (108) ! [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)))
% 14.20/3.85 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 14.20/3.85 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 14.20/3.85 | (111) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 14.20/3.85 | (112) ! [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)))))
% 14.20/3.85 | (113) ! [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)))
% 14.20/3.85 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 14.20/3.85 | (115) ! [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)))))
% 14.20/3.85 | (116) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 14.20/3.85 | (117) compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 14.20/3.85 | (118) ! [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)))
% 14.20/3.85 | (119) ! [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)))))
% 14.20/3.85 | (120) ! [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)))))
% 14.20/3.85 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 14.20/3.85 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 14.20/3.85 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 14.20/3.85 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 14.20/3.85 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 14.20/3.85 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 14.20/3.85 | (127) ! [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)))
% 14.20/3.85 | (128) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 14.20/3.86 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 14.20/3.86 | (130) ! [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))
% 14.20/3.86 | (131) ! [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))
% 14.20/3.86 | (132) ! [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)))
% 14.20/3.86 | (133) ! [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))
% 14.20/3.86 | (134) ! [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)))))
% 14.20/3.86 | (135) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 14.20/3.86 | (136) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 14.20/3.86 | (137) ! [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)))
% 14.20/3.86 | (138) ! [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)))
% 14.20/3.86 | (139) ! [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)))
% 14.20/3.86 | (140) ! [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)))))
% 14.20/3.86 | (141) ! [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))
% 14.20/3.86 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 14.20/3.86 | (143) ! [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)))))))
% 14.20/3.86 | (144) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 14.20/3.86 | (145) ! [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)))
% 14.20/3.86 | (146) ! [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)))
% 14.20/3.86 | (147) ! [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)))))
% 14.20/3.86 | (148) ! [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)))
% 14.20/3.86 | (149) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 14.20/3.86 | (150) ! [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))
% 14.20/3.86 | (151) ! [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)))
% 14.20/3.86 | (152) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 14.20/3.86 | (153) ! [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)))
% 14.20/3.87 | (154) ! [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)))
% 14.20/3.87 | (155) ! [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)))
% 14.20/3.87 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 14.20/3.87 | (157) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 14.20/3.87 | (158) ! [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)))
% 14.20/3.87 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 14.20/3.87 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 14.20/3.87 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 14.20/3.87 | (162) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 14.20/3.87 | (163) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 14.20/3.87 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 14.20/3.87 | (165) ! [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)))
% 14.20/3.87 | (166) ! [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)))
% 14.20/3.87 | (167) ! [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)))
% 14.20/3.87 | (168) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 14.20/3.87 | (169) ! [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)))
% 14.20/3.87 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 14.20/3.87 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 14.20/3.87 | (172) ! [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)))
% 14.20/3.87 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 14.20/3.87 | (174) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 14.20/3.87 | (175) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 14.20/3.87 | (176) ! [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))
% 14.20/3.87 | (177) ! [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)))
% 14.20/3.87 | (178) ! [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))
% 14.20/3.87 | (179) ! [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)))
% 14.20/3.87 | (180) ? [v0] : ? [v1] : product(v0) = v1
% 14.20/3.87 | (181) ! [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))
% 14.20/3.87 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 14.20/3.87 | (183) ! [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)))
% 14.20/3.87 | (184) ! [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)))
% 14.20/3.87 | (185) ! [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))))
% 14.20/3.87 | (186) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 14.20/3.87 | (187) ! [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)))
% 14.20/3.88 |
% 14.20/3.88 | Instantiating formula (36) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms maps(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 14.20/3.88 | (188) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_4_4) = 0) | (v1 = 0 & member(v0, all_0_4_4) = 0 & ! [v8] : ( ~ (apply(all_0_1_1, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_2_2) = v9)) & ! [v8] : ( ~ (member(v8, all_0_2_2) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_1_1, v0, v8) = v9))))
