TSTP Solution File: SET725+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET725+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 00:21:39 EDT 2022
% Result : Theorem 12.21s 3.40s
% Output : Proof 156.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET725+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 11:55:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.99 Prover 0: Preprocessing ...
% 3.26/1.36 Prover 0: Warning: ignoring some quantifiers
% 3.26/1.40 Prover 0: Constructing countermodel ...
% 4.46/1.65 Prover 0: gave up
% 4.46/1.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.76/1.70 Prover 1: Preprocessing ...
% 5.81/1.95 Prover 1: Constructing countermodel ...
% 6.12/1.99 Prover 1: gave up
% 6.12/1.99 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.12/2.03 Prover 2: Preprocessing ...
% 7.49/2.34 Prover 2: Warning: ignoring some quantifiers
% 7.49/2.36 Prover 2: Constructing countermodel ...
% 12.21/3.40 Prover 2: proved (1409ms)
% 12.21/3.40
% 12.21/3.40 No countermodel exists, formula is valid
% 12.21/3.40 % SZS status Theorem for theBenchmark
% 12.21/3.40
% 12.21/3.40 Generating proof ... Warning: ignoring some quantifiers
% 155.54/121.01 found it (size 342)
% 155.54/121.01
% 155.54/121.01 % SZS output start Proof for theBenchmark
% 155.54/121.01 Assumed formulas after preprocessing and simplification:
% 155.54/121.01 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & one_to_one(v0, v3, v4) = v7 & identity(v6, v4) = 0 & identity(v5, v3) = 0 & 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 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v10, v13, v15) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = 0) | ~ (apply(v10, v13, v15) = v17) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v16, v14) = v17) | ~ (apply(v10, v13, v15) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v16, v14) = v17) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v16, v14) = v17) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v15, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v16, v14) = v17) | ~ (member(v15, v9) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v10, v13, v15) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v15, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (member(v15, v9) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v13, v15) = v18) | ( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = v16) | ~ (apply(v9, v13, v17) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v17, v14) = v18) | ( ~ (v18 = 0) & member(v17, v11) = v18) | ( ~ (v18 = 0) & member(v14, v12) = v18) | ( ~ (v18 = 0) & member(v13, v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = v16) | ~ (apply(v8, v17, v14) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v9, v13, v17) = v18) | ( ~ (v18 = 0) & member(v17, v11) = v18) | ( ~ (v18 = 0) & member(v14, v12) = v18) | ( ~ (v18 = 0) & member(v13, v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = v16) | ~ (member(v17, v11) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v9, v13, v17) = v18) | ( ~ (v18 = 0) & apply(v8, v17, v14) = v18) | ( ~ (v18 = 0) & member(v14, v12) = v18) | ( ~ (v18 = 0) & member(v13, v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v10, v14, v17) = 0) | ~ (apply(v8, v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & apply(v9, v17, v15) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v15, v13) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v17, v15) = 0) | ~ (apply(v8, v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v14, v17) = v18) | ( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v15, v13) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v8, v14, v15) = v16) | ~ (member(v17, v12) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v10, v14, v17) = v18) | ( ~ (v18 = 0) & apply(v9, v17, v15) = v18) | ( ~ (v18 = 0) & member(v15, v13) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v10, v13, v15) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v10, v13, v15) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v15, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v10, v13, v15) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v10, v13, v15) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v12, v14, v16) = v17) | ~ (member(v15, v9) = 0) | ~ (member(v13, v9) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v10, v13, v15) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v10, v13, v15) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = v17) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v16, v11) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v12, v14, v16) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = v17) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v14, v11) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v12, v14, v16) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = v17) | ~ (member(v16, v11) = 0) | ~ (member(v14, v11) = 0) | ? [v18] : (( ~ (v18 = 0) & apply(v8, v15, v16) = v18) | ( ~ (v18 = 0) & apply(v8, v13, v14) = v18) | ( ~ (v18 = 0) & member(v15, v9) = v18) | ( ~ (v18 = 0) & member(v13, v9) = v18) | (( ~ (v17 = 0) | (v18 = 0 & apply(v12, v14, v16) = 0)) & (v17 = 0 | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17) | (((v18 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17)) & ((v17 = 0 & apply(v10, v13, v15) = 0) | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | (((v18 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17)) & ((v17 = 0 & apply(v10, v13, v15) = 0) | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17) | (((v18 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17)) & ((v17 = 0 & apply(v10, v13, v15) = 0) | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | (((v18 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17)) & ((v17 = 0 & apply(v10, v13, v15) = 0) | ( ~ (v18 = 0) & apply(v12, v14, v16) = v18))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v14, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v16, v14) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v10, v13, v15) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v14, v11) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v15, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v13, v14) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & member(v14, v11) = v17) | ( ~ (v17 = 0) & member(v13, v9) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (member(v16, v11) = 0) | ~ (member(v15, v9) = 0) | ~ (member(v14, v11) = 0) | ~ (member(v13, v9) = 0) | ? [v17] : ((v17 = 0 & apply(v12, v14, v16) = 0) | ( ~ (v17 = 0) & apply(v10, v13, v15) = v17) | ( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v13, v14) = v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v9 = v8 | ~ (compose_predicate(v15, v14, v13, v12, v11, v10) = v9) | ~ (compose_predicate(v15, v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v9, v13, v16) = 0 & apply(v8, v16, v14) = 0 & member(v16, v11) = 0) | ( ~ (v16 = 0) & member(v14, v12) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v8, v14, v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v10, v14, v16) = 0 & apply(v9, v16, v15) = 0 & member(v16, v12) = 0) | ( ~ (v16 = 0) & member(v15, v13) = v16) | ( ~ (v16 = 0) & member(v14, v11) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (equal_maps(v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v8, v12, v13) = 0) | ? [v15] : (( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (equal_maps(v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v13, v11) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v8, v12, v13) = v15) | ( ~ (v15 = 0) & member(v14, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (equal_maps(v8, v9, v10, v11) = 0) | ~ (apply(v8, 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))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (equal_maps(v8, 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(v8, v12, v13) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (member(v16, v13) = 0 & member(v15, v11) = 0 & ((v21 = 0 & v20 = 0 & v19 = 0 & apply(v10, v15, v18) = 0 & apply(v9, v18, v16) = 0 & member(v18, v12) = 0) | (v17 = 0 & apply(v8, v15, v16) = 0)) & (( ~ (v17 = 0) & apply(v8, v15, v16) = v17) | ( ! [v22] : ( ~ (apply(v10, v15, v22) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v9, v22, v16) = v23) | ( ~ (v23 = 0) & member(v22, v12) = v23))) & ! [v22] : ( ~ (apply(v9, v22, v16) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v10, v15, v22) = v23) | ( ~ (v23 = 0) & member(v22, v12) = v23))) & ! [v22] : ( ~ (member(v22, v12) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v10, v15, v22) = v23) | ( ~ (v23 = 0) & apply(v9, v22, v16) = v23))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (inverse_image3(v8, v9, v10) = v12) | ~ (apply(v8, v11, v14) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (inverse_image3(v8, v9, v10) = v12) | ~ (member(v14, v9) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & apply(v8, v11, v14) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (image3(v8, v9, v10) = v12) | ~ (apply(v8, v14, v11) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (image3(v8, v9, v10) = v12) | ~ (member(v14, v9) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & apply(v8, v14, v11) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (isomorphism(v14, v13, v12, v11, v10) = v9) | ~ (isomorphism(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (decreasing(v14, v13, v12, v11, v10) = v9) | ~ (decreasing(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (increasing(v14, v13, v12, v11, v10) = v9) | ~ (increasing(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (compose_function(v14, v13, v12, v11, v10) = v9) | ~ (compose_function(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_function(v8, v9, v10) = v13) | ~ (apply(v13, v12, v11) = v14) | ? [v15] : (( ~ (v15 = 0) & member(v12, v10) = v15) | ( ~ (v15 = 0) & member(v11, v9) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v8, v11, v12) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v8, v11, v12) = v15))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_predicate(v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v13) = v14) | ? [v15] : (( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v8, v13, v12) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v8, v13, v12) = v15))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_predicate(v8, v9, v10, v11) = 0) | ~ (apply(v8, v13, v12) = v14) | ? [v15] : (( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v10) = v15) | (( ~ (v14 = 0) | (v15 = 0 & apply(v9, v12, v13) = 0)) & (v14 = 0 | ( ~ (v15 = 0) & apply(v9, v12, v13) = v15))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (maps(v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v8, v11, v12) = 0) | ? [v14] : (( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (maps(v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v12, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v12) = v14) | ( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (maps(v8, v9, v10) = 0) | ~ (apply(v8, v11, v12) = 0) | ~ (member(v13, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (maps(v8, v9, v10) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & apply(v8, v11, v12) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (isomorphism(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0 & ((v25 = 0 & apply(v12, v15, v17) = 0) | (v24 = 0 & apply(v10, v14, v16) = 0)) & (( ~ (v25 = 0) & apply(v12, v15, v17) = v25) | ( ~ (v24 = 0) & apply(v10, v14, v16) = v24))) | ( ~ (v14 = 0) & one_to_one(v8, v9, v11) = v14) | ( ~ (v14 = 0) & maps(v8, v9, v11) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & apply(v12, v17, v15) = v18 & apply(v10, v14, v16) = 0 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & apply(v12, v15, v17) = v18 & apply(v10, v14, v16) = 0 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (injective(v8, v9, v10) = 0) | ~ (apply(v8, v12, v13) = 0) | ~ (apply(v8, v11, v13) = 0) | ? [v14] : (( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v12, v9) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (injective(v8, v9, v10) = 0) | ~ (apply(v8, v12, v13) = 0) | ~ (member(v11, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v12, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (injective(v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v12, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v12, v13) = v14) | ( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (injective(v8, v9, v10) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v12, v13) = v14) | ( ~ (v14 = 0) & apply(v8, v11, v13) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image2(v8, v9) = v11) | ~ (apply(v8, v10, v13) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image2(v8, v9) = v11) | ~ (member(v13, v9) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & apply(v8, v10, v13) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image2(v8, v9) = v11) | ~ (apply(v8, v13, v10) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image2(v8, v9) = v11) | ~ (member(v13, v9) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & apply(v8, v13, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (inverse_predicate(v13, v12, v11, v10) = v9) | ~ (inverse_predicate(v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (equal_maps(v13, v12, v11, v10) = v9) | ~ (equal_maps(v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (inverse_predicate(v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (member(v14, v11) = 0 & member(v13, v10) = 0 & ((v16 = 0 & apply(v8, v14, v13) = 0) | (v15 = 0 & apply(v9, v13, v14) = 0)) & (( ~ (v16 = 0) & apply(v8, v14, v13) = v16) | ( ~ (v15 = 0) & apply(v9, v13, v14) = v15)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (equal_maps(v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v14) & apply(v9, v13, v15) = 0 & apply(v8, v13, v14) = 0 & member(v15, v11) = 0 & member(v14, v11) = 0 & member(v13, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ((v13 = 0 & member(v8, v9) = 0) | ( ~ (v13 = 0) & member(v8, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v8, v10) = v13) | ( ~ (v13 = 0) & member(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v12, v9) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (inverse_image3(v12, v11, v10) = v9) | ~ (inverse_image3(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (image3(v12, v11, v10) = v9) | ~ (image3(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (inverse_function(v12, v11, v10) = v9) | ~ (inverse_function(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (one_to_one(v12, v11, v10) = v9) | ~ (one_to_one(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (surjective(v12, v11, v10) = v9) | ~ (surjective(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (injective(v12, v11, v10) = v9) | ~ (injective(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (maps(v12, v11, v10) = v9) | ~ (maps(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (apply(v12, v11, v10) = v9) | ~ (apply(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | (one_to_one(v8, v9, v11) = 0 & maps(v8, v9, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | member(v11, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v8, v11, v13) = 0 & member(v13, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | member(v11, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v8, v13, v11) = 0 & member(v13, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (one_to_one(v8, v9, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & surjective(v8, v9, v10) = v12) | ( ~ (v12 = 0) & injective(v8, v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (surjective(v8, v9, v10) = v11) | ? [v12] : (member(v12, v10) = 0 & ! [v13] : ( ~ (apply(v8, v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)) & ! [v13] : ( ~ (member(v13, v9) = 0) | ? [v14] : ( ~ (v14 = 0) & apply(v8, v13, v12) = v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (injective(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v13 = v12) & apply(v8, v13, v14) = 0 & apply(v8, v12, v14) = 0 & member(v14, v10) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (identity(v8, v9) = 0) | ~ (apply(v8, v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (maps(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v8, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0) | (v13 = 0 & member(v12, v9) = 0 & ! [v20] : ( ~ (apply(v8, v12, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & member(v20, v10) = v21)) & ! [v20] : ( ~ (member(v20, v10) = 0) | ? [v21] : ( ~ (v21 = 0) & apply(v8, v12, v20) = v21))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v9) = 0) | ~ (member(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (inverse_image2(v11, v10) = v9) | ~ (inverse_image2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (image2(v11, v10) = v9) | ~ (image2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (identity(v11, v10) = v9) | ~ (identity(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image2(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v8, v10, v12) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image2(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v8, v12, v10) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (surjective(v8, v9, v10) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & injective(v8, v9, v10) = 0) | ( ~ (v12 = 0) & one_to_one(v8, v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (surjective(v8, v9, v10) = 0) | ~ (member(v11, v10) = 0) | ? [v12] : (apply(v8, v12, v11) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (injective(v8, v9, v10) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & surjective(v8, v9, v10) = 0) | ( ~ (v12 = 0) & one_to_one(v8, v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (maps(v8, v9, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v12] : (apply(v8, v11, v12) = 0 & member(v12, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (product(v9) = v10) | ~ (member(v11, v9) = 0) | ~ (member(v8, v10) = 0) | member(v8, v11) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ((v12 = 0 & member(v8, v10) = 0) | (v12 = 0 & member(v8, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (identity(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & apply(v8, v11, v11) = v12 & member(v11, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & subset(v9, v8) = v11) | ( ~ (v11 = 0) & subset(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & power_set(v9) = v11 & member(v8, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (one_to_one(v8, v9, v10) = 0) | (surjective(v8, v9, v10) = 0 & injective(v8, v9, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v8, v9, v10) = 0) | ? [v11] : ((v11 = 0 & one_to_one(v8, v9, v10) = 0) | ( ~ (v11 = 0) & injective(v8, v9, v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (injective(v8, v9, v10) = 0) | ? [v11] : ((v11 = 0 & one_to_one(v8, v9, v10) = 