TSTP Solution File: SET723+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET723+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 00:21:38 EDT 2022
% Result : Theorem 15.46s 4.22s
% Output : Proof 29.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET723+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 19:54:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.61 ____ _
% 0.48/0.61 ___ / __ \_____(_)___ ________ __________
% 0.48/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.61
% 0.48/0.61 A Theorem Prover for First-Order Logic
% 0.48/0.61 (ePrincess v.1.0)
% 0.48/0.61
% 0.48/0.61 (c) Philipp Rümmer, 2009-2015
% 0.48/0.61 (c) Peter Backeman, 2014-2015
% 0.48/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.61 Bug reports to peter@backeman.se
% 0.48/0.61
% 0.48/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.61
% 0.48/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.97/0.99 Prover 0: Preprocessing ...
% 3.03/1.33 Prover 0: Warning: ignoring some quantifiers
% 3.31/1.37 Prover 0: Constructing countermodel ...
% 4.67/1.67 Prover 0: gave up
% 4.67/1.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.81/1.73 Prover 1: Preprocessing ...
% 6.01/1.97 Prover 1: Constructing countermodel ...
% 7.40/2.26 Prover 1: gave up
% 7.40/2.26 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.40/2.30 Prover 2: Preprocessing ...
% 8.69/2.59 Prover 2: Warning: ignoring some quantifiers
% 8.90/2.61 Prover 2: Constructing countermodel ...
% 15.46/4.22 Prover 2: proved (1955ms)
% 15.46/4.22
% 15.46/4.22 No countermodel exists, formula is valid
% 15.46/4.22 % SZS status Theorem for theBenchmark
% 15.46/4.22
% 15.46/4.22 Generating proof ... Warning: ignoring some quantifiers
% 27.51/7.25 found it (size 184)
% 27.51/7.25
% 27.51/7.25 % SZS output start Proof for theBenchmark
% 27.51/7.25 Assumed formulas after preprocessing and simplification:
% 27.51/7.25 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & injective(v0, v4, v5) = 0 & equal_maps(v6, v7, v3, v5) = 0 & equal_maps(v1, v2, v3, v4) = v8 & compose_function(v0, v2, v3, v4, v5) = v7 & compose_function(v0, v1, v3, v4, v5) = v6 & maps(v2, v3, v4) = 0 & maps(v1, v3, v4) = 0 & maps(v0, v4, v5) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v11, v14, v16) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = 0) | ~ (apply(v11, v14, v16) = v18) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v17, v15) = v18) | ~ (apply(v11, v14, v16) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v17, v15) = v18) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v17, v15) = v18) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v16, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v17, v15) = v18) | ~ (member(v16, v10) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v11, v14, v16) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v16, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (member(v16, v10) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v14, v16) = v19) | ( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_function(v9, v10, v11, v12, v13) = v16) | ~ (apply(v16, v14, v15) = v17) | ~ (apply(v10, v14, v18) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v18, v15) = v19) | ( ~ (v19 = 0) & member(v18, v12) = v19) | ( ~ (v19 = 0) & member(v15, v13) = v19) | ( ~ (v19 = 0) & member(v14, v11) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_function(v9, v10, v11, v12, v13) = v16) | ~ (apply(v16, v14, v15) = v17) | ~ (apply(v9, v18, v15) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v10, v14, v18) = v19) | ( ~ (v19 = 0) & member(v18, v12) = v19) | ( ~ (v19 = 0) & member(v15, v13) = v19) | ( ~ (v19 = 0) & member(v14, v11) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_function(v9, v10, v11, v12, v13) = v16) | ~ (apply(v16, v14, v15) = v17) | ~ (member(v18, v12) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v10, v14, v18) = v19) | ( ~ (v19 = 0) & apply(v9, v18, v15) = v19) | ( ~ (v19 = 0) & member(v15, v13) = v19) | ( ~ (v19 = 0) & member(v14, v11) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_predicate(v9, v10, v11, v12, v13, v14) = 0) | ~ (apply(v11, v15, v18) = 0) | ~ (apply(v9, v15, v16) = v17) | ? [v19] : (( ~ (v19 = 0) & apply(v10, v18, v16) = v19) | ( ~ (v19 = 0) & member(v18, v13) = v19) | ( ~ (v19 = 0) & member(v16, v14) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_predicate(v9, v10, v11, v12, v13, v14) = 0) | ~ (apply(v10, v18, v16) = 0) | ~ (apply(v9, v15, v16) = v17) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v15, v18) = v19) | ( ~ (v19 = 0) & member(v18, v13) = v19) | ( ~ (v19 = 0) & member(v16, v14) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (compose_predicate(v9, v10, v11, v12, v13, v14) = 0) | ~ (apply(v9, v15, v16) = v17) | ~ (member(v18, v13) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v11, v15, v18) = v19) | ( ~ (v19 = 0) & apply(v10, v18, v16) = v19) | ( ~ (v19 = 0) & member(v16, v14) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v11, v14, v16) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v11, v14, v16) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v16, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v11, v14, v16) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v11, v14, v16) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v13, v15, v17) = v18) | ~ (member(v16, v10) = 0) | ~ (member(v14, v10) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v11, v14, v16) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v11, v14, v16) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = v18) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v17, v12) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v13, v15, v17) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = v18) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v15, v12) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v13, v15, v17) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = v18) | ~ (member(v17, v12) = 0) | ~ (member(v15, v12) = 0) | ? [v19] : (( ~ (v19 = 0) & apply(v9, v16, v17) = v19) | ( ~ (v19 = 0) & apply(v9, v14, v15) = v19) | ( ~ (v19 = 0) & member(v16, v10) = v19) | ( ~ (v19 = 0) & member(v14, v10) = v19) | (( ~ (v18 = 0) | (v19 = 0 & apply(v13, v15, v17) = 0)) & (v18 = 0 | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (apply(v9, v14, v15) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18) | (((v19 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18)) & ((v18 = 0 & apply(v11, v14, v16) = 0) | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | (((v19 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18)) & ((v18 = 0 & apply(v11, v14, v16) = 0) | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18) | (((v19 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18)) & ((v18 = 0 & apply(v11, v14, v16) = 0) | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | (((v19 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18)) & ((v18 = 0 & apply(v11, v14, v16) = 0) | ( ~ (v19 = 0) & apply(v13, v15, v17) = v19))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v15, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (apply(v9, v14, v15) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (decreasing(v9, v10, v11, v12, v13) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v17, v15) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v15, v12) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (apply(v9, v14, v15) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v16, v17) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v16, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v14, v15) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & member(v15, v12) = v18) | ( ~ (v18 = 0) & member(v14, v10) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (increasing(v9, v10, v11, v12, v13) = 0) | ~ (member(v17, v12) = 0) | ~ (member(v16, v10) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v10) = 0) | ? [v18] : ((v18 = 0 & apply(v13, v15, v17) = 0) | ( ~ (v18 = 0) & apply(v11, v14, v16) = v18) | ( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v14, v15) = v18))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = v9 | ~ (compose_predicate(v16, v15, v14, v13, v12, v11) = v10) | ~ (compose_predicate(v16, v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (compose_function(v9, v10, v11, v12, v13) = v16) | ~ (apply(v16, v14, v15) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & apply(v10, v14, v17) = 0 & apply(v9, v17, v15) = 0 & member(v17, v12) = 0) | ( ~ (v17 = 0) & member(v15, v13) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (compose_predicate(v9, v10, v11, v12, v13, v14) = 0) | ~ (apply(v9, v15, v16) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & apply(v11, v15, v17) = 0 & apply(v10, v17, v16) = 0 & member(v17, v13) = 0) | ( ~ (v17 = 0) & member(v16, v14) = v17) | ( ~ (v17 = 0) & member(v15, v12) = v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (equal_maps(v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (apply(v9, v13, v14) = 0) | ? [v16] : (( ~ (v16 = 0) & member(v15, v12) = v16) | ( ~ (v16 = 0) & member(v14, v12) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (equal_maps(v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (member(v14, v12) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v9, v13, v14) = v16) | ( ~ (v16 = 0) & member(v15, v12) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (equal_maps(v9, v10, v11, v12) = 0) | ~ (apply(v9, v13, v14) = 0) | ~ (member(v15, v12) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v10, v13, v15) = v16) | ( ~ (v16 = 0) & member(v14, v12) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (equal_maps(v9, v10, v11, v12) = 0) | ~ (member(v15, v12) = 0) | ~ (member(v14, v12) = 0) | ~ (member(v13, v11) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v10, v13, v15) = v16) | ( ~ (v16 = 0) & apply(v9, v13, v14) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (compose_predicate(v9, v10, v11, v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (member(v17, v14) = 0 & member(v16, v12) = 0 & ((v22 = 0 & v21 = 0 & v20 = 0 & apply(v11, v16, v19) = 0 & apply(v10, v19, v17) = 0 & member(v19, v13) = 0) | (v18 = 0 & apply(v9, v16, v17) = 0)) & (( ~ (v18 = 0) & apply(v9, v16, v17) = v18) | ( ! [v23] : ( ~ (apply(v11, v16, v23) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v10, v23, v17) = v24) | ( ~ (v24 = 0) & member(v23, v13) = v24))) & ! [v23] : ( ~ (apply(v10, v23, v17) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v11, v16, v23) = v24) | ( ~ (v24 = 0) & member(v23, v13) = v24))) & ! [v23] : ( ~ (member(v23, v13) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v11, v16, v23) = v24) | ( ~ (v24 = 0) & apply(v10, v23, v17) = v24))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (inverse_image3(v9, v10, v11) = v13) | ~ (apply(v9, v12, v15) = 0) | ~ (member(v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v12, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (inverse_image3(v9, v10, v11) = v13) | ~ (member(v15, v10) = 0) | ~ (member(v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v9, v12, v15) = v16) | ( ~ (v16 = 0) & member(v12, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (image3(v9, v10, v11) = v13) | ~ (apply(v9, v15, v12) = 0) | ~ (member(v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v12, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (image3(v9, v10, v11) = v13) | ~ (member(v15, v10) = 0) | ~ (member(v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v9, v15, v12) = v16) | ( ~ (v16 = 0) & member(v12, v11) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = v9 | ~ (isomorphism(v15, v14, v13, v12, v11) = v10) | ~ (isomorphism(v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = v9 | ~ (decreasing(v15, v14, v13, v12, v11) = v10) | ~ (decreasing(v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = v9 | ~ (increasing(v15, v14, v13, v12, v11) = v10) | ~ (increasing(v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v10 = v9 | ~ (compose_function(v15, v14, v13, v12, v11) = v10) | ~ (compose_function(v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_function(v9, v10, v11) = v14) | ~ (apply(v14, v13, v12) = v15) | ? [v16] : (( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v9, v12, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v9, v12, v13) = v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_predicate(v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v14) = v15) | ? [v16] : (( ~ (v16 = 0) & member(v14, v12) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v9, v14, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v9, v14, v13) = v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_predicate(v9, v10, v11, v12) = 0) | ~ (apply(v9, v14, v13) = v15) | ? [v16] : (( ~ (v16 = 0) & member(v14, v12) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v13, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v13, v14) = v16))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (maps(v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v9, v12, v13) = 0) | ? [v15] : (( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (maps(v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v13, v11) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v12, v13) = v15) | ( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (maps(v9, v10, v11) = 0) | ~ (apply(v9, v12, v13) = 0) | ~ (member(v14, v11) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v12, v14) = v15) | ( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (maps(v9, v10, v11) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v11) = 0) | ~ (member(v12, v10) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v12, v14) = v15) | ( ~ (v15 = 0) & apply(v9, v12, v13) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (isomorphism(v9, v10, v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & apply(v9, v17, v18) = 0 & apply(v9, v15, v16) = 0 & member(v18, v12) = 0 & member(v17, v10) = 0 & member(v16, v12) = 0 & member(v15, v10) = 0 & ((v26 = 0 & apply(v13, v16, v18) = 0) | (v25 = 0 & apply(v11, v15, v17) = 0)) & (( ~ (v26 = 0) & apply(v13, v16, v18) = v26) | ( ~ (v25 = 0) & apply(v11, v15, v17) = v25))) | ( ~ (v15 = 0) & one_to_one(v9, v10, v12) = v15) | ( ~ (v15 = 0) & maps(v9, v10, v12) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (decreasing(v9, v10, v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v19 = 0) & apply(v13, v18, v16) = v19 & apply(v11, v15, v17) = 0 & apply(v9, v17, v18) = 0 & apply(v9, v15, v16) = 0 & member(v18, v12) = 0 & member(v17, v10) = 0 & member(v16, v12) = 0 & member(v15, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (increasing(v9, v10, v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v19 = 0) & apply(v13, v16, v18) = v19 & apply(v11, v15, v17) = 0 & apply(v9, v17, v18) = 0 & apply(v9, v15, v16) = 0 & member(v18, v12) = 0 & member(v17, v10) = 0 & member(v16, v12) = 0 & member(v15, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (injective(v9, v10, v11) = 0) | ~ (apply(v9, v13, v14) = 0) | ~ (apply(v9, v12, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v13, v10) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (injective(v9, v10, v11) = 0) | ~ (apply(v9, v13, v14) = 0) | ~ (member(v12, v10) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v12, v14) = v15) | ( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v13, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (injective(v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v13, v10) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v13, v14) = v15) | ( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (injective(v9, v10, v11) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v10) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v9, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v9, v12, v14) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (inverse_image2(v9, v10) = v12) | ~ (apply(v9, v11, v14) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & member(v14, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (inverse_image2(v9, v10) = v12) | ~ (member(v14, v10) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apply(v9, v11, v14) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (image2(v9, v10) = v12) | ~ (apply(v9, v14, v11) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & member(v14, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (image2(v9, v10) = v12) | ~ (member(v14, v10) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apply(v9, v14, v11) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (inverse_predicate(v14, v13, v12, v11) = v10) | ~ (inverse_predicate(v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (equal_maps(v14, v13, v12, v11) = v10) | ~ (equal_maps(v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (inverse_predicate(v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (member(v15, v12) = 0 & member(v14, v11) = 0 & ((v17 = 0 & apply(v9, v15, v14) = 0) | (v16 = 0 & apply(v10, v14, v15) = 0)) & (( ~ (v17 = 0) & apply(v9, v15, v14) = v17) | ( ~ (v16 = 0) & apply(v10, v14, v15) = v16)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (equal_maps(v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = v15) & apply(v10, v14, v16) = 0 & apply(v9, v14, v15) = 0 & member(v16, v12) = 0 & member(v15, v12) = 0 & member(v14, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (product(v10) = v11) | ~ (member(v9, v12) = v13) | ~ (member(v9, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & member(v12, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (difference(v11, v10) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : ((v14 = 0 & member(v9, v10) = 0) | ( ~ (v14 = 0) & member(v9, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (union(v10, v11) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & member(v9, v11) = v15 & member(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (intersection(v10, v11) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v9, v11) = v14) | ( ~ (v14 = 0) & member(v9, v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (sum(v10) = v11) | ~ (member(v13, v10) = 0) | ~ (member(v9, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v9, v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (sum(v10) = v11) | ~ (member(v9, v13) = 0) | ~ (member(v9, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (inverse_image3(v13, v12, v11) = v10) | ~ (inverse_image3(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (image3(v13, v12, v11) = v10) | ~ (image3(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (inverse_function(v13, v12, v11) = v10) | ~ (inverse_function(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (one_to_one(v13, v12, v11) = v10) | ~ (one_to_one(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (surjective(v13, v12, v11) = v10) | ~ (surjective(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (injective(v13, v12, v11) = v10) | ~ (injective(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (maps(v13, v12, v11) = v10) | ~ (maps(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (apply(v13, v12, v11) = v10) | ~ (apply(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v9, v10, v11, v12, v13) = 0) | (one_to_one(v9, v10, v12) = 0 & maps(v9, v10, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_image3(v9, v10, v11) = v13) | ~ (member(v12, v13) = 0) | member(v12, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_image3(v9, v10, v11) = v13) | ~ (member(v12, v13) = 0) | ? [v14] : (apply(v9, v12, v14) = 0 & member(v14, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (image3(v9, v10, v11) = v13) | ~ (member(v12, v13) = 0) | member(v12, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (image3(v9, v10, v11) = v13) | ~ (member(v12, v13) = 0) | ? [v14] : (apply(v9, v14, v12) = 0 & member(v14, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (one_to_one(v9, v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & surjective(v9, v10, v11) = v13) | ( ~ (v13 = 0) & injective(v9, v10, v11) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (surjective(v9, v10, v11) = v12) | ? [v13] : (member(v13, v11) = 0 & ! [v14] : ( ~ (apply(v9, v14, v13) = 0) | ? [v15] : ( ~ (v15 = 0) & member(v14, v10) = v15)) & ! [v14] : ( ~ (member(v14, v10) = 0) | ? [v15] : ( ~ (v15 = 0) & apply(v9, v14, v13) = v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (injective(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v14 = v13) & apply(v9, v14, v15) = 0 & apply(v9, v13, v15) = 0 & member(v15, v11) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (identity(v9, v10) = 0) | ~ (apply(v9, v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & member(v11, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (maps(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & ~ (v15 = v14) & apply(v9, v13, v15) = 0 & apply(v9, v13, v14) = 0 & member(v15, v11) = 0 & member(v14, v11) = 0 & member(v13, v10) = 0) | (v14 = 0 & member(v13, v10) = 0 & ! [v21] : ( ~ (apply(v9, v13, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & member(v21, v11) = v22)) & ! [v21] : ( ~ (member(v21, v11) = 0) | ? [v22] : ( ~ (v22 = 0) & apply(v9, v13, v21) = v22))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & member(v13, v10) = 0 & member(v9, v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v10, v9) = v11) | ~ (member(v9, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v9, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (power_set(v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v10) = 0) | ~ (member(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | v10 = v9 | ~ (unordered_pair(v10, v11) = v12) | ~ (member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (inverse_image2(v12, v11) = v10) | ~ (inverse_image2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (image2(v12, v11) = v10) | ~ (image2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (identity(v12, v11) = v10) | ~ (identity(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (difference(v12, v11) = v10) | ~ (difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (union(v12, v11) = v10) | ~ (union(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (intersection(v12, v11) = v10) | ~ (intersection(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (equal_set(v12, v11) = v10) | ~ (equal_set(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (member(v12, v11) = v10) | ~ (member(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_image2(v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v9, v11, v13) = 0 & member(v13, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image2(v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v9, v13, v11) = 0 & member(v13, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (surjective(v9, v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & injective(v9, v10, v11) = 0) | ( ~ (v13 = 0) & one_to_one(v9, v10, v11) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (surjective(v9, v10, v11) = 0) | ~ (member(v12, v11) = 0) | ? [v13] : (apply(v9, v13, v12) = 0 & member(v13, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (injective(v9, v10, v11) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & surjective(v9, v10, v11) = 0) | ( ~ (v13 = 0) & one_to_one(v9, v10, v11) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (maps(v9, v10, v11) = 0) | ~ (member(v12, v10) = 0) | ? [v13] : (apply(v9, v12, v13) = 0 & member(v13, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (product(v10) = v11) | ~ (member(v12, v10) = 0) | ~ (member(v9, v11) = 0) | member(v9, v12) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (difference(v11, v10) = v12) | ~ (member(v9, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v9, v11) = 0 & member(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10, v11) = v12) | ~ (member(v9, v12) = 0) | ? [v13] : ((v13 = 0 & member(v9, v11) = 0) | (v13 = 0 & member(v9, v10) = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v10, v11) = v12) | ~ (member(v9, v12) = 0) | (member(v9, v11) = 0 & member(v9, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (identity(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & apply(v9, v12, v12) = v13 & member(v12, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v9) = v10) | ~ (member(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equal_set(v9, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & subset(v10, v9) = v12) | ( ~ (v12 = 0) & subset(v9, v10) = v12))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & power_set(v10) = v12 & member(v9, v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v10) = v13 & member(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (product(v11) = v10) | ~ (product(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (sum(v11) = v10) | ~ (sum(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v10) = v11) | ~ (member(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (power_set(v11) = v10) | ~ (power_set(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (one_to_one(v9, v10, v11) = 0) | (surjective(v9, v10, v11) = 0 & injective(v9, v10, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (surjective(v9, v10, v11) = 0) | ? [v12] : ((v12 = 0 & one_to_one(v9, v10, v11) = 0) | ( ~ (v12 = 0) & injective(v9, v10, v11) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (injective(v9, v10, v11) = 0) | ? [v12] : ((v12 = 0 & one_to_one(v9, v10, v11) = 0) | ( ~ (v12 = 0) & surjective(v9, v10, v11) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (identity(v9, v10) = 0) | ~ (member(v11, v10) = 0) | apply(v9, v11, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sum(v10) = v11) | ~ (member(v9, v11) = 0) | ? [v12] : (member(v12, v10) = 0 & member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_set(v10) = v11) | ~ (member(v9, v11) = 0) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v10, v9) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & subset(v9, v10) = 0) | ( ~ (v12 = 0) & equal_set(v9, v10) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & subset(v10, v9) = 0) | ( ~ (v12 = 0) & equal_set(v9, v10) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (member(v11, v9) = 0) | member(v11, v10) = 0) & ! [v9] : ! [v10] : ( ~ (equal_set(v9, v10) = 0) | (subset(v10, v9) = 0 & subset(v9, v10) = 0)) & ! [v9] : ! [v10] : ( ~ (subset(v10, v9) = 0) | ? [v11] : ((v11 = 0 & equal_set(v9, v10) = 0) | ( ~ (v11 = 0) & subset(v9, v10) = v11))) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | ? [v11] : (power_set(v10) = v11 & member(v9, v11) = 0)) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | ? [v11] : ((v11 = 0 & equal_set(v9, v10) = 0) | ( ~ (v11 = 0) & subset(v10, v9) = v11))) & ! [v9] : ~ (member(v9, empty_set) = 0) & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : compose_predicate(v14, v13, v12, v11, v10, v9) = v15 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : isomorphism(v13, v12, v11, v10, v9) = v14 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : decreasing(v13, v12, v11, v10, v9) = v14 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : increasing(v13, v12, v11, v10, v9) = v14 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : compose_function(v13, v12, v11, v10, v9) = v14 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : inverse_predicate(v12, v11, v10, v9) = v13 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : equal_maps(v12, v11, v10, v9) = v13 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : inverse_image3(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : image3(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : inverse_function(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : one_to_one(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : surjective(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : injective(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : maps(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : ? [v12] : apply(v11, v10, v9) = v12 & ? [v9] : ? [v10] : ? [v11] : inverse_image2(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : image2(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : identity(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : unordered_pair(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : difference(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : union(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : intersection(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : equal_set(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : member(v10, v9) = v11 & ? [v9] : ? [v10] : product(v9) = v10 & ? [v9] : ? [v10] : sum(v9) = v10 & ? [v9] : ? [v10] : singleton(v9) = v10 & ? [v9] : ? [v10] : power_set(v9) = v10)
% 28.12/7.39 | 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, all_0_7_7, all_0_8_8 yields:
% 28.12/7.39 | (1) ~ (all_0_0_0 = 0) & injective(all_0_8_8, all_0_4_4, all_0_3_3) = 0 & equal_maps(all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3) = 0 & equal_maps(all_0_7_7, all_0_6_6, all_0_5_5, all_0_4_4) = all_0_0_0 & compose_function(all_0_8_8, all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1 & compose_function(all_0_8_8, all_0_7_7, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2 & maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0 & maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0 & maps(all_0_8_8, 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
% 28.48/7.45 |
% 28.48/7.45 | Applying alpha-rule on (1) yields:
% 28.48/7.45 | (2) ! [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)))
% 28.48/7.45 | (3) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 28.48/7.45 | (4) ! [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)))
% 28.48/7.45 | (5) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 28.48/7.45 | (6) ! [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)))
% 28.48/7.45 | (7) ! [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))
% 28.48/7.45 | (8) ! [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)))
% 28.48/7.45 | (9) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 28.48/7.45 | (10) ! [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)))
% 28.48/7.45 | (11) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 28.48/7.45 | (12) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 28.48/7.45 | (13) ! [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)))
% 28.48/7.45 | (14) ! [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)))
% 28.48/7.45 | (15) ! [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))
% 28.48/7.45 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 28.48/7.45 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 28.48/7.45 | (18) ! [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)))))
% 28.48/7.45 | (19) ! [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))
% 28.48/7.45 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 28.48/7.45 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 28.48/7.45 | (22) ! [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))
% 28.48/7.45 | (23) ! [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)))))
% 28.48/7.45 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 28.48/7.45 | (25) ~ (all_0_0_0 = 0)
% 28.48/7.45 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 28.48/7.45 | (27) ! [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))
% 28.48/7.45 | (28) ! [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)))
% 28.48/7.46 | (29) ! [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))
% 28.48/7.46 | (30) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 28.48/7.46 | (31) ! [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)))
% 28.48/7.46 | (32) injective(all_0_8_8, all_0_4_4, all_0_3_3) = 0
% 28.48/7.46 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 28.48/7.46 | (34) ! [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)))
% 28.48/7.46 | (35) ! [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)))
% 28.48/7.46 | (36) ! [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)))
% 28.48/7.46 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 28.48/7.46 | (38) ! [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))
% 28.48/7.46 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 28.48/7.46 | (40) ? [v0] : ? [v1] : singleton(v0) = v1
% 28.48/7.46 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 28.48/7.46 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 28.48/7.46 | (43) ! [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)))
% 28.48/7.46 | (44) ! [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)))))
% 28.48/7.46 | (45) maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0
% 28.48/7.46 | (46) ! [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)))
% 28.48/7.46 | (47) ! [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)))
% 28.48/7.46 | (48) ! [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)))
% 28.48/7.46 | (49) ! [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)))