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (188), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (189) all_0_0_0 = 0
% 14.20/3.88 |
% 14.20/3.88 | Equations (189) can reduce 71 to:
% 14.20/3.88 | (190) $false
% 14.20/3.88 |
% 14.20/3.88 |-The branch is then unsatisfiable
% 14.20/3.88 |-Branch two:
% 14.20/3.88 | (71) ~ (all_0_0_0 = 0)
% 14.20/3.88 | (192) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_4_4) = 0) | (v1 = 0 & member(v0, all_0_4_4) = 0 & ! [v8] : ( ~ (apply(all_0_1_1, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_2_2) = v9)) & ! [v8] : ( ~ (member(v8, all_0_2_2) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_1_1, v0, v8) = v9))))
% 14.20/3.88 |
% 14.20/3.88 | Instantiating (192) with all_68_0_118, all_68_1_119, all_68_2_120, all_68_3_121, all_68_4_122, all_68_5_123, all_68_6_124, all_68_7_125 yields:
% 14.20/3.88 | (193) (all_68_0_118 = 0 & all_68_1_119 = 0 & all_68_2_120 = 0 & all_68_3_121 = 0 & all_68_4_122 = 0 & ~ (all_68_5_123 = all_68_6_124) & apply(all_0_1_1, all_68_7_125, all_68_5_123) = 0 & apply(all_0_1_1, all_68_7_125, all_68_6_124) = 0 & member(all_68_5_123, all_0_2_2) = 0 & member(all_68_6_124, all_0_2_2) = 0 & member(all_68_7_125, all_0_4_4) = 0) | (all_68_6_124 = 0 & member(all_68_7_125, all_0_4_4) = 0 & ! [v0] : ( ~ (apply(all_0_1_1, all_68_7_125, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1)) & ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_68_7_125, v0) = v1)))
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (193), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (194) all_68_0_118 = 0 & all_68_1_119 = 0 & all_68_2_120 = 0 & all_68_3_121 = 0 & all_68_4_122 = 0 & ~ (all_68_5_123 = all_68_6_124) & apply(all_0_1_1, all_68_7_125, all_68_5_123) = 0 & apply(all_0_1_1, all_68_7_125, all_68_6_124) = 0 & member(all_68_5_123, all_0_2_2) = 0 & member(all_68_6_124, all_0_2_2) = 0 & member(all_68_7_125, all_0_4_4) = 0
% 14.20/3.88 |
% 14.20/3.88 | Applying alpha-rule on (194) yields:
% 14.20/3.88 | (195) all_68_4_122 = 0
% 14.20/3.88 | (196) apply(all_0_1_1, all_68_7_125, all_68_6_124) = 0
% 14.20/3.88 | (197) all_68_3_121 = 0
% 14.20/3.88 | (198) member(all_68_5_123, all_0_2_2) = 0
% 14.20/3.88 | (199) all_68_1_119 = 0
% 14.20/3.88 | (200) all_68_2_120 = 0
% 14.20/3.88 | (201) apply(all_0_1_1, all_68_7_125, all_68_5_123) = 0
% 14.20/3.88 | (202) member(all_68_7_125, all_0_4_4) = 0
% 14.20/3.88 | (203) member(all_68_6_124, all_0_2_2) = 0
% 14.20/3.88 | (204) ~ (all_68_5_123 = all_68_6_124)
% 14.20/3.88 | (205) all_68_0_118 = 0
% 14.20/3.88 |
% 14.20/3.88 | Instantiating formula (73) with all_0_1_1, all_68_5_123, all_68_7_125, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_68_7_125, all_68_5_123) = 0, yields:
% 14.20/3.88 | (206) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_68_5_123) = 0 & apply(all_0_6_6, all_68_7_125, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_68_5_123, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.88 |
% 14.20/3.88 | Instantiating formula (73) with all_0_1_1, all_68_6_124, all_68_7_125, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_68_7_125, all_68_6_124) = 0, yields:
% 14.20/3.88 | (207) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_68_6_124) = 0 & apply(all_0_6_6, all_68_7_125, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_68_6_124, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.88 |
% 14.20/3.88 | Instantiating formula (124) with all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.20/3.88 | (208) ? [v0] : (apply(all_0_6_6, all_68_7_125, v0) = 0 & member(v0, all_0_3_3) = 0)
% 14.20/3.88 |
% 14.20/3.88 | Instantiating (208) with all_81_0_126 yields:
% 14.20/3.88 | (209) apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0 & member(all_81_0_126, all_0_3_3) = 0
% 14.20/3.88 |
% 14.20/3.88 | Applying alpha-rule on (209) yields:
% 14.20/3.88 | (210) apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0
% 14.20/3.88 | (211) member(all_81_0_126, all_0_3_3) = 0
% 14.20/3.88 |
% 14.20/3.88 | Instantiating (207) with all_83_0_127, all_83_1_128, all_83_2_129, all_83_3_130 yields:
% 14.20/3.88 | (212) (all_83_0_127 = 0 & all_83_1_128 = 0 & all_83_2_129 = 0 & apply(all_0_5_5, all_83_3_130, all_68_6_124) = 0 & apply(all_0_6_6, all_68_7_125, all_83_3_130) = 0 & member(all_83_3_130, all_0_3_3) = 0) | ( ~ (all_83_3_130 = 0) & member(all_68_6_124, all_0_2_2) = all_83_3_130) | ( ~ (all_83_3_130 = 0) & member(all_68_7_125, all_0_4_4) = all_83_3_130)
% 14.20/3.88 |
% 14.20/3.88 | Instantiating (206) with all_84_0_131, all_84_1_132, all_84_2_133, all_84_3_134 yields:
% 14.20/3.88 | (213) (all_84_0_131 = 0 & all_84_1_132 = 0 & all_84_2_133 = 0 & apply(all_0_5_5, all_84_3_134, all_68_5_123) = 0 & apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0 & member(all_84_3_134, all_0_3_3) = 0) | ( ~ (all_84_3_134 = 0) & member(all_68_5_123, all_0_2_2) = all_84_3_134) | ( ~ (all_84_3_134 = 0) & member(all_68_7_125, all_0_4_4) = all_84_3_134)
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (212), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (214) (all_83_0_127 = 0 & all_83_1_128 = 0 & all_83_2_129 = 0 & apply(all_0_5_5, all_83_3_130, all_68_6_124) = 0 & apply(all_0_6_6, all_68_7_125, all_83_3_130) = 0 & member(all_83_3_130, all_0_3_3) = 0) | ( ~ (all_83_3_130 = 0) & member(all_68_6_124, all_0_2_2) = all_83_3_130)
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (214), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (215) all_83_0_127 = 0 & all_83_1_128 = 0 & all_83_2_129 = 0 & apply(all_0_5_5, all_83_3_130, all_68_6_124) = 0 & apply(all_0_6_6, all_68_7_125, all_83_3_130) = 0 & member(all_83_3_130, all_0_3_3) = 0
% 14.20/3.88 |
% 14.20/3.88 | Applying alpha-rule on (215) yields:
% 14.20/3.88 | (216) all_83_2_129 = 0
% 14.20/3.88 | (217) apply(all_0_5_5, all_83_3_130, all_68_6_124) = 0
% 14.20/3.88 | (218) all_83_1_128 = 0
% 14.20/3.88 | (219) all_83_0_127 = 0
% 14.20/3.88 | (220) apply(all_0_6_6, all_68_7_125, all_83_3_130) = 0
% 14.20/3.88 | (221) member(all_83_3_130, all_0_3_3) = 0
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (213), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (222) (all_84_0_131 = 0 & all_84_1_132 = 0 & all_84_2_133 = 0 & apply(all_0_5_5, all_84_3_134, all_68_5_123) = 0 & apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0 & member(all_84_3_134, all_0_3_3) = 0) | ( ~ (all_84_3_134 = 0) & member(all_68_5_123, all_0_2_2) = all_84_3_134)
% 14.20/3.88 |
% 14.20/3.88 +-Applying beta-rule and splitting (222), into two cases.
