TSTP Solution File: SET718+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET718+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 00:21:36 EDT 2022
% Result : Theorem 9.07s 2.68s
% Output : Proof 21.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET718+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n019.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 : Mon Jul 11 01:30:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.61/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.98 Prover 0: Preprocessing ...
% 3.33/1.32 Prover 0: Warning: ignoring some quantifiers
% 3.33/1.35 Prover 0: Constructing countermodel ...
% 4.21/1.61 Prover 0: gave up
% 4.21/1.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.63/1.66 Prover 1: Preprocessing ...
% 5.55/1.90 Prover 1: Constructing countermodel ...
% 6.01/1.95 Prover 1: gave up
% 6.01/1.95 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.01/1.98 Prover 2: Preprocessing ...
% 7.33/2.25 Prover 2: Warning: ignoring some quantifiers
% 7.33/2.27 Prover 2: Constructing countermodel ...
% 9.07/2.68 Prover 2: proved (732ms)
% 9.07/2.68
% 9.07/2.68 No countermodel exists, formula is valid
% 9.07/2.68 % SZS status Theorem for theBenchmark
% 9.07/2.68
% 9.07/2.68 Generating proof ... Warning: ignoring some quantifiers
% 20.65/5.30 found it (size 258)
% 20.65/5.30
% 20.65/5.30 % SZS output start Proof for theBenchmark
% 20.65/5.30 Assumed formulas after preprocessing and simplification:
% 20.65/5.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & one_to_one(v5, v2, v4) = v6 & one_to_one(v1, v3, v4) = 0 & one_to_one(v0, v2, v3) = 0 & compose_function(v1, v0, v2, v3, v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = 0) | ~ (apply(v9, v12, v14) = v16) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v15, v13) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v9, v12, v14) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v12, v14) = v17) | ( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (apply(v8, v12, v16) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v16, v13) = v17) | ( ~ (v17 = 0) & member(v16, v10) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (apply(v7, v16, v13) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v12, v16) = v17) | ( ~ (v17 = 0) & member(v16, v10) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (member(v16, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v12, v16) = v17) | ( ~ (v17 = 0) & apply(v7, v16, v13) = v17) | ( ~ (v17 = 0) & member(v13, v11) = v17) | ( ~ (v17 = 0) & member(v12, v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v9, v13, v16) = 0) | ~ (apply(v7, v13, v14) = v15) | ? [v17] : (( ~ (v17 = 0) & apply(v8, v16, v14) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v16, v14) = 0) | ~ (apply(v7, v13, v14) = v15) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v13, v16) = v17) | ( ~ (v17 = 0) & member(v16, v11) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v7, v13, v14) = v15) | ~ (member(v16, v11) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v9, v13, v16) = v17) | ( ~ (v17 = 0) & apply(v8, v16, v14) = v17) | ( ~ (v17 = 0) & member(v14, v12) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v14, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v11, v13, v15) = v16) | ~ (member(v14, v8) = 0) | ~ (member(v12, v8) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v9, v12, v14) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v9, v12, v14) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v15, v10) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v13, v10) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = v16) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v17] : (( ~ (v17 = 0) & apply(v7, v14, v15) = v17) | ( ~ (v17 = 0) & apply(v7, v12, v13) = v17) | ( ~ (v17 = 0) & member(v14, v8) = v17) | ( ~ (v17 = 0) & member(v12, v8) = v17) | (( ~ (v16 = 0) | (v17 = 0 & apply(v11, v13, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | (((v17 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16)) & ((v16 = 0 & apply(v9, v12, v14) = 0) | ( ~ (v17 = 0) & apply(v11, v13, v15) = v17))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v15, v13) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v13, v10) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v14, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v12, v13) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & member(v13, v10) = v16) | ( ~ (v16 = 0) & member(v12, v8) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (member(v15, v10) = 0) | ~ (member(v14, v8) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v8) = 0) | ? [v16] : ((v16 = 0 & apply(v11, v13, v15) = 0) | ( ~ (v16 = 0) & apply(v9, v12, v14) = v16) | ( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v12, v13) = v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v8 = v7 | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v8) | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v8, v12, v15) = 0 & apply(v7, v15, v13) = 0 & member(v15, v10) = 0) | ( ~ (v15 = 0) & member(v13, v11) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v7, v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v9, v13, v15) = 0 & apply(v8, v15, v14) = 0 & member(v15, v11) = 0) | ( ~ (v15 = 0) & member(v14, v12) = v15) | ( ~ (v15 = 0) & member(v13, v10) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v7, v11, v12) = 0) | ? [v14] : (( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v12, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v11, v12) = v14) | ( ~ (v14 = 0) & member(v13, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (member(v13, v10) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (member(v13, v10) = 0) | ~ (member(v12, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v14] : (( ~ (v14 = 0) & apply(v8, v11, v13) = v14) | ( ~ (v14 = 0) & apply(v7, v11, v12) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (member(v15, v12) = 0 & member(v14, v10) = 0 & ((v20 = 0 & v19 = 0 & v18 = 0 & apply(v9, v14, v17) = 0 & apply(v8, v17, v15) = 0 & member(v17, v11) = 0) | (v16 = 0 & apply(v7, v14, v15) = 0)) & (( ~ (v16 = 0) & apply(v7, v14, v15) = v16) | ( ! [v21] : ( ~ (apply(v9, v14, v21) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v8, v21, v15) = v22) | ( ~ (v22 = 0) & member(v21, v11) = v22))) & ! [v21] : ( ~ (apply(v8, v21, v15) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v9, v14, v21) = v22) | ( ~ (v22 = 0) & member(v21, v11) = v22))) & ! [v21] : ( ~ (member(v21, v11) = 0) | ? [v22] : (( ~ (v22 = 0) & apply(v9, v14, v21) = v22) | ( ~ (v22 = 0) & apply(v8, v21, v15) = v22))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image3(v7, v8, v9) = v11) | ~ (apply(v7, v10, v13) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v13, v8) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v10, v13) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image3(v7, v8, v9) = v11) | ~ (apply(v7, v13, v10) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image3(v7, v8, v9) = v11) | ~ (member(v13, v8) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & apply(v7, v13, v10) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (isomorphism(v13, v12, v11, v10, v9) = v8) | ~ (isomorphism(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (decreasing(v13, v12, v11, v10, v9) = v8) | ~ (decreasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (increasing(v13, v12, v11, v10, v9) = v8) | ~ (increasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (compose_function(v13, v12, v11, v10, v9) = v8) | ~ (compose_function(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_function(v7, v8, v9) = v12) | ~ (apply(v12, v11, v10) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v11, v9) = v14) | ( ~ (v14 = 0) & member(v10, v8) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v7, v10, v11) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v7, v10, v11) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v7, v12, v11) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v7, v12, v11) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) | ~ (apply(v7, v12, v11) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v9) = v14) | (( ~ (v13 = 0) | (v14 = 0 & apply(v8, v11, v12) = 0)) & (v13 = 0 | ( ~ (v14 = 0) & apply(v8, v11, v12) = v14))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v7, v10, v11) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v11) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v11) = 0) | ~ (member(v12, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & apply(v7, v10, v11) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0 & ((v24 = 0 & apply(v11, v14, v16) = 0) | (v23 = 0 & apply(v9, v13, v15) = 0)) & (( ~ (v24 = 0) & apply(v11, v14, v16) = v24) | ( ~ (v23 = 0) & apply(v9, v13, v15) = v23))) | ( ~ (v13 = 0) & one_to_one(v7, v8, v10) = v13) | ( ~ (v13 = 0) & maps(v7, v8, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v16, v14) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v14, v16) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (apply(v7, v10, v12) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v8) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v11, v12) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v11, v12) = v13) | ( ~ (v13 = 0) & apply(v7, v10, v12) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image2(v7, v8) = v10) | ~ (apply(v7, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image2(v7, v8) = v10) | ~ (member(v12, v8) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v9, v12) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image2(v7, v8) = v10) | ~ (apply(v7, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image2(v7, v8) = v10) | ~ (member(v12, v8) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v12, v9) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (inverse_predicate(v12, v11, v10, v9) = v8) | ~ (inverse_predicate(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (equal_maps(v12, v11, v10, v9) = v8) | ~ (equal_maps(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (inverse_predicate(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (member(v13, v10) = 0 & member(v12, v9) = 0 & ((v15 = 0 & apply(v7, v13, v12) = 0) | (v14 = 0 & apply(v8, v12, v13) = 0)) & (( ~ (v15 = 0) & apply(v7, v13, v12) = v15) | ( ~ (v14 = 0) & apply(v8, v12, v13) = v14)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equal_maps(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v7, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ((v12 = 0 & member(v7, v8) = 0) | ( ~ (v12 = 0) & member(v7, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v7, v9) = v12) | ( ~ (v12 = 0) & member(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v11, v8) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_image3(v11, v10, v9) = v8) | ~ (inverse_image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (image3(v11, v10, v9) = v8) | ~ (image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_function(v11, v10, v9) = v8) | ~ (inverse_function(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (one_to_one(v11, v10, v9) = v8) | ~ (one_to_one(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (surjective(v11, v10, v9) = v8) | ~ (surjective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (injective(v11, v10, v9) = v8) | ~ (injective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (maps(v11, v10, v9) = v8) | ~ (maps(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (apply(v11, v10, v9) = v8) | ~ (apply(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | (one_to_one(v7, v8, v10) = 0 & maps(v7, v8, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v10, v12) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v12, v10) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (one_to_one(v7, v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & surjective(v7, v8, v9) = v11) | ( ~ (v11 = 0) & injective(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (surjective(v7, v8, v9) = v10) | ? [v11] : (member(v11, v9) = 0 & ! [v12] : ( ~ (apply(v7, v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v12] : ( ~ (member(v12, v8) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v7, v12, v11) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (injective(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v12 = v11) & apply(v7, v12, v13) = 0 & apply(v7, v11, v13) = 0 & member(v13, v9) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (identity(v7, v8) = 0) | ~ (apply(v7, v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (maps(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v7, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0) | (v12 = 0 & member(v11, v8) = 0 & ! [v19] : ( ~ (apply(v7, v11, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & member(v19, v9) = v20)) & ! [v19] : ( ~ (member(v19, v9) = 0) | ? [v20] : ( ~ (v20 = 0) & apply(v7, v11, v19) = v20))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (member(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (inverse_image2(v10, v9) = v8) | ~ (inverse_image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (image2(v10, v9) = v8) | ~ (image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (identity(v10, v9) = v8) | ~ (identity(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v9, v11) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v11, v9) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & injective(v7, v8, v9) = 0) | ( ~ (v11 = 0) & one_to_one(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = 0) | ~ (member(v10, v9) = 0) | ? [v11] : (apply(v7, v11, v10) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (injective(v7, v8, v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & surjective(v7, v8, v9) = 0) | ( ~ (v11 = 0) & one_to_one(v7, v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (maps(v7, v8, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v11] : (apply(v7, v10, v11) = 0 & member(v11, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (product(v8) = v9) | ~ (member(v10, v8) = 0) | ~ (member(v7, v9) = 0) | member(v7, v10) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ((v11 = 0 & member(v7, v9) = 0) | (v11 = 0 & member(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & apply(v7, v10, v10) = v11 & member(v10, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & subset(v8, v7) = v10) | ( ~ (v10 = 0) & subset(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & power_set(v8) = v10 & member(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (one_to_one(v7, v8, v9) = 0) | (surjective(v7, v8, v9) = 0 & injective(v7, v8, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v7, v8, v9) = 0) | ? [v10] : ((v10 = 0 & one_to_one(v7, v8, v9) = 0) | ( ~ (v10 = 0) & injective(v7, v8, v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (injective(v7, v8, v9) = 0) | ? [v10] : ((v10 = 0 & one_to_one(v7, v8, v9) = 0) | ( ~ (v10 = 0) & surjective(v7, v8, v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (identity(v7, v8) = 0) | ~ (member(v9, v8) = 0) | apply(v7, v9, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v8, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v7, v8) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & subset(v8, v7) = 0) | ( ~ (v10 = 0) & equal_set(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v8, v7) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (power_set(v8) = v9 & member(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : ((v9 = 0 & equal_set(v7, v8) = 0) | ( ~ (v9 = 0) & subset(v8, v7) = v9))) & ! [v7] : ~ (member(v7, empty_set) = 0) & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : compose_predicate(v12, v11, v10, v9, v8, v7) = v13 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : isomorphism(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : decreasing(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : increasing(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : compose_function(v11, v10, v9, v8, v7) = v12 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : inverse_predicate(v10, v9, v8, v7) = v11 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : equal_maps(v10, v9, v8, v7) = v11 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_image3(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : image3(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_function(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : one_to_one(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : surjective(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : injective(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : maps(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : ? [v10] : apply(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : inverse_image2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : image2(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : identity(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : difference(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : union(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_set(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : member(v8, v7) = v9 & ? [v7] : ? [v8] : product(v7) = v8 & ? [v7] : ? [v8] : sum(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : ? [v8] : power_set(v7) = v8)
% 21.29/5.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 21.29/5.44 | (1) ~ (all_0_0_0 = 0) & one_to_one(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0 & one_to_one(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & one_to_one(all_0_6_6, all_0_4_4, all_0_3_3) = 0 & compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1 & maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v1, v9, v7) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ((v17 = 0 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (surjective(v0, v1, v2) = v3) | ? [v4] : (member(v4, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5, v4) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = v13))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1
% 21.29/5.49 |
% 21.29/5.49 | Applying alpha-rule on (1) yields:
% 21.29/5.49 | (2) ? [v0] : ? [v1] : power_set(v0) = v1
% 21.29/5.49 | (3) ! [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)))
% 21.29/5.49 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 21.29/5.49 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 21.29/5.49 | (6) ! [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))
% 21.29/5.49 | (7) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 21.29/5.49 | (8) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 21.29/5.49 | (9) ! [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)))))
% 21.29/5.49 | (10) ! [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)))
% 21.29/5.49 | (11) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 21.29/5.49 | (12) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 21.29/5.49 | (13) ! [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)))
% 21.29/5.49 | (14) ! [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)))
% 21.29/5.49 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 21.29/5.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 21.29/5.49 | (17) ! [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)))
% 21.29/5.49 | (18) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 21.29/5.49 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 21.29/5.49 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 21.29/5.49 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 21.29/5.49 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 21.29/5.49 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 21.29/5.49 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 21.29/5.49 | (25) ! [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)))
% 21.29/5.49 | (26) ! [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)))))
% 21.29/5.49 | (27) ? [v0] : ? [v1] : singleton(v0) = v1
% 21.29/5.49 | (28) ! [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)))
% 21.29/5.49 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 21.29/5.49 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 21.29/5.49 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 21.29/5.49 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 21.29/5.49 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 21.29/5.49 | (34) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 21.29/5.49 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 21.29/5.49 | (36) maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 21.29/5.50 | (37) ! [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))
% 21.29/5.50 | (38) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 21.29/5.50 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 21.29/5.50 | (40) ! [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))
% 21.29/5.50 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 21.29/5.50 | (42) ! [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))
% 21.29/5.50 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 21.29/5.50 | (44) ! [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)))
% 21.29/5.50 | (45) ! [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))
% 21.29/5.50 | (46) ~ (all_0_0_0 = 0)
% 21.29/5.50 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 21.29/5.50 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 21.29/5.50 | (49) ! [v0] : ~ (member(v0, empty_set) = 0)
% 21.29/5.50 | (50) ! [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)))
% 21.29/5.50 | (51) ! [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))
% 21.29/5.50 | (52) ! [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))
% 21.29/5.50 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 21.29/5.50 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 21.29/5.50 | (55) ! [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)))
% 21.29/5.50 | (56) ! [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)))))
% 21.29/5.50 | (57) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 21.29/5.50 | (58) ! [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)))
% 21.29/5.50 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 21.29/5.50 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 21.29/5.50 | (61) ! [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))))
% 21.29/5.50 | (62) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 21.29/5.50 | (63) ! [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)))))
% 21.29/5.50 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 21.29/5.50 | (65) one_to_one(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0