% 28.48/7.46 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 28.48/7.46 | (51) ! [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)))
% 28.48/7.46 | (52) ! [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)))
% 28.48/7.46 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 28.48/7.46 | (54) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 28.48/7.46 | (55) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 28.48/7.46 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 28.48/7.46 | (57) ! [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)))))
% 28.48/7.47 | (58) ! [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)))
% 28.48/7.47 | (59) ! [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)))))
% 28.48/7.47 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 28.48/7.47 | (61) ! [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)))
% 28.48/7.47 | (62) ! [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)))
% 28.48/7.47 | (63) ! [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)))
% 28.48/7.47 | (64) ! [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))
% 28.48/7.47 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 28.48/7.47 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 28.48/7.47 | (67) maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0
% 28.48/7.47 | (68) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 28.48/7.47 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 28.48/7.47 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 28.48/7.47 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 28.69/7.47 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 28.69/7.47 | (73) ! [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)))
% 28.69/7.47 | (74) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 28.69/7.47 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 28.69/7.47 | (76) ! [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)))
% 28.69/7.47 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 28.69/7.47 | (78) ! [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))
% 28.69/7.47 | (79) ! [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)))
% 28.69/7.47 | (80) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 28.69/7.47 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 28.69/7.47 | (82) ! [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)))))
% 28.69/7.47 | (83) ! [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)))
% 28.69/7.47 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 28.69/7.47 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 28.69/7.47 | (86) ! [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)))))
% 28.69/7.47 | (87) ! [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))))
% 28.69/7.48 | (88) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 28.69/7.48 | (89) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 28.69/7.48 | (90) ! [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))
% 28.69/7.48 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 28.69/7.48 | (92) ! [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)))))
% 28.69/7.48 | (93) ! [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)))
% 28.69/7.48 | (94) ? [v0] : ? [v1] : product(v0) = v1
% 28.69/7.48 | (95) ! [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)))
% 28.69/7.48 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 28.69/7.48 | (97) ! [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)))
% 28.69/7.48 | (98) ? [v0] : ? [v1] : power_set(v0) = v1
% 28.69/7.48 | (99) ! [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))
% 28.69/7.48 | (100) ! [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)))
% 28.69/7.48 | (101) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 28.69/7.48 | (102) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 28.69/7.48 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 28.69/7.48 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 28.69/7.48 | (105) ! [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)))
% 28.69/7.48 | (106) ! [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))
% 28.69/7.48 | (107) ! [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)))
% 28.69/7.48 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 28.69/7.48 | (109) ! [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))
% 28.69/7.48 | (110) equal_maps(all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3) = 0
% 28.69/7.48 | (111) ! [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)))))))
% 28.69/7.48 | (112) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 28.69/7.48 | (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)))
% 28.69/7.48 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 28.69/7.48 | (115) ! [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)))
% 28.69/7.49 | (116) ! [v0] : ~ (member(v0, empty_set) = 0)
% 28.69/7.49 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 28.69/7.49 | (118) ! [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)))
% 28.69/7.49 | (119) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 28.69/7.49 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 28.69/7.49 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 28.69/7.49 | (122) compose_function(all_0_8_8, all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1
% 28.69/7.49 | (123) ! [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)))
% 28.69/7.49 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 28.69/7.49 | (125) ! [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)))
% 28.69/7.49 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 28.69/7.49 | (127) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 28.69/7.49 | (128) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 28.69/7.49 | (129) ! [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)))))
% 28.69/7.49 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 28.69/7.49 | (131) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 28.69/7.49 | (132) ! [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)))))
% 28.69/7.49 | (133) ! [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)))
% 28.69/7.49 | (134) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 28.69/7.49 | (135) ! [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)))
% 28.69/7.49 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 28.69/7.49 | (137) ! [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)))
% 28.69/7.49 | (138) ! [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))))
% 28.69/7.49 | (139) ! [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)))))
% 28.69/7.49 | (140) maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0
% 28.69/7.49 | (141) ! [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)))
% 28.69/7.49 | (142) ! [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)))
% 28.69/7.49 | (143) ! [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)))
% 28.69/7.50 | (144) ! [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))
% 28.69/7.50 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 28.69/7.50 | (146) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 28.69/7.50 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 28.69/7.50 | (148) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 28.69/7.50 | (149) ! [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)))
% 28.69/7.50 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 28.69/7.50 | (151) equal_maps(all_0_7_7, all_0_6_6, all_0_5_5, all_0_4_4) = all_0_0_0
% 28.69/7.50 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 28.69/7.50 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 28.69/7.50 | (154) ! [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)))
% 28.69/7.50 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 28.69/7.50 | (156) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 28.69/7.50 | (157) ! [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)))
% 28.69/7.50 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 28.69/7.50 | (159) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 28.69/7.50 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 28.69/7.50 | (161) ! [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)))
% 28.69/7.50 | (162) ! [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)))
% 28.69/7.50 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 28.69/7.50 | (164) ! [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)))
% 28.69/7.50 | (165) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 28.69/7.50 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 28.69/7.50 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 28.69/7.50 | (168) ! [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)))))
% 28.69/7.50 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 28.69/7.50 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 28.69/7.50 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 28.69/7.50 | (172) ! [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)))))
% 28.69/7.50 | (173) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 28.69/7.50 | (174) ! [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)))
% 28.69/7.51 | (175) compose_function(all_0_8_8, all_0_7_7, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2
% 28.69/7.51 | (176) ! [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)))
% 28.69/7.51 | (177) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 28.69/7.51 | (178) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 28.69/7.51 | (179) ? [v0] : ? [v1] : sum(v0) = v1
% 28.69/7.51 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 28.69/7.51 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 28.69/7.51 | (182) ! [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)))
% 28.69/7.51 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 28.69/7.51 | (184) ! [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)))
% 28.69/7.51 | (185) ! [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))
% 28.69/7.51 | (186) ! [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)))
% 28.69/7.51 | (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)))
% 28.69/7.51 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 28.69/7.51 | (189) ! [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))
% 28.69/7.51 | (190) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 28.69/7.51 | (191) ! [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)))))
% 28.69/7.51 |
% 28.69/7.51 | Instantiating formula (99) with all_0_0_0, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms equal_maps(all_0_7_7, all_0_6_6, all_0_5_5, all_0_4_4) = all_0_0_0, yields:
% 28.69/7.51 | (192) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0, v2) = 0 & apply(all_0_7_7, v0, v1) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_5_5) = 0)
% 28.69/7.51 |
% 28.69/7.51 +-Applying beta-rule and splitting (192), into two cases.