% 14.20/3.88 |-Branch one:
% 14.20/3.88 | (223) all_84_0_131 = 0 & all_84_1_132 = 0 & all_84_2_133 = 0 & apply(all_0_5_5, all_84_3_134, all_68_5_123) = 0 & apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0 & member(all_84_3_134, all_0_3_3) = 0
% 14.20/3.89 |
% 14.20/3.89 | Applying alpha-rule on (223) yields:
% 14.20/3.89 | (224) apply(all_0_5_5, all_84_3_134, all_68_5_123) = 0
% 14.20/3.89 | (225) apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0
% 14.20/3.89 | (226) all_84_1_132 = 0
% 14.20/3.89 | (227) all_84_2_133 = 0
% 14.20/3.89 | (228) all_84_0_131 = 0
% 14.20/3.89 | (229) member(all_84_3_134, all_0_3_3) = 0
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (187) with all_68_5_123, all_68_6_124, all_84_3_134, 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_84_3_134, all_0_3_3) = 0, member(all_68_5_123, all_0_2_2) = 0, member(all_68_6_124, all_0_2_2) = 0, yields:
% 14.20/3.89 | (230) all_68_5_123 = all_68_6_124 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_84_3_134, all_68_5_123) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_84_3_134, all_68_6_124) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (67) with all_84_3_134, all_83_3_130, all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0, member(all_83_3_130, all_0_3_3) = 0, yields:
% 14.20/3.89 | (231) all_84_3_134 = all_83_3_130 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = v0) | ( ~ (v0 = 0) & member(all_84_3_134, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (67) with all_81_0_126, all_83_3_130, all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0, member(all_83_3_130, all_0_3_3) = 0, yields:
% 14.20/3.89 | (232) all_83_3_130 = all_81_0_126 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = v0) | ( ~ (v0 = 0) & member(all_81_0_126, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (67) with all_84_3_134, all_81_0_126, all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_68_7_125, all_84_3_134) = 0, member(all_81_0_126, all_0_3_3) = 0, yields:
% 14.20/3.89 | (233) all_84_3_134 = all_81_0_126 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = v0) | ( ~ (v0 = 0) & member(all_84_3_134, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (187) with all_81_0_126, all_84_3_134, all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_84_3_134, all_0_3_3) = 0, member(all_81_0_126, all_0_3_3) = 0, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.20/3.89 | (234) all_84_3_134 = all_81_0_126 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_84_3_134) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = v0))
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (232), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (235) all_83_3_130 = all_81_0_126
% 14.20/3.89 |
% 14.20/3.89 | From (235) and (217) follows:
% 14.20/3.89 | (236) apply(all_0_5_5, all_81_0_126, all_68_6_124) = 0
% 14.20/3.89 |
% 14.20/3.89 | From (235) and (220) follows:
% 14.20/3.89 | (210) apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (231), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (238) all_84_3_134 = all_83_3_130
% 14.20/3.89 |
% 14.20/3.89 | Combining equations (235,238) yields a new equation:
% 14.20/3.89 | (239) all_84_3_134 = all_81_0_126
% 14.20/3.89 |
% 14.20/3.89 | From (239) and (224) follows:
% 14.20/3.89 | (240) apply(all_0_5_5, all_81_0_126, all_68_5_123) = 0
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (230), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (241) all_68_5_123 = all_68_6_124
% 14.20/3.89 |
% 14.20/3.89 | Equations (241) can reduce 204 to:
% 14.20/3.89 | (190) $false
% 14.20/3.89 |
% 14.20/3.89 |-The branch is then unsatisfiable
% 14.20/3.89 |-Branch two:
% 14.20/3.89 | (204) ~ (all_68_5_123 = all_68_6_124)
% 14.20/3.89 | (244) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_84_3_134, all_68_5_123) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_84_3_134, all_68_6_124) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating (244) with all_115_0_138 yields:
% 14.20/3.89 | (245) ( ~ (all_115_0_138 = 0) & apply(all_0_5_5, all_84_3_134, all_68_5_123) = all_115_0_138) | ( ~ (all_115_0_138 = 0) & apply(all_0_5_5, all_84_3_134, all_68_6_124) = all_115_0_138)
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (245), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (246) ~ (all_115_0_138 = 0) & apply(all_0_5_5, all_84_3_134, all_68_5_123) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | Applying alpha-rule on (246) yields:
% 14.20/3.89 | (247) ~ (all_115_0_138 = 0)