% 21.29/5.50 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 21.29/5.50 | (67) ! [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)))
% 21.29/5.50 | (68) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 21.29/5.50 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 21.29/5.50 | (70) ! [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)))
% 21.29/5.50 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = v6))
% 21.29/5.50 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 21.29/5.50 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 21.29/5.50 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 21.29/5.50 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 21.29/5.50 | (76) ! [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)))
% 21.29/5.50 | (77) ! [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)))))
% 21.29/5.50 | (78) ! [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))
% 21.29/5.50 | (79) ! [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)))
% 21.29/5.51 | (80) ! [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)))
% 21.29/5.51 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 21.29/5.51 | (82) ! [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)))
% 21.29/5.51 | (83) ! [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)))))
% 21.29/5.51 | (84) ! [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)))
% 21.29/5.51 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 21.29/5.51 | (86) one_to_one(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 21.29/5.51 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 21.29/5.51 | (88) ! [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)))
% 21.29/5.51 | (89) ! [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)))
% 21.29/5.51 | (90) ! [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)))
% 21.29/5.51 | (91) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 21.29/5.51 | (92) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 21.29/5.51 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 21.29/5.51 | (94) ! [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)))))))
% 21.29/5.51 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 21.29/5.51 | (96) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 21.29/5.51 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 21.29/5.51 | (98) ! [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)))
% 21.29/5.51 | (99) ! [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)))
% 21.29/5.51 | (100) ! [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)))
% 21.29/5.51 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 21.29/5.51 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 21.29/5.51 | (103) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 21.29/5.51 | (104) ! [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)))
% 21.29/5.51 | (105) ! [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)))
% 21.29/5.51 | (106) ! [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)))
% 21.29/5.51 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 21.29/5.51 | (108) ! [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)))
% 21.29/5.51 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 21.29/5.51 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 21.29/5.51 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 21.29/5.52 | (112) ! [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)))
% 21.29/5.52 | (113) ! [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))
% 21.29/5.52 | (114) ! [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)))
% 21.29/5.52 | (115) ! [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)))
% 21.29/5.52 | (116) ! [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)))
% 21.70/5.52 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 21.70/5.52 | (118) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 21.70/5.52 | (119) ! [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)))
% 21.70/5.52 | (120) ! [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)))
% 21.70/5.52 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 21.70/5.52 | (122) ! [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)))
% 21.70/5.52 | (123) ! [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)))
% 21.70/5.52 | (124) ! [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)))))
% 21.70/5.52 | (125) ! [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))
% 21.70/5.52 | (126) ! [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))))
% 21.70/5.52 | (127) ! [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)))
% 21.70/5.52 | (128) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 21.70/5.52 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 21.70/5.52 | (130) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 21.70/5.52 | (131) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 21.70/5.52 | (132) ! [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))
% 21.70/5.52 | (133) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 21.70/5.52 | (134) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 21.70/5.52 | (135) ! [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)))))
% 21.70/5.52 | (136) ! [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)))
% 21.70/5.52 | (137) ! [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)))
% 21.70/5.52 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 21.70/5.52 | (139) ! [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)))
% 21.70/5.52 | (140) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 21.70/5.52 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 21.70/5.52 | (142) ! [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)))
% 21.70/5.52 | (143) ! [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)))))
% 21.70/5.52 | (144) ! [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)))))
% 21.70/5.53 | (145) ! [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)))
% 21.70/5.53 | (146) ! [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)))))
% 21.70/5.53 | (147) ! [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)))
% 21.70/5.53 | (148) ! [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)))
% 21.70/5.53 | (149) ! [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))
% 21.70/5.53 | (150) ! [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)))
% 21.70/5.53 | (151) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 21.70/5.53 | (152) ! [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)))))
% 21.70/5.53 | (153) ! [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)))
% 21.70/5.53 | (154) ! [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)))
% 21.70/5.53 | (155) ! [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)))
% 21.70/5.53 | (156) ! [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)))
% 21.70/5.53 | (157) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 21.70/5.53 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(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)))
% 21.70/5.53 | (159) compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1
% 21.70/5.53 | (160) maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 21.70/5.53 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 21.70/5.53 | (162) ! [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)))
% 21.70/5.53 | (163) ? [v0] : ? [v1] : sum(v0) = v1
% 21.70/5.53 | (164) ! [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)))
% 21.70/5.53 | (165) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 21.70/5.53 | (166) ! [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)))
% 21.70/5.53 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 21.70/5.53 | (168) ? [v0] : ? [v1] : product(v0) = v1
% 21.70/5.53 | (169) ! [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))
% 21.70/5.53 | (170) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 21.70/5.53 | (171) one_to_one(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 21.70/5.53 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 21.70/5.53 | (173) ! [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)))
% 21.70/5.53 | (174) ! [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)))))
% 21.70/5.53 | (175) ! [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)))
% 21.70/5.54 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 21.70/5.54 | (177) ! [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)))
% 21.70/5.54 | (178) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 21.70/5.54 | (179) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 21.70/5.54 | (180) ! [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)))
% 21.70/5.54 | (181) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 21.70/5.54 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 21.70/5.54 | (183) ! [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)))))
% 21.70/5.54 | (184) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 21.70/5.54 | (185) ! [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))
% 21.70/5.54 | (186) ! [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))
% 21.70/5.54 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 21.70/5.54 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 21.70/5.54 | (189) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 21.70/5.54 |
% 21.70/5.54 | Instantiating formula (137) with all_0_0_0, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms one_to_one(all_0_1_1, all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 21.70/5.54 | (190) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & surjective(all_0_1_1, all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & injective(all_0_1_1, all_0_4_4, all_0_2_2) = v0))
% 21.70/5.54 |
% 21.70/5.54 | Instantiating formula (157) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms one_to_one(all_0_5_5, all_0_3_3, all_0_2_2) = 0, yields:
% 21.70/5.54 | (191) surjective(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 21.70/5.54 |
% 21.70/5.54 | Applying alpha-rule on (191) yields:
% 21.70/5.54 | (192) surjective(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 21.70/5.54 | (193) injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 21.70/5.54 |
% 21.70/5.54 | Instantiating formula (157) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms one_to_one(all_0_6_6, all_0_4_4, all_0_3_3) = 0, yields:
% 21.70/5.54 | (194) surjective(all_0_6_6, all_0_4_4, all_0_3_3) = 0 & injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 21.70/5.54 |
% 21.70/5.54 | Applying alpha-rule on (194) yields:
% 21.70/5.54 | (195) surjective(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 21.70/5.54 | (196) injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0
% 21.70/5.54 |
% 21.70/5.54 +-Applying beta-rule and splitting (190), into two cases.
% 21.70/5.54 |-Branch one:
% 21.70/5.54 | (197) all_0_0_0 = 0
% 21.70/5.54 |
% 21.70/5.54 | Equations (197) can reduce 46 to:
% 21.70/5.54 | (198) $false
% 21.70/5.54 |
% 21.70/5.54 |-The branch is then unsatisfiable
% 21.70/5.54 |-Branch two:
% 21.70/5.54 | (46) ~ (all_0_0_0 = 0)
% 21.70/5.54 | (200) ? [v0] : (( ~ (v0 = 0) & surjective(all_0_1_1, all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & injective(all_0_1_1, all_0_4_4, all_0_2_2) = v0))