0) | ( ~ (v11 = 0) & surjective(v8, v9, v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (identity(v8, v9) = 0) | ~ (member(v10, v9) = 0) | apply(v8, v10, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v9, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & subset(v8, v9) = 0) | ( ~ (v11 = 0) & equal_set(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & subset(v9, v8) = 0) | ( ~ (v11 = 0) & equal_set(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ! [v9] : ( ~ (subset(v9, v8) = 0) | ? [v10] : ((v10 = 0 & equal_set(v8, v9) = 0) | ( ~ (v10 = 0) & subset(v8, v9) = v10))) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ? [v10] : (power_set(v9) = v10 & member(v8, v10) = 0)) & ! [v8] : ! [v9] : ( ~ (subset(v8, v9) = 0) | ? [v10] : ((v10 = 0 & equal_set(v8, v9) = 0) | ( ~ (v10 = 0) & subset(v9, v8) = v10))) & ! [v8] : ~ (member(v8, empty_set) = 0) & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : compose_predicate(v13, v12, v11, v10, v9, v8) = v14 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : isomorphism(v12, v11, v10, v9, v8) = v13 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : decreasing(v12, v11, v10, v9, v8) = v13 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : increasing(v12, v11, v10, v9, v8) = v13 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : compose_function(v12, v11, v10, v9, v8) = v13 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : inverse_predicate(v11, v10, v9, v8) = v12 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : equal_maps(v11, v10, v9, v8) = v12 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : inverse_image3(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : image3(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : inverse_function(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : one_to_one(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : surjective(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : injective(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : maps(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : ? [v11] : apply(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : inverse_image2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : image2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : identity(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : unordered_pair(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : difference(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : union(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : intersection(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : equal_set(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : subset(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : member(v9, v8) = v10 & ? [v8] : ? [v9] : product(v8) = v9 & ? [v8] : ? [v9] : sum(v8) = v9 & ? [v8] : ? [v9] : singleton(v8) = v9 & ? [v8] : ? [v9] : power_set(v8) = v9)
% 156.03/121.14 | 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 yields:
% 156.03/121.14 | (1) ~ (all_0_0_0 = 0) & one_to_one(all_0_7_7, all_0_4_4, all_0_3_3) = all_0_0_0 & identity(all_0_1_1, all_0_3_3) = 0 & identity(all_0_2_2, all_0_4_4) = 0 & compose_function(all_0_6_6, all_0_7_7, all_0_4_4, all_0_3_3, all_0_4_4) = all_0_2_2 & compose_function(all_0_7_7, all_0_5_5, all_0_3_3, all_0_4_4, all_0_3_3) = all_0_1_1 & maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0 & maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0 & maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v1, v9, v7) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ((v17 = 0 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (surjective(v0, v1, v2) = v3) | ? [v4] : (member(v4, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5, v4) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = v13))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1
% 156.24/121.19 |
% 156.24/121.19 | Applying alpha-rule on (1) yields:
% 156.24/121.20 | (2) ! [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))
% 156.24/121.20 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 156.24/121.20 | (4) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 156.24/121.20 | (5) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 156.24/121.20 | (6) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 156.24/121.20 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 156.24/121.20 | (8) ! [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)))))
% 156.24/121.20 | (9) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 156.24/121.20 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 156.24/121.20 | (11) one_to_one(all_0_7_7, all_0_4_4, all_0_3_3) = all_0_0_0
% 156.24/121.20 | (12) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 156.24/121.20 | (13) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 156.24/121.20 | (14) ! [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)))
% 156.24/121.20 | (15) ! [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)))
% 156.24/121.20 | (16) ! [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)))
% 156.24/121.20 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 156.24/121.20 | (18) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 156.24/121.20 | (19) ! [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)))
% 156.24/121.20 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 156.24/121.20 | (21) ! [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)))
% 156.24/121.20 | (22) ! [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)))))
% 156.24/121.20 | (23) ! [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))
% 156.24/121.20 | (24) ! [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)))
% 156.24/121.20 | (25) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 156.24/121.20 | (26) ! [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))
% 156.24/121.20 | (27) ! [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))
% 156.24/121.20 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 156.24/121.20 | (29) ! [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)))))
% 156.24/121.20 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 156.24/121.20 | (31) ! [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))
% 156.24/121.20 | (32) ! [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)))
% 156.24/121.20 | (33) ! [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)))
% 156.24/121.20 | (34) ? [v0] : ? [v1] : power_set(v0) = v1
% 156.24/121.20 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 156.24/121.20 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 156.24/121.20 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 156.24/121.20 | (38) ! [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)))
% 156.24/121.20 | (39) ! [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)))
% 156.24/121.21 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 156.24/121.21 | (41) ! [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)))
% 156.24/121.21 | (42) compose_function(all_0_6_6, all_0_7_7, all_0_4_4, all_0_3_3, all_0_4_4) = all_0_2_2
% 156.24/121.21 | (43) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 156.24/121.21 | (44) ! [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)))
% 156.24/121.21 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 156.24/121.21 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 156.24/121.21 | (47) ! [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)))
% 156.24/121.21 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 156.24/121.21 | (49) ! [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)))
% 156.24/121.21 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 156.24/121.21 | (51) ! [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)))))
% 156.24/121.21 | (52) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 156.24/121.21 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 156.24/121.21 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 156.24/121.21 | (55) ! [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))
% 156.24/121.21 | (56) ! [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)))
% 156.24/121.21 | (57) ! [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)))
% 156.24/121.21 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 156.24/121.21 | (59) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 156.24/121.21 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 156.24/121.21 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 156.24/121.21 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 156.24/121.21 | (63) ! [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))
% 156.24/121.21 | (64) ! [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))
% 156.24/121.21 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 156.24/121.21 | (66) ! [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)))))
% 156.24/121.21 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 156.24/121.21 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 156.24/121.21 | (69) ! [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)))
% 156.24/121.21 | (70) ! [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)))
% 156.24/121.21 | (71) identity(all_0_2_2, all_0_4_4) = 0
% 156.24/121.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 156.24/121.21 | (73) ! [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))
% 156.24/121.21 | (74) ! [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)))
% 156.24/121.21 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 156.24/121.22 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 156.24/121.22 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 156.24/121.22 | (78) ! [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)))
% 156.24/121.22 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 156.24/121.22 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 156.24/121.22 | (81) ! [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)))
% 156.24/121.22 | (82) ! [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)))
% 156.24/121.22 | (83) ? [v0] : ? [v1] : sum(v0) = v1
% 156.24/121.22 | (84) ! [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)))))
% 156.24/121.22 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15)))))))
% 156.24/121.22 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 156.24/121.22 | (87) ! [v0] : ~ (member(v0, empty_set) = 0)
% 156.24/121.22 | (88) ~ (all_0_0_0 = 0)
% 156.24/121.22 | (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)))
% 156.24/121.22 | (90) ! [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)))
% 156.24/121.22 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 156.24/121.22 | (92) ! [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)))
% 156.24/121.22 | (93) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 156.24/121.22 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 156.24/121.22 | (95) ! [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)))
% 156.24/121.22 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 156.24/121.22 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 156.24/121.22 | (98) ! [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)))
% 156.24/121.22 | (99) ! [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)))
% 156.24/121.22 | (100) ! [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)))
% 156.24/121.22 | (101) ! [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))
% 156.24/121.22 | (102) ? [v0] : ? [v1] : singleton(v0) = v1
% 156.24/121.22 | (103) ! [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)))
% 156.24/121.22 | (104) ! [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)))
% 156.24/121.22 | (105) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 156.24/121.22 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 156.24/121.22 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 156.24/121.23 | (108) ! [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))
% 156.24/121.23 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 156.24/121.23 | (110) ! [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)))
% 156.24/121.23 | (111) ! [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)))
% 156.24/121.23 | (112) ! [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)))
% 156.24/121.23 | (113) ! [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))
% 156.24/121.23 | (114) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 156.24/121.23 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 156.24/121.23 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 156.24/121.23 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 156.24/121.23 | (118) ! [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))))
% 156.24/121.23 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 156.24/121.23 | (120) compose_function(all_0_7_7, all_0_5_5, all_0_3_3, all_0_4_4, all_0_3_3) = all_0_1_1
% 156.24/121.23 | (121) ! [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)))
% 156.24/121.23 | (122) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 156.24/121.23 | (123) identity(all_0_1_1, all_0_3_3) = 0
% 156.24/121.23 | (124) ! [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)))
% 156.24/121.23 | (125) ! [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)))))
% 156.24/121.23 | (126) ! [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))))
% 156.24/121.23 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 156.24/121.23 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 156.24/121.23 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 156.24/121.23 | (130) ! [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)))
% 156.24/121.23 | (131) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 156.24/121.23 | (132) ! [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)))
% 156.24/121.23 | (133) ! [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)))))
% 156.24/121.23 | (134) ! [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)))
% 156.24/121.23 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 156.24/121.23 | (136) ! [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)))
% 156.24/121.23 | (137) ! [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)))))
% 156.24/121.23 | (138) ! [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)))
% 156.24/121.23 | (139) ! [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)))
% 156.24/121.24 | (140) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 156.24/121.24 | (141) ! [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)))))
% 156.24/121.24 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 156.24/121.24 | (143) ! [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)))
% 156.24/121.24 | (144) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 156.24/121.24 | (145) ! [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)))
% 156.24/121.24 | (146) ! [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))
% 156.24/121.24 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 156.24/121.24 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 156.24/121.24 | (149) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 156.24/121.24 | (150) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 156.24/121.24 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (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)))
% 156.24/121.24 | (152) ! [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)))
% 156.63/121.24 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 156.63/121.24 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 156.63/121.24 | (155) ! [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)))
% 156.63/121.24 | (156) ! [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)))
% 156.63/121.24 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 156.63/121.24 | (158) maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0
% 156.63/121.24 | (159) ! [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)))))
% 156.63/121.24 | (160) ! [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)))
% 156.63/121.24 | (161) maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0
% 156.63/121.24 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 156.63/121.24 | (163) ! [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)))
% 156.63/121.24 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 156.63/121.24 | (165) ! [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)))
% 156.63/121.24 | (166) ! [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))
% 156.63/121.24 | (167) ! [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)))))
% 156.63/121.24 | (168) maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0
% 156.63/121.24 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 156.63/121.24 | (170) ! [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)))
% 156.63/121.24 | (171) ? [v0] : ? [v1] : product(v0) = v1
% 156.63/121.24 | (172) ! [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)))
% 156.63/121.25 | (173) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 156.63/121.25 | (174) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 156.63/121.25 | (175) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 156.63/121.25 | (176) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 156.63/121.25 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 156.63/121.25 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 156.63/121.25 | (179) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 156.63/121.25 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 156.63/121.25 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 156.63/121.25 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 156.63/121.25 | (183) ! [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)))
% 156.63/121.25 | (184) ! [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)))
% 156.63/121.25 | (185) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 156.63/121.25 | (186) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 156.63/121.25 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 156.63/121.25 | (188) ! [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)))
% 156.63/121.25 | (189) ! [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)))))
% 156.63/121.25 | (190) ! [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))
% 156.63/121.25 | (191) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 156.63/121.25 |
% 156.63/121.25 | Instantiating formula (163) with all_0_0_0, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms one_to_one(all_0_7_7, all_0_4_4, all_0_3_3) = all_0_0_0, yields:
% 156.63/121.25 | (192) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & surjective(all_0_7_7, all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & injective(all_0_7_7, all_0_4_4, all_0_3_3) = v0))
% 156.63/121.25 |
% 156.63/121.25 +-Applying beta-rule and splitting (192), into two cases.
