TSTP Solution File: SET727+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET727+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:40 EDT 2022
% Result : Theorem 22.38s 5.91s
% Output : Proof 260.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET727+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 00:09:58 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.93/1.01 Prover 0: Preprocessing ...
% 3.38/1.38 Prover 0: Warning: ignoring some quantifiers
% 3.38/1.41 Prover 0: Constructing countermodel ...
% 4.72/1.69 Prover 0: gave up
% 4.72/1.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.72/1.74 Prover 1: Preprocessing ...
% 5.88/1.97 Prover 1: Constructing countermodel ...
% 18.34/4.97 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.50/5.03 Prover 2: Preprocessing ...
% 19.77/5.31 Prover 2: Warning: ignoring some quantifiers
% 19.77/5.33 Prover 2: Constructing countermodel ...
% 22.38/5.91 Prover 2: proved (932ms)
% 22.38/5.91 Prover 1: stopped
% 22.38/5.91
% 22.38/5.91 No countermodel exists, formula is valid
% 22.38/5.91 % SZS status Theorem for theBenchmark
% 22.38/5.91
% 22.38/5.91 Generating proof ... Warning: ignoring some quantifiers
% 258.80/213.29 found it (size 433)
% 258.80/213.29
% 258.80/213.29 % SZS output start Proof for theBenchmark
% 258.80/213.29 Assumed formulas after preprocessing and simplification:
% 258.80/213.29 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & inverse_function(v0, v3, v4) = v7 & identity(v6, v4) = 0 & identity(v5, v3) = 0 & equal_maps(v7, v2, v4, v3) = v8 & compose_function(v1, v0, v3, v4, v3) = v5 & compose_function(v0, v2, v4, v3, v4) = v6 & maps(v2, v4, v3) = 0 & maps(v1, v4, v3) = 0 & maps(v0, v3, v4) = 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)
% 259.44/213.41 | 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:
% 259.44/213.41 | (1) ~ (all_0_0_0 = 0) & inverse_function(all_0_8_8, all_0_5_5, all_0_4_4) = all_0_1_1 & identity(all_0_2_2, all_0_4_4) = 0 & identity(all_0_3_3, all_0_5_5) = 0 & equal_maps(all_0_1_1, all_0_6_6, all_0_4_4, all_0_5_5) = all_0_0_0 & compose_function(all_0_7_7, all_0_8_8, all_0_5_5, all_0_4_4, all_0_5_5) = all_0_3_3 & compose_function(all_0_8_8, all_0_6_6, all_0_4_4, all_0_5_5, all_0_4_4) = all_0_2_2 & maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0 & maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0 & maps(all_0_8_8, all_0_5_5, all_0_4_4) = 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
% 259.51/213.47 |
% 259.51/213.47 | Applying alpha-rule on (1) yields:
% 259.51/213.47 | (2) ! [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)))
% 259.51/213.47 | (3) ! [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)))
% 259.51/213.47 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 259.51/213.47 | (5) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 259.51/213.47 | (6) ! [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)))
% 259.51/213.47 | (7) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 259.51/213.47 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 259.51/213.47 | (9) ! [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))
% 259.51/213.47 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 259.51/213.47 | (11) ! [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)))
% 259.51/213.47 | (12) ~ (all_0_0_0 = 0)
% 259.51/213.47 | (13) ! [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)))
% 259.51/213.47 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 259.51/213.47 | (15) ! [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)))
% 259.51/213.47 | (16) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 259.51/213.47 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 259.51/213.47 | (18) ! [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)))
% 259.51/213.48 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 259.51/213.48 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 259.51/213.48 | (21) ! [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))
% 259.51/213.48 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 259.51/213.48 | (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)))))
% 259.51/213.48 | (24) ! [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))
% 259.51/213.48 | (25) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 259.51/213.48 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 259.51/213.48 | (27) ! [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)))
% 259.51/213.48 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 259.51/213.48 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 259.51/213.48 | (30) ! [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)))
% 259.51/213.48 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 259.51/213.48 | (32) ! [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)))))
% 259.51/213.48 | (33) ! [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)))))
% 259.51/213.48 | (34) ! [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)))
% 259.51/213.48 | (35) identity(all_0_2_2, all_0_4_4) = 0
% 259.51/213.48 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 259.51/213.48 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 259.51/213.48 | (38) ! [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)))
% 259.51/213.48 | (39) ! [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)))
% 259.51/213.48 | (40) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 259.51/213.48 | (41) inverse_function(all_0_8_8, all_0_5_5, all_0_4_4) = all_0_1_1
% 259.51/213.48 | (42) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 259.51/213.48 | (43) ! [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)))
% 259.51/213.48 | (44) ! [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)))
% 259.51/213.48 | (45) ! [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)))
% 259.51/213.48 | (46) ! [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))
% 259.51/213.48 | (47) ! [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))
% 259.51/213.48 | (48) ! [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)))
% 259.51/213.48 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 259.51/213.48 | (50) ! [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)))
% 259.51/213.49 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 259.51/213.49 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 259.51/213.49 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 259.51/213.49 | (54) ! [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)))
% 259.51/213.49 | (55) ! [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)))
% 259.51/213.49 | (56) ! [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)))
% 259.51/213.49 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 259.51/213.49 | (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(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)))
% 259.51/213.49 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 259.51/213.49 | (60) ! [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)))
% 259.51/213.49 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 259.51/213.49 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 259.51/213.49 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 259.51/213.49 | (64) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 259.51/213.49 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 259.51/213.49 | (66) ! [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)))))
% 259.51/213.49 | (67) ! [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)))
% 259.51/213.49 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 259.51/213.49 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 259.51/213.49 | (70) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 259.51/213.49 | (71) ! [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))
% 259.51/213.49 | (72) ! [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)))
% 259.51/213.49 | (73) ! [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)))
% 259.51/213.49 | (74) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 259.51/213.49 | (75) ! [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)))
% 259.51/213.49 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 259.51/213.49 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 259.51/213.49 | (78) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 259.51/213.49 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 259.51/213.49 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 259.51/213.49 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 259.51/213.49 | (82) ! [v0] : ~ (member(v0, empty_set) = 0)
% 259.51/213.49 | (83) ! [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))))
% 259.51/213.49 | (84) equal_maps(all_0_1_1, all_0_6_6, all_0_4_4, all_0_5_5) = all_0_0_0
% 259.51/213.49 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 259.51/213.49 | (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)))))
% 259.51/213.50 | (87) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 259.51/213.50 | (88) maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0
% 259.51/213.50 | (89) ! [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)))
% 259.51/213.50 | (90) ! [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)))))
% 259.51/213.50 | (91) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 259.51/213.50 | (92) identity(all_0_3_3, all_0_5_5) = 0
% 259.51/213.50 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 259.51/213.50 | (94) compose_function(all_0_8_8, all_0_6_6, all_0_4_4, all_0_5_5, all_0_4_4) = all_0_2_2
% 259.51/213.50 | (95) ! [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)))
% 259.51/213.50 | (96) ! [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)))))
% 259.51/213.50 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 259.51/213.50 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 259.51/213.50 | (99) ! [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)))
% 259.51/213.50 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 259.51/213.50 | (101) ! [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)))
% 259.51/213.50 | (102) ? [v0] : ? [v1] : product(v0) = v1
% 259.51/213.50 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 259.51/213.50 | (104) ! [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)))
% 259.51/213.50 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 259.51/213.50 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 259.51/213.50 | (107) ! [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)))))
% 259.51/213.50 | (108) ! [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)))
% 259.51/213.50 | (109) ! [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))
% 259.51/213.50 | (110) ! [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)))
% 259.51/213.50 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 259.51/213.50 | (112) ! [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)))
% 259.51/213.50 | (113) ! [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))))
% 259.51/213.50 | (114) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 259.51/213.50 | (115) ! [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)))
% 259.51/213.50 | (116) ! [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)))
% 259.51/213.51 | (117) ! [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))
% 259.51/213.51 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 259.51/213.51 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, 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)))))
% 259.51/213.51 | (120) maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0
% 259.51/213.51 | (121) ! [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)))))
% 259.51/213.51 | (122) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 259.51/213.51 | (123) ! [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)))
% 259.51/213.51 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 259.51/213.51 | (125) ! [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)))
% 259.51/213.51 | (126) ! [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)))
% 259.51/213.51 | (127) ! [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))
% 259.51/213.51 | (128) ! [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)))
% 259.51/213.51 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 259.51/213.51 | (130) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 259.51/213.51 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 259.51/213.51 | (132) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 259.51/213.51 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 259.51/213.51 | (134) ! [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)))
% 259.51/213.51 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 259.51/213.51 | (136) ! [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)))
% 259.95/213.51 | (137) ! [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))
% 259.95/213.51 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 259.95/213.51 | (139) ! [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)))
% 259.95/213.51 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 259.95/213.51 | (141) ! [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)))
% 259.95/213.51 | (142) ! [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)))
% 259.95/213.51 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 259.95/213.51 | (144) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 259.95/213.51 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 259.95/213.51 | (146) ! [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))
% 259.95/213.51 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 259.95/213.51 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 259.95/213.51 | (149) ! [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)))))))
% 259.95/213.52 | (150) ! [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)))
% 259.95/213.52 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 259.95/213.52 | (152) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 259.95/213.52 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 259.95/213.52 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 259.95/213.52 | (155) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 259.95/213.52 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 259.95/213.52 | (157) ? [v0] : ? [v1] : singleton(v0) = v1
% 259.95/213.52 | (158) ! [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))
% 259.95/213.52 | (159) ! [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))
% 259.95/213.52 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 259.95/213.52 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 259.95/213.52 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 259.95/213.52 | (163) ! [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)))))
% 259.95/213.52 | (164) ! [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)))
% 259.95/213.52 | (165) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 259.95/213.52 | (166) ! [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)))))
% 259.95/213.52 | (167) compose_function(all_0_7_7, all_0_8_8, all_0_5_5, all_0_4_4, all_0_5_5) = all_0_3_3
% 259.95/213.52 | (168) ! [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))
% 259.95/213.52 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 259.95/213.52 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 259.95/213.52 | (171) ! [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)))
% 259.95/213.52 | (172) ! [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))
% 259.95/213.52 | (173) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 259.95/213.52 | (174) ! [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)))
% 259.95/213.52 | (175) maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0
% 259.95/213.52 | (176) ! [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)))
% 259.95/213.52 | (177) ! [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)))
% 259.95/213.52 | (178) ! [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)))
% 259.95/213.52 | (179) ! [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)))))
% 259.95/213.52 | (180) ! [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)))
% 259.95/213.53 | (181) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 259.95/213.53 | (182) ! [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)))
% 259.95/213.53 | (183) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 259.95/213.53 | (184) ? [v0] : ? [v1] : power_set(v0) = v1
% 259.95/213.53 | (185) ! [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)))))
% 259.95/213.53 | (186) ! [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)))
% 259.95/213.53 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 259.95/213.53 | (188) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 259.95/213.53 | (189) ? [v0] : ? [v1] : sum(v0) = v1
% 259.95/213.53 | (190) ! [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)))
% 259.95/213.53 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 259.95/213.53 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (24) with all_0_0_0, all_0_5_5, all_0_4_4, all_0_6_6, all_0_1_1 and discharging atoms equal_maps(all_0_1_1, all_0_6_6, all_0_4_4, all_0_5_5) = all_0_0_0, yields:
% 259.95/213.53 | (193) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_1_1, v0, v1) = 0 & apply(all_0_6_6, v0, v2) = 0 & member(v2, all_0_5_5) = 0 & member(v1, all_0_5_5) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.53 |
% 259.95/213.53 +-Applying beta-rule and splitting (193), into two cases.