% 21.70/5.54 |
% 21.70/5.54 | Instantiating (200) with all_71_0_118 yields:
% 21.70/5.54 | (201) ( ~ (all_71_0_118 = 0) & surjective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118) | ( ~ (all_71_0_118 = 0) & injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118)
% 21.70/5.54 |
% 21.70/5.54 +-Applying beta-rule and splitting (201), into two cases.
% 21.70/5.54 |-Branch one:
% 21.70/5.54 | (202) ~ (all_71_0_118 = 0) & surjective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118
% 21.70/5.54 |
% 21.70/5.54 | Applying alpha-rule on (202) yields:
% 21.70/5.54 | (203) ~ (all_71_0_118 = 0)
% 21.70/5.54 | (204) surjective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118
% 21.70/5.54 |
% 21.70/5.54 | Instantiating formula (61) with all_71_0_118, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms surjective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118, yields:
% 21.70/5.54 | (205) all_71_0_118 = 0 | ? [v0] : (member(v0, all_0_2_2) = 0 & ! [v1] : ( ~ (apply(all_0_1_1, 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_1_1, v1, v0) = v2)))
% 21.70/5.54 |
% 21.70/5.54 +-Applying beta-rule and splitting (205), into two cases.
% 21.70/5.54 |-Branch one:
% 21.70/5.54 | (206) all_71_0_118 = 0
% 21.70/5.54 |
% 21.70/5.54 | Equations (206) can reduce 203 to:
% 21.70/5.54 | (198) $false
% 21.70/5.54 |
% 21.70/5.54 |-The branch is then unsatisfiable
% 21.70/5.54 |-Branch two:
% 21.70/5.54 | (203) ~ (all_71_0_118 = 0)
% 21.70/5.54 | (209) ? [v0] : (member(v0, all_0_2_2) = 0 & ! [v1] : ( ~ (apply(all_0_1_1, 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_1_1, v1, v0) = v2)))
% 21.70/5.54 |
% 21.70/5.54 | Instantiating (209) with all_86_0_119 yields:
% 21.70/5.54 | (210) member(all_86_0_119, all_0_2_2) = 0 & ! [v0] : ( ~ (apply(all_0_1_1, v0, all_86_0_119) = 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_1_1, v0, all_86_0_119) = v1))
% 21.70/5.54 |
% 21.70/5.54 | Applying alpha-rule on (210) yields:
% 21.70/5.54 | (211) member(all_86_0_119, all_0_2_2) = 0
% 21.70/5.54 | (212) ! [v0] : ( ~ (apply(all_0_1_1, v0, all_86_0_119) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1))
% 21.70/5.54 | (213) ! [v0] : ( ~ (member(v0, all_0_4_4) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, v0, all_86_0_119) = v1))
% 21.70/5.54 |
% 21.70/5.54 | Instantiating formula (15) with all_86_0_119, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms surjective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_86_0_119, all_0_2_2) = 0, yields:
% 21.70/5.54 | (214) ? [v0] : (apply(all_0_5_5, v0, all_86_0_119) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.54 |
% 21.70/5.54 | Instantiating (214) with all_94_0_120 yields:
% 21.70/5.54 | (215) apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0 & member(all_94_0_120, all_0_3_3) = 0
% 21.70/5.54 |
% 21.70/5.54 | Applying alpha-rule on (215) yields:
% 21.70/5.54 | (216) apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0
% 21.70/5.55 | (217) member(all_94_0_120, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (64) with all_94_0_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_94_0_120, all_0_3_3) = 0, yields:
% 21.70/5.55 | (218) ? [v0] : (apply(all_0_5_5, all_94_0_120, v0) = 0 & member(v0, all_0_2_2) = 0)
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (15) with all_94_0_120, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms surjective(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_94_0_120, all_0_3_3) = 0, yields:
% 21.70/5.55 | (219) ? [v0] : (apply(all_0_6_6, v0, all_94_0_120) = 0 & member(v0, all_0_4_4) = 0)
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (219) with all_101_0_121 yields:
% 21.70/5.55 | (220) apply(all_0_6_6, all_101_0_121, all_94_0_120) = 0 & member(all_101_0_121, all_0_4_4) = 0
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (220) yields:
% 21.70/5.55 | (221) apply(all_0_6_6, all_101_0_121, all_94_0_120) = 0
% 21.70/5.55 | (222) member(all_101_0_121, all_0_4_4) = 0
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (218) with all_103_0_122 yields:
% 21.70/5.55 | (223) apply(all_0_5_5, all_94_0_120, all_103_0_122) = 0 & member(all_103_0_122, all_0_2_2) = 0
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (223) yields:
% 21.70/5.55 | (224) apply(all_0_5_5, all_94_0_120, all_103_0_122) = 0
% 21.70/5.55 | (225) member(all_103_0_122, all_0_2_2) = 0
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (98) with all_86_0_119, all_103_0_122, all_94_0_120, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0, member(all_103_0_122, all_0_2_2) = 0, yields:
% 21.70/5.55 | (226) all_103_0_122 = all_86_0_119 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_94_0_120, all_103_0_122) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (15) with all_103_0_122, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms surjective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_103_0_122, all_0_2_2) = 0, yields:
% 21.70/5.55 | (227) ? [v0] : (apply(all_0_5_5, v0, all_103_0_122) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (64) with all_101_0_121, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_101_0_121, all_0_4_4) = 0, yields:
% 21.70/5.55 | (228) ? [v0] : (apply(all_0_6_6, all_101_0_121, v0) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (213) with all_101_0_121 and discharging atoms member(all_101_0_121, all_0_4_4) = 0, yields:
% 21.70/5.55 | (229) ? [v0] : ( ~ (v0 = 0) & apply(all_0_1_1, all_101_0_121, all_86_0_119) = v0)
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (229) with all_110_0_123 yields:
% 21.70/5.55 | (230) ~ (all_110_0_123 = 0) & apply(all_0_1_1, all_101_0_121, all_86_0_119) = all_110_0_123
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (230) yields:
% 21.70/5.55 | (231) ~ (all_110_0_123 = 0)
% 21.70/5.55 | (232) apply(all_0_1_1, all_101_0_121, all_86_0_119) = all_110_0_123
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (228) with all_112_0_124 yields:
% 21.70/5.55 | (233) apply(all_0_6_6, all_101_0_121, all_112_0_124) = 0 & member(all_112_0_124, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (233) yields:
% 21.70/5.55 | (234) apply(all_0_6_6, all_101_0_121, all_112_0_124) = 0
% 21.70/5.55 | (235) member(all_112_0_124, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (227) with all_114_0_125 yields:
% 21.70/5.55 | (236) apply(all_0_5_5, all_114_0_125, all_103_0_122) = 0 & member(all_114_0_125, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (236) yields:
% 21.70/5.55 | (237) apply(all_0_5_5, all_114_0_125, all_103_0_122) = 0
% 21.70/5.55 | (238) member(all_114_0_125, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (226), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (239) all_103_0_122 = all_86_0_119
% 21.70/5.55 |
% 21.70/5.55 | From (239) and (237) follows:
% 21.70/5.55 | (240) apply(all_0_5_5, all_114_0_125, all_86_0_119) = 0
% 21.70/5.55 |
% 21.70/5.55 | From (239) and (224) follows:
% 21.70/5.55 | (216) apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0
% 21.70/5.55 |
% 21.70/5.55 | From (239) and (225) follows:
% 21.70/5.55 | (211) member(all_86_0_119, all_0_2_2) = 0
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (84) with all_86_0_119, all_94_0_120, all_114_0_125, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0, member(all_114_0_125, all_0_3_3) = 0, yields:
% 21.70/5.55 | (243) all_114_0_125 = all_94_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_114_0_125, all_86_0_119) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (80) with all_112_0_124, all_110_0_123, all_0_1_1, all_86_0_119, all_101_0_121, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_101_0_121, all_86_0_119) = all_110_0_123, member(all_112_0_124, all_0_3_3) = 0, yields:
% 21.70/5.55 | (244) all_110_0_123 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = v0) | ( ~ (v0 = 0) & member(all_101_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (98) with all_94_0_120, all_112_0_124, all_101_0_121, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_101_0_121, all_94_0_120) = 0, member(all_112_0_124, all_0_3_3) = 0, yields:
% 21.70/5.55 | (245) all_112_0_124 = all_94_0_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = v0) | ( ~ (v0 = 0) & member(all_101_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0))
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (245), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (246) all_112_0_124 = all_94_0_120
% 21.70/5.55 |
% 21.70/5.55 | From (246) and (234) follows:
% 21.70/5.55 | (221) apply(all_0_6_6, all_101_0_121, all_94_0_120) = 0
% 21.70/5.55 |
% 21.70/5.55 | From (246) and (235) follows:
% 21.70/5.55 | (217) member(all_94_0_120, all_0_3_3) = 0
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (243), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (249) all_114_0_125 = all_94_0_120
% 21.70/5.55 |
% 21.70/5.55 | From (249) and (240) follows:
% 21.70/5.55 | (216) apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (244), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (251) all_110_0_123 = 0
% 21.70/5.55 |
% 21.70/5.55 | Equations (251) can reduce 231 to:
% 21.70/5.55 | (198) $false
% 21.70/5.55 |
% 21.70/5.55 |-The branch is then unsatisfiable
% 21.70/5.55 |-Branch two:
% 21.70/5.55 | (231) ~ (all_110_0_123 = 0)
% 21.70/5.55 | (254) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = v0) | ( ~ (v0 = 0) & member(all_101_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.55 |
% 21.70/5.55 | Instantiating (254) with all_145_0_130 yields:
% 21.70/5.55 | (255) ( ~ (all_145_0_130 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & member(all_101_0_121, all_0_4_4) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & member(all_86_0_119, all_0_2_2) = all_145_0_130)
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (255), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (256) ( ~ (all_145_0_130 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & member(all_101_0_121, all_0_4_4) = all_145_0_130)
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (256), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (257) ( ~ (all_145_0_130 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = all_145_0_130) | ( ~ (all_145_0_130 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_145_0_130)
% 21.70/5.55 |
% 21.70/5.55 +-Applying beta-rule and splitting (257), into two cases.
% 21.70/5.55 |-Branch one:
% 21.70/5.55 | (258) ~ (all_145_0_130 = 0) & apply(all_0_5_5, all_112_0_124, all_86_0_119) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (258) yields:
% 21.70/5.55 | (259) ~ (all_145_0_130 = 0)
% 21.70/5.55 | (260) apply(all_0_5_5, all_112_0_124, all_86_0_119) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | From (246) and (260) follows:
% 21.70/5.55 | (261) apply(all_0_5_5, all_94_0_120, all_86_0_119) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (19) with all_0_5_5, all_94_0_120, all_86_0_119, all_145_0_130, 0 and discharging atoms apply(all_0_5_5, all_94_0_120, all_86_0_119) = all_145_0_130, apply(all_0_5_5, all_94_0_120, all_86_0_119) = 0, yields:
% 21.70/5.55 | (262) all_145_0_130 = 0
% 21.70/5.55 |
% 21.70/5.55 | Equations (262) can reduce 259 to:
% 21.70/5.55 | (198) $false
% 21.70/5.55 |