% 156.63/121.25 |-Branch one:
% 156.63/121.25 | (193) all_0_0_0 = 0
% 156.63/121.25 |
% 156.63/121.25 | Equations (193) can reduce 88 to:
% 156.63/121.25 | (194) $false
% 156.63/121.25 |
% 156.63/121.25 |-The branch is then unsatisfiable
% 156.63/121.25 |-Branch two:
% 156.63/121.25 | (88) ~ (all_0_0_0 = 0)
% 156.63/121.25 | (196) ? [v0] : (( ~ (v0 = 0) & surjective(all_0_7_7, all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & injective(all_0_7_7, all_0_4_4, all_0_3_3) = v0))
% 156.63/121.25 |
% 156.63/121.25 | Instantiating (196) with all_68_0_119 yields:
% 156.63/121.25 | (197) ( ~ (all_68_0_119 = 0) & surjective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119) | ( ~ (all_68_0_119 = 0) & injective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119)
% 156.63/121.25 |
% 156.63/121.25 +-Applying beta-rule and splitting (197), into two cases.
% 156.63/121.25 |-Branch one:
% 156.63/121.25 | (198) ~ (all_68_0_119 = 0) & surjective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119
% 156.63/121.25 |
% 156.63/121.25 | Applying alpha-rule on (198) yields:
% 156.63/121.25 | (199) ~ (all_68_0_119 = 0)
% 156.63/121.25 | (200) surjective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119
% 156.63/121.25 |
% 156.63/121.25 | Instantiating formula (126) with all_68_0_119, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms surjective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119, yields:
% 156.63/121.25 | (201) all_68_0_119 = 0 | ? [v0] : (member(v0, all_0_3_3) = 0 & ! [v1] : ( ~ (apply(all_0_7_7, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_4_4) = v2)) & ! [v1] : ( ~ (member(v1, all_0_4_4) = 0) | ? [v2] : ( ~ (v2 = 0) & apply(all_0_7_7, v1, v0) = v2)))
% 156.63/121.25 |
% 156.63/121.25 +-Applying beta-rule and splitting (201), into two cases.
% 156.63/121.25 |-Branch one:
% 156.63/121.25 | (202) all_68_0_119 = 0
% 156.63/121.25 |
% 156.63/121.25 | Equations (202) can reduce 199 to:
% 156.63/121.25 | (194) $false
% 156.63/121.25 |
% 156.63/121.25 |-The branch is then unsatisfiable
% 156.63/121.25 |-Branch two:
% 156.63/121.25 | (199) ~ (all_68_0_119 = 0)
% 156.63/121.25 | (205) ? [v0] : (member(v0, all_0_3_3) = 0 & ! [v1] : ( ~ (apply(all_0_7_7, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_4_4) = v2)) & ! [v1] : ( ~ (member(v1, all_0_4_4) = 0) | ? [v2] : ( ~ (v2 = 0) & apply(all_0_7_7, v1, v0) = v2)))
% 156.63/121.25 |
% 156.63/121.25 | Instantiating (205) with all_83_0_120 yields:
% 156.63/121.25 | (206) member(all_83_0_120, all_0_3_3) = 0 & ! [v0] : ( ~ (apply(all_0_7_7, v0, all_83_0_120) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1)) & ! [v0] : ( ~ (member(v0, all_0_4_4) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_7_7, v0, all_83_0_120) = v1))
% 156.63/121.25 |
% 156.63/121.25 | Applying alpha-rule on (206) yields:
% 156.63/121.25 | (207) member(all_83_0_120, all_0_3_3) = 0
% 156.63/121.25 | (208) ! [v0] : ( ~ (apply(all_0_7_7, v0, all_83_0_120) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1))
% 156.63/121.25 | (209) ! [v0] : ( ~ (member(v0, all_0_4_4) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_7_7, v0, all_83_0_120) = v1))
% 156.63/121.25 |
% 156.63/121.25 | Instantiating formula (115) with all_83_0_120, all_0_3_3, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_3_3) = 0, member(all_83_0_120, all_0_3_3) = 0, yields:
% 156.63/121.25 | (210) apply(all_0_1_1, all_83_0_120, all_83_0_120) = 0
% 156.63/121.25 |
% 156.63/121.25 | Instantiating formula (92) with all_0_1_1, all_83_0_120, all_83_0_120, all_0_3_3, all_0_4_4, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms compose_function(all_0_7_7, all_0_5_5, all_0_3_3, all_0_4_4, all_0_3_3) = all_0_1_1, apply(all_0_1_1, all_83_0_120, all_83_0_120) = 0, yields:
% 156.63/121.26 | (211) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, all_83_0_120, v0) = 0 & apply(all_0_7_7, v0, all_83_0_120) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_83_0_120, all_0_3_3) = v0))
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (211) with all_104_0_124, all_104_1_125, all_104_2_126, all_104_3_127 yields:
% 156.63/121.26 | (212) (all_104_0_124 = 0 & all_104_1_125 = 0 & all_104_2_126 = 0 & apply(all_0_5_5, all_83_0_120, all_104_3_127) = 0 & apply(all_0_7_7, all_104_3_127, all_83_0_120) = 0 & member(all_104_3_127, all_0_4_4) = 0) | ( ~ (all_104_3_127 = 0) & member(all_83_0_120, all_0_3_3) = all_104_3_127)
% 156.63/121.26 |
% 156.63/121.26 +-Applying beta-rule and splitting (212), into two cases.
% 156.63/121.26 |-Branch one:
% 156.63/121.26 | (213) all_104_0_124 = 0 & all_104_1_125 = 0 & all_104_2_126 = 0 & apply(all_0_5_5, all_83_0_120, all_104_3_127) = 0 & apply(all_0_7_7, all_104_3_127, all_83_0_120) = 0 & member(all_104_3_127, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (213) yields:
% 156.63/121.26 | (214) all_104_1_125 = 0
% 156.63/121.26 | (215) member(all_104_3_127, all_0_4_4) = 0
% 156.63/121.26 | (216) apply(all_0_5_5, all_83_0_120, all_104_3_127) = 0
% 156.63/121.26 | (217) all_104_0_124 = 0
% 156.63/121.26 | (218) all_104_2_126 = 0
% 156.63/121.26 | (219) apply(all_0_7_7, all_104_3_127, all_83_0_120) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (209) with all_104_3_127 and discharging atoms member(all_104_3_127, all_0_4_4) = 0, yields:
% 156.63/121.26 | (220) ? [v0] : ( ~ (v0 = 0) & apply(all_0_7_7, all_104_3_127, all_83_0_120) = v0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (220) with all_121_0_131 yields:
% 156.63/121.26 | (221) ~ (all_121_0_131 = 0) & apply(all_0_7_7, all_104_3_127, all_83_0_120) = all_121_0_131
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (221) yields:
% 156.63/121.26 | (222) ~ (all_121_0_131 = 0)
% 156.63/121.26 | (223) apply(all_0_7_7, all_104_3_127, all_83_0_120) = all_121_0_131
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (142) with all_0_7_7, all_104_3_127, all_83_0_120, all_121_0_131, 0 and discharging atoms apply(all_0_7_7, all_104_3_127, all_83_0_120) = all_121_0_131, apply(all_0_7_7, all_104_3_127, all_83_0_120) = 0, yields:
% 156.63/121.26 | (224) all_121_0_131 = 0
% 156.63/121.26 |
% 156.63/121.26 | Equations (224) can reduce 222 to:
% 156.63/121.26 | (194) $false
% 156.63/121.26 |
% 156.63/121.26 |-The branch is then unsatisfiable
% 156.63/121.26 |-Branch two:
% 156.63/121.26 | (226) ~ (all_104_3_127 = 0) & member(all_83_0_120, all_0_3_3) = all_104_3_127
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (226) yields:
% 156.63/121.26 | (227) ~ (all_104_3_127 = 0)
% 156.63/121.26 | (228) member(all_83_0_120, all_0_3_3) = all_104_3_127
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (157) with all_83_0_120, all_0_3_3, all_104_3_127, 0 and discharging atoms member(all_83_0_120, all_0_3_3) = all_104_3_127, member(all_83_0_120, all_0_3_3) = 0, yields:
% 156.63/121.26 | (229) all_104_3_127 = 0
% 156.63/121.26 |
% 156.63/121.26 | Equations (229) can reduce 227 to:
% 156.63/121.26 | (194) $false
% 156.63/121.26 |
% 156.63/121.26 |-The branch is then unsatisfiable
% 156.63/121.26 |-Branch two:
% 156.63/121.26 | (231) ~ (all_68_0_119 = 0) & injective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (231) yields:
% 156.63/121.26 | (199) ~ (all_68_0_119 = 0)
% 156.63/121.26 | (233) injective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (64) with all_68_0_119, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms injective(all_0_7_7, all_0_4_4, all_0_3_3) = all_68_0_119, yields:
% 156.63/121.26 | (234) all_68_0_119 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_7_7, v1, v2) = 0 & apply(all_0_7_7, v0, v2) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.26 |
% 156.63/121.26 +-Applying beta-rule and splitting (234), into two cases.
% 156.63/121.26 |-Branch one:
% 156.63/121.26 | (202) all_68_0_119 = 0
% 156.63/121.26 |
% 156.63/121.26 | Equations (202) can reduce 199 to:
% 156.63/121.26 | (194) $false
% 156.63/121.26 |
% 156.63/121.26 |-The branch is then unsatisfiable
% 156.63/121.26 |-Branch two:
% 156.63/121.26 | (199) ~ (all_68_0_119 = 0)
% 156.63/121.26 | (238) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_7_7, v1, v2) = 0 & apply(all_0_7_7, v0, v2) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (238) with all_83_0_153, all_83_1_154, all_83_2_155 yields:
% 156.63/121.26 | (239) ~ (all_83_1_154 = all_83_2_155) & apply(all_0_7_7, all_83_1_154, all_83_0_153) = 0 & apply(all_0_7_7, all_83_2_155, all_83_0_153) = 0 & member(all_83_0_153, all_0_3_3) = 0 & member(all_83_1_154, all_0_4_4) = 0 & member(all_83_2_155, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (239) yields:
% 156.63/121.26 | (240) member(all_83_1_154, all_0_4_4) = 0
% 156.63/121.26 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.26 | (242) member(all_83_0_153, all_0_3_3) = 0
% 156.63/121.26 | (243) member(all_83_2_155, all_0_4_4) = 0
% 156.63/121.26 | (244) apply(all_0_7_7, all_83_2_155, all_83_0_153) = 0
% 156.63/121.26 | (245) apply(all_0_7_7, all_83_1_154, all_83_0_153) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (20) with all_83_0_153, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.63/121.26 | (246) ? [v0] : (apply(all_0_5_5, all_83_0_153, v0) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (20) with all_83_0_153, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.63/121.26 | (247) ? [v0] : (apply(all_0_6_6, all_83_0_153, v0) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (115) with all_83_0_153, all_0_3_3, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_3_3) = 0, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.63/121.26 | (248) apply(all_0_1_1, all_83_0_153, all_83_0_153) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (20) with all_83_1_154, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, yields:
% 156.63/121.26 | (249) ? [v0] : (apply(all_0_7_7, all_83_1_154, v0) = 0 & member(v0, all_0_3_3) = 0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (115) with all_83_1_154, all_0_4_4, all_0_2_2 and discharging atoms identity(all_0_2_2, all_0_4_4) = 0, member(all_83_1_154, all_0_4_4) = 0, yields:
% 156.63/121.26 | (250) apply(all_0_2_2, all_83_1_154, all_83_1_154) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (15) with all_83_2_155, all_83_1_154, all_83_0_153, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, member(all_83_0_153, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.26 | (251) all_83_1_154 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_83_2_155) = v0))
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (15) with all_83_2_155, all_83_1_154, all_83_0_153, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_83_0_153, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.26 | (252) all_83_1_154 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_83_2_155) = v0))
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (20) with all_83_2_155, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.26 | (253) ? [v0] : (apply(all_0_7_7, all_83_2_155, v0) = 0 & member(v0, all_0_3_3) = 0)
% 156.63/121.26 |
% 156.63/121.26 | Instantiating formula (115) with all_83_2_155, all_0_4_4, all_0_2_2 and discharging atoms identity(all_0_2_2, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.26 | (254) apply(all_0_2_2, all_83_2_155, all_83_2_155) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (247) with all_91_0_156 yields:
% 156.63/121.26 | (255) apply(all_0_6_6, all_83_0_153, all_91_0_156) = 0 & member(all_91_0_156, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (255) yields:
% 156.63/121.26 | (256) apply(all_0_6_6, all_83_0_153, all_91_0_156) = 0
% 156.63/121.26 | (257) member(all_91_0_156, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (253) with all_93_0_157 yields:
% 156.63/121.26 | (258) apply(all_0_7_7, all_83_2_155, all_93_0_157) = 0 & member(all_93_0_157, all_0_3_3) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (258) yields:
% 156.63/121.26 | (259) apply(all_0_7_7, all_83_2_155, all_93_0_157) = 0
% 156.63/121.26 | (260) member(all_93_0_157, all_0_3_3) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (246) with all_95_0_158 yields:
% 156.63/121.26 | (261) apply(all_0_5_5, all_83_0_153, all_95_0_158) = 0 & member(all_95_0_158, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (261) yields:
% 156.63/121.26 | (262) apply(all_0_5_5, all_83_0_153, all_95_0_158) = 0
% 156.63/121.26 | (263) member(all_95_0_158, all_0_4_4) = 0
% 156.63/121.26 |
% 156.63/121.26 | Instantiating (249) with all_97_0_159 yields:
% 156.63/121.26 | (264) apply(all_0_7_7, all_83_1_154, all_97_0_159) = 0 & member(all_97_0_159, all_0_3_3) = 0
% 156.63/121.26 |
% 156.63/121.26 | Applying alpha-rule on (264) yields:
% 156.63/121.26 | (265) apply(all_0_7_7, all_83_1_154, all_97_0_159) = 0
% 156.63/121.26 | (266) member(all_97_0_159, all_0_3_3) = 0
% 156.63/121.26 |
% 156.63/121.26 +-Applying beta-rule and splitting (252), into two cases.