% 259.95/213.53 |-Branch one:
% 259.95/213.53 | (194) all_0_0_0 = 0
% 259.95/213.53 |
% 259.95/213.53 | Equations (194) can reduce 12 to:
% 259.95/213.53 | (195) $false
% 259.95/213.53 |
% 259.95/213.53 |-The branch is then unsatisfiable
% 259.95/213.53 |-Branch two:
% 259.95/213.53 | (12) ~ (all_0_0_0 = 0)
% 259.95/213.53 | (197) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_1_1, v0, v1) = 0 & apply(all_0_6_6, v0, v2) = 0 & member(v2, all_0_5_5) = 0 & member(v1, all_0_5_5) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.53 |
% 259.95/213.53 | Instantiating (197) with all_68_0_120, all_68_1_121, all_68_2_122 yields:
% 259.95/213.53 | (198) ~ (all_68_0_120 = all_68_1_121) & apply(all_0_1_1, all_68_2_122, all_68_1_121) = 0 & apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0 & member(all_68_0_120, all_0_5_5) = 0 & member(all_68_1_121, all_0_5_5) = 0 & member(all_68_2_122, all_0_4_4) = 0
% 259.95/213.53 |
% 259.95/213.53 | Applying alpha-rule on (198) yields:
% 259.95/213.53 | (199) member(all_68_1_121, all_0_5_5) = 0
% 259.95/213.53 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.53 | (201) member(all_68_2_122, all_0_4_4) = 0
% 259.95/213.53 | (202) member(all_68_0_120, all_0_5_5) = 0
% 259.95/213.53 | (203) apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0
% 259.95/213.53 | (204) apply(all_0_1_1, all_68_2_122, all_68_1_121) = 0
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (86) with 0, all_0_1_1, all_68_2_122, all_68_1_121, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms inverse_function(all_0_8_8, all_0_5_5, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_68_2_122, all_68_1_121) = 0, yields:
% 259.95/213.53 | (205) ? [v0] : ((v0 = 0 & apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (69) with all_68_0_120, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.53 | (206) ? [v0] : (apply(all_0_8_8, all_68_0_120, v0) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (111) with all_68_0_120, all_0_5_5, all_0_3_3 and discharging atoms identity(all_0_3_3, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.53 | (207) apply(all_0_3_3, all_68_0_120, all_68_0_120) = 0
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (141) with all_68_0_120, all_68_1_121, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.53 | (208) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_1_121) = v0) | ( ~ (v0 = 0) & member(all_68_0_120, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (69) with all_68_1_121, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.53 | (209) ? [v0] : (apply(all_0_8_8, all_68_1_121, v0) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (111) with all_68_1_121, all_0_5_5, all_0_3_3 and discharging atoms identity(all_0_3_3, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.53 | (210) apply(all_0_3_3, all_68_1_121, all_68_1_121) = 0
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.53 | (211) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (69) with all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.53 | (212) ? [v0] : (apply(all_0_6_6, all_68_2_122, v0) = 0 & member(v0, all_0_5_5) = 0)
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_68_2_122, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.53 | (213) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (69) with all_68_2_122, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.53 | (214) ? [v0] : (apply(all_0_7_7, all_68_2_122, v0) = 0 & member(v0, all_0_5_5) = 0)
% 259.95/213.53 |
% 259.95/213.53 | Instantiating formula (111) with all_68_2_122, all_0_4_4, all_0_2_2 and discharging atoms identity(all_0_2_2, all_0_4_4) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.53 | (215) apply(all_0_2_2, all_68_2_122, all_68_2_122) = 0
% 259.95/213.54 |
% 259.95/213.54 | Instantiating (212) with all_76_0_123 yields:
% 259.95/213.54 | (216) apply(all_0_6_6, all_68_2_122, all_76_0_123) = 0 & member(all_76_0_123, all_0_5_5) = 0
% 259.95/213.54 |
% 259.95/213.54 | Applying alpha-rule on (216) yields:
% 259.95/213.54 | (217) apply(all_0_6_6, all_68_2_122, all_76_0_123) = 0
% 259.95/213.54 | (218) member(all_76_0_123, all_0_5_5) = 0
% 259.95/213.54 |
% 259.95/213.54 | Instantiating (206) with all_78_0_124 yields:
% 259.95/213.54 | (219) apply(all_0_8_8, all_68_0_120, all_78_0_124) = 0 & member(all_78_0_124, all_0_4_4) = 0
% 259.95/213.54 |
% 259.95/213.54 | Applying alpha-rule on (219) yields:
% 259.95/213.54 | (220) apply(all_0_8_8, all_68_0_120, all_78_0_124) = 0
% 259.95/213.54 | (221) member(all_78_0_124, all_0_4_4) = 0
% 259.95/213.54 |
% 259.95/213.54 | Instantiating (214) with all_80_0_125 yields:
% 259.95/213.54 | (222) apply(all_0_7_7, all_68_2_122, all_80_0_125) = 0 & member(all_80_0_125, all_0_5_5) = 0
% 259.95/213.54 |
% 259.95/213.54 | Applying alpha-rule on (222) yields:
% 259.95/213.54 | (223) apply(all_0_7_7, all_68_2_122, all_80_0_125) = 0
% 259.95/213.54 | (224) member(all_80_0_125, all_0_5_5) = 0
% 259.95/213.54 |
% 259.95/213.54 | Instantiating (209) with all_82_0_126 yields:
% 259.95/213.54 | (225) apply(all_0_8_8, all_68_1_121, all_82_0_126) = 0 & member(all_82_0_126, all_0_4_4) = 0
% 259.95/213.54 |
% 259.95/213.54 | Applying alpha-rule on (225) yields:
% 259.95/213.54 | (226) apply(all_0_8_8, all_68_1_121, all_82_0_126) = 0
% 259.95/213.54 | (227) member(all_82_0_126, all_0_4_4) = 0
% 259.95/213.54 |
% 259.95/213.54 | Instantiating (205) with all_84_0_127 yields:
% 259.95/213.54 | (228) (all_84_0_127 = 0 & apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0) | ( ~ (all_84_0_127 = 0) & member(all_68_1_121, all_0_5_5) = all_84_0_127) | ( ~ (all_84_0_127 = 0) & member(all_68_2_122, all_0_4_4) = all_84_0_127)
% 259.95/213.54 |
% 259.95/213.54 +-Applying beta-rule and splitting (228), into two cases.
% 259.95/213.54 |-Branch one:
% 259.95/213.54 | (229) (all_84_0_127 = 0 & apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0) | ( ~ (all_84_0_127 = 0) & member(all_68_1_121, all_0_5_5) = all_84_0_127)
% 259.95/213.54 |
% 259.95/213.54 +-Applying beta-rule and splitting (229), into two cases.
% 259.95/213.54 |-Branch one:
% 259.95/213.54 | (230) all_84_0_127 = 0 & apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0
% 259.95/213.54 |
% 259.95/213.54 | Applying alpha-rule on (230) yields:
% 259.95/213.54 | (231) all_84_0_127 = 0
% 259.95/213.54 | (232) apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0
% 259.95/213.54 |
% 259.95/213.54 +-Applying beta-rule and splitting (208), into two cases.
% 259.95/213.54 |-Branch one:
% 259.95/213.54 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.54 |
% 259.95/213.54 | Equations (233) can reduce 200 to:
% 259.95/213.54 | (195) $false
% 259.95/213.54 |
% 259.95/213.54 |-The branch is then unsatisfiable
% 259.95/213.54 |-Branch two:
% 259.95/213.54 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.54 | (236) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_1_121) = v0) | ( ~ (v0 = 0) & member(all_68_0_120, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.54 |
% 259.95/213.54 +-Applying beta-rule and splitting (213), into two cases.