% 14.20/3.89 | (248) apply(all_0_5_5, all_84_3_134, all_68_5_123) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | From (239) and (248) follows:
% 14.20/3.89 | (249) apply(all_0_5_5, all_81_0_126, all_68_5_123) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (161) with all_0_5_5, all_81_0_126, all_68_5_123, 0, all_115_0_138 and discharging atoms apply(all_0_5_5, all_81_0_126, all_68_5_123) = all_115_0_138, apply(all_0_5_5, all_81_0_126, all_68_5_123) = 0, yields:
% 14.20/3.89 | (250) all_115_0_138 = 0
% 14.20/3.89 |
% 14.20/3.89 | Equations (250) can reduce 247 to:
% 14.20/3.89 | (190) $false
% 14.20/3.89 |
% 14.20/3.89 |-The branch is then unsatisfiable
% 14.20/3.89 |-Branch two:
% 14.20/3.89 | (252) ~ (all_115_0_138 = 0) & apply(all_0_5_5, all_84_3_134, all_68_6_124) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | Applying alpha-rule on (252) yields:
% 14.20/3.89 | (247) ~ (all_115_0_138 = 0)
% 14.20/3.89 | (254) apply(all_0_5_5, all_84_3_134, all_68_6_124) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | From (239) and (254) follows:
% 14.20/3.89 | (255) apply(all_0_5_5, all_81_0_126, all_68_6_124) = all_115_0_138
% 14.20/3.89 |
% 14.20/3.89 | Instantiating formula (161) with all_0_5_5, all_81_0_126, all_68_6_124, 0, all_115_0_138 and discharging atoms apply(all_0_5_5, all_81_0_126, all_68_6_124) = all_115_0_138, apply(all_0_5_5, all_81_0_126, all_68_6_124) = 0, yields:
% 14.20/3.89 | (250) all_115_0_138 = 0
% 14.20/3.89 |
% 14.20/3.89 | Equations (250) can reduce 247 to:
% 14.20/3.89 | (190) $false
% 14.20/3.89 |
% 14.20/3.89 |-The branch is then unsatisfiable
% 14.20/3.89 |-Branch two:
% 14.20/3.89 | (258) ~ (all_84_3_134 = all_83_3_130)
% 14.20/3.89 | (259) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = v0) | ( ~ (v0 = 0) & member(all_84_3_134, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating (259) with all_112_0_144 yields:
% 14.20/3.89 | (260) ( ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144) | ( ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144) | ( ~ (all_112_0_144 = 0) & member(all_68_7_125, all_0_4_4) = all_112_0_144)
% 14.20/3.89 |
% 14.20/3.89 | Equations (235) can reduce 258 to:
% 14.20/3.89 | (261) ~ (all_84_3_134 = all_81_0_126)
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (234), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (239) all_84_3_134 = all_81_0_126
% 14.20/3.89 |
% 14.20/3.89 | Equations (239) can reduce 261 to:
% 14.20/3.89 | (190) $false
% 14.20/3.89 |
% 14.20/3.89 |-The branch is then unsatisfiable
% 14.20/3.89 |-Branch two:
% 14.20/3.89 | (261) ~ (all_84_3_134 = all_81_0_126)
% 14.20/3.89 | (265) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_84_3_134) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = v0))
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (233), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (239) all_84_3_134 = all_81_0_126
% 14.20/3.89 |
% 14.20/3.89 | Equations (239) can reduce 261 to:
% 14.20/3.89 | (190) $false
% 14.20/3.89 |
% 14.20/3.89 |-The branch is then unsatisfiable
% 14.20/3.89 |-Branch two:
% 14.20/3.89 | (261) ~ (all_84_3_134 = all_81_0_126)
% 14.20/3.89 | (269) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = v0) | ( ~ (v0 = 0) & member(all_84_3_134, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.20/3.89 |
% 14.20/3.89 | Instantiating (269) with all_142_0_153 yields:
% 14.20/3.89 | (270) ( ~ (all_142_0_153 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153) | ( ~ (all_142_0_153 = 0) & member(all_84_3_134, all_0_3_3) = all_142_0_153) | ( ~ (all_142_0_153 = 0) & member(all_68_7_125, all_0_4_4) = all_142_0_153)
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (270), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (271) ( ~ (all_142_0_153 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153) | ( ~ (all_142_0_153 = 0) & member(all_84_3_134, all_0_3_3) = all_142_0_153)
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (271), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (272) ~ (all_142_0_153 = 0) & apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153
% 14.20/3.89 |
% 14.20/3.89 | Applying alpha-rule on (272) yields:
% 14.20/3.89 | (273) ~ (all_142_0_153 = 0)
% 14.20/3.89 | (274) apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (260), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (275) ( ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144) | ( ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144)
% 14.20/3.89 |
% 14.20/3.89 +-Applying beta-rule and splitting (275), into two cases.
