TSTP Solution File: SET771+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET771+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:58 EDT 2022
% Result : Theorem 6.66s 2.15s
% Output : Proof 12.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET771+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 06:20:57 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.61/0.59 ____ _
% 0.61/0.59 ___ / __ \_____(_)___ ________ __________
% 0.61/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.59
% 0.61/0.59 A Theorem Prover for First-Order Logic
% 0.61/0.59 (ePrincess v.1.0)
% 0.61/0.59
% 0.61/0.59 (c) Philipp Rümmer, 2009-2015
% 0.61/0.59 (c) Peter Backeman, 2014-2015
% 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.59 Bug reports to peter@backeman.se
% 0.61/0.59
% 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.59
% 0.61/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.03/1.03 Prover 0: Preprocessing ...
% 3.61/1.40 Prover 0: Warning: ignoring some quantifiers
% 3.61/1.43 Prover 0: Constructing countermodel ...
% 4.49/1.66 Prover 0: gave up
% 4.49/1.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.49/1.71 Prover 1: Preprocessing ...
% 5.79/1.98 Prover 1: Constructing countermodel ...
% 6.66/2.15 Prover 1: proved (492ms)
% 6.66/2.15
% 6.66/2.15 No countermodel exists, formula is valid
% 6.66/2.15 % SZS status Theorem for theBenchmark
% 6.66/2.15
% 6.66/2.15 Generating proof ... found it (size 232)
% 11.94/3.31
% 11.94/3.31 % SZS output start Proof for theBenchmark
% 11.94/3.31 Assumed formulas after preprocessing and simplification:
% 11.94/3.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & equivalence(v3, v1) = v4 & maps(v0, v1, v2) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = v13) | ~ (apply(v5, v14, v11) = 0) | ? [v15] : ? [v16] : ((apply(v6, v10, v14) = v16 & member(v14, v8) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))) | (member(v11, v9) = v16 & member(v10, v7) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v14, v12) = 0) | ~ (apply(v5, v11, v12) = v13) | ? [v15] : ? [v16] : ((apply(v7, v11, v14) = v16 & member(v14, v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))) | (member(v12, v10) = v16 & member(v11, v8) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v9, v11, v13) = v19 & apply(v7, v10, v12) = v18 & member(v13, v8) = v17 & member(v12, v6) = v16 & member(v11, v8) = v15 & member(v10, v6) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | (( ~ (v19 = 0) | v18 = 0) & ( ~ (v18 = 0) | v19 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (decreasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v9, v13, v11) = v19 & apply(v7, v10, v12) = v18 & member(v13, v8) = v17 & member(v12, v6) = v16 & member(v11, v8) = v15 & member(v10, v6) = v14 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (increasing(v5, v6, v7, v8, v9) = 0) | ~ (apply(v5, v12, v13) = 0) | ~ (apply(v5, v10, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v9, v11, v13) = v19 & apply(v7, v10, v12) = v18 & member(v13, v8) = v17 & member(v12, v6) = v16 & member(v11, v8) = v15 & member(v10, v6) = v14 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v6 = v5 | ~ (compose_predicate(v12, v11, v10, v9, v8, v7) = v6) | ~ (compose_predicate(v12, v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose_function(v5, v6, v7, v8, v9) = v12) | ~ (apply(v12, v10, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & apply(v6, v10, v13) = 0 & apply(v5, v13, v11) = 0 & member(v13, v8) = 0) | (member(v11, v9) = v14 & member(v10, v7) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = 0) | ~ (apply(v5, v11, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & apply(v7, v11, v13) = 0 & apply(v6, v13, v12) = 0 & member(v13, v9) = 0) | (member(v12, v10) = v14 & member(v11, v8) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (equal_maps(v5, v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (apply(v5, v9, v10) = 0) | ? [v12] : ? [v13] : ? [v14] : (member(v11, v8) = v14 & member(v10, v8) = v13 & member(v9, v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (compose_predicate(v5, v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (apply(v5, v12, v13) = v14 & member(v13, v10) = 0 & member(v12, v8) = 0 & ( ~ (v14 = 0) | ! [v19] : ( ~ (apply(v6, v19, v13) = 0) | ? [v20] : ? [v21] : (apply(v7, v12, v19) = v21 & member(v19, v9) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0))))) & (v14 = 0 | (v18 = 0 & v17 = 0 & v16 = 0 & apply(v7, v12, v15) = 0 & apply(v6, v15, v13) = 0 & member(v15, v9) = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image3(v5, v6, v7) = v9) | ~ (apply(v5, v8, v11) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & member(v11, v6) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image3(v5, v6, v7) = v9) | ~ (apply(v5, v11, v8) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & member(v11, v6) = v12) | ( ~ (v12 = 0) & member(v8, v7) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (isomorphism(v11, v10, v9, v8, v7) = v6) | ~ (isomorphism(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (decreasing(v11, v10, v9, v8, v7) = v6) | ~ (decreasing(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (increasing(v11, v10, v9, v8, v7) = v6) | ~ (increasing(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v6 = v5 | ~ (compose_function(v11, v10, v9, v8, v7) = v6) | ~ (compose_function(v11, v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_function(v5, v6, v7) = v10) | ~ (apply(v10, v9, v8) = v11) | ? [v12] : ? [v13] : ? [v14] : (apply(v5, v8, v9) = v14 & member(v9, v7) = v13 & member(v8, v6) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (( ~ (v14 = 0) | v11 = 0) & ( ~ (v11 = 0) | v14 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_predicate(v5, v6, v7, v8) = 0) | ~ (apply(v5, v10, v9) = v11) | ? [v12] : ? [v13] : ? [v14] : (apply(v6, v9, v10) = v14 & member(v10, v8) = v13 & member(v9, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | (( ~ (v14 = 0) | v11 = 0) & ( ~ (v11 = 0) | v14 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (maps(v5, v6, v7) = 0) | ~ (apply(v5, v8, v10) = 0) | ~ (apply(v5, v8, v9) = 0) | ? [v11] : ? [v12] : ? [v13] : (member(v10, v7) = v13 & member(v9, v7) = v12 & member(v8, v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v9) = v10) | ~ (apply(v5, v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v5, v8, v9) = v14 & member(v9, v6) = v13 & member(v8, v6) = v12 & member(v7, v6) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence_class(v7, v6, v5) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : (apply(v5, v7, v8) = v12 & member(v8, v6) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v9) = v10) | ~ (apply(v6, v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v6, v8, v9) = v14 & member(v9, v5) = v13 & member(v8, v5) = v12 & member(v7, v5) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (isomorphism(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & apply(v9, v12, v14) = v22 & apply(v7, v11, v13) = v21 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0 & ( ~ (v22 = 0) | ~ (v21 = 0)) & (v22 = 0 | v21 = 0)) | (one_to_one(v5, v6, v8) = v12 & maps(v5, v6, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (decreasing(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v9, v14, v12) = v15 & apply(v7, v11, v13) = 0 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (increasing(v5, v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v9, v12, v14) = v15 & apply(v7, v11, v13) = 0 & apply(v5, v13, v14) = 0 & apply(v5, v11, v12) = 0 & member(v14, v8) = 0 & member(v13, v6) = 0 & member(v12, v8) = 0 & member(v11, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (injective(v5, v6, v7) = 0) | ~ (apply(v5, v9, v10) = 0) | ~ (apply(v5, v8, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (member(v10, v7) = v13 & member(v9, v6) = v12 & member(v8, v6) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (inverse_image2(v5, v6) = v8) | ~ (apply(v5, v7, v10) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (image2(v5, v6) = v8) | ~ (apply(v5, v10, v7) = 0) | ~ (member(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (inverse_predicate(v10, v9, v8, v7) = v6) | ~ (inverse_predicate(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (equal_maps(v10, v9, v8, v7) = v6) | ~ (equal_maps(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (inverse_predicate(v5, v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v6, v10, v11) = v12 & apply(v5, v11, v10) = v13 & member(v11, v8) = 0 & member(v10, v7) = 0 & ( ~ (v13 = 0) | ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_maps(v5, v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & apply(v6, v10, v12) = 0 & apply(v5, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v10 & member(v5, v6) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v11 & member(v5, v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (partition(v5, v6) = 0) | ~ (member(v9, v7) = 0) | ~ (member(v8, v5) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v8) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (equivalence_class(v9, v8, v7) = v6) | ~ (equivalence_class(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (inverse_image3(v9, v8, v7) = v6) | ~ (inverse_image3(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (image3(v9, v8, v7) = v6) | ~ (image3(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (inverse_function(v9, v8, v7) = v6) | ~ (inverse_function(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (one_to_one(v9, v8, v7) = v6) | ~ (one_to_one(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (surjective(v9, v8, v7) = v6) | ~ (surjective(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (injective(v9, v8, v7) = v6) | ~ (injective(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (maps(v9, v8, v7) = v6) | ~ (maps(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (apply(v9, v8, v7) = v6) | ~ (apply(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (equivalence_class(v7, v6, v5) = v9) | ~ (member(v8, v9) = 0) | (apply(v5, v7, v8) = 0 & member(v8, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v5, v6, v7, v8, v9) = 0) | (one_to_one(v5, v6, v8) = 0 & maps(v5, v6, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | member(v8, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v5, v8, v10) = 0 & member(v10, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | member(v8, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image3(v5, v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v5, v10, v8) = 0 & member(v10, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (pre_order(v5, v6) = 0) | ~ (apply(v5, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (partition(v5, v6) = 0) | ~ (subset(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (surjective(v5, v6, v7) = v8) | ? [v9] : (member(v9, v7) = 0 & ! [v10] : ( ~ (apply(v5, v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v6) = v11)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (injective(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v10 = v9) & apply(v5, v10, v11) = 0 & apply(v5, v9, v11) = 0 & member(v11, v7) = 0 & member(v10, v6) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (identity(v5, v6) = 0) | ~ (apply(v5, v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (maps(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v11 = v10) & apply(v5, v9, v11) = 0 & apply(v5, v9, v10) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0 & member(v9, v6) = 0) | (v10 = 0 & member(v9, v6) = 0 & ! [v17] : ( ~ (apply(v5, v9, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & member(v17, v7) = v18))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (apply(v3, v5, v6) = v7) | ~ (apply(v0, v5, v8) = 0) | ? [v9] : ? [v10] : ((apply(v0, v6, v8) = v10 & member(v8, v2) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))) | (member(v6, v1) = v10 & member(v5, v1) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (pre_order(v8, v7) = v6) | ~ (pre_order(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equivalence(v8, v7) = v6) | ~ (equivalence(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (partition(v8, v7) = v6) | ~ (partition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (inverse_image2(v8, v7) = v6) | ~ (inverse_image2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (image2(v8, v7) = v6) | ~ (image2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (identity(v8, v7) = v6) | ~ (identity(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (equivalence(v6, v5) = 0) | ~ (apply(v6, v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (apply(v6, v8, v7) = v11 & member(v8, v5) = v10 & member(v7, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (inverse_image2(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : (apply(v5, v7, v9) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (image2(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : (apply(v5, v9, v7) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v5, v6, v7) = v8) | ? [v9] : ? [v10] : (one_to_one(v5, v6, v7) = v9 & injective(v5, v6, v7) = v10 & ( ~ (v9 = 0) | (v10 = 0 & v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v5, v6, v7) = 0) | ~ (member(v8, v7) = 0) | ? [v9] : (apply(v5, v9, v8) = 0 & member(v9, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (maps(v5, v6, v7) = 0) | ~ (member(v8, v6) = 0) | ? [v9] : (apply(v5, v8, v9) = 0 & member(v9, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ? [v10] : (member(v5, v7) = v10 & member(v5, v6) = v9 & (v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pre_order(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = 0) & apply(v5, v9, v10) = 0 & apply(v5, v8, v10) = v16 & apply(v5, v8, v9) = 0 & member(v10, v6) = 0 & member(v9, v6) = 0 & member(v8, v6) = 0) | (v9 = 0 & ~ (v10 = 0) & apply(v5, v8, v8) = v10 & member(v8, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equivalence(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = 0) & apply(v6, v9, v10) = 0 & apply(v6, v8, v10) = v16 & apply(v6, v8, v9) = 0 & member(v10, v5) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & ~ (v13 = 0) & apply(v6, v9, v8) = v13 & apply(v6, v8, v9) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v9 = 0 & ~ (v10 = 0) & apply(v6, v8, v8) = v10 & member(v8, v5) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (partition(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v11 = 0 & v10 = 0 & ~ (v9 = v8) & member(v12, v9) = 0 & member(v12, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0) | (v9 = 0 & ~ (v10 = 0) & subset(v8, v6) = v10 & member(v8, v5) = 0) | (v9 = 0 & member(v8, v6) = 0 & ! [v15] : ( ~ (member(v8, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v15, v5) = v16))))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | ? [v8] : (member(v8, v6) = 0 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (identity(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v5, v8, v8) = v9 & member(v8, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : ? [v9] : (subset(v6, v5) = v9 & subset(v5, v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (partition(v5, v6) = 0) | ~ (member(v7, v6) = 0) | ? [v8] : (member(v8, v5) = 0 & member(v7, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (disjoint(v5, v6) = 0) | ~ (member(v7, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (surjective(v5, v6, v7) = 0) | ? [v8] : ? [v9] : (one_to_one(v5, v6, v7) = v9 & injective(v5, v6, v7) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (apply(v3, v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & v8 = 0 & apply(v0, v6, v7) = 0 & apply(v0, v5, v7) = 0 & member(v7, v2) = 0) | (member(v6, v1) = v8 & member(v5, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ~ (member(v5, empty_set) = 0))
% 12.10/3.39 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 12.10/3.39 | (1) ~ (all_0_0_0 = 0) & equivalence(all_0_1_1, all_0_3_3) = all_0_0_0 & maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0 & ! [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] : ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [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] : ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [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] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0))))) & ! [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] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) & ! [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] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0))) & ! [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) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [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) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [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] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [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] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) | ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0)))) & ! [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 | ~ (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] : (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] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [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(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & 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) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [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] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [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 | ~ (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] : (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] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) & ! [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] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [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] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = 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 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) & ! [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] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) & ! [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 