% 21.70/5.55 |-The branch is then unsatisfiable
% 21.70/5.55 |-Branch two:
% 21.70/5.55 | (264) ~ (all_145_0_130 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (264) yields:
% 21.70/5.55 | (259) ~ (all_145_0_130 = 0)
% 21.70/5.55 | (266) apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | From (246) and (266) follows:
% 21.70/5.55 | (267) apply(all_0_6_6, all_101_0_121, all_94_0_120) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (19) with all_0_6_6, all_101_0_121, all_94_0_120, all_145_0_130, 0 and discharging atoms apply(all_0_6_6, all_101_0_121, all_94_0_120) = all_145_0_130, apply(all_0_6_6, all_101_0_121, all_94_0_120) = 0, yields:
% 21.70/5.55 | (262) all_145_0_130 = 0
% 21.70/5.55 |
% 21.70/5.55 | Equations (262) can reduce 259 to:
% 21.70/5.55 | (198) $false
% 21.70/5.55 |
% 21.70/5.55 |-The branch is then unsatisfiable
% 21.70/5.55 |-Branch two:
% 21.70/5.55 | (270) ~ (all_145_0_130 = 0) & member(all_101_0_121, all_0_4_4) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Applying alpha-rule on (270) yields:
% 21.70/5.55 | (259) ~ (all_145_0_130 = 0)
% 21.70/5.55 | (272) member(all_101_0_121, all_0_4_4) = all_145_0_130
% 21.70/5.55 |
% 21.70/5.55 | Instantiating formula (59) with all_101_0_121, all_0_4_4, all_145_0_130, 0 and discharging atoms member(all_101_0_121, all_0_4_4) = all_145_0_130, member(all_101_0_121, all_0_4_4) = 0, yields:
% 21.70/5.55 | (262) all_145_0_130 = 0
% 21.70/5.55 |
% 21.70/5.55 | Equations (262) can reduce 259 to:
% 21.70/5.55 | (198) $false
% 21.70/5.55 |
% 21.70/5.55 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (275) ~ (all_145_0_130 = 0) & member(all_86_0_119, all_0_2_2) = all_145_0_130
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (275) yields:
% 21.70/5.56 | (259) ~ (all_145_0_130 = 0)
% 21.70/5.56 | (277) member(all_86_0_119, all_0_2_2) = all_145_0_130
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_86_0_119, all_0_2_2, all_145_0_130, 0 and discharging atoms member(all_86_0_119, all_0_2_2) = all_145_0_130, member(all_86_0_119, all_0_2_2) = 0, yields:
% 21.70/5.56 | (262) all_145_0_130 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (262) can reduce 259 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (280) ~ (all_114_0_125 = all_94_0_120)
% 21.70/5.56 | (281) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_114_0_125, all_86_0_119) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.56 |
% 21.70/5.56 | Instantiating (281) with all_141_0_135 yields:
% 21.70/5.56 | (282) ( ~ (all_141_0_135 = 0) & apply(all_0_5_5, all_114_0_125, all_86_0_119) = all_141_0_135) | ( ~ (all_141_0_135 = 0) & member(all_94_0_120, all_0_3_3) = all_141_0_135) | ( ~ (all_141_0_135 = 0) & member(all_86_0_119, all_0_2_2) = all_141_0_135)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (282), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (283) ( ~ (all_141_0_135 = 0) & apply(all_0_5_5, all_114_0_125, all_86_0_119) = all_141_0_135) | ( ~ (all_141_0_135 = 0) & member(all_94_0_120, all_0_3_3) = all_141_0_135)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (283), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (284) ~ (all_141_0_135 = 0) & apply(all_0_5_5, all_114_0_125, all_86_0_119) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (284) yields:
% 21.70/5.56 | (285) ~ (all_141_0_135 = 0)
% 21.70/5.56 | (286) apply(all_0_5_5, all_114_0_125, all_86_0_119) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (19) with all_0_5_5, all_114_0_125, all_86_0_119, all_141_0_135, 0 and discharging atoms apply(all_0_5_5, all_114_0_125, all_86_0_119) = all_141_0_135, apply(all_0_5_5, all_114_0_125, all_86_0_119) = 0, yields:
% 21.70/5.56 | (287) all_141_0_135 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (287) can reduce 285 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (289) ~ (all_141_0_135 = 0) & member(all_94_0_120, all_0_3_3) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (289) yields:
% 21.70/5.56 | (285) ~ (all_141_0_135 = 0)
% 21.70/5.56 | (291) member(all_94_0_120, all_0_3_3) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_94_0_120, all_0_3_3, all_141_0_135, 0 and discharging atoms member(all_94_0_120, all_0_3_3) = all_141_0_135, member(all_94_0_120, all_0_3_3) = 0, yields:
% 21.70/5.56 | (287) all_141_0_135 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (287) can reduce 285 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (294) ~ (all_141_0_135 = 0) & member(all_86_0_119, all_0_2_2) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (294) yields:
% 21.70/5.56 | (285) ~ (all_141_0_135 = 0)
% 21.70/5.56 | (296) member(all_86_0_119, all_0_2_2) = all_141_0_135
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_86_0_119, all_0_2_2, all_141_0_135, 0 and discharging atoms member(all_86_0_119, all_0_2_2) = all_141_0_135, member(all_86_0_119, all_0_2_2) = 0, yields:
% 21.70/5.56 | (287) all_141_0_135 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (287) can reduce 285 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (299) ~ (all_112_0_124 = all_94_0_120)
% 21.70/5.56 | (300) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = v0) | ( ~ (v0 = 0) & member(all_101_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0))
% 21.70/5.56 |
% 21.70/5.56 | Instantiating (300) with all_137_0_159 yields:
% 21.70/5.56 | (301) ( ~ (all_137_0_159 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_137_0_159) | ( ~ (all_137_0_159 = 0) & member(all_101_0_121, all_0_4_4) = all_137_0_159) | ( ~ (all_137_0_159 = 0) & member(all_94_0_120, all_0_3_3) = all_137_0_159)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (301), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (302) ( ~ (all_137_0_159 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_137_0_159) | ( ~ (all_137_0_159 = 0) & member(all_101_0_121, all_0_4_4) = all_137_0_159)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (302), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (303) ~ (all_137_0_159 = 0) & apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (303) yields:
% 21.70/5.56 | (304) ~ (all_137_0_159 = 0)
% 21.70/5.56 | (305) apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (19) with all_0_6_6, all_101_0_121, all_112_0_124, all_137_0_159, 0 and discharging atoms apply(all_0_6_6, all_101_0_121, all_112_0_124) = all_137_0_159, apply(all_0_6_6, all_101_0_121, all_112_0_124) = 0, yields:
% 21.70/5.56 | (306) all_137_0_159 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (306) can reduce 304 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (308) ~ (all_137_0_159 = 0) & member(all_101_0_121, all_0_4_4) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (308) yields:
% 21.70/5.56 | (304) ~ (all_137_0_159 = 0)
% 21.70/5.56 | (310) member(all_101_0_121, all_0_4_4) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_101_0_121, all_0_4_4, all_137_0_159, 0 and discharging atoms member(all_101_0_121, all_0_4_4) = all_137_0_159, member(all_101_0_121, all_0_4_4) = 0, yields:
% 21.70/5.56 | (306) all_137_0_159 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (306) can reduce 304 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (313) ~ (all_137_0_159 = 0) & member(all_94_0_120, all_0_3_3) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (313) yields:
% 21.70/5.56 | (304) ~ (all_137_0_159 = 0)
% 21.70/5.56 | (315) member(all_94_0_120, all_0_3_3) = all_137_0_159
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_94_0_120, all_0_3_3, all_137_0_159, 0 and discharging atoms member(all_94_0_120, all_0_3_3) = all_137_0_159, member(all_94_0_120, all_0_3_3) = 0, yields:
% 21.70/5.56 | (306) all_137_0_159 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (306) can reduce 304 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (318) ~ (all_103_0_122 = all_86_0_119)
% 21.70/5.56 | (319) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_94_0_120, all_103_0_122) = v0) | ( ~ (v0 = 0) & member(all_94_0_120, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_119, all_0_2_2) = v0))
% 21.70/5.56 |
% 21.70/5.56 | Instantiating (319) with all_120_0_224 yields:
% 21.70/5.56 | (320) ( ~ (all_120_0_224 = 0) & apply(all_0_5_5, all_94_0_120, all_103_0_122) = all_120_0_224) | ( ~ (all_120_0_224 = 0) & member(all_94_0_120, all_0_3_3) = all_120_0_224) | ( ~ (all_120_0_224 = 0) & member(all_86_0_119, all_0_2_2) = all_120_0_224)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (320), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (321) ( ~ (all_120_0_224 = 0) & apply(all_0_5_5, all_94_0_120, all_103_0_122) = all_120_0_224) | ( ~ (all_120_0_224 = 0) & member(all_94_0_120, all_0_3_3) = all_120_0_224)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (321), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (322) ~ (all_120_0_224 = 0) & apply(all_0_5_5, all_94_0_120, all_103_0_122) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (322) yields:
% 21.70/5.56 | (323) ~ (all_120_0_224 = 0)
% 21.70/5.56 | (324) apply(all_0_5_5, all_94_0_120, all_103_0_122) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (19) with all_0_5_5, all_94_0_120, all_103_0_122, all_120_0_224, 0 and discharging atoms apply(all_0_5_5, all_94_0_120, all_103_0_122) = all_120_0_224, apply(all_0_5_5, all_94_0_120, all_103_0_122) = 0, yields:
% 21.70/5.56 | (325) all_120_0_224 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (325) can reduce 323 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (327) ~ (all_120_0_224 = 0) & member(all_94_0_120, all_0_3_3) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (327) yields:
% 21.70/5.56 | (323) ~ (all_120_0_224 = 0)
% 21.70/5.56 | (329) member(all_94_0_120, all_0_3_3) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_94_0_120, all_0_3_3, all_120_0_224, 0 and discharging atoms member(all_94_0_120, all_0_3_3) = all_120_0_224, member(all_94_0_120, all_0_3_3) = 0, yields:
% 21.70/5.56 | (325) all_120_0_224 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (325) can reduce 323 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (332) ~ (all_120_0_224 = 0) & member(all_86_0_119, all_0_2_2) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (332) yields:
% 21.70/5.56 | (323) ~ (all_120_0_224 = 0)
% 21.70/5.56 | (334) member(all_86_0_119, all_0_2_2) = all_120_0_224
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (59) with all_86_0_119, all_0_2_2, all_120_0_224, 0 and discharging atoms member(all_86_0_119, all_0_2_2) = all_120_0_224, member(all_86_0_119, all_0_2_2) = 0, yields:
% 21.70/5.56 | (325) all_120_0_224 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (325) can reduce 323 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (337) ~ (all_71_0_118 = 0) & injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118
% 21.70/5.56 |
% 21.70/5.56 | Applying alpha-rule on (337) yields:
% 21.70/5.56 | (203) ~ (all_71_0_118 = 0)
% 21.70/5.56 | (339) injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118
% 21.70/5.56 |
% 21.70/5.56 | Instantiating formula (132) with all_71_0_118, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms injective(all_0_1_1, all_0_4_4, all_0_2_2) = all_71_0_118, yields:
% 21.70/5.56 | (340) all_71_0_118 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 21.70/5.56 |
% 21.70/5.56 +-Applying beta-rule and splitting (340), into two cases.