% 14.20/3.89 |-Branch one:
% 14.20/3.89 | (276) ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.89 |
% 14.20/3.89 | Applying alpha-rule on (276) yields:
% 14.20/3.89 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.89 | (278) apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | From (235) and (278) follows:
% 14.20/3.90 | (279) apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_81_0_126, all_142_0_153, 0 and discharging atoms apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153, apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0, yields:
% 14.20/3.90 | (280) all_142_0_153 = 0
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_81_0_126, all_112_0_144, all_142_0_153 and discharging atoms apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_142_0_153, apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144, yields:
% 14.20/3.90 | (281) all_142_0_153 = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Combining equations (281,280) yields a new equation:
% 14.20/3.90 | (282) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Simplifying 282 yields:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (285) ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (285) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (287) member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (123) with all_84_3_134, all_0_3_3, all_112_0_144, 0 and discharging atoms member(all_84_3_134, all_0_3_3) = all_112_0_144, member(all_84_3_134, all_0_3_3) = 0, yields:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (290) ~ (all_112_0_144 = 0) & member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (290) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (292) member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_112_0_144, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_112_0_144, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (295) ~ (all_142_0_153 = 0) & member(all_84_3_134, all_0_3_3) = all_142_0_153
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (295) yields:
% 14.20/3.90 | (273) ~ (all_142_0_153 = 0)
% 14.20/3.90 | (297) member(all_84_3_134, all_0_3_3) = all_142_0_153
% 14.20/3.90 |
% 14.20/3.90 +-Applying beta-rule and splitting (260), into two cases.
% 14.20/3.90 |-Branch one:
% 14.20/3.90 | (275) ( ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144) | ( ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144)
% 14.20/3.90 |
% 14.20/3.90 +-Applying beta-rule and splitting (275), into two cases.
% 14.20/3.90 |-Branch one:
% 14.20/3.90 | (276) ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (276) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (278) apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | From (235) and (278) follows:
% 14.20/3.90 | (279) apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_81_0_126, all_112_0_144, 0 and discharging atoms apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144, apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0, yields:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (285) ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (285) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (287) member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (123) with all_84_3_134, all_0_3_3, all_142_0_153, 0 and discharging atoms member(all_84_3_134, all_0_3_3) = all_142_0_153, member(all_84_3_134, all_0_3_3) = 0, yields:
% 14.20/3.90 | (280) all_142_0_153 = 0
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (123) with all_84_3_134, all_0_3_3, all_112_0_144, all_142_0_153 and discharging atoms member(all_84_3_134, all_0_3_3) = all_142_0_153, member(all_84_3_134, all_0_3_3) = all_112_0_144, yields:
% 14.20/3.90 | (281) all_142_0_153 = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Combining equations (280,281) yields a new equation:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (290) ~ (all_112_0_144 = 0) & member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (290) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (292) member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_112_0_144, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_112_0_144, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.20/3.90 | (283) all_112_0_144 = 0
% 14.20/3.90 |
% 14.20/3.90 | Equations (283) can reduce 277 to:
% 14.20/3.90 | (190) $false
% 14.20/3.90 |
% 14.20/3.90 |-The branch is then unsatisfiable
% 14.20/3.90 |-Branch two:
% 14.20/3.90 | (317) ~ (all_142_0_153 = 0) & member(all_68_7_125, all_0_4_4) = all_142_0_153
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (317) yields:
% 14.20/3.90 | (273) ~ (all_142_0_153 = 0)
% 14.20/3.90 | (319) member(all_68_7_125, all_0_4_4) = all_142_0_153
% 14.20/3.90 |
% 14.20/3.90 +-Applying beta-rule and splitting (260), into two cases.
% 14.20/3.90 |-Branch one:
% 14.20/3.90 | (275) ( ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144) | ( ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144)
% 14.20/3.90 |
% 14.20/3.90 +-Applying beta-rule and splitting (275), into two cases.
% 14.20/3.90 |-Branch one:
% 14.20/3.90 | (276) ~ (all_112_0_144 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Applying alpha-rule on (276) yields:
% 14.20/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.20/3.90 | (278) apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | From (235) and (278) follows:
% 14.20/3.90 | (279) apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144