% 259.95/213.54 |-Branch one:
% 259.95/213.54 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.54 |
% 259.95/213.54 | Equations (233) can reduce 200 to:
% 259.95/213.54 | (195) $false
% 259.95/213.54 |
% 259.95/213.54 |-The branch is then unsatisfiable
% 259.95/213.54 |-Branch two:
% 259.95/213.54 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.54 | (240) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (240) with all_96_0_129 yields:
% 259.95/213.55 | (241) ( ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129) | ( ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129)
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (211), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 | (245) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (139) with all_0_2_2, all_68_2_122, all_68_2_122, all_0_4_4, all_0_5_5, all_0_4_4, all_0_6_6, all_0_8_8 and discharging atoms compose_function(all_0_8_8, all_0_6_6, all_0_4_4, all_0_5_5, all_0_4_4) = all_0_2_2, apply(all_0_2_2, all_68_2_122, all_68_2_122) = 0, yields:
% 259.95/213.55 | (246) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_6_6, all_68_2_122, v0) = 0 & apply(all_0_8_8, v0, all_68_2_122) = 0 & member(v0, all_0_5_5) = 0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (139) with all_0_3_3, all_68_0_120, all_68_0_120, all_0_5_5, all_0_4_4, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms compose_function(all_0_7_7, all_0_8_8, all_0_5_5, all_0_4_4, all_0_5_5) = all_0_3_3, apply(all_0_3_3, all_68_0_120, all_68_0_120) = 0, yields:
% 259.95/213.55 | (247) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_7_7, v0, all_68_0_120) = 0 & apply(all_0_8_8, all_68_0_120, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_68_0_120, all_0_5_5) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (139) with all_0_3_3, all_68_1_121, all_68_1_121, all_0_5_5, all_0_4_4, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms compose_function(all_0_7_7, all_0_8_8, all_0_5_5, all_0_4_4, all_0_5_5) = all_0_3_3, apply(all_0_3_3, all_68_1_121, all_68_1_121) = 0, yields:
% 259.95/213.55 | (248) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_7_7, v0, all_68_1_121) = 0 & apply(all_0_8_8, all_68_1_121, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (69) with all_82_0_126, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_82_0_126, all_0_4_4) = 0, yields:
% 259.95/213.55 | (249) ? [v0] : (apply(all_0_6_6, all_82_0_126, v0) = 0 & member(v0, all_0_5_5) = 0)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_82_0_126, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_82_0_126, all_0_4_4) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (250) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (69) with all_82_0_126, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_82_0_126, all_0_4_4) = 0, yields:
% 259.95/213.55 | (251) ? [v0] : (apply(all_0_7_7, all_82_0_126, v0) = 0 & member(v0, all_0_5_5) = 0)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (141) with all_68_2_122, all_82_0_126, all_68_1_121, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0, member(all_82_0_126, all_0_4_4) = 0, yields:
% 259.95/213.55 | (252) all_82_0_126 = all_68_2_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_82_0_126) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (69) with all_80_0_125, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, member(all_80_0_125, all_0_5_5) = 0, yields:
% 259.95/213.55 | (253) ? [v0] : (apply(all_0_8_8, all_80_0_125, v0) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_78_0_124, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_78_0_124, all_0_4_4) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (254) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_78_0_124, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_78_0_124, all_0_4_4) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (255) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_76_0_123, all_68_0_120, all_82_0_126, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_82_0_126, all_0_4_4) = 0, member(all_76_0_123, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.55 | (256) all_76_0_123 = all_68_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_82_0_126, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_82_0_126, all_68_0_120) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_76_0_123, all_68_1_121, all_78_0_124, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_78_0_124, all_0_4_4) = 0, member(all_76_0_123, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (257) all_76_0_123 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_76_0_123, all_68_1_121, all_68_2_122, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_76_0_123, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.55 | (258) all_76_0_123 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_76_0_123, all_68_1_121, all_82_0_126, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_82_0_126, all_0_4_4) = 0, member(all_76_0_123, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (259) all_76_0_123 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (178) with all_76_0_123, all_68_1_121, all_78_0_124, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_78_0_124, all_0_4_4) = 0, member(all_76_0_123, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.55 | (260) all_76_0_123 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (69) with all_76_0_123, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, member(all_76_0_123, all_0_5_5) = 0, yields:
% 259.95/213.55 | (261) ? [v0] : (apply(all_0_8_8, all_76_0_123, v0) = 0 & member(v0, all_0_4_4) = 0)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (261) with all_119_0_131 yields:
% 259.95/213.55 | (262) apply(all_0_8_8, all_76_0_123, all_119_0_131) = 0 & member(all_119_0_131, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (262) yields:
% 259.95/213.55 | (263) apply(all_0_8_8, all_76_0_123, all_119_0_131) = 0
% 259.95/213.55 | (264) member(all_119_0_131, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (251) with all_121_0_132 yields:
% 259.95/213.55 | (265) apply(all_0_7_7, all_82_0_126, all_121_0_132) = 0 & member(all_121_0_132, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (265) yields:
% 259.95/213.55 | (266) apply(all_0_7_7, all_82_0_126, all_121_0_132) = 0
% 259.95/213.55 | (267) member(all_121_0_132, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (249) with all_123_0_133 yields:
% 259.95/213.55 | (268) apply(all_0_6_6, all_82_0_126, all_123_0_133) = 0 & member(all_123_0_133, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (268) yields:
% 259.95/213.55 | (269) apply(all_0_6_6, all_82_0_126, all_123_0_133) = 0
% 259.95/213.55 | (270) member(all_123_0_133, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (248) with all_127_0_135, all_127_1_136, all_127_2_137, all_127_3_138 yields:
% 259.95/213.55 | (271) (all_127_0_135 = 0 & all_127_1_136 = 0 & all_127_2_137 = 0 & apply(all_0_7_7, all_127_3_138, all_68_1_121) = 0 & apply(all_0_8_8, all_68_1_121, all_127_3_138) = 0 & member(all_127_3_138, all_0_4_4) = 0) | ( ~ (all_127_3_138 = 0) & member(all_68_1_121, all_0_5_5) = all_127_3_138)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (247) with all_128_0_139, all_128_1_140, all_128_2_141, all_128_3_142 yields:
% 259.95/213.55 | (272) (all_128_0_139 = 0 & all_128_1_140 = 0 & all_128_2_141 = 0 & apply(all_0_7_7, all_128_3_142, all_68_0_120) = 0 & apply(all_0_8_8, all_68_0_120, all_128_3_142) = 0 & member(all_128_3_142, all_0_4_4) = 0) | ( ~ (all_128_3_142 = 0) & member(all_68_0_120, all_0_5_5) = all_128_3_142)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (246) with all_129_0_143, all_129_1_144, all_129_2_145, all_129_3_146 yields:
% 259.95/213.55 | (273) (all_129_0_143 = 0 & all_129_1_144 = 0 & all_129_2_145 = 0 & apply(all_0_6_6, all_68_2_122, all_129_3_146) = 0 & apply(all_0_8_8, all_129_3_146, all_68_2_122) = 0 & member(all_129_3_146, all_0_5_5) = 0) | ( ~ (all_129_3_146 = 0) & member(all_68_2_122, all_0_4_4) = all_129_3_146)
% 259.95/213.55 |
% 259.95/213.55 | Instantiating (253) with all_132_0_148 yields:
% 259.95/213.55 | (274) apply(all_0_8_8, all_80_0_125, all_132_0_148) = 0 & member(all_132_0_148, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (274) yields:
% 259.95/213.55 | (275) apply(all_0_8_8, all_80_0_125, all_132_0_148) = 0
% 259.95/213.55 | (276) member(all_132_0_148, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (252), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (277) all_82_0_126 = all_68_2_122
% 259.95/213.55 |
% 259.95/213.55 | From (277) and (269) follows:
% 259.95/213.55 | (278) apply(all_0_6_6, all_68_2_122, all_123_0_133) = 0
% 259.95/213.55 |
% 259.95/213.55 | From (277) and (266) follows:
% 259.95/213.55 | (279) apply(all_0_7_7, all_68_2_122, all_121_0_132) = 0
% 259.95/213.55 |
% 259.95/213.55 | From (277) and (226) follows:
% 259.95/213.55 | (232) apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0
% 259.95/213.55 |
% 259.95/213.55 | From (277) and (227) follows:
% 259.95/213.55 | (201) member(all_68_2_122, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (256), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (282) all_76_0_123 = all_68_0_120
% 259.95/213.55 |
% 259.95/213.55 | From (282) and (217) follows:
% 259.95/213.55 | (203) apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0
% 259.95/213.55 |
% 259.95/213.55 | From (282) and (263) follows:
% 259.95/213.55 | (284) apply(all_0_8_8, all_68_0_120, all_119_0_131) = 0
% 259.95/213.55 |
% 259.95/213.55 | From (282) and (218) follows:
% 259.95/213.55 | (202) member(all_68_0_120, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (254), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 | (289) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (255), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 | (293) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (250), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 | (297) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (273), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (298) all_129_0_143 = 0 & all_129_1_144 = 0 & all_129_2_145 = 0 & apply(all_0_6_6, all_68_2_122, all_129_3_146) = 0 & apply(all_0_8_8, all_129_3_146, all_68_2_122) = 0 & member(all_129_3_146, all_0_5_5) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (298) yields:
% 259.95/213.55 | (299) all_129_1_144 = 0
% 259.95/213.55 | (300) apply(all_0_8_8, all_129_3_146, all_68_2_122) = 0
% 259.95/213.55 | (301) apply(all_0_6_6, all_68_2_122, all_129_3_146) = 0
% 259.95/213.55 | (302) member(all_129_3_146, all_0_5_5) = 0
% 259.95/213.55 | (303) all_129_2_145 = 0
% 259.95/213.55 | (304) all_129_0_143 = 0
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (271), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (305) all_127_0_135 = 0 & all_127_1_136 = 0 & all_127_2_137 = 0 & apply(all_0_7_7, all_127_3_138, all_68_1_121) = 0 & apply(all_0_8_8, all_68_1_121, all_127_3_138) = 0 & member(all_127_3_138, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (305) yields:
% 259.95/213.55 | (306) apply(all_0_8_8, all_68_1_121, all_127_3_138) = 0
% 259.95/213.55 | (307) member(all_127_3_138, all_0_4_4) = 0
% 259.95/213.55 | (308) all_127_1_136 = 0
% 259.95/213.55 | (309) all_127_2_137 = 0
% 259.95/213.55 | (310) all_127_0_135 = 0
% 259.95/213.55 | (311) apply(all_0_7_7, all_127_3_138, all_68_1_121) = 0
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (260), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (312) all_76_0_123 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Combining equations (312,282) yields a new equation:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (315) ~ (all_76_0_123 = all_68_1_121)
% 259.95/213.55 | (316) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Equations (282) can reduce 315 to:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (257), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (312) all_76_0_123 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Combining equations (312,282) yields a new equation:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (315) ~ (all_76_0_123 = all_68_1_121)
% 259.95/213.55 | (322) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_78_0_124, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Equations (282) can reduce 315 to:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (258), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (312) all_76_0_123 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Combining equations (312,282) yields a new equation:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (315) ~ (all_76_0_123 = all_68_1_121)
% 259.95/213.55 | (328) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Equations (282) can reduce 315 to:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (259), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (312) all_76_0_123 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Combining equations (312,282) yields a new equation:
% 259.95/213.55 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.55 |
% 259.95/213.55 | Equations (233) can reduce 200 to:
% 259.95/213.55 | (195) $false
% 259.95/213.55 |
% 259.95/213.55 |-The branch is then unsatisfiable
% 259.95/213.55 |-Branch two:
% 259.95/213.55 | (315) ~ (all_76_0_123 = all_68_1_121)
% 259.95/213.55 | (334) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_82_0_126, all_68_1_121) = v0))
% 259.95/213.55 |
% 259.95/213.55 | Equations (282) can reduce 315 to:
% 259.95/213.55 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.55 |
% 259.95/213.55 +-Applying beta-rule and splitting (272), into two cases.