% 28.69/7.51 |-Branch one:
% 28.69/7.51 | (193) all_0_0_0 = 0
% 28.69/7.51 |
% 28.69/7.51 | Equations (193) can reduce 25 to:
% 28.69/7.51 | (194) $false
% 28.69/7.51 |
% 28.69/7.51 |-The branch is then unsatisfiable
% 28.69/7.51 |-Branch two:
% 28.69/7.51 | (25) ~ (all_0_0_0 = 0)
% 28.69/7.51 | (196) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_6_6, v0, v2) = 0 & apply(all_0_7_7, v0, v1) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_5_5) = 0)
% 28.69/7.51 |
% 28.69/7.51 | Instantiating (196) with all_70_0_122, all_70_1_123, all_70_2_124 yields:
% 28.69/7.51 | (197) ~ (all_70_0_122 = all_70_1_123) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0 & apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0 & member(all_70_0_122, all_0_4_4) = 0 & member(all_70_1_123, all_0_4_4) = 0 & member(all_70_2_124, all_0_5_5) = 0
% 28.69/7.51 |
% 28.69/7.51 | Applying alpha-rule on (197) yields:
% 28.69/7.51 | (198) member(all_70_1_123, all_0_4_4) = 0
% 28.69/7.51 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.51 | (200) member(all_70_0_122, all_0_4_4) = 0
% 28.69/7.51 | (201) apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0
% 28.69/7.51 | (202) member(all_70_2_124, all_0_5_5) = 0
% 28.69/7.51 | (203) apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0
% 28.69/7.51 |
% 28.69/7.51 | Instantiating formula (63) with all_70_1_123, all_70_0_122, all_70_2_124, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0, apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0, member(all_70_0_122, all_0_4_4) = 0, yields:
% 28.69/7.51 | (204) all_70_0_122 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.51 |
% 28.69/7.51 | Instantiating formula (37) with all_70_0_122, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_70_0_122, all_0_4_4) = 0, yields:
% 28.69/7.51 | (205) ? [v0] : (apply(all_0_8_8, all_70_0_122, v0) = 0 & member(v0, all_0_3_3) = 0)
% 28.69/7.51 |
% 28.69/7.51 | Instantiating formula (63) with all_70_0_122, all_70_1_123, all_70_2_124, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.52 | (206) all_70_0_122 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_1_123) = v0) | ( ~ (v0 = 0) & member(all_70_0_122, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (37) with all_70_1_123, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.52 | (207) ? [v0] : (apply(all_0_8_8, all_70_1_123, v0) = 0 & member(v0, all_0_3_3) = 0)
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (187) with all_70_0_122, all_70_1_123, all_70_2_124, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, member(all_70_0_122, all_0_4_4) = 0, member(all_70_1_123, all_0_4_4) = 0, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.52 | (208) all_70_0_122 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_1_123) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (37) with all_70_2_124, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.52 | (209) ? [v0] : (apply(all_0_6_6, all_70_2_124, v0) = 0 & member(v0, all_0_4_4) = 0)
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (187) with all_70_0_122, all_70_1_123, all_70_2_124, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0, member(all_70_0_122, all_0_4_4) = 0, member(all_70_1_123, all_0_4_4) = 0, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.52 | (210) all_70_0_122 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (37) with all_70_2_124, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.52 | (211) ? [v0] : (apply(all_0_7_7, all_70_2_124, v0) = 0 & member(v0, all_0_4_4) = 0)
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (211) with all_77_0_125 yields:
% 28.69/7.52 | (212) apply(all_0_7_7, all_70_2_124, all_77_0_125) = 0 & member(all_77_0_125, all_0_4_4) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (212) yields:
% 28.69/7.52 | (213) apply(all_0_7_7, all_70_2_124, all_77_0_125) = 0
% 28.69/7.52 | (214) member(all_77_0_125, all_0_4_4) = 0
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (209) with all_79_0_126 yields:
% 28.69/7.52 | (215) apply(all_0_6_6, all_70_2_124, all_79_0_126) = 0 & member(all_79_0_126, all_0_4_4) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (215) yields:
% 28.69/7.52 | (216) apply(all_0_6_6, all_70_2_124, all_79_0_126) = 0
% 28.69/7.52 | (217) member(all_79_0_126, all_0_4_4) = 0
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (205) with all_81_0_127 yields:
% 28.69/7.52 | (218) apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0 & member(all_81_0_127, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (218) yields:
% 28.69/7.52 | (219) apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0
% 28.69/7.52 | (220) member(all_81_0_127, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (207) with all_83_0_128 yields:
% 28.69/7.52 | (221) apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0 & member(all_83_0_128, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (221) yields:
% 28.69/7.52 | (222) apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0
% 28.69/7.52 | (223) member(all_83_0_128, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 +-Applying beta-rule and splitting (206), into two cases.
% 28.69/7.52 |-Branch one:
% 28.69/7.52 | (224) all_70_0_122 = all_70_1_123
% 28.69/7.52 |
% 28.69/7.52 | Equations (224) can reduce 199 to:
% 28.69/7.52 | (194) $false
% 28.69/7.52 |
% 28.69/7.52 |-The branch is then unsatisfiable
% 28.69/7.52 |-Branch two:
% 28.69/7.52 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.52 | (227) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_1_123) = v0) | ( ~ (v0 = 0) & member(all_70_0_122, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.52 |
% 28.69/7.52 +-Applying beta-rule and splitting (204), into two cases.
% 28.69/7.52 |-Branch one:
% 28.69/7.52 | (224) all_70_0_122 = all_70_1_123
% 28.69/7.52 |
% 28.69/7.52 | Equations (224) can reduce 199 to:
% 28.69/7.52 | (194) $false
% 28.69/7.52 |
% 28.69/7.52 |-The branch is then unsatisfiable
% 28.69/7.52 |-Branch two:
% 28.69/7.52 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.52 | (231) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.52 |
% 28.69/7.52 +-Applying beta-rule and splitting (210), into two cases.
% 28.69/7.52 |-Branch one:
% 28.69/7.52 | (224) all_70_0_122 = all_70_1_123
% 28.69/7.52 |
% 28.69/7.52 | Equations (224) can reduce 199 to:
% 28.69/7.52 | (194) $false
% 28.69/7.52 |
% 28.69/7.52 |-The branch is then unsatisfiable
% 28.69/7.52 |-Branch two:
% 28.69/7.52 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.52 | (235) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = v0))
% 28.69/7.52 |
% 28.69/7.52 +-Applying beta-rule and splitting (208), into two cases.
% 28.69/7.52 |-Branch one:
% 28.69/7.52 | (224) all_70_0_122 = all_70_1_123
% 28.69/7.52 |
% 28.69/7.52 | Equations (224) can reduce 199 to:
% 28.69/7.52 | (194) $false
% 28.69/7.52 |
% 28.69/7.52 |-The branch is then unsatisfiable
% 28.69/7.52 |-Branch two:
% 28.69/7.52 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.52 | (239) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_1_123) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (63) with all_79_0_126, all_70_0_122, all_70_2_124, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, apply(all_0_6_6, all_70_2_124, all_79_0_126) = 0, member(all_70_0_122, all_0_4_4) = 0, yields:
% 28.69/7.52 | (240) all_79_0_126 = all_70_0_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & member(all_79_0_126, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (13) with all_83_0_128, all_70_0_122, all_70_1_123, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms injective(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_83_0_128, all_0_3_3) = 0, member(all_70_0_122, all_0_4_4) = 0, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.52 | (241) all_70_0_122 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_83_0_128) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (137) with all_81_0_127, all_83_0_128, all_70_2_124, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms equal_maps(all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3) = 0, member(all_83_0_128, all_0_3_3) = 0, member(all_81_0_127, all_0_3_3) = 0, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.52 | (242) all_83_0_128 = all_81_0_127 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_1_1, all_70_2_124, all_81_0_127) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_70_2_124, all_83_0_128) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (37) with all_79_0_126, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_79_0_126, all_0_4_4) = 0, yields:
% 28.69/7.52 | (243) ? [v0] : (apply(all_0_8_8, all_79_0_126, v0) = 0 & member(v0, all_0_3_3) = 0)
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (63) with all_70_1_123, all_77_0_125, all_70_2_124, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_5_5, all_0_4_4) = 0, apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0, member(all_77_0_125, all_0_4_4) = 0, yields:
% 28.69/7.52 | (244) all_77_0_125 = all_70_1_123 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_77_0_125) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.52 |
% 28.69/7.52 | Instantiating formula (37) with all_77_0_125, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_77_0_125, all_0_4_4) = 0, yields:
% 28.69/7.52 | (245) ? [v0] : (apply(all_0_8_8, all_77_0_125, v0) = 0 & member(v0, all_0_3_3) = 0)
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (245) with all_127_0_133 yields:
% 28.69/7.52 | (246) apply(all_0_8_8, all_77_0_125, all_127_0_133) = 0 & member(all_127_0_133, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (246) yields:
% 28.69/7.52 | (247) apply(all_0_8_8, all_77_0_125, all_127_0_133) = 0
% 28.69/7.52 | (248) member(all_127_0_133, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Instantiating (243) with all_129_0_134 yields:
% 28.69/7.52 | (249) apply(all_0_8_8, all_79_0_126, all_129_0_134) = 0 & member(all_129_0_134, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 | Applying alpha-rule on (249) yields:
% 28.69/7.52 | (250) apply(all_0_8_8, all_79_0_126, all_129_0_134) = 0
% 28.69/7.52 | (251) member(all_129_0_134, all_0_3_3) = 0
% 28.69/7.52 |
% 28.69/7.52 +-Applying beta-rule and splitting (240), into two cases.