% 14.20/3.90 |
% 14.20/3.90 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_81_0_126, all_112_0_144, 0 and discharging atoms apply(all_0_6_6, all_68_7_125, all_81_0_126) = all_112_0_144, apply(all_0_6_6, all_68_7_125, all_81_0_126) = 0, yields:
% 14.68/3.90 | (283) all_112_0_144 = 0
% 14.68/3.90 |
% 14.68/3.90 | Equations (283) can reduce 277 to:
% 14.68/3.90 | (190) $false
% 14.68/3.90 |
% 14.68/3.90 |-The branch is then unsatisfiable
% 14.68/3.90 |-Branch two:
% 14.68/3.90 | (285) ~ (all_112_0_144 = 0) & member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.68/3.90 |
% 14.68/3.90 | Applying alpha-rule on (285) yields:
% 14.68/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.68/3.90 | (287) member(all_84_3_134, all_0_3_3) = all_112_0_144
% 14.68/3.90 |
% 14.68/3.90 | Instantiating formula (123) with all_84_3_134, all_0_3_3, all_112_0_144, 0 and discharging atoms member(all_84_3_134, all_0_3_3) = all_112_0_144, member(all_84_3_134, all_0_3_3) = 0, yields:
% 14.68/3.90 | (283) all_112_0_144 = 0
% 14.68/3.90 |
% 14.68/3.90 | Equations (283) can reduce 277 to:
% 14.68/3.90 | (190) $false
% 14.68/3.90 |
% 14.68/3.90 |-The branch is then unsatisfiable
% 14.68/3.90 |-Branch two:
% 14.68/3.90 | (290) ~ (all_112_0_144 = 0) & member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.68/3.90 |
% 14.68/3.90 | Applying alpha-rule on (290) yields:
% 14.68/3.90 | (277) ~ (all_112_0_144 = 0)
% 14.68/3.90 | (292) member(all_68_7_125, all_0_4_4) = all_112_0_144
% 14.68/3.90 |
% 14.68/3.90 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_142_0_153, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_142_0_153, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.68/3.90 | (280) all_142_0_153 = 0
% 14.68/3.90 |
% 14.68/3.90 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_112_0_144, all_142_0_153 and discharging atoms member(all_68_7_125, all_0_4_4) = all_142_0_153, member(all_68_7_125, all_0_4_4) = all_112_0_144, yields:
% 14.68/3.90 | (281) all_142_0_153 = all_112_0_144
% 14.68/3.90 |
% 14.68/3.90 | Combining equations (280,281) yields a new equation:
% 14.68/3.90 | (283) all_112_0_144 = 0
% 14.68/3.90 |
% 14.68/3.90 | Equations (283) can reduce 277 to:
% 14.68/3.90 | (190) $false
% 14.68/3.90 |
% 14.68/3.90 |-The branch is then unsatisfiable
% 14.68/3.90 |-Branch two:
% 14.68/3.90 | (339) ~ (all_83_3_130 = all_81_0_126)
% 14.68/3.90 | (340) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = v0) | ( ~ (v0 = 0) & member(all_81_0_126, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.68/3.90 |
% 14.68/3.90 | Instantiating (340) with all_108_0_162 yields:
% 14.68/3.90 | (341) ( ~ (all_108_0_162 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_108_0_162) | ( ~ (all_108_0_162 = 0) & member(all_81_0_126, all_0_3_3) = all_108_0_162) | ( ~ (all_108_0_162 = 0) & member(all_68_7_125, all_0_4_4) = all_108_0_162)
% 14.68/3.90 |
% 14.68/3.90 +-Applying beta-rule and splitting (341), into two cases.
% 14.68/3.90 |-Branch one:
% 14.68/3.90 | (342) ( ~ (all_108_0_162 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_108_0_162) | ( ~ (all_108_0_162 = 0) & member(all_81_0_126, all_0_3_3) = all_108_0_162)
% 14.68/3.90 |
% 14.68/3.90 +-Applying beta-rule and splitting (342), into two cases.
% 14.68/3.90 |-Branch one:
% 14.68/3.90 | (343) ~ (all_108_0_162 = 0) & apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_108_0_162
% 14.68/3.90 |
% 14.68/3.90 | Applying alpha-rule on (343) yields:
% 14.68/3.90 | (344) ~ (all_108_0_162 = 0)
% 14.68/3.90 | (345) apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_108_0_162
% 14.68/3.90 |
% 14.68/3.90 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_83_3_130, all_108_0_162, 0 and discharging atoms apply(all_0_6_6, all_68_7_125, all_83_3_130) = all_108_0_162, apply(all_0_6_6, all_68_7_125, all_83_3_130) = 0, yields:
% 14.68/3.90 | (346) all_108_0_162 = 0
% 14.68/3.90 |
% 14.68/3.90 | Equations (346) can reduce 344 to:
% 14.68/3.90 | (190) $false
% 14.68/3.90 |
% 14.68/3.90 |-The branch is then unsatisfiable
% 14.68/3.90 |-Branch two:
% 14.68/3.90 | (348) ~ (all_108_0_162 = 0) & member(all_81_0_126, all_0_3_3) = all_108_0_162
% 14.68/3.90 |
% 14.68/3.90 | Applying alpha-rule on (348) yields:
% 14.68/3.90 | (344) ~ (all_108_0_162 = 0)
% 14.68/3.90 | (350) member(all_81_0_126, all_0_3_3) = all_108_0_162
% 14.68/3.90 |
% 14.68/3.90 | Instantiating formula (123) with all_81_0_126, all_0_3_3, all_108_0_162, 0 and discharging atoms member(all_81_0_126, all_0_3_3) = all_108_0_162, member(all_81_0_126, all_0_3_3) = 0, yields:
% 14.68/3.90 | (346) all_108_0_162 = 0
% 14.68/3.90 |
% 14.68/3.90 | Equations (346) can reduce 344 to:
% 14.68/3.90 | (190) $false
% 14.68/3.90 |
% 14.68/3.90 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (353) ~ (all_108_0_162 = 0) & member(all_68_7_125, all_0_4_4) = all_108_0_162
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (353) yields:
% 14.68/3.91 | (344) ~ (all_108_0_162 = 0)
% 14.68/3.91 | (355) member(all_68_7_125, all_0_4_4) = all_108_0_162
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_108_0_162, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_108_0_162, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.68/3.91 | (346) all_108_0_162 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (346) can reduce 344 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (358) ~ (all_84_3_134 = 0) & member(all_68_5_123, all_0_2_2) = all_84_3_134