% 259.95/213.55 |-Branch one:
% 259.95/213.55 | (336) all_128_0_139 = 0 & all_128_1_140 = 0 & all_128_2_141 = 0 & apply(all_0_7_7, all_128_3_142, all_68_0_120) = 0 & apply(all_0_8_8, all_68_0_120, all_128_3_142) = 0 & member(all_128_3_142, all_0_4_4) = 0
% 259.95/213.55 |
% 259.95/213.55 | Applying alpha-rule on (336) yields:
% 259.95/213.55 | (337) all_128_1_140 = 0
% 259.95/213.55 | (338) member(all_128_3_142, all_0_4_4) = 0
% 259.95/213.55 | (339) apply(all_0_7_7, all_128_3_142, all_68_0_120) = 0
% 259.95/213.55 | (340) all_128_0_139 = 0
% 259.95/213.55 | (341) apply(all_0_8_8, all_68_0_120, all_128_3_142) = 0
% 259.95/213.55 | (342) all_128_2_141 = 0
% 259.95/213.55 |
% 259.95/213.55 | Instantiating formula (141) with all_129_3_146, all_68_0_120, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, apply(all_0_6_6, all_68_2_122, all_129_3_146) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.56 | (343) all_129_3_146 = all_68_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & member(all_129_3_146, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_123_0_133, all_68_0_120, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, apply(all_0_6_6, all_68_2_122, all_123_0_133) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.56 | (344) all_123_0_133 = all_68_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & member(all_123_0_133, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_127_3_138, all_68_2_122, all_68_1_121, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, apply(all_0_8_8, all_68_1_121, all_127_3_138) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.56 | (345) all_127_3_138 = all_68_2_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = v0) | ( ~ (v0 = 0) & member(all_127_3_138, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_68_0_120, all_68_1_121, all_132_0_148, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_132_0_148, all_0_4_4) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.56 | (346) all_68_0_120 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_132_0_148, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_132_0_148, all_68_1_121) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_123_0_133, all_129_3_146, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, apply(all_0_6_6, all_68_2_122, all_123_0_133) = 0, member(all_129_3_146, all_0_5_5) = 0, yields:
% 259.95/213.56 | (347) all_129_3_146 = all_123_0_133 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = v0) | ( ~ (v0 = 0) & member(all_123_0_133, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_129_3_146, all_68_0_120, all_68_2_122, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_5_5) = 0, member(all_129_3_146, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.56 | (348) all_129_3_146 = all_68_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_68_2_122, all_127_3_138, all_68_1_121, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0, member(all_127_3_138, all_0_4_4) = 0, yields:
% 259.95/213.56 | (349) all_127_3_138 = all_68_2_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_127_3_138) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_119_0_131, all_127_3_138, all_68_0_120, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, apply(all_0_8_8, all_68_0_120, all_119_0_131) = 0, member(all_127_3_138, all_0_4_4) = 0, yields:
% 259.95/213.56 | (350) all_127_3_138 = all_119_0_131 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_0_120, all_127_3_138) = v0) | ( ~ (v0 = 0) & member(all_119_0_131, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_68_0_120, all_0_5_5) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_68_2_122, all_128_3_142, all_123_0_133, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms maps(all_0_8_8, all_0_5_5, all_0_4_4) = 0, member(all_128_3_142, all_0_4_4) = 0, member(all_123_0_133, all_0_5_5) = 0, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.56 | (351) all_128_3_142 = all_68_2_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_123_0_133, all_128_3_142) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_123_0_133, all_68_2_122) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (141) with all_80_0_125, all_121_0_132, all_68_2_122, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, apply(all_0_7_7, all_68_2_122, all_80_0_125) = 0, member(all_121_0_132, all_0_5_5) = 0, yields:
% 259.95/213.56 | (352) all_121_0_132 = all_80_0_125 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_121_0_132) = v0) | ( ~ (v0 = 0) & member(all_80_0_125, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_80_0_125, all_68_0_120, all_119_0_131, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_119_0_131, all_0_4_4) = 0, member(all_80_0_125, all_0_5_5) = 0, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.56 | (353) all_80_0_125 = all_68_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_80_0_125) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_0_120) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_68_1_121, all_123_0_133, all_119_0_131, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_123_0_133, all_0_5_5) = 0, member(all_119_0_131, all_0_4_4) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.56 | (354) all_123_0_133 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_123_0_133) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (178) with all_68_1_121, all_121_0_132, all_119_0_131, all_0_5_5, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_5_5) = 0, member(all_121_0_132, all_0_5_5) = 0, member(all_119_0_131, all_0_4_4) = 0, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.56 | (355) all_121_0_132 = all_68_1_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_121_0_132) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = v0))
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (352), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (356) all_121_0_132 = all_80_0_125
% 259.95/213.56 |
% 259.95/213.56 | From (356) and (279) follows:
% 259.95/213.56 | (223) apply(all_0_7_7, all_68_2_122, all_80_0_125) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (347), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (358) all_129_3_146 = all_123_0_133
% 259.95/213.56 |
% 259.95/213.56 | From (358) and (301) follows:
% 259.95/213.56 | (278) apply(all_0_6_6, all_68_2_122, all_123_0_133) = 0
% 259.95/213.56 |
% 259.95/213.56 | From (358) and (300) follows:
% 259.95/213.56 | (360) apply(all_0_8_8, all_123_0_133, all_68_2_122) = 0
% 259.95/213.56 |
% 259.95/213.56 | From (358) and (302) follows:
% 259.95/213.56 | (270) member(all_123_0_133, all_0_5_5) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (348), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (362) all_129_3_146 = all_68_0_120
% 259.95/213.56 |
% 259.95/213.56 | Combining equations (362,358) yields a new equation:
% 259.95/213.56 | (363) all_123_0_133 = all_68_0_120
% 259.95/213.56 |
% 259.95/213.56 | From (363) and (360) follows:
% 259.95/213.56 | (364) apply(all_0_8_8, all_68_0_120, all_68_2_122) = 0
% 259.95/213.56 |
% 259.95/213.56 | From (363) and (270) follows:
% 259.95/213.56 | (202) member(all_68_0_120, all_0_5_5) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (345), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (366) all_127_3_138 = all_68_2_122
% 259.95/213.56 |
% 259.95/213.56 | From (366) and (311) follows:
% 259.95/213.56 | (367) apply(all_0_7_7, all_68_2_122, all_68_1_121) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (350), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (368) all_127_3_138 = all_119_0_131
% 259.95/213.56 |
% 259.95/213.56 | Combining equations (368,366) yields a new equation:
% 259.95/213.56 | (369) all_119_0_131 = all_68_2_122
% 259.95/213.56 |
% 259.95/213.56 | Simplifying 369 yields:
% 259.95/213.56 | (370) all_119_0_131 = all_68_2_122
% 259.95/213.56 |
% 259.95/213.56 | From (370) and (284) follows:
% 259.95/213.56 | (364) apply(all_0_8_8, all_68_0_120, all_68_2_122) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (355), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (372) all_121_0_132 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Combining equations (356,372) yields a new equation:
% 259.95/213.56 | (373) all_80_0_125 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Simplifying 373 yields:
% 259.95/213.56 | (374) all_80_0_125 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | From (374) and (223) follows:
% 259.95/213.56 | (367) apply(all_0_7_7, all_68_2_122, all_68_1_121) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (354), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (376) all_123_0_133 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Combining equations (363,376) yields a new equation:
% 259.95/213.56 | (377) all_68_0_120 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Simplifying 377 yields:
% 259.95/213.56 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Equations (233) can reduce 200 to:
% 259.95/213.56 | (195) $false
% 259.95/213.56 |
% 259.95/213.56 |-The branch is then unsatisfiable
% 259.95/213.56 |-Branch two:
% 259.95/213.56 | (380) ~ (all_123_0_133 = all_68_1_121)
% 259.95/213.56 | (381) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_123_0_133) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Equations (363) can reduce 380 to:
% 259.95/213.56 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (346), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Equations (233) can reduce 200 to:
% 259.95/213.56 | (195) $false
% 259.95/213.56 |
% 259.95/213.56 |-The branch is then unsatisfiable
% 259.95/213.56 |-Branch two:
% 259.95/213.56 | (200) ~ (all_68_0_120 = all_68_1_121)
% 259.95/213.56 | (386) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_132_0_148, all_68_0_120) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_132_0_148, all_68_1_121) = v0))
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (351), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (387) all_128_3_142 = all_68_2_122
% 259.95/213.56 |
% 259.95/213.56 | From (387) and (339) follows:
% 259.95/213.56 | (388) apply(all_0_7_7, all_68_2_122, all_68_0_120) = 0
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (353), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (389) all_80_0_125 = all_68_0_120
% 259.95/213.56 |
% 259.95/213.56 | Combining equations (374,389) yields a new equation:
% 259.95/213.56 | (233) all_68_0_120 = all_68_1_121
% 259.95/213.56 |
% 259.95/213.56 | Equations (233) can reduce 200 to:
% 259.95/213.56 | (195) $false
% 259.95/213.56 |
% 259.95/213.56 |-The branch is then unsatisfiable
% 259.95/213.56 |-Branch two:
% 259.95/213.56 | (392) ~ (all_80_0_125 = all_68_0_120)
% 259.95/213.56 | (393) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_80_0_125) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_0_120) = v0))
% 259.95/213.56 |
% 259.95/213.56 | Instantiating (393) with all_256_0_179 yields:
% 259.95/213.56 | (394) ( ~ (all_256_0_179 = 0) & apply(all_0_7_7, all_119_0_131, all_80_0_125) = all_256_0_179) | ( ~ (all_256_0_179 = 0) & apply(all_0_7_7, all_119_0_131, all_68_0_120) = all_256_0_179)
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (394), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (395) ~ (all_256_0_179 = 0) & apply(all_0_7_7, all_119_0_131, all_80_0_125) = all_256_0_179
% 259.95/213.56 |
% 259.95/213.56 | Applying alpha-rule on (395) yields:
% 259.95/213.56 | (396) ~ (all_256_0_179 = 0)
% 259.95/213.56 | (397) apply(all_0_7_7, all_119_0_131, all_80_0_125) = all_256_0_179
% 259.95/213.56 |
% 259.95/213.56 | From (370)(374) and (397) follows:
% 259.95/213.56 | (398) apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_256_0_179
% 259.95/213.56 |
% 259.95/213.56 +-Applying beta-rule and splitting (241), into two cases.
% 259.95/213.56 |-Branch one:
% 259.95/213.56 | (399) ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129
% 259.95/213.56 |
% 259.95/213.56 | Applying alpha-rule on (399) yields:
% 259.95/213.56 | (400) ~ (all_96_0_129 = 0)
% 259.95/213.56 | (401) apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129
% 259.95/213.56 |
% 259.95/213.56 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_0_120, 0, all_96_0_129 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129, apply(all_0_7_7, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.57 | (402) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (402) can reduce 400 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (404) ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (404) yields:
% 259.95/213.57 | (400) ~ (all_96_0_129 = 0)
% 259.95/213.57 | (406) apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_1_121, all_96_0_129, all_256_0_179 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_256_0_179, apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129, yields:
% 259.95/213.57 | (407) all_256_0_179 = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_1_121, 0, all_256_0_179 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_256_0_179, apply(all_0_7_7, all_68_2_122, all_68_1_121) = 0, yields:
% 259.95/213.57 | (408) all_256_0_179 = 0
% 259.95/213.57 |
% 259.95/213.57 | Combining equations (407,408) yields a new equation:
% 259.95/213.57 | (409) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Simplifying 409 yields:
% 259.95/213.57 | (402) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (402) can reduce 400 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (412) ~ (all_256_0_179 = 0) & apply(all_0_7_7, all_119_0_131, all_68_0_120) = all_256_0_179
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (412) yields:
% 259.95/213.57 | (396) ~ (all_256_0_179 = 0)
% 259.95/213.57 | (414) apply(all_0_7_7, all_119_0_131, all_68_0_120) = all_256_0_179
% 259.95/213.57 |
% 259.95/213.57 | From (370) and (414) follows:
% 259.95/213.57 | (415) apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_256_0_179
% 259.95/213.57 |
% 259.95/213.57 +-Applying beta-rule and splitting (241), into two cases.