% 21.70/5.56 |-Branch one:
% 21.70/5.56 | (206) all_71_0_118 = 0
% 21.70/5.56 |
% 21.70/5.56 | Equations (206) can reduce 203 to:
% 21.70/5.56 | (198) $false
% 21.70/5.56 |
% 21.70/5.56 |-The branch is then unsatisfiable
% 21.70/5.56 |-Branch two:
% 21.70/5.56 | (203) ~ (all_71_0_118 = 0)
% 21.70/5.56 | (344) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 21.70/5.56 |
% 21.70/5.57 | Instantiating (344) with all_86_0_229, all_86_1_230, all_86_2_231 yields:
% 21.70/5.57 | (345) ~ (all_86_1_230 = all_86_2_231) & apply(all_0_1_1, all_86_1_230, all_86_0_229) = 0 & apply(all_0_1_1, all_86_2_231, all_86_0_229) = 0 & member(all_86_0_229, all_0_2_2) = 0 & member(all_86_1_230, all_0_4_4) = 0 & member(all_86_2_231, all_0_4_4) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (345) yields:
% 21.70/5.57 | (346) apply(all_0_1_1, all_86_2_231, all_86_0_229) = 0
% 21.70/5.57 | (347) apply(all_0_1_1, all_86_1_230, all_86_0_229) = 0
% 21.70/5.57 | (348) ~ (all_86_1_230 = all_86_2_231)
% 21.70/5.57 | (349) member(all_86_0_229, all_0_2_2) = 0
% 21.70/5.57 | (350) member(all_86_2_231, all_0_4_4) = 0
% 21.70/5.57 | (351) member(all_86_1_230, all_0_4_4) = 0
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (108) with all_0_1_1, all_86_0_229, all_86_1_230, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_86_1_230, all_86_0_229) = 0, yields:
% 21.70/5.57 | (352) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_86_0_229) = 0 & apply(all_0_6_6, all_86_1_230, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_86_1_230, all_0_4_4) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (108) with all_0_1_1, all_86_0_229, all_86_2_231, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3, all_0_2_2) = all_0_1_1, apply(all_0_1_1, all_86_2_231, all_86_0_229) = 0, yields:
% 21.70/5.57 | (353) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_86_0_229) = 0 & apply(all_0_6_6, all_86_2_231, v0) = 0 & member(v0, all_0_3_3) = 0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_86_2_231, all_0_4_4) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (15) with all_86_0_229, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms surjective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, member(all_86_0_229, all_0_2_2) = 0, yields:
% 21.70/5.57 | (354) ? [v0] : (apply(all_0_5_5, v0, all_86_0_229) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (64) with all_86_1_230, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_86_1_230, all_0_4_4) = 0, yields:
% 21.70/5.57 | (355) ? [v0] : (apply(all_0_6_6, all_86_1_230, v0) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (64) with all_86_2_231, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_86_2_231, all_0_4_4) = 0, yields:
% 21.70/5.57 | (356) ? [v0] : (apply(all_0_6_6, all_86_2_231, v0) = 0 & member(v0, all_0_3_3) = 0)
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (356) with all_93_0_232 yields:
% 21.70/5.57 | (357) apply(all_0_6_6, all_86_2_231, all_93_0_232) = 0 & member(all_93_0_232, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (357) yields:
% 21.70/5.57 | (358) apply(all_0_6_6, all_86_2_231, all_93_0_232) = 0
% 21.70/5.57 | (359) member(all_93_0_232, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (355) with all_95_0_233 yields:
% 21.70/5.57 | (360) apply(all_0_6_6, all_86_1_230, all_95_0_233) = 0 & member(all_95_0_233, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (360) yields:
% 21.70/5.57 | (361) apply(all_0_6_6, all_86_1_230, all_95_0_233) = 0
% 21.70/5.57 | (362) member(all_95_0_233, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (354) with all_97_0_234 yields:
% 21.70/5.57 | (363) apply(all_0_5_5, all_97_0_234, all_86_0_229) = 0 & member(all_97_0_234, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (363) yields:
% 21.70/5.57 | (364) apply(all_0_5_5, all_97_0_234, all_86_0_229) = 0
% 21.70/5.57 | (365) member(all_97_0_234, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (353) with all_99_0_235, all_99_1_236, all_99_2_237, all_99_3_238 yields:
% 21.70/5.57 | (366) (all_99_0_235 = 0 & all_99_1_236 = 0 & all_99_2_237 = 0 & apply(all_0_5_5, all_99_3_238, all_86_0_229) = 0 & apply(all_0_6_6, all_86_2_231, all_99_3_238) = 0 & member(all_99_3_238, all_0_3_3) = 0) | ( ~ (all_99_3_238 = 0) & member(all_86_0_229, all_0_2_2) = all_99_3_238) | ( ~ (all_99_3_238 = 0) & member(all_86_2_231, all_0_4_4) = all_99_3_238)
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (352) with all_100_0_239, all_100_1_240, all_100_2_241, all_100_3_242 yields:
% 21.70/5.57 | (367) (all_100_0_239 = 0 & all_100_1_240 = 0 & all_100_2_241 = 0 & apply(all_0_5_5, all_100_3_242, all_86_0_229) = 0 & apply(all_0_6_6, all_86_1_230, all_100_3_242) = 0 & member(all_100_3_242, all_0_3_3) = 0) | ( ~ (all_100_3_242 = 0) & member(all_86_0_229, all_0_2_2) = all_100_3_242) | ( ~ (all_100_3_242 = 0) & member(all_86_1_230, all_0_4_4) = all_100_3_242)
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (366), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (368) (all_99_0_235 = 0 & all_99_1_236 = 0 & all_99_2_237 = 0 & apply(all_0_5_5, all_99_3_238, all_86_0_229) = 0 & apply(all_0_6_6, all_86_2_231, all_99_3_238) = 0 & member(all_99_3_238, all_0_3_3) = 0) | ( ~ (all_99_3_238 = 0) & member(all_86_0_229, all_0_2_2) = all_99_3_238)
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (368), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (369) all_99_0_235 = 0 & all_99_1_236 = 0 & all_99_2_237 = 0 & apply(all_0_5_5, all_99_3_238, all_86_0_229) = 0 & apply(all_0_6_6, all_86_2_231, all_99_3_238) = 0 & member(all_99_3_238, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (369) yields:
% 21.70/5.57 | (370) apply(all_0_5_5, all_99_3_238, all_86_0_229) = 0
% 21.70/5.57 | (371) member(all_99_3_238, all_0_3_3) = 0
% 21.70/5.57 | (372) all_99_1_236 = 0
% 21.70/5.57 | (373) all_99_0_235 = 0
% 21.70/5.57 | (374) all_99_2_237 = 0
% 21.70/5.57 | (375) apply(all_0_6_6, all_86_2_231, all_99_3_238) = 0
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (367), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (376) (all_100_0_239 = 0 & all_100_1_240 = 0 & all_100_2_241 = 0 & apply(all_0_5_5, all_100_3_242, all_86_0_229) = 0 & apply(all_0_6_6, all_86_1_230, all_100_3_242) = 0 & member(all_100_3_242, all_0_3_3) = 0) | ( ~ (all_100_3_242 = 0) & member(all_86_0_229, all_0_2_2) = all_100_3_242)
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (376), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (377) all_100_0_239 = 0 & all_100_1_240 = 0 & all_100_2_241 = 0 & apply(all_0_5_5, all_100_3_242, all_86_0_229) = 0 & apply(all_0_6_6, all_86_1_230, all_100_3_242) = 0 & member(all_100_3_242, all_0_3_3) = 0
% 21.70/5.57 |
% 21.70/5.57 | Applying alpha-rule on (377) yields:
% 21.70/5.57 | (378) all_100_0_239 = 0
% 21.70/5.57 | (379) all_100_1_240 = 0
% 21.70/5.57 | (380) apply(all_0_5_5, all_100_3_242, all_86_0_229) = 0
% 21.70/5.57 | (381) apply(all_0_6_6, all_86_1_230, all_100_3_242) = 0
% 21.70/5.57 | (382) member(all_100_3_242, all_0_3_3) = 0
% 21.70/5.57 | (383) all_100_2_241 = 0
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (70) with all_95_0_233, all_100_3_242, all_86_1_230, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_86_1_230, all_100_3_242) = 0, apply(all_0_6_6, all_86_1_230, all_95_0_233) = 0, yields:
% 21.70/5.57 | (384) all_100_3_242 = all_95_0_233 | ? [v0] : (( ~ (v0 = 0) & member(all_100_3_242, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_95_0_233, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_1_230, all_0_4_4) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (145) with all_99_3_238, all_86_1_230, all_86_2_231, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms injective(all_0_6_6, all_0_4_4, all_0_3_3) = 0, member(all_99_3_238, all_0_3_3) = 0, member(all_86_1_230, all_0_4_4) = 0, member(all_86_2_231, all_0_4_4) = 0, yields:
% 21.70/5.57 | (385) all_86_1_230 = all_86_2_231 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_86_1_230, all_99_3_238) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_86_2_231, all_99_3_238) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (98) with all_93_0_232, all_97_0_234, all_86_2_231, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_4_4, all_0_3_3) = 0, apply(all_0_6_6, all_86_2_231, all_93_0_232) = 0, member(all_97_0_234, all_0_3_3) = 0, yields:
% 21.70/5.57 | (386) all_97_0_234 = all_93_0_232 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_86_2_231, all_97_0_234) = v0) | ( ~ (v0 = 0) & member(all_93_0_232, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_2_231, all_0_4_4) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (84) with all_86_0_229, all_100_3_242, all_97_0_234, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_100_3_242, all_86_0_229) = 0, member(all_97_0_234, all_0_3_3) = 0, yields:
% 21.70/5.57 | (387) all_100_3_242 = all_97_0_234 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = v0) | ( ~ (v0 = 0) & member(all_100_3_242, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating formula (84) with all_86_0_229, all_99_3_238, all_97_0_234, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_3_3, all_0_2_2) = 0, apply(all_0_5_5, all_99_3_238, all_86_0_229) = 0, member(all_97_0_234, all_0_3_3) = 0, yields:
% 21.70/5.57 | (388) all_99_3_238 = all_97_0_234 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = v0) | ( ~ (v0 = 0) & member(all_99_3_238, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0))
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (388), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (389) all_99_3_238 = all_97_0_234
% 21.70/5.57 |
% 21.70/5.57 | From (389) and (370) follows:
% 21.70/5.57 | (364) apply(all_0_5_5, all_97_0_234, all_86_0_229) = 0
% 21.70/5.57 |
% 21.70/5.57 | From (389) and (375) follows:
% 21.70/5.57 | (391) apply(all_0_6_6, all_86_2_231, all_97_0_234) = 0
% 21.70/5.57 |
% 21.70/5.57 +-Applying beta-rule and splitting (385), into two cases.