% 156.63/121.26 |-Branch one:
% 156.63/121.26 | (267) all_83_1_154 = all_83_2_155
% 156.63/121.26 |
% 156.63/121.26 | Equations (267) can reduce 241 to:
% 156.63/121.26 | (194) $false
% 156.63/121.26 |
% 156.63/121.26 |-The branch is then unsatisfiable
% 156.63/121.26 |-Branch two:
% 156.63/121.26 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.26 | (270) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (270) with all_103_0_160 yields:
% 156.63/121.27 | (271) ( ~ (all_103_0_160 = 0) & apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_103_0_160) | ( ~ (all_103_0_160 = 0) & apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_103_0_160)
% 156.63/121.27 |
% 156.63/121.27 +-Applying beta-rule and splitting (251), into two cases.
% 156.63/121.27 |-Branch one:
% 156.63/121.27 | (267) all_83_1_154 = all_83_2_155
% 156.63/121.27 |
% 156.63/121.27 | Equations (267) can reduce 241 to:
% 156.63/121.27 | (194) $false
% 156.63/121.27 |
% 156.63/121.27 |-The branch is then unsatisfiable
% 156.63/121.27 |-Branch two:
% 156.63/121.27 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.27 | (275) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (92) with all_0_1_1, all_83_0_153, all_83_0_153, all_0_3_3, all_0_4_4, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms compose_function(all_0_7_7, all_0_5_5, all_0_3_3, all_0_4_4, all_0_3_3) = all_0_1_1, apply(all_0_1_1, all_83_0_153, all_83_0_153) = 0, yields:
% 156.63/121.27 | (276) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, all_83_0_153, v0) = 0 & apply(all_0_7_7, v0, all_83_0_153) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (92) with all_0_2_2, all_83_1_154, all_83_1_154, all_0_4_4, all_0_3_3, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms compose_function(all_0_6_6, all_0_7_7, all_0_4_4, all_0_3_3, all_0_4_4) = all_0_2_2, apply(all_0_2_2, all_83_1_154, all_83_1_154) = 0, yields:
% 156.63/121.27 | (277) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_6_6, v0, all_83_1_154) = 0 & apply(all_0_7_7, all_83_1_154, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_83_1_154, all_0_4_4) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (92) with all_0_2_2, all_83_2_155, all_83_2_155, all_0_4_4, all_0_3_3, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms compose_function(all_0_6_6, all_0_7_7, all_0_4_4, all_0_3_3, all_0_4_4) = all_0_2_2, apply(all_0_2_2, all_83_2_155, all_83_2_155) = 0, yields:
% 156.63/121.27 | (278) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_6_6, v0, all_83_2_155) = 0 & apply(all_0_7_7, all_83_2_155, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_83_2_155, all_0_4_4) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (99) with all_93_0_157, all_83_0_153, all_83_2_155, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, apply(all_0_7_7, all_83_2_155, all_93_0_157) = 0, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.63/121.27 | (279) all_93_0_157 = all_83_0_153 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_83_0_153) = v0) | ( ~ (v0 = 0) & member(all_93_0_157, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_2_155, all_0_4_4) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (20) with all_97_0_159, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, member(all_97_0_159, all_0_3_3) = 0, yields:
% 156.63/121.27 | (280) ? [v0] : (apply(all_0_5_5, all_97_0_159, v0) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (15) with all_83_1_154, all_83_2_155, all_97_0_159, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_97_0_159, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.27 | (281) all_83_1_154 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_97_0_159, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_97_0_159, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (20) with all_97_0_159, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_97_0_159, all_0_3_3) = 0, yields:
% 156.63/121.27 | (282) ? [v0] : (apply(all_0_6_6, all_97_0_159, v0) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (20) with all_95_0_158, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_95_0_158, all_0_4_4) = 0, yields:
% 156.63/121.27 | (283) ? [v0] : (apply(all_0_7_7, all_95_0_158, v0) = 0 & member(v0, all_0_3_3) = 0)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (15) with all_83_1_154, all_83_2_155, all_93_0_157, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, member(all_93_0_157, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.27 | (284) all_83_1_154 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_93_0_157, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_93_0_157, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (15) with all_83_1_154, all_83_2_155, all_93_0_157, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_93_0_157, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.27 | (285) all_83_1_154 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (20) with all_93_0_157, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_93_0_157, all_0_3_3) = 0, yields:
% 156.63/121.27 | (286) ? [v0] : (apply(all_0_6_6, all_93_0_157, v0) = 0 & member(v0, all_0_4_4) = 0)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (15) with all_93_0_157, all_97_0_159, all_83_1_154, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_97_0_159, all_0_3_3) = 0, member(all_93_0_157, all_0_3_3) = 0, member(all_83_1_154, all_0_4_4) = 0, yields:
% 156.63/121.27 | (287) all_97_0_159 = all_93_0_157 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_97_0_159) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_93_0_157) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating formula (15) with all_91_0_156, all_83_2_155, all_93_0_157, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_93_0_157, all_0_3_3) = 0, member(all_91_0_156, all_0_4_4) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.27 | (288) all_91_0_156 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_91_0_156) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = v0))
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (282) with all_114_0_162 yields:
% 156.63/121.27 | (289) apply(all_0_6_6, all_97_0_159, all_114_0_162) = 0 & member(all_114_0_162, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Applying alpha-rule on (289) yields:
% 156.63/121.27 | (290) apply(all_0_6_6, all_97_0_159, all_114_0_162) = 0
% 156.63/121.27 | (291) member(all_114_0_162, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (280) with all_116_0_163 yields:
% 156.63/121.27 | (292) apply(all_0_5_5, all_97_0_159, all_116_0_163) = 0 & member(all_116_0_163, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Applying alpha-rule on (292) yields:
% 156.63/121.27 | (293) apply(all_0_5_5, all_97_0_159, all_116_0_163) = 0
% 156.63/121.27 | (294) member(all_116_0_163, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (278) with all_118_0_164, all_118_1_165, all_118_2_166, all_118_3_167 yields:
% 156.63/121.27 | (295) (all_118_0_164 = 0 & all_118_1_165 = 0 & all_118_2_166 = 0 & apply(all_0_6_6, all_118_3_167, all_83_2_155) = 0 & apply(all_0_7_7, all_83_2_155, all_118_3_167) = 0 & member(all_118_3_167, all_0_3_3) = 0) | ( ~ (all_118_3_167 = 0) & member(all_83_2_155, all_0_4_4) = all_118_3_167)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (286) with all_119_0_168 yields:
% 156.63/121.27 | (296) apply(all_0_6_6, all_93_0_157, all_119_0_168) = 0 & member(all_119_0_168, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Applying alpha-rule on (296) yields:
% 156.63/121.27 | (297) apply(all_0_6_6, all_93_0_157, all_119_0_168) = 0
% 156.63/121.27 | (298) member(all_119_0_168, all_0_4_4) = 0
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (283) with all_121_0_169 yields:
% 156.63/121.27 | (299) apply(all_0_7_7, all_95_0_158, all_121_0_169) = 0 & member(all_121_0_169, all_0_3_3) = 0
% 156.63/121.27 |
% 156.63/121.27 | Applying alpha-rule on (299) yields:
% 156.63/121.27 | (300) apply(all_0_7_7, all_95_0_158, all_121_0_169) = 0
% 156.63/121.27 | (301) member(all_121_0_169, all_0_3_3) = 0
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (277) with all_123_0_170, all_123_1_171, all_123_2_172, all_123_3_173 yields:
% 156.63/121.27 | (302) (all_123_0_170 = 0 & all_123_1_171 = 0 & all_123_2_172 = 0 & apply(all_0_6_6, all_123_3_173, all_83_1_154) = 0 & apply(all_0_7_7, all_83_1_154, all_123_3_173) = 0 & member(all_123_3_173, all_0_3_3) = 0) | ( ~ (all_123_3_173 = 0) & member(all_83_1_154, all_0_4_4) = all_123_3_173)
% 156.63/121.27 |
% 156.63/121.27 | Instantiating (276) with all_126_0_175, all_126_1_176, all_126_2_177, all_126_3_178 yields:
% 156.63/121.27 | (303) (all_126_0_175 = 0 & all_126_1_176 = 0 & all_126_2_177 = 0 & apply(all_0_5_5, all_83_0_153, all_126_3_178) = 0 & apply(all_0_7_7, all_126_3_178, all_83_0_153) = 0 & member(all_126_3_178, all_0_4_4) = 0) | ( ~ (all_126_3_178 = 0) & member(all_83_0_153, all_0_3_3) = all_126_3_178)
% 156.63/121.27 |
% 156.63/121.27 +-Applying beta-rule and splitting (279), into two cases.
% 156.63/121.27 |-Branch one:
% 156.63/121.27 | (304) all_93_0_157 = all_83_0_153
% 156.63/121.27 |
% 156.63/121.27 | From (304) and (297) follows:
% 156.63/121.27 | (305) apply(all_0_6_6, all_83_0_153, all_119_0_168) = 0
% 156.63/121.27 |
% 156.63/121.27 | From (304) and (259) follows:
% 156.63/121.27 | (244) apply(all_0_7_7, all_83_2_155, all_83_0_153) = 0
% 156.63/121.27 |
% 156.63/121.27 +-Applying beta-rule and splitting (302), into two cases.
% 156.63/121.27 |-Branch one:
% 156.63/121.27 | (307) all_123_0_170 = 0 & all_123_1_171 = 0 & all_123_2_172 = 0 & apply(all_0_6_6, all_123_3_173, all_83_1_154) = 0 & apply(all_0_7_7, all_83_1_154, all_123_3_173) = 0 & member(all_123_3_173, all_0_3_3) = 0
% 156.63/121.27 |
% 156.63/121.27 | Applying alpha-rule on (307) yields:
% 156.63/121.27 | (308) apply(all_0_7_7, all_83_1_154, all_123_3_173) = 0
% 156.63/121.27 | (309) all_123_0_170 = 0
% 156.63/121.27 | (310) all_123_1_171 = 0
% 156.63/121.27 | (311) all_123_2_172 = 0
% 156.63/121.27 | (312) apply(all_0_6_6, all_123_3_173, all_83_1_154) = 0
% 156.63/121.27 | (313) member(all_123_3_173, all_0_3_3) = 0
% 156.63/121.27 |
% 156.63/121.27 +-Applying beta-rule and splitting (287), into two cases.