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = 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)))) & ! [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))))) & ! [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] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (apply(all_0_1_1, v0, v1) = v2) | ~ (apply(all_0_4_4, v0, v3) = 0) | ? [v4] : ? [v5] : ((apply(all_0_4_4, v1, v3) = v5 & member(v3, all_0_2_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))) | (member(v1, all_0_3_3) = v5 & member(v0, all_0_3_3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [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] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [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] : ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [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] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 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] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 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 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 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] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [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] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 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(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (apply(all_0_1_1, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & apply(all_0_4_4, v1, v2) = 0 & apply(all_0_4_4, v0, v2) = 0 & member(v2, all_0_2_2) = 0) | (member(v1, all_0_3_3) = v3 & member(v0, all_0_3_3) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 12.47/3.43 |
% 12.47/3.43 | Applying alpha-rule on (1) yields:
% 12.47/3.43 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 12.47/3.43 | (3) ! [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) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))))
% 12.47/3.43 | (4) ! [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))))
% 12.47/3.43 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 12.47/3.43 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 12.47/3.43 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0)))
% 12.47/3.43 | (8) ! [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))
% 12.47/3.43 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 12.47/3.43 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 12.47/3.43 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 12.47/3.43 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 12.47/3.43 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 12.47/3.43 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 12.47/3.43 | (15) maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0
% 12.47/3.43 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 12.47/3.43 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 12.47/3.43 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 12.47/3.43 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 12.47/3.43 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0))
% 12.47/3.43 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 12.47/3.43 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 12.47/3.43 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 12.47/3.44 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 12.47/3.44 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 12.47/3.44 | (26) ! [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] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0)))))
% 12.47/3.44 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))
% 12.47/3.44 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 12.47/3.44 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 12.47/3.44 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 12.47/3.44 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0))
% 12.47/3.44 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11)))))
% 12.47/3.44 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 12.47/3.44 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 12.47/3.44 | (35) ! [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] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0))))
% 12.47/3.44 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 12.47/3.44 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 12.47/3.44 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 12.47/3.44 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 12.47/3.44 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 12.47/3.44 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 12.47/3.44 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 12.47/3.44 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 12.47/3.44 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0))))
% 12.47/3.44 | (45) ! [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))
% 12.47/3.44 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 12.47/3.44 | (47) ! [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] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 12.47/3.44 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 12.47/3.44 | (49) ! [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))
% 12.47/3.44 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 12.47/3.44 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 12.47/3.44 | (52) ! [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))
% 12.47/3.44 | (53) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 12.47/3.44 | (54) ! [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))
% 12.47/3.45 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (apply(all_0_1_1, v0, v1) = v2) | ~ (apply(all_0_4_4, v0, v3) = 0) | ? [v4] : ? [v5] : ((apply(all_0_4_4, v1, v3) = v5 & member(v3, all_0_2_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))) | (member(v1, all_0_3_3) = v5 & member(v0, all_0_3_3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 12.47/3.45 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 12.47/3.45 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 12.47/3.45 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0))