% 28.69/7.52 |-Branch one:
% 28.69/7.52 | (252) all_79_0_126 = all_70_0_122
% 28.69/7.52 |
% 28.69/7.52 | From (252) and (216) follows:
% 28.69/7.52 | (203) apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0
% 28.69/7.52 |
% 28.69/7.52 | From (252) and (250) follows:
% 28.69/7.52 | (254) apply(all_0_8_8, all_70_0_122, all_129_0_134) = 0
% 28.69/7.52 |
% 28.69/7.52 | From (252) and (217) follows:
% 28.69/7.53 | (200) member(all_70_0_122, all_0_4_4) = 0
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (241), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (224) all_70_0_122 = all_70_1_123
% 28.69/7.53 |
% 28.69/7.53 | Equations (224) can reduce 199 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (199) ~ (all_70_0_122 = all_70_1_123)
% 28.69/7.53 | (259) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_83_0_128) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = v0))
% 28.69/7.53 |
% 28.69/7.53 | Instantiating (259) with all_138_0_135 yields:
% 28.69/7.53 | (260) ( ~ (all_138_0_135 = 0) & apply(all_0_8_8, all_70_0_122, all_83_0_128) = all_138_0_135) | ( ~ (all_138_0_135 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_138_0_135)
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (260), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (261) ~ (all_138_0_135 = 0) & apply(all_0_8_8, all_70_0_122, all_83_0_128) = all_138_0_135
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (261) yields:
% 28.69/7.53 | (262) ~ (all_138_0_135 = 0)
% 28.69/7.53 | (263) apply(all_0_8_8, all_70_0_122, all_83_0_128) = all_138_0_135
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (244), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (264) all_77_0_125 = all_70_1_123
% 28.69/7.53 |
% 28.69/7.53 | From (264) and (213) follows:
% 28.69/7.53 | (201) apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0
% 28.69/7.53 |
% 28.69/7.53 | From (264) and (247) follows:
% 28.69/7.53 | (266) apply(all_0_8_8, all_70_1_123, all_127_0_133) = 0
% 28.69/7.53 |
% 28.69/7.53 | From (264) and (214) follows:
% 28.69/7.53 | (198) member(all_70_1_123, all_0_4_4) = 0
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (187) with all_129_0_134, all_81_0_127, all_70_0_122, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, member(all_129_0_134, all_0_3_3) = 0, member(all_81_0_127, all_0_3_3) = 0, member(all_70_0_122, all_0_4_4) = 0, yields:
% 28.69/7.53 | (268) all_129_0_134 = all_81_0_127 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_129_0_134) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = v0))
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (63) with all_83_0_128, all_127_0_133, all_70_1_123, all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_4_4, all_0_3_3) = 0, apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0, member(all_127_0_133, all_0_3_3) = 0, yields:
% 28.69/7.53 | (269) all_127_0_133 = all_83_0_128 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_127_0_133) = v0) | ( ~ (v0 = 0) & member(all_83_0_128, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0))
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (269), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (270) all_127_0_133 = all_83_0_128
% 28.69/7.53 |
% 28.69/7.53 | From (270) and (266) follows:
% 28.69/7.53 | (222) apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0
% 28.69/7.53 |
% 28.69/7.53 | From (270) and (248) follows:
% 28.69/7.53 | (223) member(all_83_0_128, all_0_3_3) = 0
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (268), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (273) all_129_0_134 = all_81_0_127
% 28.69/7.53 |
% 28.69/7.53 | From (273) and (254) follows:
% 28.69/7.53 | (219) apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0
% 28.69/7.53 |
% 28.69/7.53 | From (273) and (251) follows:
% 28.69/7.53 | (220) member(all_81_0_127, all_0_3_3) = 0
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (242), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (276) all_83_0_128 = all_81_0_127
% 28.69/7.53 |
% 28.69/7.53 | From (276) and (263) follows:
% 28.69/7.53 | (277) apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_138_0_135
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (150) with all_0_8_8, all_70_0_122, all_81_0_127, all_138_0_135, 0 and discharging atoms apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_138_0_135, apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0, yields:
% 28.69/7.53 | (278) all_138_0_135 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (278) can reduce 262 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (280) ~ (all_83_0_128 = all_81_0_127)
% 28.69/7.53 | (281) ? [v0] : (( ~ (v0 = 0) & apply(all_0_1_1, all_70_2_124, all_81_0_127) = v0) | ( ~ (v0 = 0) & apply(all_0_2_2, all_70_2_124, all_83_0_128) = v0))
% 28.69/7.53 |
% 28.69/7.53 | Instantiating (281) with all_238_0_801 yields:
% 28.69/7.53 | (282) ( ~ (all_238_0_801 = 0) & apply(all_0_1_1, all_70_2_124, all_81_0_127) = all_238_0_801) | ( ~ (all_238_0_801 = 0) & apply(all_0_2_2, all_70_2_124, all_83_0_128) = all_238_0_801)
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (282), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (283) ~ (all_238_0_801 = 0) & apply(all_0_1_1, all_70_2_124, all_81_0_127) = all_238_0_801
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (283) yields:
% 28.69/7.53 | (284) ~ (all_238_0_801 = 0)
% 28.69/7.53 | (285) apply(all_0_1_1, all_70_2_124, all_81_0_127) = all_238_0_801
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (93) with all_70_0_122, all_238_0_801, all_0_1_1, all_81_0_127, all_70_2_124, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms compose_function(all_0_8_8, all_0_6_6, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_1_1, apply(all_0_1_1, all_70_2_124, all_81_0_127) = all_238_0_801, member(all_70_0_122, all_0_4_4) = 0, yields:
% 28.69/7.53 | (286) all_238_0_801 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = v0) | ( ~ (v0 = 0) & member(all_81_0_127, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (286), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (287) all_238_0_801 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (287) can reduce 284 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (284) ~ (all_238_0_801 = 0)
% 28.69/7.53 | (290) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = v0) | ( ~ (v0 = 0) & member(all_81_0_127, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.53 |
% 28.69/7.53 | Instantiating (290) with all_301_0_813 yields:
% 28.69/7.53 | (291) ( ~ (all_301_0_813 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & member(all_81_0_127, all_0_3_3) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & member(all_70_2_124, all_0_5_5) = all_301_0_813)
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (291), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (292) ( ~ (all_301_0_813 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & member(all_81_0_127, all_0_3_3) = all_301_0_813)
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (292), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (293) ( ~ (all_301_0_813 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813) | ( ~ (all_301_0_813 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813)
% 28.69/7.53 |
% 28.69/7.53 +-Applying beta-rule and splitting (293), into two cases.
% 28.69/7.53 |-Branch one:
% 28.69/7.53 | (294) ~ (all_301_0_813 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (294) yields:
% 28.69/7.53 | (295) ~ (all_301_0_813 = 0)
% 28.69/7.53 | (296) apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (150) with all_0_6_6, all_70_2_124, all_70_0_122, all_301_0_813, 0 and discharging atoms apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_301_0_813, apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0, yields:
% 28.69/7.53 | (297) all_301_0_813 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (297) can reduce 295 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (299) ~ (all_301_0_813 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (299) yields:
% 28.69/7.53 | (295) ~ (all_301_0_813 = 0)
% 28.69/7.53 | (301) apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (150) with all_0_8_8, all_70_0_122, all_81_0_127, all_301_0_813, 0 and discharging atoms apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_301_0_813, apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0, yields:
% 28.69/7.53 | (297) all_301_0_813 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (297) can reduce 295 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (304) ~ (all_301_0_813 = 0) & member(all_81_0_127, all_0_3_3) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (304) yields:
% 28.69/7.53 | (295) ~ (all_301_0_813 = 0)
% 28.69/7.53 | (306) member(all_81_0_127, all_0_3_3) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (136) with all_81_0_127, all_0_3_3, all_301_0_813, 0 and discharging atoms member(all_81_0_127, all_0_3_3) = all_301_0_813, member(all_81_0_127, all_0_3_3) = 0, yields:
% 28.69/7.53 | (297) all_301_0_813 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (297) can reduce 295 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.53 |-Branch two:
% 28.69/7.53 | (309) ~ (all_301_0_813 = 0) & member(all_70_2_124, all_0_5_5) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Applying alpha-rule on (309) yields:
% 28.69/7.53 | (295) ~ (all_301_0_813 = 0)
% 28.69/7.53 | (311) member(all_70_2_124, all_0_5_5) = all_301_0_813
% 28.69/7.53 |
% 28.69/7.53 | Instantiating formula (136) with all_70_2_124, all_0_5_5, all_301_0_813, 0 and discharging atoms member(all_70_2_124, all_0_5_5) = all_301_0_813, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.53 | (297) all_301_0_813 = 0
% 28.69/7.53 |
% 28.69/7.53 | Equations (297) can reduce 295 to:
% 28.69/7.53 | (194) $false
% 28.69/7.53 |
% 28.69/7.53 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (314) ~ (all_238_0_801 = 0) & apply(all_0_2_2, all_70_2_124, all_83_0_128) = all_238_0_801
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (314) yields:
% 28.69/7.54 | (284) ~ (all_238_0_801 = 0)