% 156.63/121.27 |-Branch one:
% 156.63/121.27 | (314) all_97_0_159 = all_93_0_157
% 156.63/121.27 |
% 156.63/121.28 | Combining equations (304,314) yields a new equation:
% 156.63/121.28 | (315) all_97_0_159 = all_83_0_153
% 156.63/121.28 |
% 156.63/121.28 | From (315) and (293) follows:
% 156.63/121.28 | (316) apply(all_0_5_5, all_83_0_153, all_116_0_163) = 0
% 156.63/121.28 |
% 156.63/121.28 | From (315) and (290) follows:
% 156.63/121.28 | (317) apply(all_0_6_6, all_83_0_153, all_114_0_162) = 0
% 156.63/121.28 |
% 156.63/121.28 | From (315) and (265) follows:
% 156.63/121.28 | (245) apply(all_0_7_7, all_83_1_154, all_83_0_153) = 0
% 156.63/121.28 |
% 156.63/121.28 | From (315) and (266) follows:
% 156.63/121.28 | (242) member(all_83_0_153, all_0_3_3) = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (303), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (320) all_126_0_175 = 0 & all_126_1_176 = 0 & all_126_2_177 = 0 & apply(all_0_5_5, all_83_0_153, all_126_3_178) = 0 & apply(all_0_7_7, all_126_3_178, all_83_0_153) = 0 & member(all_126_3_178, all_0_4_4) = 0
% 156.63/121.28 |
% 156.63/121.28 | Applying alpha-rule on (320) yields:
% 156.63/121.28 | (321) apply(all_0_7_7, all_126_3_178, all_83_0_153) = 0
% 156.63/121.28 | (322) all_126_1_176 = 0
% 156.63/121.28 | (323) member(all_126_3_178, all_0_4_4) = 0
% 156.63/121.28 | (324) apply(all_0_5_5, all_83_0_153, all_126_3_178) = 0
% 156.63/121.28 | (325) all_126_2_177 = 0
% 156.63/121.28 | (326) all_126_0_175 = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (295), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (327) all_118_0_164 = 0 & all_118_1_165 = 0 & all_118_2_166 = 0 & apply(all_0_6_6, all_118_3_167, all_83_2_155) = 0 & apply(all_0_7_7, all_83_2_155, all_118_3_167) = 0 & member(all_118_3_167, all_0_3_3) = 0
% 156.63/121.28 |
% 156.63/121.28 | Applying alpha-rule on (327) yields:
% 156.63/121.28 | (328) apply(all_0_7_7, all_83_2_155, all_118_3_167) = 0
% 156.63/121.28 | (329) all_118_0_164 = 0
% 156.63/121.28 | (330) apply(all_0_6_6, all_118_3_167, all_83_2_155) = 0
% 156.63/121.28 | (331) all_118_1_165 = 0
% 156.63/121.28 | (332) all_118_2_166 = 0
% 156.63/121.28 | (333) member(all_118_3_167, all_0_3_3) = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (281), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (267) all_83_1_154 = all_83_2_155
% 156.63/121.28 |
% 156.63/121.28 | Equations (267) can reduce 241 to:
% 156.63/121.28 | (194) $false
% 156.63/121.28 |
% 156.63/121.28 |-The branch is then unsatisfiable
% 156.63/121.28 |-Branch two:
% 156.63/121.28 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.28 | (337) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_97_0_159, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_97_0_159, all_83_2_155) = v0))
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (284), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (267) all_83_1_154 = all_83_2_155
% 156.63/121.28 |
% 156.63/121.28 | Equations (267) can reduce 241 to:
% 156.63/121.28 | (194) $false
% 156.63/121.28 |
% 156.63/121.28 |-The branch is then unsatisfiable
% 156.63/121.28 |-Branch two:
% 156.63/121.28 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.28 | (341) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_93_0_157, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_93_0_157, all_83_2_155) = v0))
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (285), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (267) all_83_1_154 = all_83_2_155
% 156.63/121.28 |
% 156.63/121.28 | Equations (267) can reduce 241 to:
% 156.63/121.28 | (194) $false
% 156.63/121.28 |
% 156.63/121.28 |-The branch is then unsatisfiable
% 156.63/121.28 |-Branch two:
% 156.63/121.28 | (241) ~ (all_83_1_154 = all_83_2_155)
% 156.63/121.28 | (345) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_1_154) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating (345) with all_160_0_182 yields:
% 156.63/121.28 | (346) ( ~ (all_160_0_182 = 0) & apply(all_0_6_6, all_93_0_157, all_83_1_154) = all_160_0_182) | ( ~ (all_160_0_182 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_160_0_182)
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (99) with all_95_0_158, all_126_3_178, all_83_0_153, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, apply(all_0_5_5, all_83_0_153, all_95_0_158) = 0, member(all_126_3_178, all_0_4_4) = 0, yields:
% 156.63/121.28 | (347) all_126_3_178 = all_95_0_158 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_126_3_178) = v0) | ( ~ (v0 = 0) & member(all_95_0_158, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (99) with all_83_2_155, all_119_0_168, all_118_3_167, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, apply(all_0_6_6, all_118_3_167, all_83_2_155) = 0, member(all_119_0_168, all_0_4_4) = 0, yields:
% 156.63/121.28 | (348) all_119_0_168 = all_83_2_155 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_118_3_167, all_119_0_168) = v0) | ( ~ (v0 = 0) & member(all_118_3_167, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_2_155, all_0_4_4) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (99) with all_114_0_162, all_119_0_168, all_83_0_153, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, apply(all_0_6_6, all_83_0_153, all_114_0_162) = 0, member(all_119_0_168, all_0_4_4) = 0, yields:
% 156.63/121.28 | (349) all_119_0_168 = all_114_0_162 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_119_0_168) = v0) | ( ~ (v0 = 0) & member(all_114_0_162, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (15) with all_119_0_168, all_91_0_156, all_121_0_169, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_3_3, all_0_4_4) = 0, member(all_121_0_169, all_0_3_3) = 0, member(all_119_0_168, all_0_4_4) = 0, member(all_91_0_156, all_0_4_4) = 0, yields:
% 156.63/121.28 | (350) all_119_0_168 = all_91_0_156 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_121_0_169, all_119_0_168) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_121_0_169, all_91_0_156) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (99) with all_123_3_173, all_118_3_167, all_83_1_154, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, apply(all_0_7_7, all_83_1_154, all_123_3_173) = 0, member(all_118_3_167, all_0_3_3) = 0, yields:
% 156.63/121.28 | (351) all_123_3_173 = all_118_3_167 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_118_3_167) = v0) | ( ~ (v0 = 0) & member(all_123_3_173, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_1_154, all_0_4_4) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (15) with all_118_3_167, all_121_0_169, all_83_2_155, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_121_0_169, all_0_3_3) = 0, member(all_118_3_167, all_0_3_3) = 0, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.63/121.28 | (352) all_121_0_169 = all_118_3_167 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_121_0_169) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_118_3_167) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (99) with all_126_3_178, all_116_0_163, all_83_0_153, all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_4_4) = 0, apply(all_0_5_5, all_83_0_153, all_126_3_178) = 0, member(all_116_0_163, all_0_4_4) = 0, yields:
% 156.63/121.28 | (353) all_126_3_178 = all_116_0_163 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_116_0_163) = v0) | ( ~ (v0 = 0) & member(all_126_3_178, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.63/121.28 |
% 156.63/121.28 | Instantiating formula (15) with all_83_0_153, all_121_0_169, all_116_0_163, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_4_4, all_0_3_3) = 0, member(all_121_0_169, all_0_3_3) = 0, member(all_116_0_163, all_0_4_4) = 0, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.63/121.28 | (354) all_121_0_169 = all_83_0_153 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_116_0_163, all_121_0_169) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_116_0_163, all_83_0_153) = v0))
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (353), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (355) all_126_3_178 = all_116_0_163
% 156.63/121.28 |
% 156.63/121.28 | From (355) and (324) follows:
% 156.63/121.28 | (316) apply(all_0_5_5, all_83_0_153, all_116_0_163) = 0
% 156.63/121.28 |
% 156.63/121.28 | From (355) and (321) follows:
% 156.63/121.28 | (357) apply(all_0_7_7, all_116_0_163, all_83_0_153) = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (347), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (358) all_126_3_178 = all_95_0_158
% 156.63/121.28 |
% 156.63/121.28 | Combining equations (358,355) yields a new equation:
% 156.63/121.28 | (359) all_116_0_163 = all_95_0_158
% 156.63/121.28 |
% 156.63/121.28 | From (359) and (357) follows:
% 156.63/121.28 | (360) apply(all_0_7_7, all_95_0_158, all_83_0_153) = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (354), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (361) all_121_0_169 = all_83_0_153
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (352), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (362) all_121_0_169 = all_118_3_167
% 156.63/121.28 |
% 156.63/121.28 | Combining equations (362,361) yields a new equation:
% 156.63/121.28 | (363) all_118_3_167 = all_83_0_153
% 156.63/121.28 |
% 156.63/121.28 | Simplifying 363 yields:
% 156.63/121.28 | (364) all_118_3_167 = all_83_0_153
% 156.63/121.28 |
% 156.63/121.28 | From (364) and (330) follows:
% 156.63/121.28 | (365) apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0
% 156.63/121.28 |
% 156.63/121.28 | From (364) and (333) follows:
% 156.63/121.28 | (242) member(all_83_0_153, all_0_3_3) = 0
% 156.63/121.28 |
% 156.63/121.28 +-Applying beta-rule and splitting (271), into two cases.
% 156.63/121.28 |-Branch one:
% 156.63/121.28 | (367) ~ (all_103_0_160 = 0) & apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_103_0_160
% 156.63/121.28 |
% 156.63/121.28 | Applying alpha-rule on (367) yields:
% 156.63/121.28 | (368) ~ (all_103_0_160 = 0)
% 156.83/121.28 | (369) apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_103_0_160
% 156.83/121.28 |
% 156.83/121.28 +-Applying beta-rule and splitting (349), into two cases.