% 259.95/213.57 |-Branch one:
% 259.95/213.57 | (399) ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (399) yields:
% 259.95/213.57 | (400) ~ (all_96_0_129 = 0)
% 259.95/213.57 | (401) apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_0_120, all_96_0_129, all_256_0_179 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_256_0_179, apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_96_0_129, yields:
% 259.95/213.57 | (407) all_256_0_179 = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_0_120, 0, all_256_0_179 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_0_120) = all_256_0_179, apply(all_0_7_7, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.57 | (408) all_256_0_179 = 0
% 259.95/213.57 |
% 259.95/213.57 | Combining equations (407,408) yields a new equation:
% 259.95/213.57 | (409) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Simplifying 409 yields:
% 259.95/213.57 | (402) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (402) can reduce 400 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (404) ~ (all_96_0_129 = 0) & apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (404) yields:
% 259.95/213.57 | (400) ~ (all_96_0_129 = 0)
% 259.95/213.57 | (406) apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_1_121, 0, all_96_0_129 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_96_0_129, apply(all_0_7_7, all_68_2_122, all_68_1_121) = 0, yields:
% 259.95/213.57 | (402) all_96_0_129 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (402) can reduce 400 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (429) ~ (all_128_3_142 = all_68_2_122)
% 259.95/213.57 | (430) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_123_0_133, all_128_3_142) = v0) | ( ~ (v0 = 0) & apply(all_0_8_8, all_123_0_133, all_68_2_122) = v0))
% 259.95/213.57 |
% 259.95/213.57 | Instantiating (430) with all_252_0_2275 yields:
% 259.95/213.57 | (431) ( ~ (all_252_0_2275 = 0) & apply(all_0_8_8, all_123_0_133, all_128_3_142) = all_252_0_2275) | ( ~ (all_252_0_2275 = 0) & apply(all_0_8_8, all_123_0_133, all_68_2_122) = all_252_0_2275)
% 259.95/213.57 |
% 259.95/213.57 +-Applying beta-rule and splitting (431), into two cases.
% 259.95/213.57 |-Branch one:
% 259.95/213.57 | (432) ~ (all_252_0_2275 = 0) & apply(all_0_8_8, all_123_0_133, all_128_3_142) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (432) yields:
% 259.95/213.57 | (433) ~ (all_252_0_2275 = 0)
% 259.95/213.57 | (434) apply(all_0_8_8, all_123_0_133, all_128_3_142) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | From (363) and (434) follows:
% 259.95/213.57 | (435) apply(all_0_8_8, all_68_0_120, all_128_3_142) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_8_8, all_68_0_120, all_128_3_142, all_252_0_2275, 0 and discharging atoms apply(all_0_8_8, all_68_0_120, all_128_3_142) = all_252_0_2275, apply(all_0_8_8, all_68_0_120, all_128_3_142) = 0, yields:
% 259.95/213.57 | (436) all_252_0_2275 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (436) can reduce 433 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (438) ~ (all_252_0_2275 = 0) & apply(all_0_8_8, all_123_0_133, all_68_2_122) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (438) yields:
% 259.95/213.57 | (433) ~ (all_252_0_2275 = 0)
% 259.95/213.57 | (440) apply(all_0_8_8, all_123_0_133, all_68_2_122) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | From (363) and (440) follows:
% 259.95/213.57 | (441) apply(all_0_8_8, all_68_0_120, all_68_2_122) = all_252_0_2275
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_8_8, all_68_0_120, all_68_2_122, 0, all_252_0_2275 and discharging atoms apply(all_0_8_8, all_68_0_120, all_68_2_122) = all_252_0_2275, apply(all_0_8_8, all_68_0_120, all_68_2_122) = 0, yields:
% 259.95/213.57 | (436) all_252_0_2275 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (436) can reduce 433 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (444) ~ (all_121_0_132 = all_68_1_121)
% 259.95/213.57 | (445) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_121_0_132) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = v0))
% 259.95/213.57 |
% 259.95/213.57 | Instantiating (445) with all_240_0_3136 yields:
% 259.95/213.57 | (446) ( ~ (all_240_0_3136 = 0) & apply(all_0_7_7, all_119_0_131, all_121_0_132) = all_240_0_3136) | ( ~ (all_240_0_3136 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = all_240_0_3136)
% 259.95/213.57 |
% 259.95/213.57 +-Applying beta-rule and splitting (446), into two cases.
% 259.95/213.57 |-Branch one:
% 259.95/213.57 | (447) ~ (all_240_0_3136 = 0) & apply(all_0_7_7, all_119_0_131, all_121_0_132) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (447) yields:
% 259.95/213.57 | (448) ~ (all_240_0_3136 = 0)
% 259.95/213.57 | (449) apply(all_0_7_7, all_119_0_131, all_121_0_132) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | From (370)(356) and (449) follows:
% 259.95/213.57 | (450) apply(all_0_7_7, all_68_2_122, all_80_0_125) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_80_0_125, all_240_0_3136, 0 and discharging atoms apply(all_0_7_7, all_68_2_122, all_80_0_125) = all_240_0_3136, apply(all_0_7_7, all_68_2_122, all_80_0_125) = 0, yields:
% 259.95/213.57 | (451) all_240_0_3136 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (451) can reduce 448 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (453) ~ (all_240_0_3136 = 0) & apply(all_0_7_7, all_119_0_131, all_68_1_121) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (453) yields:
% 259.95/213.57 | (448) ~ (all_240_0_3136 = 0)
% 259.95/213.57 | (455) apply(all_0_7_7, all_119_0_131, all_68_1_121) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | From (370) and (455) follows:
% 259.95/213.57 | (456) apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_240_0_3136
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_68_1_121, 0, all_240_0_3136 and discharging atoms apply(all_0_7_7, all_68_2_122, all_68_1_121) = all_240_0_3136, apply(all_0_7_7, all_68_2_122, all_68_1_121) = 0, yields:
% 259.95/213.57 | (451) all_240_0_3136 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (451) can reduce 448 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (459) ~ (all_127_3_138 = all_119_0_131)
% 259.95/213.57 | (460) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_0_120, all_127_3_138) = v0) | ( ~ (v0 = 0) & member(all_119_0_131, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_68_0_120, all_0_5_5) = v0))
% 259.95/213.57 |
% 259.95/213.57 | Instantiating (460) with all_236_0_6431 yields:
% 259.95/213.57 | (461) ( ~ (all_236_0_6431 = 0) & apply(all_0_8_8, all_68_0_120, all_127_3_138) = all_236_0_6431) | ( ~ (all_236_0_6431 = 0) & member(all_119_0_131, all_0_4_4) = all_236_0_6431) | ( ~ (all_236_0_6431 = 0) & member(all_68_0_120, all_0_5_5) = all_236_0_6431)
% 259.95/213.57 |
% 259.95/213.57 +-Applying beta-rule and splitting (461), into two cases.
% 259.95/213.57 |-Branch one:
% 259.95/213.57 | (462) ( ~ (all_236_0_6431 = 0) & apply(all_0_8_8, all_68_0_120, all_127_3_138) = all_236_0_6431) | ( ~ (all_236_0_6431 = 0) & member(all_119_0_131, all_0_4_4) = all_236_0_6431)
% 259.95/213.57 |
% 259.95/213.57 +-Applying beta-rule and splitting (462), into two cases.
% 259.95/213.57 |-Branch one:
% 259.95/213.57 | (463) ~ (all_236_0_6431 = 0) & apply(all_0_8_8, all_68_0_120, all_127_3_138) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (463) yields:
% 259.95/213.57 | (464) ~ (all_236_0_6431 = 0)
% 259.95/213.57 | (465) apply(all_0_8_8, all_68_0_120, all_127_3_138) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | From (366) and (465) follows:
% 259.95/213.57 | (466) apply(all_0_8_8, all_68_0_120, all_68_2_122) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (52) with all_0_8_8, all_68_0_120, all_68_2_122, 0, all_236_0_6431 and discharging atoms apply(all_0_8_8, all_68_0_120, all_68_2_122) = all_236_0_6431, apply(all_0_8_8, all_68_0_120, all_68_2_122) = 0, yields:
% 259.95/213.57 | (467) all_236_0_6431 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (467) can reduce 464 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (469) ~ (all_236_0_6431 = 0) & member(all_119_0_131, all_0_4_4) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (469) yields:
% 259.95/213.57 | (464) ~ (all_236_0_6431 = 0)
% 259.95/213.57 | (471) member(all_119_0_131, all_0_4_4) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (77) with all_119_0_131, all_0_4_4, all_236_0_6431, 0 and discharging atoms member(all_119_0_131, all_0_4_4) = all_236_0_6431, member(all_119_0_131, all_0_4_4) = 0, yields:
% 259.95/213.57 | (467) all_236_0_6431 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (467) can reduce 464 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.57 |-Branch two:
% 259.95/213.57 | (474) ~ (all_236_0_6431 = 0) & member(all_68_0_120, all_0_5_5) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Applying alpha-rule on (474) yields:
% 259.95/213.57 | (464) ~ (all_236_0_6431 = 0)
% 259.95/213.57 | (476) member(all_68_0_120, all_0_5_5) = all_236_0_6431
% 259.95/213.57 |
% 259.95/213.57 | Instantiating formula (77) with all_68_0_120, all_0_5_5, all_236_0_6431, 0 and discharging atoms member(all_68_0_120, all_0_5_5) = all_236_0_6431, member(all_68_0_120, all_0_5_5) = 0, yields:
% 259.95/213.57 | (467) all_236_0_6431 = 0
% 259.95/213.57 |
% 259.95/213.57 | Equations (467) can reduce 464 to:
% 259.95/213.57 | (195) $false
% 259.95/213.57 |
% 259.95/213.57 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (479) ~ (all_127_3_138 = all_68_2_122)
% 259.95/213.58 | (480) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = v0) | ( ~ (v0 = 0) & member(all_127_3_138, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0))
% 259.95/213.58 |
% 259.95/213.58 | Instantiating (480) with all_232_0_9323 yields:
% 259.95/213.58 | (481) ( ~ (all_232_0_9323 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_232_0_9323) | ( ~ (all_232_0_9323 = 0) & member(all_127_3_138, all_0_4_4) = all_232_0_9323) | ( ~ (all_232_0_9323 = 0) & member(all_68_1_121, all_0_5_5) = all_232_0_9323)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (481), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (482) ( ~ (all_232_0_9323 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_232_0_9323) | ( ~ (all_232_0_9323 = 0) & member(all_127_3_138, all_0_4_4) = all_232_0_9323)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (482), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (483) ~ (all_232_0_9323 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (483) yields:
% 259.95/213.58 | (484) ~ (all_232_0_9323 = 0)
% 259.95/213.58 | (485) apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (52) with all_0_8_8, all_68_1_121, all_68_2_122, all_232_0_9323, 0 and discharging atoms apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_232_0_9323, apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0, yields:
% 259.95/213.58 | (486) all_232_0_9323 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (486) can reduce 484 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (488) ~ (all_232_0_9323 = 0) & member(all_127_3_138, all_0_4_4) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (488) yields:
% 259.95/213.58 | (484) ~ (all_232_0_9323 = 0)
% 259.95/213.58 | (490) member(all_127_3_138, all_0_4_4) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (77) with all_127_3_138, all_0_4_4, all_232_0_9323, 0 and discharging atoms member(all_127_3_138, all_0_4_4) = all_232_0_9323, member(all_127_3_138, all_0_4_4) = 0, yields:
% 259.95/213.58 | (486) all_232_0_9323 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (486) can reduce 484 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (493) ~ (all_232_0_9323 = 0) & member(all_68_1_121, all_0_5_5) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (493) yields:
% 259.95/213.58 | (484) ~ (all_232_0_9323 = 0)
% 259.95/213.58 | (495) member(all_68_1_121, all_0_5_5) = all_232_0_9323
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_232_0_9323, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_232_0_9323, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.58 | (486) all_232_0_9323 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (486) can reduce 484 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (498) ~ (all_129_3_146 = all_68_0_120)
% 259.95/213.58 | (499) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0))
% 259.95/213.58 |
% 259.95/213.58 | Instantiating (499) with all_228_0_10963 yields:
% 259.95/213.58 | (500) ( ~ (all_228_0_10963 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_228_0_10963) | ( ~ (all_228_0_10963 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_228_0_10963)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (500), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (501) ~ (all_228_0_10963 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_228_0_10963