% 21.70/5.57 |-Branch one:
% 21.70/5.57 | (392) all_86_1_230 = all_86_2_231
% 21.70/5.57 |
% 21.70/5.57 | Equations (392) can reduce 348 to:
% 21.70/5.57 | (198) $false
% 21.70/5.57 |
% 21.70/5.57 |-The branch is then unsatisfiable
% 21.70/5.57 |-Branch two:
% 21.70/5.57 | (348) ~ (all_86_1_230 = all_86_2_231)
% 21.70/5.57 | (395) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_86_1_230, all_99_3_238) = v0) | ( ~ (v0 = 0) & apply(all_0_6_6, all_86_2_231, all_99_3_238) = v0))
% 21.70/5.57 |
% 21.70/5.57 | Instantiating (395) with all_141_0_253 yields:
% 21.70/5.57 | (396) ( ~ (all_141_0_253 = 0) & apply(all_0_6_6, all_86_1_230, all_99_3_238) = all_141_0_253) | ( ~ (all_141_0_253 = 0) & apply(all_0_6_6, all_86_2_231, all_99_3_238) = all_141_0_253)
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (386), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (397) all_97_0_234 = all_93_0_232
% 21.70/5.58 |
% 21.70/5.58 | Combining equations (397,389) yields a new equation:
% 21.70/5.58 | (398) all_99_3_238 = all_93_0_232
% 21.70/5.58 |
% 21.70/5.58 | From (397) and (364) follows:
% 21.70/5.58 | (399) apply(all_0_5_5, all_93_0_232, all_86_0_229) = 0
% 21.70/5.58 |
% 21.70/5.58 | From (397) and (391) follows:
% 21.70/5.58 | (358) apply(all_0_6_6, all_86_2_231, all_93_0_232) = 0
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (387), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (401) all_100_3_242 = all_97_0_234
% 21.70/5.58 |
% 21.70/5.58 | Combining equations (397,401) yields a new equation:
% 21.70/5.58 | (402) all_100_3_242 = all_93_0_232
% 21.70/5.58 |
% 21.70/5.58 | From (402) and (382) follows:
% 21.70/5.58 | (359) member(all_93_0_232, all_0_3_3) = 0
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (384), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (404) all_100_3_242 = all_95_0_233
% 21.70/5.58 |
% 21.70/5.58 | Combining equations (404,402) yields a new equation:
% 21.70/5.58 | (405) all_95_0_233 = all_93_0_232
% 21.70/5.58 |
% 21.70/5.58 | Simplifying 405 yields:
% 21.70/5.58 | (406) all_95_0_233 = all_93_0_232
% 21.70/5.58 |
% 21.70/5.58 | From (406) and (361) follows:
% 21.70/5.58 | (407) apply(all_0_6_6, all_86_1_230, all_93_0_232) = 0
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (396), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (408) ~ (all_141_0_253 = 0) & apply(all_0_6_6, all_86_1_230, all_99_3_238) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (408) yields:
% 21.70/5.58 | (409) ~ (all_141_0_253 = 0)
% 21.70/5.58 | (410) apply(all_0_6_6, all_86_1_230, all_99_3_238) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | From (398) and (410) follows:
% 21.70/5.58 | (411) apply(all_0_6_6, all_86_1_230, all_93_0_232) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (19) with all_0_6_6, all_86_1_230, all_93_0_232, 0, all_141_0_253 and discharging atoms apply(all_0_6_6, all_86_1_230, all_93_0_232) = all_141_0_253, apply(all_0_6_6, all_86_1_230, all_93_0_232) = 0, yields:
% 21.70/5.58 | (412) all_141_0_253 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (412) can reduce 409 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (414) ~ (all_141_0_253 = 0) & apply(all_0_6_6, all_86_2_231, all_99_3_238) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (414) yields:
% 21.70/5.58 | (409) ~ (all_141_0_253 = 0)
% 21.70/5.58 | (416) apply(all_0_6_6, all_86_2_231, all_99_3_238) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | From (398) and (416) follows:
% 21.70/5.58 | (417) apply(all_0_6_6, all_86_2_231, all_93_0_232) = all_141_0_253
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (19) with all_0_6_6, all_86_2_231, all_93_0_232, all_141_0_253, 0 and discharging atoms apply(all_0_6_6, all_86_2_231, all_93_0_232) = all_141_0_253, apply(all_0_6_6, all_86_2_231, all_93_0_232) = 0, yields:
% 21.70/5.58 | (412) all_141_0_253 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (412) can reduce 409 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (420) ~ (all_100_3_242 = all_95_0_233)
% 21.70/5.58 | (421) ? [v0] : (( ~ (v0 = 0) & member(all_100_3_242, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_95_0_233, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_1_230, all_0_4_4) = v0))
% 21.70/5.58 |
% 21.70/5.58 | Instantiating (421) with all_154_0_276 yields:
% 21.70/5.58 | (422) ( ~ (all_154_0_276 = 0) & member(all_100_3_242, all_0_3_3) = all_154_0_276) | ( ~ (all_154_0_276 = 0) & member(all_95_0_233, all_0_3_3) = all_154_0_276) | ( ~ (all_154_0_276 = 0) & member(all_86_1_230, all_0_4_4) = all_154_0_276)
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (422), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (423) ( ~ (all_154_0_276 = 0) & member(all_100_3_242, all_0_3_3) = all_154_0_276) | ( ~ (all_154_0_276 = 0) & member(all_95_0_233, all_0_3_3) = all_154_0_276)
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (423), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (424) ~ (all_154_0_276 = 0) & member(all_100_3_242, all_0_3_3) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (424) yields:
% 21.70/5.58 | (425) ~ (all_154_0_276 = 0)
% 21.70/5.58 | (426) member(all_100_3_242, all_0_3_3) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | From (402) and (426) follows:
% 21.70/5.58 | (427) member(all_93_0_232, all_0_3_3) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (59) with all_93_0_232, all_0_3_3, all_154_0_276, 0 and discharging atoms member(all_93_0_232, all_0_3_3) = all_154_0_276, member(all_93_0_232, all_0_3_3) = 0, yields:
% 21.70/5.58 | (428) all_154_0_276 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (428) can reduce 425 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (430) ~ (all_154_0_276 = 0) & member(all_95_0_233, all_0_3_3) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (430) yields:
% 21.70/5.58 | (425) ~ (all_154_0_276 = 0)
% 21.70/5.58 | (432) member(all_95_0_233, all_0_3_3) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (59) with all_95_0_233, all_0_3_3, all_154_0_276, 0 and discharging atoms member(all_95_0_233, all_0_3_3) = all_154_0_276, member(all_95_0_233, all_0_3_3) = 0, yields:
% 21.70/5.58 | (428) all_154_0_276 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (428) can reduce 425 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (435) ~ (all_154_0_276 = 0) & member(all_86_1_230, all_0_4_4) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (435) yields:
% 21.70/5.58 | (425) ~ (all_154_0_276 = 0)
% 21.70/5.58 | (437) member(all_86_1_230, all_0_4_4) = all_154_0_276
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (59) with all_86_1_230, all_0_4_4, all_154_0_276, 0 and discharging atoms member(all_86_1_230, all_0_4_4) = all_154_0_276, member(all_86_1_230, all_0_4_4) = 0, yields:
% 21.70/5.58 | (428) all_154_0_276 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (428) can reduce 425 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (440) ~ (all_100_3_242 = all_97_0_234)
% 21.70/5.58 | (441) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = v0) | ( ~ (v0 = 0) & member(all_100_3_242, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0))
% 21.70/5.58 |
% 21.70/5.58 | Instantiating (441) with all_150_0_332 yields:
% 21.70/5.58 | (442) ( ~ (all_150_0_332 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_150_0_332) | ( ~ (all_150_0_332 = 0) & member(all_100_3_242, all_0_3_3) = all_150_0_332) | ( ~ (all_150_0_332 = 0) & member(all_86_0_229, all_0_2_2) = all_150_0_332)
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (442), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (443) ( ~ (all_150_0_332 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_150_0_332) | ( ~ (all_150_0_332 = 0) & member(all_100_3_242, all_0_3_3) = all_150_0_332)
% 21.70/5.58 |
% 21.70/5.58 +-Applying beta-rule and splitting (443), into two cases.
% 21.70/5.58 |-Branch one:
% 21.70/5.58 | (444) ~ (all_150_0_332 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (444) yields:
% 21.70/5.58 | (445) ~ (all_150_0_332 = 0)
% 21.70/5.58 | (446) apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | From (397) and (446) follows:
% 21.70/5.58 | (447) apply(all_0_5_5, all_93_0_232, all_86_0_229) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (19) with all_0_5_5, all_93_0_232, all_86_0_229, 0, all_150_0_332 and discharging atoms apply(all_0_5_5, all_93_0_232, all_86_0_229) = all_150_0_332, apply(all_0_5_5, all_93_0_232, all_86_0_229) = 0, yields:
% 21.70/5.58 | (448) all_150_0_332 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (448) can reduce 445 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (450) ~ (all_150_0_332 = 0) & member(all_100_3_242, all_0_3_3) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (450) yields:
% 21.70/5.58 | (445) ~ (all_150_0_332 = 0)
% 21.70/5.58 | (452) member(all_100_3_242, all_0_3_3) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (59) with all_100_3_242, all_0_3_3, all_150_0_332, 0 and discharging atoms member(all_100_3_242, all_0_3_3) = all_150_0_332, member(all_100_3_242, all_0_3_3) = 0, yields:
% 21.70/5.58 | (448) all_150_0_332 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (448) can reduce 445 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (455) ~ (all_150_0_332 = 0) & member(all_86_0_229, all_0_2_2) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Applying alpha-rule on (455) yields:
% 21.70/5.58 | (445) ~ (all_150_0_332 = 0)
% 21.70/5.58 | (457) member(all_86_0_229, all_0_2_2) = all_150_0_332
% 21.70/5.58 |
% 21.70/5.58 | Instantiating formula (59) with all_86_0_229, all_0_2_2, all_150_0_332, 0 and discharging atoms member(all_86_0_229, all_0_2_2) = all_150_0_332, member(all_86_0_229, all_0_2_2) = 0, yields:
% 21.70/5.58 | (448) all_150_0_332 = 0
% 21.70/5.58 |
% 21.70/5.58 | Equations (448) can reduce 445 to:
% 21.70/5.58 | (198) $false
% 21.70/5.58 |
% 21.70/5.58 |-The branch is then unsatisfiable
% 21.70/5.58 |-Branch two:
% 21.70/5.58 | (460) ~ (all_97_0_234 = all_93_0_232)
% 21.70/5.58 | (461) ? [v0] : (( ~ (v0 = 0) & apply(all_0_6_6, all_86_2_231, all_97_0_234) = v0) | ( ~ (v0 = 0) & member(all_93_0_232, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_2_231, all_0_4_4) = v0))
% 21.70/5.58 |
% 21.70/5.58 | Instantiating (461) with all_146_0_403 yields:
% 21.70/5.59 | (462) ( ~ (all_146_0_403 = 0) & apply(all_0_6_6, all_86_2_231, all_97_0_234) = all_146_0_403) | ( ~ (all_146_0_403 = 0) & member(all_93_0_232, all_0_3_3) = all_146_0_403) | ( ~ (all_146_0_403 = 0) & member(all_86_2_231, all_0_4_4) = all_146_0_403)
% 21.70/5.59 |
% 21.70/5.59 +-Applying beta-rule and splitting (462), into two cases.