% 156.83/121.28 |-Branch one:
% 156.83/121.28 | (370) all_119_0_168 = all_114_0_162
% 156.83/121.28 |
% 156.83/121.28 | From (370) and (305) follows:
% 156.83/121.28 | (317) apply(all_0_6_6, all_83_0_153, all_114_0_162) = 0
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (348), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (372) all_119_0_168 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | Combining equations (370,372) yields a new equation:
% 156.83/121.29 | (373) all_114_0_162 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | Simplifying 373 yields:
% 156.83/121.29 | (374) all_114_0_162 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | From (374) and (317) follows:
% 156.83/121.29 | (365) apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (350), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (376) all_119_0_168 = all_91_0_156
% 156.83/121.29 |
% 156.83/121.29 | Combining equations (376,372) yields a new equation:
% 156.83/121.29 | (377) all_91_0_156 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | Simplifying 377 yields:
% 156.83/121.29 | (378) all_91_0_156 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | From (378) and (256) follows:
% 156.83/121.29 | (365) apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (346), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (380) ~ (all_160_0_182 = 0) & apply(all_0_6_6, all_93_0_157, all_83_1_154) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (380) yields:
% 156.83/121.29 | (381) ~ (all_160_0_182 = 0)
% 156.83/121.29 | (382) apply(all_0_6_6, all_93_0_157, all_83_1_154) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 | From (304) and (382) follows:
% 156.83/121.29 | (383) apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (351), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (384) all_123_3_173 = all_118_3_167
% 156.83/121.29 |
% 156.83/121.29 | Combining equations (364,384) yields a new equation:
% 156.83/121.29 | (385) all_123_3_173 = all_83_0_153
% 156.83/121.29 |
% 156.83/121.29 | From (385) and (312) follows:
% 156.83/121.29 | (386) apply(all_0_6_6, all_83_0_153, all_83_1_154) = 0
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_1_154, all_103_0_160, all_160_0_182 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_160_0_182, apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_103_0_160, yields:
% 156.83/121.29 | (387) all_160_0_182 = all_103_0_160
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_1_154, 0, all_160_0_182 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_1_154) = all_160_0_182, apply(all_0_6_6, all_83_0_153, all_83_1_154) = 0, yields:
% 156.83/121.29 | (388) all_160_0_182 = 0
% 156.83/121.29 |
% 156.83/121.29 | Combining equations (387,388) yields a new equation:
% 156.83/121.29 | (389) all_103_0_160 = 0
% 156.83/121.29 |
% 156.83/121.29 | Simplifying 389 yields:
% 156.83/121.29 | (390) all_103_0_160 = 0
% 156.83/121.29 |
% 156.83/121.29 | Equations (390) can reduce 368 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (392) ~ (all_123_3_173 = all_118_3_167)
% 156.83/121.29 | (393) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_118_3_167) = v0) | ( ~ (v0 = 0) & member(all_123_3_173, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_1_154, all_0_4_4) = v0))
% 156.83/121.29 |
% 156.83/121.29 | Instantiating (393) with all_255_0_279 yields:
% 156.83/121.29 | (394) ( ~ (all_255_0_279 = 0) & apply(all_0_7_7, all_83_1_154, all_118_3_167) = all_255_0_279) | ( ~ (all_255_0_279 = 0) & member(all_123_3_173, all_0_3_3) = all_255_0_279) | ( ~ (all_255_0_279 = 0) & member(all_83_1_154, all_0_4_4) = all_255_0_279)
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (394), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (395) ( ~ (all_255_0_279 = 0) & apply(all_0_7_7, all_83_1_154, all_118_3_167) = all_255_0_279) | ( ~ (all_255_0_279 = 0) & member(all_123_3_173, all_0_3_3) = all_255_0_279)
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (395), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (396) ~ (all_255_0_279 = 0) & apply(all_0_7_7, all_83_1_154, all_118_3_167) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (396) yields:
% 156.83/121.29 | (397) ~ (all_255_0_279 = 0)
% 156.83/121.29 | (398) apply(all_0_7_7, all_83_1_154, all_118_3_167) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | From (364) and (398) follows:
% 156.83/121.29 | (399) apply(all_0_7_7, all_83_1_154, all_83_0_153) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (142) with all_0_7_7, all_83_1_154, all_83_0_153, all_255_0_279, 0 and discharging atoms apply(all_0_7_7, all_83_1_154, all_83_0_153) = all_255_0_279, apply(all_0_7_7, all_83_1_154, all_83_0_153) = 0, yields:
% 156.83/121.29 | (400) all_255_0_279 = 0
% 156.83/121.29 |
% 156.83/121.29 | Equations (400) can reduce 397 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (402) ~ (all_255_0_279 = 0) & member(all_123_3_173, all_0_3_3) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (402) yields:
% 156.83/121.29 | (397) ~ (all_255_0_279 = 0)
% 156.83/121.29 | (404) member(all_123_3_173, all_0_3_3) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (157) with all_123_3_173, all_0_3_3, all_255_0_279, 0 and discharging atoms member(all_123_3_173, all_0_3_3) = all_255_0_279, member(all_123_3_173, all_0_3_3) = 0, yields:
% 156.83/121.29 | (400) all_255_0_279 = 0
% 156.83/121.29 |
% 156.83/121.29 | Equations (400) can reduce 397 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (407) ~ (all_255_0_279 = 0) & member(all_83_1_154, all_0_4_4) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (407) yields:
% 156.83/121.29 | (397) ~ (all_255_0_279 = 0)
% 156.83/121.29 | (409) member(all_83_1_154, all_0_4_4) = all_255_0_279
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (157) with all_83_1_154, all_0_4_4, all_255_0_279, 0 and discharging atoms member(all_83_1_154, all_0_4_4) = all_255_0_279, member(all_83_1_154, all_0_4_4) = 0, yields:
% 156.83/121.29 | (400) all_255_0_279 = 0
% 156.83/121.29 |
% 156.83/121.29 | Equations (400) can reduce 397 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (412) ~ (all_160_0_182 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (412) yields:
% 156.83/121.29 | (381) ~ (all_160_0_182 = 0)
% 156.83/121.29 | (414) apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 | From (304) and (414) follows:
% 156.83/121.29 | (415) apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_160_0_182
% 156.83/121.29 |
% 156.83/121.29 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_2_155, 0, all_160_0_182 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_160_0_182, apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0, yields:
% 156.83/121.29 | (388) all_160_0_182 = 0
% 156.83/121.29 |
% 156.83/121.29 | Equations (388) can reduce 381 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (418) ~ (all_119_0_168 = all_91_0_156)
% 156.83/121.29 | (419) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_121_0_169, all_119_0_168) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_121_0_169, all_91_0_156) = v0))
% 156.83/121.29 |
% 156.83/121.29 | Instantiating (419) with all_235_0_558 yields:
% 156.83/121.29 | (420) ( ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_119_0_168) = all_235_0_558) | ( ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_91_0_156) = all_235_0_558)
% 156.83/121.29 |
% 156.83/121.29 | Equations (372) can reduce 418 to:
% 156.83/121.29 | (421) ~ (all_91_0_156 = all_83_2_155)
% 156.83/121.29 |
% 156.83/121.29 | Simplifying 421 yields:
% 156.83/121.29 | (422) ~ (all_91_0_156 = all_83_2_155)
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (288), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (378) all_91_0_156 = all_83_2_155
% 156.83/121.29 |
% 156.83/121.29 | Equations (378) can reduce 422 to:
% 156.83/121.29 | (194) $false
% 156.83/121.29 |
% 156.83/121.29 |-The branch is then unsatisfiable
% 156.83/121.29 |-Branch two:
% 156.83/121.29 | (422) ~ (all_91_0_156 = all_83_2_155)
% 156.83/121.29 | (426) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_91_0_156) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = v0))
% 156.83/121.29 |
% 156.83/121.29 | Instantiating (426) with all_252_0_562 yields:
% 156.83/121.29 | (427) ( ~ (all_252_0_562 = 0) & apply(all_0_6_6, all_93_0_157, all_91_0_156) = all_252_0_562) | ( ~ (all_252_0_562 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_252_0_562)
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (427), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (428) ~ (all_252_0_562 = 0) & apply(all_0_6_6, all_93_0_157, all_91_0_156) = all_252_0_562
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (428) yields:
% 156.83/121.29 | (429) ~ (all_252_0_562 = 0)
% 156.83/121.29 | (430) apply(all_0_6_6, all_93_0_157, all_91_0_156) = all_252_0_562
% 156.83/121.29 |
% 156.83/121.29 | From (304) and (430) follows:
% 156.83/121.29 | (431) apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_252_0_562
% 156.83/121.29 |
% 156.83/121.29 +-Applying beta-rule and splitting (420), into two cases.
% 156.83/121.29 |-Branch one:
% 156.83/121.29 | (432) ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_119_0_168) = all_235_0_558
% 156.83/121.29 |
% 156.83/121.29 | Applying alpha-rule on (432) yields:
% 156.83/121.30 | (433) ~ (all_235_0_558 = 0)
% 156.83/121.30 | (434) apply(all_0_6_6, all_121_0_169, all_119_0_168) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | From (361)(372) and (434) follows:
% 156.83/121.30 | (435) apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_2_155, 0, all_235_0_558 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_235_0_558, apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0, yields:
% 156.83/121.30 | (436) all_235_0_558 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (436) can reduce 433 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (438) ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (438) yields:
% 156.83/121.30 | (433) ~ (all_235_0_558 = 0)
% 156.83/121.30 | (440) apply(all_0_6_6, all_121_0_169, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | From (361) and (440) follows:
% 156.83/121.30 | (441) apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_91_0_156, all_252_0_562, 0 and discharging atoms apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_252_0_562, apply(all_0_6_6, all_83_0_153, all_91_0_156) = 0, yields:
% 156.83/121.30 | (442) all_252_0_562 = 0
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_91_0_156, all_235_0_558, all_252_0_562 and discharging atoms apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_252_0_562, apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_235_0_558, yields:
% 156.83/121.30 | (443) all_252_0_562 = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Combining equations (442,443) yields a new equation:
% 156.83/121.30 | (436) all_235_0_558 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (436) can reduce 433 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (446) ~ (all_252_0_562 = 0) & apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_252_0_562
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (446) yields:
% 156.83/121.30 | (429) ~ (all_252_0_562 = 0)
% 156.83/121.30 | (448) apply(all_0_6_6, all_93_0_157, all_83_2_155) = all_252_0_562
% 156.83/121.30 |
% 156.83/121.30 | From (304) and (448) follows:
% 156.83/121.30 | (449) apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_252_0_562
% 156.83/121.30 |
% 156.83/121.30 +-Applying beta-rule and splitting (420), into two cases.
% 156.83/121.30 |-Branch one:
% 156.83/121.30 | (432) ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_119_0_168) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (432) yields:
% 156.83/121.30 | (433) ~ (all_235_0_558 = 0)
% 156.83/121.30 | (434) apply(all_0_6_6, all_121_0_169, all_119_0_168) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | From (361)(372) and (434) follows:
% 156.83/121.30 | (435) apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_2_155, all_235_0_558, all_252_0_562 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_252_0_562, apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_235_0_558, yields:
% 156.83/121.30 | (443) all_252_0_562 = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_2_155, 0, all_252_0_562 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_252_0_562, apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0, yields:
% 156.83/121.30 | (442) all_252_0_562 = 0
% 156.83/121.30 |
% 156.83/121.30 | Combining equations (443,442) yields a new equation:
% 156.83/121.30 | (456) all_235_0_558 = 0
% 156.83/121.30 |
% 156.83/121.30 | Simplifying 456 yields:
% 156.83/121.30 | (436) all_235_0_558 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (436) can reduce 433 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (438) ~ (all_235_0_558 = 0) & apply(all_0_6_6, all_121_0_169, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (438) yields:
% 156.83/121.30 | (433) ~ (all_235_0_558 = 0)
% 156.83/121.30 | (440) apply(all_0_6_6, all_121_0_169, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | From (361) and (440) follows:
% 156.83/121.30 | (441) apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_235_0_558
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_91_0_156, all_235_0_558, 0 and discharging atoms apply(all_0_6_6, all_83_0_153, all_91_0_156) = all_235_0_558, apply(all_0_6_6, all_83_0_153, all_91_0_156) = 0, yields:
% 156.83/121.30 | (436) all_235_0_558 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (436) can reduce 433 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (465) ~ (all_119_0_168 = all_83_2_155)
% 156.83/121.30 | (466) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_118_3_167, all_119_0_168) = v0) | ( ~ (v0 = 0) & member(all_118_3_167, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_2_155, all_0_4_4) = v0))
% 156.83/121.30 |
% 156.83/121.30 | Instantiating (466) with all_231_0_1160 yields:
% 156.83/121.30 | (467) ( ~ (all_231_0_1160 = 0) & apply(all_0_6_6, all_118_3_167, all_119_0_168) = all_231_0_1160) | ( ~ (all_231_0_1160 = 0) & member(all_118_3_167, all_0_3_3) = all_231_0_1160) | ( ~ (all_231_0_1160 = 0) & member(all_83_2_155, all_0_4_4) = all_231_0_1160)
% 156.83/121.30 |
% 156.83/121.30 +-Applying beta-rule and splitting (467), into two cases.
% 156.83/121.30 |-Branch one:
% 156.83/121.30 | (468) ( ~ (all_231_0_1160 = 0) & apply(all_0_6_6, all_118_3_167, all_119_0_168) = all_231_0_1160) | ( ~ (all_231_0_1160 = 0) & member(all_118_3_167, all_0_3_3) = all_231_0_1160)
% 156.83/121.30 |
% 156.83/121.30 +-Applying beta-rule and splitting (468), into two cases.