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (501) yields:
% 259.95/213.58 | (502) ~ (all_228_0_10963 = 0)
% 259.95/213.58 | (503) apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_228_0_10963
% 259.95/213.58 |
% 259.95/213.58 | From (358) and (503) follows:
% 259.95/213.58 | (504) apply(all_0_6_6, all_68_2_122, all_123_0_133) = all_228_0_10963
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_123_0_133, all_228_0_10963, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_123_0_133) = all_228_0_10963, apply(all_0_6_6, all_68_2_122, all_123_0_133) = 0, yields:
% 259.95/213.58 | (505) all_228_0_10963 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (505) can reduce 502 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (507) ~ (all_228_0_10963 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_228_0_10963
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (507) yields:
% 259.95/213.58 | (502) ~ (all_228_0_10963 = 0)
% 259.95/213.58 | (509) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_228_0_10963
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_228_0_10963, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_228_0_10963, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.58 | (505) all_228_0_10963 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (505) can reduce 502 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (512) ~ (all_129_3_146 = all_123_0_133)
% 259.95/213.58 | (513) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = v0) | ( ~ (v0 = 0) & member(all_123_0_133, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.58 |
% 259.95/213.58 | Instantiating (513) with all_224_0_11944 yields:
% 259.95/213.58 | (514) ( ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944) | ( ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944) | ( ~ (all_224_0_11944 = 0) & member(all_68_2_122, all_0_4_4) = all_224_0_11944)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (343), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (362) all_129_3_146 = all_68_0_120
% 259.95/213.58 |
% 259.95/213.58 | Equations (362) can reduce 512 to:
% 259.95/213.58 | (516) ~ (all_123_0_133 = all_68_0_120)
% 259.95/213.58 |
% 259.95/213.58 | Simplifying 516 yields:
% 259.95/213.58 | (517) ~ (all_123_0_133 = all_68_0_120)
% 259.95/213.58 |
% 259.95/213.58 | From (362) and (301) follows:
% 259.95/213.58 | (203) apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (349), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (366) all_127_3_138 = all_68_2_122
% 259.95/213.58 |
% 259.95/213.58 | From (366) and (307) follows:
% 259.95/213.58 | (201) member(all_68_2_122, all_0_4_4) = 0
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (344), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (363) all_123_0_133 = all_68_0_120
% 259.95/213.58 |
% 259.95/213.58 | Equations (363) can reduce 517 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (517) ~ (all_123_0_133 = all_68_0_120)
% 259.95/213.58 | (524) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & member(all_123_0_133, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.58 |
% 259.95/213.58 | Instantiating (524) with all_254_0_15158 yields:
% 259.95/213.58 | (525) ( ~ (all_254_0_15158 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158) | ( ~ (all_254_0_15158 = 0) & member(all_123_0_133, all_0_5_5) = all_254_0_15158) | ( ~ (all_254_0_15158 = 0) & member(all_68_2_122, all_0_4_4) = all_254_0_15158)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (525), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (526) ( ~ (all_254_0_15158 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158) | ( ~ (all_254_0_15158 = 0) & member(all_123_0_133, all_0_5_5) = all_254_0_15158)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (526), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (527) ~ (all_254_0_15158 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (527) yields:
% 259.95/213.58 | (528) ~ (all_254_0_15158 = 0)
% 259.95/213.58 | (529) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (514), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (530) ( ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944) | ( ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944)
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (530), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.58 | (531) ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (531) yields:
% 259.95/213.58 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.58 | (533) apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | From (362) and (533) follows:
% 259.95/213.58 | (534) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_254_0_15158, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.58 | (535) all_254_0_15158 = 0
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_224_0_11944, all_254_0_15158 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_254_0_15158, apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944, yields:
% 259.95/213.58 | (536) all_254_0_15158 = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Combining equations (536,535) yields a new equation:
% 259.95/213.58 | (537) all_224_0_11944 = 0
% 259.95/213.58 |
% 259.95/213.58 | Simplifying 537 yields:
% 259.95/213.58 | (538) all_224_0_11944 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (538) can reduce 532 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (540) ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (540) yields:
% 259.95/213.58 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.58 | (542) member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (77) with all_123_0_133, all_0_5_5, all_224_0_11944, 0 and discharging atoms member(all_123_0_133, all_0_5_5) = all_224_0_11944, member(all_123_0_133, all_0_5_5) = 0, yields:
% 259.95/213.58 | (538) all_224_0_11944 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (538) can reduce 532 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (545) ~ (all_224_0_11944 = 0) & member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (545) yields:
% 259.95/213.58 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.58 | (547) member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 259.95/213.58 |
% 259.95/213.58 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_224_0_11944, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_224_0_11944, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.58 | (538) all_224_0_11944 = 0
% 259.95/213.58 |
% 259.95/213.58 | Equations (538) can reduce 532 to:
% 259.95/213.58 | (195) $false
% 259.95/213.58 |
% 259.95/213.58 |-The branch is then unsatisfiable
% 259.95/213.58 |-Branch two:
% 259.95/213.58 | (550) ~ (all_254_0_15158 = 0) & member(all_123_0_133, all_0_5_5) = all_254_0_15158
% 259.95/213.58 |
% 259.95/213.58 | Applying alpha-rule on (550) yields:
% 259.95/213.58 | (528) ~ (all_254_0_15158 = 0)
% 259.95/213.58 | (552) member(all_123_0_133, all_0_5_5) = all_254_0_15158
% 259.95/213.58 |
% 259.95/213.58 +-Applying beta-rule and splitting (514), into two cases.
% 259.95/213.58 |-Branch one:
% 259.95/213.59 | (530) ( ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944) | ( ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944)
% 259.95/213.59 |
% 259.95/213.59 +-Applying beta-rule and splitting (530), into two cases.
% 259.95/213.59 |-Branch one:
% 259.95/213.59 | (531) ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (531) yields:
% 259.95/213.59 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.59 | (533) apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | From (362) and (533) follows:
% 259.95/213.59 | (534) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_224_0_11944, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.59 | (538) all_224_0_11944 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (538) can reduce 532 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (540) ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (540) yields:
% 259.95/213.59 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.59 | (542) member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_123_0_133, all_0_5_5, all_254_0_15158, 0 and discharging atoms member(all_123_0_133, all_0_5_5) = all_254_0_15158, member(all_123_0_133, all_0_5_5) = 0, yields:
% 259.95/213.59 | (535) all_254_0_15158 = 0
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_123_0_133, all_0_5_5, all_224_0_11944, all_254_0_15158 and discharging atoms member(all_123_0_133, all_0_5_5) = all_254_0_15158, member(all_123_0_133, all_0_5_5) = all_224_0_11944, yields:
% 259.95/213.59 | (536) all_254_0_15158 = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Combining equations (535,536) yields a new equation:
% 259.95/213.59 | (538) all_224_0_11944 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (538) can reduce 532 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (545) ~ (all_224_0_11944 = 0) & member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (545) yields:
% 259.95/213.59 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.59 | (547) member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_224_0_11944, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_224_0_11944, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.59 | (538) all_224_0_11944 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (538) can reduce 532 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (572) ~ (all_254_0_15158 = 0) & member(all_68_2_122, all_0_4_4) = all_254_0_15158
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (572) yields:
% 259.95/213.59 | (528) ~ (all_254_0_15158 = 0)
% 259.95/213.59 | (574) member(all_68_2_122, all_0_4_4) = all_254_0_15158
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_254_0_15158, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_254_0_15158, member(all_68_2_122, all_0_4_4) = 0, yields:
% 259.95/213.59 | (535) all_254_0_15158 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (535) can reduce 528 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (479) ~ (all_127_3_138 = all_68_2_122)
% 259.95/213.59 | (578) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_127_3_138) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 259.95/213.59 |
% 259.95/213.59 | Instantiating (578) with all_237_0_22220 yields:
% 259.95/213.59 | (579) ( ~ (all_237_0_22220 = 0) & apply(all_0_8_8, all_68_1_121, all_127_3_138) = all_237_0_22220) | ( ~ (all_237_0_22220 = 0) & member(all_68_1_121, all_0_5_5) = all_237_0_22220) | ( ~ (all_237_0_22220 = 0) & member(all_68_2_122, all_0_4_4) = all_237_0_22220)
% 259.95/213.59 |
% 259.95/213.59 +-Applying beta-rule and splitting (579), into two cases.
% 259.95/213.59 |-Branch one:
% 259.95/213.59 | (580) ( ~ (all_237_0_22220 = 0) & apply(all_0_8_8, all_68_1_121, all_127_3_138) = all_237_0_22220) | ( ~ (all_237_0_22220 = 0) & member(all_68_1_121, all_0_5_5) = all_237_0_22220)
% 259.95/213.59 |
% 259.95/213.59 +-Applying beta-rule and splitting (580), into two cases.
% 259.95/213.59 |-Branch one:
% 259.95/213.59 | (581) ~ (all_237_0_22220 = 0) & apply(all_0_8_8, all_68_1_121, all_127_3_138) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (581) yields:
% 259.95/213.59 | (582) ~ (all_237_0_22220 = 0)
% 259.95/213.59 | (583) apply(all_0_8_8, all_68_1_121, all_127_3_138) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (52) with all_0_8_8, all_68_1_121, all_127_3_138, all_237_0_22220, 0 and discharging atoms apply(all_0_8_8, all_68_1_121, all_127_3_138) = all_237_0_22220, apply(all_0_8_8, all_68_1_121, all_127_3_138) = 0, yields:
% 259.95/213.59 | (584) all_237_0_22220 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (584) can reduce 582 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (586) ~ (all_237_0_22220 = 0) & member(all_68_1_121, all_0_5_5) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (586) yields:
% 259.95/213.59 | (582) ~ (all_237_0_22220 = 0)
% 259.95/213.59 | (588) member(all_68_1_121, all_0_5_5) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_237_0_22220, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_237_0_22220, member(all_68_1_121, all_0_5_5) = 0, yields:
% 259.95/213.59 | (584) all_237_0_22220 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (584) can reduce 582 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (591) ~ (all_237_0_22220 = 0) & member(all_68_2_122, all_0_4_4) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (591) yields:
% 259.95/213.59 | (582) ~ (all_237_0_22220 = 0)
% 259.95/213.59 | (593) member(all_68_2_122, all_0_4_4) = all_237_0_22220
% 259.95/213.59 |
% 259.95/213.59 +-Applying beta-rule and splitting (514), into two cases.