% 28.69/7.54 | (316) apply(all_0_2_2, all_70_2_124, all_83_0_128) = all_238_0_801
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (93) with all_70_1_123, all_238_0_801, all_0_2_2, all_83_0_128, all_70_2_124, all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms compose_function(all_0_8_8, all_0_7_7, all_0_5_5, all_0_4_4, all_0_3_3) = all_0_2_2, apply(all_0_2_2, all_70_2_124, all_83_0_128) = all_238_0_801, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.54 | (317) all_238_0_801 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = v0) | ( ~ (v0 = 0) & member(all_83_0_128, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (317), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (287) all_238_0_801 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (287) can reduce 284 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (284) ~ (all_238_0_801 = 0)
% 28.69/7.54 | (321) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = v0) | ( ~ (v0 = 0) & member(all_83_0_128, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.54 |
% 28.69/7.54 | Instantiating (321) with all_301_0_818 yields:
% 28.69/7.54 | (322) ( ~ (all_301_0_818 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & member(all_83_0_128, all_0_3_3) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & member(all_70_2_124, all_0_5_5) = all_301_0_818)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (322), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (323) ( ~ (all_301_0_818 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & member(all_83_0_128, all_0_3_3) = all_301_0_818)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (323), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (324) ( ~ (all_301_0_818 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818) | ( ~ (all_301_0_818 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (324), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (325) ~ (all_301_0_818 = 0) & apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (325) yields:
% 28.69/7.54 | (326) ~ (all_301_0_818 = 0)
% 28.69/7.54 | (327) apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (150) with all_0_7_7, all_70_2_124, all_70_1_123, all_301_0_818, 0 and discharging atoms apply(all_0_7_7, all_70_2_124, all_70_1_123) = all_301_0_818, apply(all_0_7_7, all_70_2_124, all_70_1_123) = 0, yields:
% 28.69/7.54 | (328) all_301_0_818 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (328) can reduce 326 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (330) ~ (all_301_0_818 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (330) yields:
% 28.69/7.54 | (326) ~ (all_301_0_818 = 0)
% 28.69/7.54 | (332) apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (150) with all_0_8_8, all_70_1_123, all_83_0_128, all_301_0_818, 0 and discharging atoms apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_301_0_818, apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0, yields:
% 28.69/7.54 | (328) all_301_0_818 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (328) can reduce 326 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (335) ~ (all_301_0_818 = 0) & member(all_83_0_128, all_0_3_3) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (335) yields:
% 28.69/7.54 | (326) ~ (all_301_0_818 = 0)
% 28.69/7.54 | (337) member(all_83_0_128, all_0_3_3) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (136) with all_83_0_128, all_0_3_3, all_301_0_818, 0 and discharging atoms member(all_83_0_128, all_0_3_3) = all_301_0_818, member(all_83_0_128, all_0_3_3) = 0, yields:
% 28.69/7.54 | (328) all_301_0_818 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (328) can reduce 326 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (340) ~ (all_301_0_818 = 0) & member(all_70_2_124, all_0_5_5) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (340) yields:
% 28.69/7.54 | (326) ~ (all_301_0_818 = 0)
% 28.69/7.54 | (342) member(all_70_2_124, all_0_5_5) = all_301_0_818
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (136) with all_70_2_124, all_0_5_5, all_301_0_818, 0 and discharging atoms member(all_70_2_124, all_0_5_5) = all_301_0_818, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.54 | (328) all_301_0_818 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (328) can reduce 326 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (345) ~ (all_129_0_134 = all_81_0_127)
% 28.69/7.54 | (346) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_129_0_134) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = v0))
% 28.69/7.54 |
% 28.69/7.54 | Instantiating (346) with all_219_0_822 yields:
% 28.69/7.54 | (347) ( ~ (all_219_0_822 = 0) & apply(all_0_8_8, all_70_0_122, all_129_0_134) = all_219_0_822) | ( ~ (all_219_0_822 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_219_0_822)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (347), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (348) ~ (all_219_0_822 = 0) & apply(all_0_8_8, all_70_0_122, all_129_0_134) = all_219_0_822
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (348) yields:
% 28.69/7.54 | (349) ~ (all_219_0_822 = 0)
% 28.69/7.54 | (350) apply(all_0_8_8, all_70_0_122, all_129_0_134) = all_219_0_822
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (150) with all_0_8_8, all_70_0_122, all_129_0_134, all_219_0_822, 0 and discharging atoms apply(all_0_8_8, all_70_0_122, all_129_0_134) = all_219_0_822, apply(all_0_8_8, all_70_0_122, all_129_0_134) = 0, yields:
% 28.69/7.54 | (351) all_219_0_822 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (351) can reduce 349 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (353) ~ (all_219_0_822 = 0) & apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_219_0_822
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (353) yields:
% 28.69/7.54 | (349) ~ (all_219_0_822 = 0)
% 28.69/7.54 | (355) apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_219_0_822
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (150) with all_0_8_8, all_70_0_122, all_81_0_127, all_219_0_822, 0 and discharging atoms apply(all_0_8_8, all_70_0_122, all_81_0_127) = all_219_0_822, apply(all_0_8_8, all_70_0_122, all_81_0_127) = 0, yields:
% 28.69/7.54 | (351) all_219_0_822 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (351) can reduce 349 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (358) ~ (all_127_0_133 = all_83_0_128)
% 28.69/7.54 | (359) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_70_1_123, all_127_0_133) = v0) | ( ~ (v0 = 0) & member(all_83_0_128, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0))
% 28.69/7.54 |
% 28.69/7.54 | Instantiating (359) with all_215_0_835 yields:
% 28.69/7.54 | (360) ( ~ (all_215_0_835 = 0) & apply(all_0_8_8, all_70_1_123, all_127_0_133) = all_215_0_835) | ( ~ (all_215_0_835 = 0) & member(all_83_0_128, all_0_3_3) = all_215_0_835) | ( ~ (all_215_0_835 = 0) & member(all_70_1_123, all_0_4_4) = all_215_0_835)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (360), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (361) ( ~ (all_215_0_835 = 0) & apply(all_0_8_8, all_70_1_123, all_127_0_133) = all_215_0_835) | ( ~ (all_215_0_835 = 0) & member(all_83_0_128, all_0_3_3) = all_215_0_835)
% 28.69/7.54 |
% 28.69/7.54 +-Applying beta-rule and splitting (361), into two cases.
% 28.69/7.54 |-Branch one:
% 28.69/7.54 | (362) ~ (all_215_0_835 = 0) & apply(all_0_8_8, all_70_1_123, all_127_0_133) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (362) yields:
% 28.69/7.54 | (363) ~ (all_215_0_835 = 0)
% 28.69/7.54 | (364) apply(all_0_8_8, all_70_1_123, all_127_0_133) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (150) with all_0_8_8, all_70_1_123, all_127_0_133, all_215_0_835, 0 and discharging atoms apply(all_0_8_8, all_70_1_123, all_127_0_133) = all_215_0_835, apply(all_0_8_8, all_70_1_123, all_127_0_133) = 0, yields:
% 28.69/7.54 | (365) all_215_0_835 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (365) can reduce 363 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (367) ~ (all_215_0_835 = 0) & member(all_83_0_128, all_0_3_3) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (367) yields:
% 28.69/7.54 | (363) ~ (all_215_0_835 = 0)
% 28.69/7.54 | (369) member(all_83_0_128, all_0_3_3) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.54 | Instantiating formula (136) with all_83_0_128, all_0_3_3, all_215_0_835, 0 and discharging atoms member(all_83_0_128, all_0_3_3) = all_215_0_835, member(all_83_0_128, all_0_3_3) = 0, yields:
% 28.69/7.54 | (365) all_215_0_835 = 0
% 28.69/7.54 |
% 28.69/7.54 | Equations (365) can reduce 363 to:
% 28.69/7.54 | (194) $false
% 28.69/7.54 |
% 28.69/7.54 |-The branch is then unsatisfiable
% 28.69/7.54 |-Branch two:
% 28.69/7.54 | (372) ~ (all_215_0_835 = 0) & member(all_70_1_123, all_0_4_4) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.54 | Applying alpha-rule on (372) yields:
% 28.69/7.54 | (363) ~ (all_215_0_835 = 0)
% 28.69/7.54 | (374) member(all_70_1_123, all_0_4_4) = all_215_0_835
% 28.69/7.54 |
% 28.69/7.55 | Instantiating formula (136) with all_70_1_123, all_0_4_4, all_215_0_835, 0 and discharging atoms member(all_70_1_123, all_0_4_4) = all_215_0_835, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.55 | (365) all_215_0_835 = 0
% 28.69/7.55 |
% 28.69/7.55 | Equations (365) can reduce 363 to:
% 28.69/7.55 | (194) $false
% 28.69/7.55 |
% 28.69/7.55 |-The branch is then unsatisfiable
% 28.69/7.55 |-Branch two:
% 28.69/7.55 | (377) ~ (all_77_0_125 = all_70_1_123)
% 28.69/7.55 | (378) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_70_2_124, all_77_0_125) = v0) | ( ~ (v0 = 0) & member(all_70_1_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 28.69/7.55 |
% 28.69/7.55 | Instantiating (378) with all_147_0_873 yields:
% 28.69/7.55 | (379) ( ~ (all_147_0_873 = 0) & apply(all_0_7_7, all_70_2_124, all_77_0_125) = all_147_0_873) | ( ~ (all_147_0_873 = 0) & member(all_70_1_123, all_0_4_4) = all_147_0_873) | ( ~ (all_147_0_873 = 0) & member(all_70_2_124, all_0_5_5) = all_147_0_873)
% 28.69/7.55 |
% 28.69/7.55 +-Applying beta-rule and splitting (379), into two cases.