% 156.83/121.30 |-Branch one:
% 156.83/121.30 | (469) ~ (all_231_0_1160 = 0) & apply(all_0_6_6, all_118_3_167, all_119_0_168) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (469) yields:
% 156.83/121.30 | (470) ~ (all_231_0_1160 = 0)
% 156.83/121.30 | (471) apply(all_0_6_6, all_118_3_167, all_119_0_168) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | From (364)(370) and (471) follows:
% 156.83/121.30 | (472) apply(all_0_6_6, all_83_0_153, all_114_0_162) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_114_0_162, all_231_0_1160, 0 and discharging atoms apply(all_0_6_6, all_83_0_153, all_114_0_162) = all_231_0_1160, apply(all_0_6_6, all_83_0_153, all_114_0_162) = 0, yields:
% 156.83/121.30 | (473) all_231_0_1160 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (473) can reduce 470 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (475) ~ (all_231_0_1160 = 0) & member(all_118_3_167, all_0_3_3) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (475) yields:
% 156.83/121.30 | (470) ~ (all_231_0_1160 = 0)
% 156.83/121.30 | (477) member(all_118_3_167, all_0_3_3) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | From (364) and (477) follows:
% 156.83/121.30 | (478) member(all_83_0_153, all_0_3_3) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (157) with all_83_0_153, all_0_3_3, all_231_0_1160, 0 and discharging atoms member(all_83_0_153, all_0_3_3) = all_231_0_1160, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.83/121.30 | (473) all_231_0_1160 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (473) can reduce 470 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (481) ~ (all_231_0_1160 = 0) & member(all_83_2_155, all_0_4_4) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Applying alpha-rule on (481) yields:
% 156.83/121.30 | (470) ~ (all_231_0_1160 = 0)
% 156.83/121.30 | (483) member(all_83_2_155, all_0_4_4) = all_231_0_1160
% 156.83/121.30 |
% 156.83/121.30 | Instantiating formula (157) with all_83_2_155, all_0_4_4, all_231_0_1160, 0 and discharging atoms member(all_83_2_155, all_0_4_4) = all_231_0_1160, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.83/121.30 | (473) all_231_0_1160 = 0
% 156.83/121.30 |
% 156.83/121.30 | Equations (473) can reduce 470 to:
% 156.83/121.30 | (194) $false
% 156.83/121.30 |
% 156.83/121.30 |-The branch is then unsatisfiable
% 156.83/121.30 |-Branch two:
% 156.83/121.30 | (486) ~ (all_119_0_168 = all_114_0_162)
% 156.83/121.30 | (487) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_83_0_153, all_119_0_168) = v0) | ( ~ (v0 = 0) & member(all_114_0_162, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.83/121.30 |
% 156.83/121.30 | Instantiating (487) with all_227_0_3082 yields:
% 156.83/121.30 | (488) ( ~ (all_227_0_3082 = 0) & apply(all_0_6_6, all_83_0_153, all_119_0_168) = all_227_0_3082) | ( ~ (all_227_0_3082 = 0) & member(all_114_0_162, all_0_4_4) = all_227_0_3082) | ( ~ (all_227_0_3082 = 0) & member(all_83_0_153, all_0_3_3) = all_227_0_3082)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (488), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (489) ( ~ (all_227_0_3082 = 0) & apply(all_0_6_6, all_83_0_153, all_119_0_168) = all_227_0_3082) | ( ~ (all_227_0_3082 = 0) & member(all_114_0_162, all_0_4_4) = all_227_0_3082)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (489), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (490) ~ (all_227_0_3082 = 0) & apply(all_0_6_6, all_83_0_153, all_119_0_168) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (490) yields:
% 156.83/121.31 | (491) ~ (all_227_0_3082 = 0)
% 156.83/121.31 | (492) apply(all_0_6_6, all_83_0_153, all_119_0_168) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_119_0_168, all_227_0_3082, 0 and discharging atoms apply(all_0_6_6, all_83_0_153, all_119_0_168) = all_227_0_3082, apply(all_0_6_6, all_83_0_153, all_119_0_168) = 0, yields:
% 156.83/121.31 | (493) all_227_0_3082 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (493) can reduce 491 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (495) ~ (all_227_0_3082 = 0) & member(all_114_0_162, all_0_4_4) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (495) yields:
% 156.83/121.31 | (491) ~ (all_227_0_3082 = 0)
% 156.83/121.31 | (497) member(all_114_0_162, all_0_4_4) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (157) with all_114_0_162, all_0_4_4, all_227_0_3082, 0 and discharging atoms member(all_114_0_162, all_0_4_4) = all_227_0_3082, member(all_114_0_162, all_0_4_4) = 0, yields:
% 156.83/121.31 | (493) all_227_0_3082 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (493) can reduce 491 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (500) ~ (all_227_0_3082 = 0) & member(all_83_0_153, all_0_3_3) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (500) yields:
% 156.83/121.31 | (491) ~ (all_227_0_3082 = 0)
% 156.83/121.31 | (502) member(all_83_0_153, all_0_3_3) = all_227_0_3082
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (157) with all_83_0_153, all_0_3_3, all_227_0_3082, 0 and discharging atoms member(all_83_0_153, all_0_3_3) = all_227_0_3082, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.83/121.31 | (493) all_227_0_3082 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (493) can reduce 491 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (505) ~ (all_103_0_160 = 0) & apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_103_0_160
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (505) yields:
% 156.83/121.31 | (368) ~ (all_103_0_160 = 0)
% 156.83/121.31 | (507) apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_103_0_160
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_6_6, all_83_0_153, all_83_2_155, 0, all_103_0_160 and discharging atoms apply(all_0_6_6, all_83_0_153, all_83_2_155) = all_103_0_160, apply(all_0_6_6, all_83_0_153, all_83_2_155) = 0, yields:
% 156.83/121.31 | (390) all_103_0_160 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (390) can reduce 368 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (510) ~ (all_121_0_169 = all_118_3_167)
% 156.83/121.31 | (511) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_121_0_169) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_118_3_167) = v0))
% 156.83/121.31 |
% 156.83/121.31 | Instantiating (511) with all_215_0_5858 yields:
% 156.83/121.31 | (512) ( ~ (all_215_0_5858 = 0) & apply(all_0_7_7, all_83_2_155, all_121_0_169) = all_215_0_5858) | ( ~ (all_215_0_5858 = 0) & apply(all_0_7_7, all_83_2_155, all_118_3_167) = all_215_0_5858)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (512), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (513) ~ (all_215_0_5858 = 0) & apply(all_0_7_7, all_83_2_155, all_121_0_169) = all_215_0_5858
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (513) yields:
% 156.83/121.31 | (514) ~ (all_215_0_5858 = 0)
% 156.83/121.31 | (515) apply(all_0_7_7, all_83_2_155, all_121_0_169) = all_215_0_5858
% 156.83/121.31 |
% 156.83/121.31 | From (361) and (515) follows:
% 156.83/121.31 | (516) apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_215_0_5858
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_7_7, all_83_2_155, all_83_0_153, all_215_0_5858, 0 and discharging atoms apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_215_0_5858, apply(all_0_7_7, all_83_2_155, all_83_0_153) = 0, yields:
% 156.83/121.31 | (517) all_215_0_5858 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (517) can reduce 514 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (519) ~ (all_215_0_5858 = 0) & apply(all_0_7_7, all_83_2_155, all_118_3_167) = all_215_0_5858
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (519) yields:
% 156.83/121.31 | (514) ~ (all_215_0_5858 = 0)
% 156.83/121.31 | (521) apply(all_0_7_7, all_83_2_155, all_118_3_167) = all_215_0_5858
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_7_7, all_83_2_155, all_118_3_167, all_215_0_5858, 0 and discharging atoms apply(all_0_7_7, all_83_2_155, all_118_3_167) = all_215_0_5858, apply(all_0_7_7, all_83_2_155, all_118_3_167) = 0, yields:
% 156.83/121.31 | (517) all_215_0_5858 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (517) can reduce 514 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (524) ~ (all_121_0_169 = all_83_0_153)
% 156.83/121.31 | (525) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_116_0_163, all_121_0_169) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_116_0_163, all_83_0_153) = v0))
% 156.83/121.31 |
% 156.83/121.31 | Instantiating (525) with all_211_0_6340 yields:
% 156.83/121.31 | (526) ( ~ (all_211_0_6340 = 0) & apply(all_0_7_7, all_116_0_163, all_121_0_169) = all_211_0_6340) | ( ~ (all_211_0_6340 = 0) & apply(all_0_7_7, all_116_0_163, all_83_0_153) = all_211_0_6340)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (526), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (527) ~ (all_211_0_6340 = 0) & apply(all_0_7_7, all_116_0_163, all_121_0_169) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (527) yields:
% 156.83/121.31 | (528) ~ (all_211_0_6340 = 0)
% 156.83/121.31 | (529) apply(all_0_7_7, all_116_0_163, all_121_0_169) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | From (359) and (529) follows:
% 156.83/121.31 | (530) apply(all_0_7_7, all_95_0_158, all_121_0_169) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_7_7, all_95_0_158, all_121_0_169, all_211_0_6340, 0 and discharging atoms apply(all_0_7_7, all_95_0_158, all_121_0_169) = all_211_0_6340, apply(all_0_7_7, all_95_0_158, all_121_0_169) = 0, yields:
% 156.83/121.31 | (531) all_211_0_6340 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (531) can reduce 528 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (533) ~ (all_211_0_6340 = 0) & apply(all_0_7_7, all_116_0_163, all_83_0_153) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | Applying alpha-rule on (533) yields:
% 156.83/121.31 | (528) ~ (all_211_0_6340 = 0)
% 156.83/121.31 | (535) apply(all_0_7_7, all_116_0_163, all_83_0_153) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | From (359) and (535) follows:
% 156.83/121.31 | (536) apply(all_0_7_7, all_95_0_158, all_83_0_153) = all_211_0_6340
% 156.83/121.31 |
% 156.83/121.31 | Instantiating formula (142) with all_0_7_7, all_95_0_158, all_83_0_153, 0, all_211_0_6340 and discharging atoms apply(all_0_7_7, all_95_0_158, all_83_0_153) = all_211_0_6340, apply(all_0_7_7, all_95_0_158, all_83_0_153) = 0, yields:
% 156.83/121.31 | (531) all_211_0_6340 = 0
% 156.83/121.31 |
% 156.83/121.31 | Equations (531) can reduce 528 to:
% 156.83/121.31 | (194) $false
% 156.83/121.31 |
% 156.83/121.31 |-The branch is then unsatisfiable
% 156.83/121.31 |-Branch two:
% 156.83/121.31 | (539) ~ (all_126_3_178 = all_95_0_158)
% 156.83/121.31 | (540) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_126_3_178) = v0) | ( ~ (v0 = 0) & member(all_95_0_158, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.83/121.31 |
% 156.83/121.31 | Instantiating (540) with all_207_0_7341 yields:
% 156.83/121.31 | (541) ( ~ (all_207_0_7341 = 0) & apply(all_0_5_5, all_83_0_153, all_126_3_178) = all_207_0_7341) | ( ~ (all_207_0_7341 = 0) & member(all_95_0_158, all_0_4_4) = all_207_0_7341) | ( ~ (all_207_0_7341 = 0) & member(all_83_0_153, all_0_3_3) = all_207_0_7341)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (541), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (542) ( ~ (all_207_0_7341 = 0) & apply(all_0_5_5, all_83_0_153, all_126_3_178) = all_207_0_7341) | ( ~ (all_207_0_7341 = 0) & member(all_95_0_158, all_0_4_4) = all_207_0_7341)
% 156.83/121.31 |
% 156.83/121.31 +-Applying beta-rule and splitting (542), into two cases.
% 156.83/121.31 |-Branch one:
% 156.83/121.31 | (543) ~ (all_207_0_7341 = 0) & apply(all_0_5_5, all_83_0_153, all_126_3_178) = all_207_0_7341
% 156.83/121.31 |
% 156.83/121.32 | Applying alpha-rule on (543) yields:
% 156.83/121.32 | (544) ~ (all_207_0_7341 = 0)
% 156.83/121.32 | (545) apply(all_0_5_5, all_83_0_153, all_126_3_178) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | From (355) and (545) follows:
% 156.83/121.32 | (546) apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (142) with all_0_5_5, all_83_0_153, all_116_0_163, all_207_0_7341, 0 and discharging atoms apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_207_0_7341, apply(all_0_5_5, all_83_0_153, all_116_0_163) = 0, yields:
% 156.83/121.32 | (547) all_207_0_7341 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (547) can reduce 544 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (549) ~ (all_207_0_7341 = 0) & member(all_95_0_158, all_0_4_4) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (549) yields:
% 156.83/121.32 | (544) ~ (all_207_0_7341 = 0)
% 156.83/121.32 | (551) member(all_95_0_158, all_0_4_4) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_95_0_158, all_0_4_4, all_207_0_7341, 0 and discharging atoms member(all_95_0_158, all_0_4_4) = all_207_0_7341, member(all_95_0_158, all_0_4_4) = 0, yields:
% 156.83/121.32 | (547) all_207_0_7341 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (547) can reduce 544 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (554) ~ (all_207_0_7341 = 0) & member(all_83_0_153, all_0_3_3) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (554) yields:
% 156.83/121.32 | (544) ~ (all_207_0_7341 = 0)
% 156.83/121.32 | (556) member(all_83_0_153, all_0_3_3) = all_207_0_7341
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_83_0_153, all_0_3_3, all_207_0_7341, 0 and discharging atoms member(all_83_0_153, all_0_3_3) = all_207_0_7341, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.83/121.32 | (547) all_207_0_7341 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (547) can reduce 544 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (559) ~ (all_126_3_178 = all_116_0_163)
% 156.83/121.32 | (560) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_83_0_153, all_116_0_163) = v0) | ( ~ (v0 = 0) & member(all_126_3_178, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_83_0_153, all_0_3_3) = v0))
% 156.83/121.32 |
% 156.83/121.32 | Instantiating (560) with all_203_0_8684 yields:
% 156.83/121.32 | (561) ( ~ (all_203_0_8684 = 0) & apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_203_0_8684) | ( ~ (all_203_0_8684 = 0) & member(all_126_3_178, all_0_4_4) = all_203_0_8684) | ( ~ (all_203_0_8684 = 0) & member(all_83_0_153, all_0_3_3) = all_203_0_8684)
% 156.83/121.32 |
% 156.83/121.32 +-Applying beta-rule and splitting (561), into two cases.