% 21.70/5.59 |-Branch one:
% 21.70/5.59 | (463) ( ~ (all_146_0_403 = 0) & apply(all_0_6_6, all_86_2_231, all_97_0_234) = all_146_0_403) | ( ~ (all_146_0_403 = 0) & member(all_93_0_232, all_0_3_3) = all_146_0_403)
% 21.70/5.59 |
% 21.70/5.59 +-Applying beta-rule and splitting (463), into two cases.
% 21.70/5.59 |-Branch one:
% 21.70/5.59 | (464) ~ (all_146_0_403 = 0) & apply(all_0_6_6, all_86_2_231, all_97_0_234) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (464) yields:
% 21.70/5.59 | (465) ~ (all_146_0_403 = 0)
% 21.70/5.59 | (466) apply(all_0_6_6, all_86_2_231, all_97_0_234) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (19) with all_0_6_6, all_86_2_231, all_97_0_234, 0, all_146_0_403 and discharging atoms apply(all_0_6_6, all_86_2_231, all_97_0_234) = all_146_0_403, apply(all_0_6_6, all_86_2_231, all_97_0_234) = 0, yields:
% 21.70/5.59 | (467) all_146_0_403 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (467) can reduce 465 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (469) ~ (all_146_0_403 = 0) & member(all_93_0_232, all_0_3_3) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (469) yields:
% 21.70/5.59 | (465) ~ (all_146_0_403 = 0)
% 21.70/5.59 | (471) member(all_93_0_232, all_0_3_3) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_93_0_232, all_0_3_3, all_146_0_403, 0 and discharging atoms member(all_93_0_232, all_0_3_3) = all_146_0_403, member(all_93_0_232, all_0_3_3) = 0, yields:
% 21.70/5.59 | (467) all_146_0_403 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (467) can reduce 465 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (474) ~ (all_146_0_403 = 0) & member(all_86_2_231, all_0_4_4) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (474) yields:
% 21.70/5.59 | (465) ~ (all_146_0_403 = 0)
% 21.70/5.59 | (476) member(all_86_2_231, all_0_4_4) = all_146_0_403
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_2_231, all_0_4_4, all_146_0_403, 0 and discharging atoms member(all_86_2_231, all_0_4_4) = all_146_0_403, member(all_86_2_231, all_0_4_4) = 0, yields:
% 21.70/5.59 | (467) all_146_0_403 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (467) can reduce 465 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (479) ~ (all_99_3_238 = all_97_0_234)
% 21.70/5.59 | (480) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = v0) | ( ~ (v0 = 0) & member(all_99_3_238, all_0_3_3) = v0) | ( ~ (v0 = 0) & member(all_86_0_229, all_0_2_2) = v0))
% 21.70/5.59 |
% 21.70/5.59 | Instantiating (480) with all_138_0_824 yields:
% 21.70/5.59 | (481) ( ~ (all_138_0_824 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_138_0_824) | ( ~ (all_138_0_824 = 0) & member(all_99_3_238, all_0_3_3) = all_138_0_824) | ( ~ (all_138_0_824 = 0) & member(all_86_0_229, all_0_2_2) = all_138_0_824)
% 21.70/5.59 |
% 21.70/5.59 +-Applying beta-rule and splitting (481), into two cases.
% 21.70/5.59 |-Branch one:
% 21.70/5.59 | (482) ( ~ (all_138_0_824 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_138_0_824) | ( ~ (all_138_0_824 = 0) & member(all_99_3_238, all_0_3_3) = all_138_0_824)
% 21.70/5.59 |
% 21.70/5.59 +-Applying beta-rule and splitting (482), into two cases.
% 21.70/5.59 |-Branch one:
% 21.70/5.59 | (483) ~ (all_138_0_824 = 0) & apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (483) yields:
% 21.70/5.59 | (484) ~ (all_138_0_824 = 0)
% 21.70/5.59 | (485) apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (19) with all_0_5_5, all_97_0_234, all_86_0_229, all_138_0_824, 0 and discharging atoms apply(all_0_5_5, all_97_0_234, all_86_0_229) = all_138_0_824, apply(all_0_5_5, all_97_0_234, all_86_0_229) = 0, yields:
% 21.70/5.59 | (486) all_138_0_824 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (486) can reduce 484 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (488) ~ (all_138_0_824 = 0) & member(all_99_3_238, all_0_3_3) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (488) yields:
% 21.70/5.59 | (484) ~ (all_138_0_824 = 0)
% 21.70/5.59 | (490) member(all_99_3_238, all_0_3_3) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_99_3_238, all_0_3_3, all_138_0_824, 0 and discharging atoms member(all_99_3_238, all_0_3_3) = all_138_0_824, member(all_99_3_238, all_0_3_3) = 0, yields:
% 21.70/5.59 | (486) all_138_0_824 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (486) can reduce 484 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (493) ~ (all_138_0_824 = 0) & member(all_86_0_229, all_0_2_2) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (493) yields:
% 21.70/5.59 | (484) ~ (all_138_0_824 = 0)
% 21.70/5.59 | (495) member(all_86_0_229, all_0_2_2) = all_138_0_824
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_0_229, all_0_2_2, all_138_0_824, 0 and discharging atoms member(all_86_0_229, all_0_2_2) = all_138_0_824, member(all_86_0_229, all_0_2_2) = 0, yields:
% 21.70/5.59 | (486) all_138_0_824 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (486) can reduce 484 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (498) ~ (all_100_3_242 = 0) & member(all_86_0_229, all_0_2_2) = all_100_3_242
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (498) yields:
% 21.70/5.59 | (499) ~ (all_100_3_242 = 0)
% 21.70/5.59 | (500) member(all_86_0_229, all_0_2_2) = all_100_3_242
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_0_229, all_0_2_2, all_100_3_242, 0 and discharging atoms member(all_86_0_229, all_0_2_2) = all_100_3_242, member(all_86_0_229, all_0_2_2) = 0, yields:
% 21.70/5.59 | (501) all_100_3_242 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (501) can reduce 499 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (503) ~ (all_100_3_242 = 0) & member(all_86_1_230, all_0_4_4) = all_100_3_242
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (503) yields:
% 21.70/5.59 | (499) ~ (all_100_3_242 = 0)
% 21.70/5.59 | (505) member(all_86_1_230, all_0_4_4) = all_100_3_242
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_1_230, all_0_4_4, all_100_3_242, 0 and discharging atoms member(all_86_1_230, all_0_4_4) = all_100_3_242, member(all_86_1_230, all_0_4_4) = 0, yields:
% 21.70/5.59 | (501) all_100_3_242 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (501) can reduce 499 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (508) ~ (all_99_3_238 = 0) & member(all_86_0_229, all_0_2_2) = all_99_3_238
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (508) yields:
% 21.70/5.59 | (509) ~ (all_99_3_238 = 0)
% 21.70/5.59 | (510) member(all_86_0_229, all_0_2_2) = all_99_3_238
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_0_229, all_0_2_2, all_99_3_238, 0 and discharging atoms member(all_86_0_229, all_0_2_2) = all_99_3_238, member(all_86_0_229, all_0_2_2) = 0, yields:
% 21.70/5.59 | (511) all_99_3_238 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (511) can reduce 509 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 |-Branch two:
% 21.70/5.59 | (513) ~ (all_99_3_238 = 0) & member(all_86_2_231, all_0_4_4) = all_99_3_238
% 21.70/5.59 |
% 21.70/5.59 | Applying alpha-rule on (513) yields:
% 21.70/5.59 | (509) ~ (all_99_3_238 = 0)
% 21.70/5.59 | (515) member(all_86_2_231, all_0_4_4) = all_99_3_238
% 21.70/5.59 |
% 21.70/5.59 | Instantiating formula (59) with all_86_2_231, all_0_4_4, all_99_3_238, 0 and discharging atoms member(all_86_2_231, all_0_4_4) = all_99_3_238, member(all_86_2_231, all_0_4_4) = 0, yields:
% 21.70/5.59 | (511) all_99_3_238 = 0
% 21.70/5.59 |
% 21.70/5.59 | Equations (511) can reduce 509 to:
% 21.70/5.59 | (198) $false
% 21.70/5.59 |
% 21.70/5.59 |-The branch is then unsatisfiable
% 21.70/5.59 % SZS output end Proof for theBenchmark
% 21.70/5.59
% 21.70/5.59 4987ms
%------------------------------------------------------------------------------