% 28.69/7.55 |-Branch one:
% 28.69/7.55 | (380) ( ~ (all_147_0_873 = 0) & apply(all_0_7_7, all_70_2_124, all_77_0_125) = all_147_0_873) | ( ~ (all_147_0_873 = 0) & member(all_70_1_123, all_0_4_4) = all_147_0_873)
% 28.69/7.55 |
% 28.69/7.55 +-Applying beta-rule and splitting (380), into two cases.
% 28.69/7.55 |-Branch one:
% 28.69/7.55 | (381) ~ (all_147_0_873 = 0) & apply(all_0_7_7, all_70_2_124, all_77_0_125) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Applying alpha-rule on (381) yields:
% 28.69/7.55 | (382) ~ (all_147_0_873 = 0)
% 28.69/7.55 | (383) apply(all_0_7_7, all_70_2_124, all_77_0_125) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Instantiating formula (150) with all_0_7_7, all_70_2_124, all_77_0_125, all_147_0_873, 0 and discharging atoms apply(all_0_7_7, all_70_2_124, all_77_0_125) = all_147_0_873, apply(all_0_7_7, all_70_2_124, all_77_0_125) = 0, yields:
% 28.69/7.55 | (384) all_147_0_873 = 0
% 28.69/7.55 |
% 28.69/7.55 | Equations (384) can reduce 382 to:
% 28.69/7.55 | (194) $false
% 28.69/7.55 |
% 28.69/7.55 |-The branch is then unsatisfiable
% 28.69/7.55 |-Branch two:
% 28.69/7.55 | (386) ~ (all_147_0_873 = 0) & member(all_70_1_123, all_0_4_4) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Applying alpha-rule on (386) yields:
% 28.69/7.55 | (382) ~ (all_147_0_873 = 0)
% 28.69/7.55 | (388) member(all_70_1_123, all_0_4_4) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Instantiating formula (136) with all_70_1_123, all_0_4_4, all_147_0_873, 0 and discharging atoms member(all_70_1_123, all_0_4_4) = all_147_0_873, member(all_70_1_123, all_0_4_4) = 0, yields:
% 28.69/7.55 | (384) all_147_0_873 = 0
% 28.69/7.55 |
% 28.69/7.55 | Equations (384) can reduce 382 to:
% 28.69/7.55 | (194) $false
% 28.69/7.55 |
% 28.69/7.55 |-The branch is then unsatisfiable
% 28.69/7.55 |-Branch two:
% 28.69/7.55 | (391) ~ (all_147_0_873 = 0) & member(all_70_2_124, all_0_5_5) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Applying alpha-rule on (391) yields:
% 28.69/7.55 | (382) ~ (all_147_0_873 = 0)
% 28.69/7.55 | (393) member(all_70_2_124, all_0_5_5) = all_147_0_873
% 28.69/7.55 |
% 28.69/7.55 | Instantiating formula (136) with all_70_2_124, all_0_5_5, all_147_0_873, 0 and discharging atoms member(all_70_2_124, all_0_5_5) = all_147_0_873, member(all_70_2_124, all_0_5_5) = 0, yields:
% 28.69/7.55 | (384) all_147_0_873 = 0
% 28.69/7.55 |
% 28.69/7.55 | Equations (384) can reduce 382 to:
% 28.69/7.55 | (194) $false
% 28.69/7.55 |
% 28.69/7.55 |-The branch is then unsatisfiable
% 28.69/7.55 |-Branch two:
% 28.69/7.55 | (396) ~ (all_138_0_135 = 0) & apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_138_0_135
% 28.69/7.55 |
% 28.69/7.55 | Applying alpha-rule on (396) yields:
% 28.69/7.55 | (262) ~ (all_138_0_135 = 0)
% 28.69/7.55 | (398) apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_138_0_135
% 28.69/7.55 |
% 28.69/7.55 | Instantiating formula (150) with all_0_8_8, all_70_1_123, all_83_0_128, all_138_0_135, 0 and discharging atoms apply(all_0_8_8, all_70_1_123, all_83_0_128) = all_138_0_135, apply(all_0_8_8, all_70_1_123, all_83_0_128) = 0, yields:
% 28.69/7.55 | (278) all_138_0_135 = 0
% 28.69/7.55 |
% 28.69/7.55 | Equations (278) can reduce 262 to:
% 28.69/7.55 | (194) $false
% 28.69/7.55 |
% 28.69/7.55 |-The branch is then unsatisfiable
% 28.69/7.55 |-Branch two:
% 28.69/7.55 | (401) ~ (all_79_0_126 = all_70_0_122)
% 28.69/7.55 | (402) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = v0) | ( ~ (v0 = 0) & member(all_79_0_126, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_70_2_124, all_0_5_5) = v0))
% 29.02/7.55 |
% 29.02/7.55 | Instantiating (402) with all_135_0_916 yields:
% 29.02/7.55 | (403) ( ~ (all_135_0_916 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_135_0_916) | ( ~ (all_135_0_916 = 0) & member(all_79_0_126, all_0_4_4) = all_135_0_916) | ( ~ (all_135_0_916 = 0) & member(all_70_2_124, all_0_5_5) = all_135_0_916)
% 29.02/7.55 |
% 29.02/7.55 +-Applying beta-rule and splitting (403), into two cases.
% 29.02/7.55 |-Branch one:
% 29.02/7.55 | (404) ( ~ (all_135_0_916 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_135_0_916) | ( ~ (all_135_0_916 = 0) & member(all_79_0_126, all_0_4_4) = all_135_0_916)
% 29.02/7.55 |
% 29.02/7.55 +-Applying beta-rule and splitting (404), into two cases.
% 29.02/7.55 |-Branch one:
% 29.02/7.55 | (405) ~ (all_135_0_916 = 0) & apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Applying alpha-rule on (405) yields:
% 29.02/7.55 | (406) ~ (all_135_0_916 = 0)
% 29.02/7.55 | (407) apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Instantiating formula (150) with all_0_6_6, all_70_2_124, all_70_0_122, all_135_0_916, 0 and discharging atoms apply(all_0_6_6, all_70_2_124, all_70_0_122) = all_135_0_916, apply(all_0_6_6, all_70_2_124, all_70_0_122) = 0, yields:
% 29.02/7.55 | (408) all_135_0_916 = 0
% 29.02/7.55 |
% 29.02/7.55 | Equations (408) can reduce 406 to:
% 29.02/7.55 | (194) $false
% 29.02/7.55 |
% 29.02/7.55 |-The branch is then unsatisfiable
% 29.02/7.55 |-Branch two:
% 29.02/7.55 | (410) ~ (all_135_0_916 = 0) & member(all_79_0_126, all_0_4_4) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Applying alpha-rule on (410) yields:
% 29.02/7.55 | (406) ~ (all_135_0_916 = 0)
% 29.02/7.55 | (412) member(all_79_0_126, all_0_4_4) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Instantiating formula (136) with all_79_0_126, all_0_4_4, all_135_0_916, 0 and discharging atoms member(all_79_0_126, all_0_4_4) = all_135_0_916, member(all_79_0_126, all_0_4_4) = 0, yields:
% 29.02/7.55 | (408) all_135_0_916 = 0
% 29.02/7.55 |
% 29.02/7.55 | Equations (408) can reduce 406 to:
% 29.02/7.55 | (194) $false
% 29.02/7.55 |
% 29.02/7.55 |-The branch is then unsatisfiable
% 29.02/7.55 |-Branch two:
% 29.02/7.55 | (415) ~ (all_135_0_916 = 0) & member(all_70_2_124, all_0_5_5) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Applying alpha-rule on (415) yields:
% 29.02/7.55 | (406) ~ (all_135_0_916 = 0)
% 29.02/7.55 | (417) member(all_70_2_124, all_0_5_5) = all_135_0_916
% 29.02/7.55 |
% 29.02/7.55 | Instantiating formula (136) with all_70_2_124, all_0_5_5, all_135_0_916, 0 and discharging atoms member(all_70_2_124, all_0_5_5) = all_135_0_916, member(all_70_2_124, all_0_5_5) = 0, yields:
% 29.02/7.55 | (408) all_135_0_916 = 0
% 29.02/7.55 |
% 29.02/7.55 | Equations (408) can reduce 406 to:
% 29.02/7.55 | (194) $false
% 29.02/7.55 |
% 29.02/7.55 |-The branch is then unsatisfiable
% 29.02/7.55 % SZS output end Proof for theBenchmark
% 29.02/7.55
% 29.02/7.55 6929ms
%------------------------------------------------------------------------------