% 156.83/121.32 |-Branch one:
% 156.83/121.32 | (562) ( ~ (all_203_0_8684 = 0) & apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_203_0_8684) | ( ~ (all_203_0_8684 = 0) & member(all_126_3_178, all_0_4_4) = all_203_0_8684)
% 156.83/121.32 |
% 156.83/121.32 +-Applying beta-rule and splitting (562), into two cases.
% 156.83/121.32 |-Branch one:
% 156.83/121.32 | (563) ~ (all_203_0_8684 = 0) & apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (563) yields:
% 156.83/121.32 | (564) ~ (all_203_0_8684 = 0)
% 156.83/121.32 | (565) apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (142) with all_0_5_5, all_83_0_153, all_116_0_163, all_203_0_8684, 0 and discharging atoms apply(all_0_5_5, all_83_0_153, all_116_0_163) = all_203_0_8684, apply(all_0_5_5, all_83_0_153, all_116_0_163) = 0, yields:
% 156.83/121.32 | (566) all_203_0_8684 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (566) can reduce 564 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (568) ~ (all_203_0_8684 = 0) & member(all_126_3_178, all_0_4_4) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (568) yields:
% 156.83/121.32 | (564) ~ (all_203_0_8684 = 0)
% 156.83/121.32 | (570) member(all_126_3_178, all_0_4_4) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_126_3_178, all_0_4_4, all_203_0_8684, 0 and discharging atoms member(all_126_3_178, all_0_4_4) = all_203_0_8684, member(all_126_3_178, all_0_4_4) = 0, yields:
% 156.83/121.32 | (566) all_203_0_8684 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (566) can reduce 564 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (573) ~ (all_203_0_8684 = 0) & member(all_83_0_153, all_0_3_3) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (573) yields:
% 156.83/121.32 | (564) ~ (all_203_0_8684 = 0)
% 156.83/121.32 | (575) member(all_83_0_153, all_0_3_3) = all_203_0_8684
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_83_0_153, all_0_3_3, all_203_0_8684, 0 and discharging atoms member(all_83_0_153, all_0_3_3) = all_203_0_8684, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.83/121.32 | (566) all_203_0_8684 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (566) can reduce 564 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (578) ~ (all_118_3_167 = 0) & member(all_83_2_155, all_0_4_4) = all_118_3_167
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (578) yields:
% 156.83/121.32 | (579) ~ (all_118_3_167 = 0)
% 156.83/121.32 | (580) member(all_83_2_155, all_0_4_4) = all_118_3_167
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_83_2_155, all_0_4_4, all_118_3_167, 0 and discharging atoms member(all_83_2_155, all_0_4_4) = all_118_3_167, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.83/121.32 | (581) all_118_3_167 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (581) can reduce 579 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (583) ~ (all_126_3_178 = 0) & member(all_83_0_153, all_0_3_3) = all_126_3_178
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (583) yields:
% 156.83/121.32 | (584) ~ (all_126_3_178 = 0)
% 156.83/121.32 | (585) member(all_83_0_153, all_0_3_3) = all_126_3_178
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (157) with all_83_0_153, all_0_3_3, all_126_3_178, 0 and discharging atoms member(all_83_0_153, all_0_3_3) = all_126_3_178, member(all_83_0_153, all_0_3_3) = 0, yields:
% 156.83/121.32 | (586) all_126_3_178 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (586) can reduce 584 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (588) ~ (all_97_0_159 = all_93_0_157)
% 156.83/121.32 | (589) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_97_0_159) = v0) | ( ~ (v0 = 0) & apply(all_0_7_7, all_83_1_154, all_93_0_157) = v0))
% 156.83/121.32 |
% 156.83/121.32 | Instantiating (589) with all_141_0_33458 yields:
% 156.83/121.32 | (590) ( ~ (all_141_0_33458 = 0) & apply(all_0_7_7, all_83_1_154, all_97_0_159) = all_141_0_33458) | ( ~ (all_141_0_33458 = 0) & apply(all_0_7_7, all_83_1_154, all_93_0_157) = all_141_0_33458)
% 156.83/121.32 |
% 156.83/121.32 +-Applying beta-rule and splitting (590), into two cases.
% 156.83/121.32 |-Branch one:
% 156.83/121.32 | (591) ~ (all_141_0_33458 = 0) & apply(all_0_7_7, all_83_1_154, all_97_0_159) = all_141_0_33458
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (591) yields:
% 156.83/121.32 | (592) ~ (all_141_0_33458 = 0)
% 156.83/121.32 | (593) apply(all_0_7_7, all_83_1_154, all_97_0_159) = all_141_0_33458
% 156.83/121.32 |
% 156.83/121.32 | Instantiating formula (142) with all_0_7_7, all_83_1_154, all_97_0_159, all_141_0_33458, 0 and discharging atoms apply(all_0_7_7, all_83_1_154, all_97_0_159) = all_141_0_33458, apply(all_0_7_7, all_83_1_154, all_97_0_159) = 0, yields:
% 156.83/121.32 | (594) all_141_0_33458 = 0
% 156.83/121.32 |
% 156.83/121.32 | Equations (594) can reduce 592 to:
% 156.83/121.32 | (194) $false
% 156.83/121.32 |
% 156.83/121.32 |-The branch is then unsatisfiable
% 156.83/121.32 |-Branch two:
% 156.83/121.32 | (596) ~ (all_141_0_33458 = 0) & apply(all_0_7_7, all_83_1_154, all_93_0_157) = all_141_0_33458
% 156.83/121.32 |
% 156.83/121.32 | Applying alpha-rule on (596) yields:
% 156.83/121.32 | (592) ~ (all_141_0_33458 = 0)
% 156.83/121.32 | (598) apply(all_0_7_7, all_83_1_154, all_93_0_157) = all_141_0_33458
% 156.83/121.32 |
% 156.83/121.32 | From (304) and (598) follows:
% 156.83/121.33 | (599) apply(all_0_7_7, all_83_1_154, all_83_0_153) = all_141_0_33458
% 156.83/121.33 |
% 156.83/121.33 | Instantiating formula (142) with all_0_7_7, all_83_1_154, all_83_0_153, all_141_0_33458, 0 and discharging atoms apply(all_0_7_7, all_83_1_154, all_83_0_153) = all_141_0_33458, apply(all_0_7_7, all_83_1_154, all_83_0_153) = 0, yields:
% 156.83/121.33 | (594) all_141_0_33458 = 0
% 156.83/121.33 |
% 156.83/121.33 | Equations (594) can reduce 592 to:
% 156.83/121.33 | (194) $false
% 156.83/121.33 |
% 156.83/121.33 |-The branch is then unsatisfiable
% 156.83/121.33 |-Branch two:
% 156.83/121.33 | (602) ~ (all_123_3_173 = 0) & member(all_83_1_154, all_0_4_4) = all_123_3_173
% 156.83/121.33 |
% 156.83/121.33 | Applying alpha-rule on (602) yields:
% 156.83/121.33 | (603) ~ (all_123_3_173 = 0)
% 156.83/121.33 | (604) member(all_83_1_154, all_0_4_4) = all_123_3_173
% 156.83/121.33 |
% 156.83/121.33 | Instantiating formula (157) with all_83_1_154, all_0_4_4, all_123_3_173, 0 and discharging atoms member(all_83_1_154, all_0_4_4) = all_123_3_173, member(all_83_1_154, all_0_4_4) = 0, yields:
% 156.83/121.33 | (605) all_123_3_173 = 0
% 156.83/121.33 |
% 156.83/121.33 | Equations (605) can reduce 603 to:
% 156.83/121.33 | (194) $false
% 156.83/121.33 |
% 156.83/121.33 |-The branch is then unsatisfiable
% 156.83/121.33 |-Branch two:
% 156.83/121.33 | (607) ~ (all_93_0_157 = all_83_0_153)
% 156.83/121.33 | (608) ? [v0] : (( ~ (v0 = 0) & apply(all_0_7_7, all_83_2_155, all_83_0_153) = v0) | ( ~ (v0 = 0) & member(all_93_0_157, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_83_2_155, all_0_4_4) = v0))
% 156.83/121.33 |
% 156.83/121.33 | Instantiating (608) with all_133_0_33489 yields:
% 156.83/121.33 | (609) ( ~ (all_133_0_33489 = 0) & apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_133_0_33489) | ( ~ (all_133_0_33489 = 0) & member(all_93_0_157, all_0_3_3) = all_133_0_33489) | ( ~ (all_133_0_33489 = 0) & member(all_83_2_155, all_0_4_4) = all_133_0_33489)
% 156.83/121.33 |
% 156.83/121.33 +-Applying beta-rule and splitting (609), into two cases.
% 156.83/121.33 |-Branch one:
% 156.83/121.33 | (610) ( ~ (all_133_0_33489 = 0) & apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_133_0_33489) | ( ~ (all_133_0_33489 = 0) & member(all_93_0_157, all_0_3_3) = all_133_0_33489)
% 156.83/121.33 |
% 156.83/121.33 +-Applying beta-rule and splitting (610), into two cases.
% 156.83/121.33 |-Branch one:
% 156.83/121.33 | (611) ~ (all_133_0_33489 = 0) & apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Applying alpha-rule on (611) yields:
% 156.83/121.33 | (612) ~ (all_133_0_33489 = 0)
% 156.83/121.33 | (613) apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Instantiating formula (142) with all_0_7_7, all_83_2_155, all_83_0_153, all_133_0_33489, 0 and discharging atoms apply(all_0_7_7, all_83_2_155, all_83_0_153) = all_133_0_33489, apply(all_0_7_7, all_83_2_155, all_83_0_153) = 0, yields:
% 156.83/121.33 | (614) all_133_0_33489 = 0
% 156.83/121.33 |
% 156.83/121.33 | Equations (614) can reduce 612 to:
% 156.83/121.33 | (194) $false
% 156.83/121.33 |
% 156.83/121.33 |-The branch is then unsatisfiable
% 156.83/121.33 |-Branch two:
% 156.83/121.33 | (616) ~ (all_133_0_33489 = 0) & member(all_93_0_157, all_0_3_3) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Applying alpha-rule on (616) yields:
% 156.83/121.33 | (612) ~ (all_133_0_33489 = 0)
% 156.83/121.33 | (618) member(all_93_0_157, all_0_3_3) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Instantiating formula (157) with all_93_0_157, all_0_3_3, all_133_0_33489, 0 and discharging atoms member(all_93_0_157, all_0_3_3) = all_133_0_33489, member(all_93_0_157, all_0_3_3) = 0, yields:
% 156.83/121.33 | (614) all_133_0_33489 = 0
% 156.83/121.33 |
% 156.83/121.33 | Equations (614) can reduce 612 to:
% 156.83/121.33 | (194) $false
% 156.83/121.33 |
% 156.83/121.33 |-The branch is then unsatisfiable
% 156.83/121.33 |-Branch two:
% 156.83/121.33 | (621) ~ (all_133_0_33489 = 0) & member(all_83_2_155, all_0_4_4) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Applying alpha-rule on (621) yields:
% 156.83/121.33 | (612) ~ (all_133_0_33489 = 0)
% 156.83/121.33 | (623) member(all_83_2_155, all_0_4_4) = all_133_0_33489
% 156.83/121.33 |
% 156.83/121.33 | Instantiating formula (157) with all_83_2_155, all_0_4_4, all_133_0_33489, 0 and discharging atoms member(all_83_2_155, all_0_4_4) = all_133_0_33489, member(all_83_2_155, all_0_4_4) = 0, yields:
% 156.83/121.33 | (614) all_133_0_33489 = 0
% 156.83/121.33 |
% 156.83/121.33 | Equations (614) can reduce 612 to:
% 156.83/121.33 | (194) $false
% 156.83/121.33 |
% 156.83/121.33 |-The branch is then unsatisfiable
% 156.83/121.33 % SZS output end Proof for theBenchmark
% 156.83/121.33
% 156.83/121.33 120740ms
%------------------------------------------------------------------------------