% 259.95/213.59 |-Branch one:
% 259.95/213.59 | (530) ( ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944) | ( ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944)
% 259.95/213.59 |
% 259.95/213.59 +-Applying beta-rule and splitting (530), into two cases.
% 259.95/213.59 |-Branch one:
% 259.95/213.59 | (531) ~ (all_224_0_11944 = 0) & apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (531) yields:
% 259.95/213.59 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.59 | (533) apply(all_0_6_6, all_68_2_122, all_129_3_146) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | From (362) and (533) follows:
% 259.95/213.59 | (534) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_224_0_11944, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_224_0_11944, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 259.95/213.59 | (538) all_224_0_11944 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (538) can reduce 532 to:
% 259.95/213.59 | (195) $false
% 259.95/213.59 |
% 259.95/213.59 |-The branch is then unsatisfiable
% 259.95/213.59 |-Branch two:
% 259.95/213.59 | (540) ~ (all_224_0_11944 = 0) & member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Applying alpha-rule on (540) yields:
% 259.95/213.59 | (532) ~ (all_224_0_11944 = 0)
% 259.95/213.59 | (542) member(all_123_0_133, all_0_5_5) = all_224_0_11944
% 259.95/213.59 |
% 259.95/213.59 | Instantiating formula (77) with all_123_0_133, all_0_5_5, all_224_0_11944, 0 and discharging atoms member(all_123_0_133, all_0_5_5) = all_224_0_11944, member(all_123_0_133, all_0_5_5) = 0, yields:
% 259.95/213.59 | (538) all_224_0_11944 = 0
% 259.95/213.59 |
% 259.95/213.59 | Equations (538) can reduce 532 to:
% 260.31/213.59 | (195) $false
% 260.31/213.59 |
% 260.31/213.59 |-The branch is then unsatisfiable
% 260.31/213.59 |-Branch two:
% 260.31/213.59 | (545) ~ (all_224_0_11944 = 0) & member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 260.31/213.59 |
% 260.31/213.59 | Applying alpha-rule on (545) yields:
% 260.31/213.59 | (532) ~ (all_224_0_11944 = 0)
% 260.31/213.59 | (547) member(all_68_2_122, all_0_4_4) = all_224_0_11944
% 260.31/213.59 |
% 260.31/213.59 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_237_0_22220, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_237_0_22220, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.59 | (584) all_237_0_22220 = 0
% 260.31/213.59 |
% 260.31/213.59 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_224_0_11944, all_237_0_22220 and discharging atoms member(all_68_2_122, all_0_4_4) = all_237_0_22220, member(all_68_2_122, all_0_4_4) = all_224_0_11944, yields:
% 260.31/213.59 | (610) all_237_0_22220 = all_224_0_11944
% 260.31/213.59 |
% 260.31/213.59 | Combining equations (584,610) yields a new equation:
% 260.31/213.59 | (538) all_224_0_11944 = 0
% 260.31/213.59 |
% 260.31/213.59 | Equations (538) can reduce 532 to:
% 260.31/213.59 | (195) $false
% 260.31/213.59 |
% 260.31/213.59 |-The branch is then unsatisfiable
% 260.31/213.59 |-Branch two:
% 260.31/213.59 | (498) ~ (all_129_3_146 = all_68_0_120)
% 260.31/213.59 | (614) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = v0) | ( ~ (v0 = 0) & member(all_129_3_146, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 260.31/213.59 |
% 260.31/213.59 | Instantiating (614) with all_233_0_25335 yields:
% 260.31/213.59 | (615) ( ~ (all_233_0_25335 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_233_0_25335) | ( ~ (all_233_0_25335 = 0) & member(all_129_3_146, all_0_5_5) = all_233_0_25335) | ( ~ (all_233_0_25335 = 0) & member(all_68_2_122, all_0_4_4) = all_233_0_25335)
% 260.31/213.59 |
% 260.31/213.59 +-Applying beta-rule and splitting (615), into two cases.
% 260.31/213.59 |-Branch one:
% 260.31/213.59 | (616) ( ~ (all_233_0_25335 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_233_0_25335) | ( ~ (all_233_0_25335 = 0) & member(all_129_3_146, all_0_5_5) = all_233_0_25335)
% 260.31/213.59 |
% 260.31/213.59 +-Applying beta-rule and splitting (616), into two cases.
% 260.31/213.59 |-Branch one:
% 260.31/213.59 | (617) ~ (all_233_0_25335 = 0) & apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_233_0_25335
% 260.31/213.59 |
% 260.31/213.59 | Applying alpha-rule on (617) yields:
% 260.31/213.59 | (618) ~ (all_233_0_25335 = 0)
% 260.31/213.59 | (619) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_233_0_25335
% 260.31/213.59 |
% 260.31/213.59 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_233_0_25335, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_233_0_25335, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 260.31/213.59 | (620) all_233_0_25335 = 0
% 260.31/213.59 |
% 260.31/213.59 | Equations (620) can reduce 618 to:
% 260.31/213.59 | (195) $false
% 260.31/213.59 |
% 260.31/213.59 |-The branch is then unsatisfiable
% 260.31/213.59 |-Branch two:
% 260.31/213.59 | (622) ~ (all_233_0_25335 = 0) & member(all_129_3_146, all_0_5_5) = all_233_0_25335
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (622) yields:
% 260.31/213.60 | (618) ~ (all_233_0_25335 = 0)
% 260.31/213.60 | (624) member(all_129_3_146, all_0_5_5) = all_233_0_25335
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_129_3_146, all_0_5_5, all_233_0_25335, 0 and discharging atoms member(all_129_3_146, all_0_5_5) = all_233_0_25335, member(all_129_3_146, all_0_5_5) = 0, yields:
% 260.31/213.60 | (620) all_233_0_25335 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (620) can reduce 618 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (627) ~ (all_233_0_25335 = 0) & member(all_68_2_122, all_0_4_4) = all_233_0_25335
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (627) yields:
% 260.31/213.60 | (618) ~ (all_233_0_25335 = 0)
% 260.31/213.60 | (629) member(all_68_2_122, all_0_4_4) = all_233_0_25335
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_233_0_25335, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_233_0_25335, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.60 | (620) all_233_0_25335 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (620) can reduce 618 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (632) ~ (all_121_0_132 = all_80_0_125)
% 260.31/213.60 | (633) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_68_2_122, all_121_0_132) = v0) | ( ~ (v0 = 0) & member(all_80_0_125, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 260.31/213.60 |
% 260.31/213.60 | Instantiating (633) with all_220_0_28315 yields:
% 260.31/213.60 | (634) ( ~ (all_220_0_28315 = 0) & apply(all_0_7_7, all_68_2_122, all_121_0_132) = all_220_0_28315) | ( ~ (all_220_0_28315 = 0) & member(all_80_0_125, all_0_5_5) = all_220_0_28315) | ( ~ (all_220_0_28315 = 0) & member(all_68_2_122, all_0_4_4) = all_220_0_28315)
% 260.31/213.60 |
% 260.31/213.60 +-Applying beta-rule and splitting (345), into two cases.
% 260.31/213.60 |-Branch one:
% 260.31/213.60 | (366) all_127_3_138 = all_68_2_122
% 260.31/213.60 |
% 260.31/213.60 | From (366) and (307) follows:
% 260.31/213.60 | (201) member(all_68_2_122, all_0_4_4) = 0
% 260.31/213.60 |
% 260.31/213.60 +-Applying beta-rule and splitting (634), into two cases.
% 260.31/213.60 |-Branch one:
% 260.31/213.60 | (637) ( ~ (all_220_0_28315 = 0) & apply(all_0_7_7, all_68_2_122, all_121_0_132) = all_220_0_28315) | ( ~ (all_220_0_28315 = 0) & member(all_80_0_125, all_0_5_5) = all_220_0_28315)
% 260.31/213.60 |
% 260.31/213.60 +-Applying beta-rule and splitting (637), into two cases.
% 260.31/213.60 |-Branch one:
% 260.31/213.60 | (638) ~ (all_220_0_28315 = 0) & apply(all_0_7_7, all_68_2_122, all_121_0_132) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (638) yields:
% 260.31/213.60 | (639) ~ (all_220_0_28315 = 0)
% 260.31/213.60 | (640) apply(all_0_7_7, all_68_2_122, all_121_0_132) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (52) with all_0_7_7, all_68_2_122, all_121_0_132, all_220_0_28315, 0 and discharging atoms apply(all_0_7_7, all_68_2_122, all_121_0_132) = all_220_0_28315, apply(all_0_7_7, all_68_2_122, all_121_0_132) = 0, yields:
% 260.31/213.60 | (641) all_220_0_28315 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (641) can reduce 639 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (643) ~ (all_220_0_28315 = 0) & member(all_80_0_125, all_0_5_5) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (643) yields:
% 260.31/213.60 | (639) ~ (all_220_0_28315 = 0)
% 260.31/213.60 | (645) member(all_80_0_125, all_0_5_5) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_80_0_125, all_0_5_5, all_220_0_28315, 0 and discharging atoms member(all_80_0_125, all_0_5_5) = all_220_0_28315, member(all_80_0_125, all_0_5_5) = 0, yields:
% 260.31/213.60 | (641) all_220_0_28315 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (641) can reduce 639 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (648) ~ (all_220_0_28315 = 0) & member(all_68_2_122, all_0_4_4) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (648) yields:
% 260.31/213.60 | (639) ~ (all_220_0_28315 = 0)
% 260.31/213.60 | (650) member(all_68_2_122, all_0_4_4) = all_220_0_28315
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_220_0_28315, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_220_0_28315, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.60 | (641) all_220_0_28315 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (641) can reduce 639 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (479) ~ (all_127_3_138 = all_68_2_122)
% 260.31/213.60 | (480) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = v0) | ( ~ (v0 = 0) & member(all_127_3_138, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0))
% 260.31/213.60 |
% 260.31/213.60 | Instantiating (480) with all_229_0_112211 yields:
% 260.31/213.60 | (655) ( ~ (all_229_0_112211 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_229_0_112211) | ( ~ (all_229_0_112211 = 0) & member(all_127_3_138, all_0_4_4) = all_229_0_112211) | ( ~ (all_229_0_112211 = 0) & member(all_68_1_121, all_0_5_5) = all_229_0_112211)
% 260.31/213.60 |
% 260.31/213.60 +-Applying beta-rule and splitting (655), into two cases.
% 260.31/213.60 |-Branch one:
% 260.31/213.60 | (656) ( ~ (all_229_0_112211 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_229_0_112211) | ( ~ (all_229_0_112211 = 0) & member(all_127_3_138, all_0_4_4) = all_229_0_112211)
% 260.31/213.60 |
% 260.31/213.60 +-Applying beta-rule and splitting (656), into two cases.