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (358) yields:
% 14.68/3.91 | (359) ~ (all_84_3_134 = 0)
% 14.68/3.91 | (360) member(all_68_5_123, all_0_2_2) = all_84_3_134
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (123) with all_68_5_123, all_0_2_2, all_84_3_134, 0 and discharging atoms member(all_68_5_123, all_0_2_2) = all_84_3_134, member(all_68_5_123, all_0_2_2) = 0, yields:
% 14.68/3.91 | (361) all_84_3_134 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (361) can reduce 359 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (363) ~ (all_84_3_134 = 0) & member(all_68_7_125, all_0_4_4) = all_84_3_134
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (363) yields:
% 14.68/3.91 | (359) ~ (all_84_3_134 = 0)
% 14.68/3.91 | (365) member(all_68_7_125, all_0_4_4) = all_84_3_134
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_84_3_134, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_84_3_134, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.68/3.91 | (361) all_84_3_134 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (361) can reduce 359 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (368) ~ (all_83_3_130 = 0) & member(all_68_6_124, all_0_2_2) = all_83_3_130
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (368) yields:
% 14.68/3.91 | (369) ~ (all_83_3_130 = 0)
% 14.68/3.91 | (370) member(all_68_6_124, all_0_2_2) = all_83_3_130
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (123) with all_68_6_124, all_0_2_2, all_83_3_130, 0 and discharging atoms member(all_68_6_124, all_0_2_2) = all_83_3_130, member(all_68_6_124, all_0_2_2) = 0, yields:
% 14.68/3.91 | (371) all_83_3_130 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (371) can reduce 369 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (373) ~ (all_83_3_130 = 0) & member(all_68_7_125, all_0_4_4) = all_83_3_130
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (373) yields:
% 14.68/3.91 | (369) ~ (all_83_3_130 = 0)
% 14.68/3.91 | (375) member(all_68_7_125, all_0_4_4) = all_83_3_130
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_83_3_130, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_83_3_130, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.68/3.91 | (371) all_83_3_130 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (371) can reduce 369 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (378) all_68_6_124 = 0 & member(all_68_7_125, all_0_4_4) = 0 & ! [v0] : ( ~ (apply(all_0_1_1, all_68_7_125, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1)) & ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_68_7_125, v0) = v1))
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (378) yields:
% 14.68/3.91 | (379) all_68_6_124 = 0
% 14.68/3.91 | (202) member(all_68_7_125, all_0_4_4) = 0
% 14.68/3.91 | (381) ! [v0] : ( ~ (apply(all_0_1_1, all_68_7_125, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1))
% 14.68/3.91 | (382) ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, all_68_7_125, v0) = v1))
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (124) with all_68_7_125, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.68/3.91 | (208) ? [v0] : (apply(all_0_6_6, all_68_7_125, v0) = 0 & member(v0, all_0_3_3) = 0)
% 14.68/3.91 |
% 14.68/3.91 | Instantiating (208) with all_82_0_188 yields:
% 14.68/3.91 | (384) apply(all_0_6_6, all_68_7_125, all_82_0_188) = 0 & member(all_82_0_188, all_0_3_3) = 0
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (384) yields:
% 14.68/3.91 | (385) apply(all_0_6_6, all_68_7_125, all_82_0_188) = 0
% 14.68/3.91 | (386) member(all_82_0_188, all_0_3_3) = 0
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (124) with all_82_0_188, 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_82_0_188, all_0_3_3) = 0, yields:
% 14.68/3.91 | (387) ? [v0] : (apply(all_0_5_5, all_82_0_188, v0) = 0 & member(v0, all_0_2_2) = 0)
% 14.68/3.91 |
% 14.68/3.91 | Instantiating (387) with all_89_0_189 yields:
% 14.68/3.91 | (388) apply(all_0_5_5, all_82_0_188, all_89_0_189) = 0 & member(all_89_0_189, all_0_2_2) = 0
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (388) yields:
% 14.68/3.91 | (389) apply(all_0_5_5, all_82_0_188, all_89_0_189) = 0
% 14.68/3.91 | (390) member(all_89_0_189, all_0_2_2) = 0
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (382) with all_89_0_189 and discharging atoms member(all_89_0_189, all_0_2_2) = 0, yields:
% 14.68/3.91 | (391) ? [v0] : ( ~ (v0 = 0) & apply(all_0_1_1, all_68_7_125, all_89_0_189) = v0)
% 14.68/3.91 |
% 14.68/3.91 | Instantiating (391) with all_96_0_190 yields:
% 14.68/3.91 | (392) ~ (all_96_0_190 = 0) & apply(all_0_1_1, all_68_7_125, all_89_0_189) = all_96_0_190
% 14.68/3.91 |
% 14.68/3.91 | Applying alpha-rule on (392) yields:
% 14.68/3.91 | (393) ~ (all_96_0_190 = 0)
% 14.68/3.91 | (394) apply(all_0_1_1, all_68_7_125, all_89_0_189) = all_96_0_190
% 14.68/3.91 |
% 14.68/3.91 | Instantiating formula (4) with all_82_0_188, all_96_0_190, all_0_1_1, all_89_0_189, all_68_7_125, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_68_7_125, all_89_0_189) = all_96_0_190, member(all_82_0_188, all_0_3_3) = 0, yields:
% 14.68/3.91 | (395) all_96_0_190 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = v0) | ( ~ (v0 = 0) & member(all_89_0_189, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.68/3.91 |
% 14.68/3.91 +-Applying beta-rule and splitting (395), into two cases.