% 260.31/213.60 |-Branch one:
% 260.31/213.60 | (657) ~ (all_229_0_112211 = 0) & apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (657) yields:
% 260.31/213.60 | (658) ~ (all_229_0_112211 = 0)
% 260.31/213.60 | (659) apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (52) with all_0_8_8, all_68_1_121, all_68_2_122, all_229_0_112211, 0 and discharging atoms apply(all_0_8_8, all_68_1_121, all_68_2_122) = all_229_0_112211, apply(all_0_8_8, all_68_1_121, all_68_2_122) = 0, yields:
% 260.31/213.60 | (660) all_229_0_112211 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (660) can reduce 658 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (662) ~ (all_229_0_112211 = 0) & member(all_127_3_138, all_0_4_4) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (662) yields:
% 260.31/213.60 | (658) ~ (all_229_0_112211 = 0)
% 260.31/213.60 | (664) member(all_127_3_138, all_0_4_4) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_127_3_138, all_0_4_4, all_229_0_112211, 0 and discharging atoms member(all_127_3_138, all_0_4_4) = all_229_0_112211, member(all_127_3_138, all_0_4_4) = 0, yields:
% 260.31/213.60 | (660) all_229_0_112211 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (660) can reduce 658 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (667) ~ (all_229_0_112211 = 0) & member(all_68_1_121, all_0_5_5) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (667) yields:
% 260.31/213.60 | (658) ~ (all_229_0_112211 = 0)
% 260.31/213.60 | (669) member(all_68_1_121, all_0_5_5) = all_229_0_112211
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_229_0_112211, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_229_0_112211, member(all_68_1_121, all_0_5_5) = 0, yields:
% 260.31/213.60 | (660) all_229_0_112211 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (660) can reduce 658 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (672) ~ (all_128_3_142 = 0) & member(all_68_0_120, all_0_5_5) = all_128_3_142
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (672) yields:
% 260.31/213.60 | (673) ~ (all_128_3_142 = 0)
% 260.31/213.60 | (674) member(all_68_0_120, all_0_5_5) = all_128_3_142
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_0_120, all_0_5_5, all_128_3_142, 0 and discharging atoms member(all_68_0_120, all_0_5_5) = all_128_3_142, member(all_68_0_120, all_0_5_5) = 0, yields:
% 260.31/213.60 | (675) all_128_3_142 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (675) can reduce 673 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (677) ~ (all_127_3_138 = 0) & member(all_68_1_121, all_0_5_5) = all_127_3_138
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (677) yields:
% 260.31/213.60 | (678) ~ (all_127_3_138 = 0)
% 260.31/213.60 | (679) member(all_68_1_121, all_0_5_5) = all_127_3_138
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_127_3_138, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_127_3_138, member(all_68_1_121, all_0_5_5) = 0, yields:
% 260.31/213.60 | (680) all_127_3_138 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (680) can reduce 678 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (682) ~ (all_129_3_146 = 0) & member(all_68_2_122, all_0_4_4) = all_129_3_146
% 260.31/213.60 |
% 260.31/213.60 | Applying alpha-rule on (682) yields:
% 260.31/213.60 | (683) ~ (all_129_3_146 = 0)
% 260.31/213.60 | (684) member(all_68_2_122, all_0_4_4) = all_129_3_146
% 260.31/213.60 |
% 260.31/213.60 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_129_3_146, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_129_3_146, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.60 | (685) all_129_3_146 = 0
% 260.31/213.60 |
% 260.31/213.60 | Equations (685) can reduce 683 to:
% 260.31/213.60 | (195) $false
% 260.31/213.60 |
% 260.31/213.60 |-The branch is then unsatisfiable
% 260.31/213.60 |-Branch two:
% 260.31/213.60 | (687) ~ (all_76_0_123 = all_68_0_120)
% 260.31/213.60 | (688) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_82_0_126, all_76_0_123) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_82_0_126, all_68_0_120) = v0))
% 260.31/213.60 |
% 260.31/213.60 | Instantiating (688) with all_142_0_123028 yields:
% 260.31/213.60 | (689) ( ~ (all_142_0_123028 = 0) & apply(all_0_6_6, all_82_0_126, all_76_0_123) = all_142_0_123028) | ( ~ (all_142_0_123028 = 0) & apply(all_0_6_6, all_82_0_126, all_68_0_120) = all_142_0_123028)
% 260.31/213.61 |
% 260.31/213.61 +-Applying beta-rule and splitting (689), into two cases.
% 260.31/213.61 |-Branch one:
% 260.31/213.61 | (690) ~ (all_142_0_123028 = 0) & apply(all_0_6_6, all_82_0_126, all_76_0_123) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (690) yields:
% 260.31/213.61 | (691) ~ (all_142_0_123028 = 0)
% 260.31/213.61 | (692) apply(all_0_6_6, all_82_0_126, all_76_0_123) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | From (277) and (692) follows:
% 260.31/213.61 | (693) apply(all_0_6_6, all_68_2_122, all_76_0_123) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_76_0_123, all_142_0_123028, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_76_0_123) = all_142_0_123028, apply(all_0_6_6, all_68_2_122, all_76_0_123) = 0, yields:
% 260.31/213.61 | (694) all_142_0_123028 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (694) can reduce 691 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (696) ~ (all_142_0_123028 = 0) & apply(all_0_6_6, all_82_0_126, all_68_0_120) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (696) yields:
% 260.31/213.61 | (691) ~ (all_142_0_123028 = 0)
% 260.31/213.61 | (698) apply(all_0_6_6, all_82_0_126, all_68_0_120) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | From (277) and (698) follows:
% 260.31/213.61 | (699) apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_142_0_123028
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (52) with all_0_6_6, all_68_2_122, all_68_0_120, all_142_0_123028, 0 and discharging atoms apply(all_0_6_6, all_68_2_122, all_68_0_120) = all_142_0_123028, apply(all_0_6_6, all_68_2_122, all_68_0_120) = 0, yields:
% 260.31/213.61 | (694) all_142_0_123028 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (694) can reduce 691 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (702) ~ (all_82_0_126 = all_68_2_122)
% 260.31/213.61 | (703) ? [v0] : (( ~ (v0 = 0) & apply(all_0_8_8, all_68_1_121, all_82_0_126) = v0) | ( ~ (v0 = 0) & member(all_68_1_121, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_68_2_122, all_0_4_4) = v0))
% 260.31/213.61 |
% 260.31/213.61 | Instantiating (703) with all_138_0_123052 yields:
% 260.31/213.61 | (704) ( ~ (all_138_0_123052 = 0) & apply(all_0_8_8, all_68_1_121, all_82_0_126) = all_138_0_123052) | ( ~ (all_138_0_123052 = 0) & member(all_68_1_121, all_0_5_5) = all_138_0_123052) | ( ~ (all_138_0_123052 = 0) & member(all_68_2_122, all_0_4_4) = all_138_0_123052)
% 260.31/213.61 |
% 260.31/213.61 +-Applying beta-rule and splitting (704), into two cases.
% 260.31/213.61 |-Branch one:
% 260.31/213.61 | (705) ( ~ (all_138_0_123052 = 0) & apply(all_0_8_8, all_68_1_121, all_82_0_126) = all_138_0_123052) | ( ~ (all_138_0_123052 = 0) & member(all_68_1_121, all_0_5_5) = all_138_0_123052)
% 260.31/213.61 |
% 260.31/213.61 +-Applying beta-rule and splitting (705), into two cases.
% 260.31/213.61 |-Branch one:
% 260.31/213.61 | (706) ~ (all_138_0_123052 = 0) & apply(all_0_8_8, all_68_1_121, all_82_0_126) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (706) yields:
% 260.31/213.61 | (707) ~ (all_138_0_123052 = 0)
% 260.31/213.61 | (708) apply(all_0_8_8, all_68_1_121, all_82_0_126) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (52) with all_0_8_8, all_68_1_121, all_82_0_126, all_138_0_123052, 0 and discharging atoms apply(all_0_8_8, all_68_1_121, all_82_0_126) = all_138_0_123052, apply(all_0_8_8, all_68_1_121, all_82_0_126) = 0, yields:
% 260.31/213.61 | (709) all_138_0_123052 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (709) can reduce 707 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (711) ~ (all_138_0_123052 = 0) & member(all_68_1_121, all_0_5_5) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (711) yields:
% 260.31/213.61 | (707) ~ (all_138_0_123052 = 0)
% 260.31/213.61 | (713) member(all_68_1_121, all_0_5_5) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_138_0_123052, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_138_0_123052, member(all_68_1_121, all_0_5_5) = 0, yields:
% 260.31/213.61 | (709) all_138_0_123052 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (709) can reduce 707 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (716) ~ (all_138_0_123052 = 0) & member(all_68_2_122, all_0_4_4) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (716) yields:
% 260.31/213.61 | (707) ~ (all_138_0_123052 = 0)
% 260.31/213.61 | (718) member(all_68_2_122, all_0_4_4) = all_138_0_123052
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_138_0_123052, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_138_0_123052, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.61 | (709) all_138_0_123052 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (709) can reduce 707 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (721) ~ (all_84_0_127 = 0) & member(all_68_1_121, all_0_5_5) = all_84_0_127
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (721) yields:
% 260.31/213.61 | (722) ~ (all_84_0_127 = 0)
% 260.31/213.61 | (723) member(all_68_1_121, all_0_5_5) = all_84_0_127
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (77) with all_68_1_121, all_0_5_5, all_84_0_127, 0 and discharging atoms member(all_68_1_121, all_0_5_5) = all_84_0_127, member(all_68_1_121, all_0_5_5) = 0, yields:
% 260.31/213.61 | (231) all_84_0_127 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (231) can reduce 722 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 |-Branch two:
% 260.31/213.61 | (726) ~ (all_84_0_127 = 0) & member(all_68_2_122, all_0_4_4) = all_84_0_127
% 260.31/213.61 |
% 260.31/213.61 | Applying alpha-rule on (726) yields:
% 260.31/213.61 | (722) ~ (all_84_0_127 = 0)
% 260.31/213.61 | (728) member(all_68_2_122, all_0_4_4) = all_84_0_127
% 260.31/213.61 |
% 260.31/213.61 | Instantiating formula (77) with all_68_2_122, all_0_4_4, all_84_0_127, 0 and discharging atoms member(all_68_2_122, all_0_4_4) = all_84_0_127, member(all_68_2_122, all_0_4_4) = 0, yields:
% 260.31/213.61 | (231) all_84_0_127 = 0
% 260.31/213.61 |
% 260.31/213.61 | Equations (231) can reduce 722 to:
% 260.31/213.61 | (195) $false
% 260.31/213.61 |
% 260.31/213.61 |-The branch is then unsatisfiable
% 260.31/213.61 % SZS output end Proof for theBenchmark
% 260.31/213.61
% 260.31/213.61 213010ms
%------------------------------------------------------------------------------