% 14.68/3.91 |-Branch one:
% 14.68/3.91 | (396) all_96_0_190 = 0
% 14.68/3.91 |
% 14.68/3.91 | Equations (396) can reduce 393 to:
% 14.68/3.91 | (190) $false
% 14.68/3.91 |
% 14.68/3.91 |-The branch is then unsatisfiable
% 14.68/3.91 |-Branch two:
% 14.68/3.91 | (393) ~ (all_96_0_190 = 0)
% 14.68/3.91 | (399) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = v0) | ( ~ (v0 = 0) & member(all_89_0_189, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_68_7_125, all_0_4_4) = v0))
% 14.68/3.91 |
% 14.68/3.91 | Instantiating (399) with all_105_0_191 yields:
% 14.68/3.91 | (400) ( ~ (all_105_0_191 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & member(all_89_0_189, all_0_2_2) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & member(all_68_7_125, all_0_4_4) = all_105_0_191)
% 14.68/3.91 |
% 14.68/3.91 +-Applying beta-rule and splitting (400), into two cases.
% 14.68/3.91 |-Branch one:
% 14.68/3.91 | (401) ( ~ (all_105_0_191 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & member(all_89_0_189, all_0_2_2) = all_105_0_191)
% 14.68/3.91 |
% 14.68/3.91 +-Applying beta-rule and splitting (401), into two cases.
% 14.68/3.91 |-Branch one:
% 14.68/3.91 | (402) ( ~ (all_105_0_191 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191) | ( ~ (all_105_0_191 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191)
% 14.75/3.91 |
% 14.75/3.91 +-Applying beta-rule and splitting (402), into two cases.
% 14.75/3.91 |-Branch one:
% 14.75/3.91 | (403) ~ (all_105_0_191 = 0) & apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Applying alpha-rule on (403) yields:
% 14.75/3.91 | (404) ~ (all_105_0_191 = 0)
% 14.75/3.91 | (405) apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Instantiating formula (161) with all_0_5_5, all_82_0_188, all_89_0_189, all_105_0_191, 0 and discharging atoms apply(all_0_5_5, all_82_0_188, all_89_0_189) = all_105_0_191, apply(all_0_5_5, all_82_0_188, all_89_0_189) = 0, yields:
% 14.75/3.91 | (406) all_105_0_191 = 0
% 14.75/3.91 |
% 14.75/3.91 | Equations (406) can reduce 404 to:
% 14.75/3.91 | (190) $false
% 14.75/3.91 |
% 14.75/3.91 |-The branch is then unsatisfiable
% 14.75/3.91 |-Branch two:
% 14.75/3.91 | (408) ~ (all_105_0_191 = 0) & apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Applying alpha-rule on (408) yields:
% 14.75/3.91 | (404) ~ (all_105_0_191 = 0)
% 14.75/3.91 | (410) apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Instantiating formula (161) with all_0_6_6, all_68_7_125, all_82_0_188, all_105_0_191, 0 and discharging atoms apply(all_0_6_6, all_68_7_125, all_82_0_188) = all_105_0_191, apply(all_0_6_6, all_68_7_125, all_82_0_188) = 0, yields:
% 14.75/3.91 | (406) all_105_0_191 = 0
% 14.75/3.91 |
% 14.75/3.91 | Equations (406) can reduce 404 to:
% 14.75/3.91 | (190) $false
% 14.75/3.91 |
% 14.75/3.91 |-The branch is then unsatisfiable
% 14.75/3.91 |-Branch two:
% 14.75/3.91 | (413) ~ (all_105_0_191 = 0) & member(all_89_0_189, all_0_2_2) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Applying alpha-rule on (413) yields:
% 14.75/3.91 | (404) ~ (all_105_0_191 = 0)
% 14.75/3.91 | (415) member(all_89_0_189, all_0_2_2) = all_105_0_191
% 14.75/3.91 |
% 14.75/3.91 | Instantiating formula (123) with all_89_0_189, all_0_2_2, all_105_0_191, 0 and discharging atoms member(all_89_0_189, all_0_2_2) = all_105_0_191, member(all_89_0_189, all_0_2_2) = 0, yields:
% 14.75/3.92 | (406) all_105_0_191 = 0
% 14.75/3.92 |
% 14.75/3.92 | Equations (406) can reduce 404 to:
% 14.75/3.92 | (190) $false
% 14.75/3.92 |
% 14.75/3.92 |-The branch is then unsatisfiable
% 14.75/3.92 |-Branch two:
% 14.75/3.92 | (418) ~ (all_105_0_191 = 0) & member(all_68_7_125, all_0_4_4) = all_105_0_191
% 14.75/3.92 |
% 14.75/3.92 | Applying alpha-rule on (418) yields:
% 14.75/3.92 | (404) ~ (all_105_0_191 = 0)
% 14.75/3.92 | (420) member(all_68_7_125, all_0_4_4) = all_105_0_191
% 14.75/3.92 |
% 14.75/3.92 | Instantiating formula (123) with all_68_7_125, all_0_4_4, all_105_0_191, 0 and discharging atoms member(all_68_7_125, all_0_4_4) = all_105_0_191, member(all_68_7_125, all_0_4_4) = 0, yields:
% 14.75/3.92 | (406) all_105_0_191 = 0
% 14.75/3.92 |
% 14.75/3.92 | Equations (406) can reduce 404 to:
% 14.75/3.92 | (190) $false
% 14.75/3.92 |
% 14.75/3.92 |-The branch is then unsatisfiable
% 14.75/3.92 % SZS output end Proof for theBenchmark
% 14.75/3.92
% 14.75/3.92 3306ms
%------------------------------------------------------------------------------