% 12.47/3.45 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 12.47/3.45 | (60) ! [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] : ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))
% 12.47/3.45 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 12.47/3.45 | (62) ! [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)))
% 12.47/3.45 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 12.47/3.45 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 12.47/3.45 | (65) ! [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))
% 12.47/3.45 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 12.47/3.45 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 12.47/3.45 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 12.47/3.45 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 12.47/3.45 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 12.47/3.45 | (71) ! [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))
% 12.47/3.45 | (72) ! [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)))
% 12.47/3.45 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 12.47/3.45 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0)))
% 12.47/3.45 | (75) ~ (all_0_0_0 = 0)
% 12.47/3.45 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (one_to_one(v0, v1, v2) = v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 12.47/3.45 | (77) ! [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))
% 12.47/3.45 | (78) ! [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)))))
% 12.47/3.45 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 12.47/3.45 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 12.47/3.45 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 12.47/3.45 | (82) ! [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))
% 12.47/3.45 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 12.47/3.45 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 12.47/3.45 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 12.47/3.45 | (86) ! [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))
% 12.47/3.45 | (87) ! [v0] : ~ (member(v0, empty_set) = 0)
% 12.47/3.45 | (88) ! [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(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & 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) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 12.47/3.46 | (89) ! [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] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 12.47/3.46 | (90) ! [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))
% 12.47/3.46 | (91) equivalence(all_0_1_1, all_0_3_3) = all_0_0_0
% 12.47/3.46 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 12.47/3.46 | (93) ! [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] : ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))
% 12.47/3.46 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 12.47/3.46 | (95) ! [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) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))))
% 12.47/3.46 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 12.47/3.46 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 12.47/3.46 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 12.47/3.46 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 12.47/3.46 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 12.47/3.46 | (101) ! [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] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) | ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0))))
% 12.47/3.46 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 12.47/3.46 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 12.47/3.46 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 12.47/3.46 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 12.47/3.46 | (106) ! [v0] : ! [v1] : ( ~ (apply(all_0_1_1, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & apply(all_0_4_4, v1, v2) = 0 & apply(all_0_4_4, v0, v2) = 0 & member(v2, all_0_2_2) = 0) | (member(v1, all_0_3_3) = v3 & member(v0, all_0_3_3) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 12.47/3.46 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 12.47/3.46 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 12.47/3.46 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0))
% 12.47/3.46 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 12.47/3.46 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 12.47/3.46 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 12.47/3.46 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0)))
% 12.47/3.46 | (114) ! [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))
% 12.47/3.46 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5))
% 12.47/3.46 |
% 12.47/3.46 | Instantiating formula (74) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equivalence(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 12.47/3.47 | (116) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_3_3) = 0))
% 12.47/3.47 |
% 12.47/3.47 +-Applying beta-rule and splitting (116), into two cases.
% 12.47/3.47 |-Branch one:
% 12.47/3.47 | (117) all_0_0_0 = 0
% 12.47/3.47 |
% 12.47/3.47 | Equations (117) can reduce 75 to:
% 12.47/3.47 | (118) $false
% 12.47/3.47 |
% 12.47/3.47 |-The branch is then unsatisfiable
% 12.47/3.47 |-Branch two:
% 12.47/3.47 | (75) ~ (all_0_0_0 = 0)
% 12.47/3.47 | (120) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_3_3) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_3_3) = 0 & member(v0, all_0_3_3) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_3_3) = 0))
% 12.47/3.47 |
% 12.47/3.47 | Instantiating (120) with all_10_0_5, all_10_1_6, all_10_2_7, all_10_3_8, all_10_4_9, all_10_5_10, all_10_6_11, all_10_7_12, all_10_8_13 yields:
% 12.47/3.47 | (121) (all_10_1_6 = 0 & all_10_2_7 = 0 & all_10_3_8 = 0 & all_10_4_9 = 0 & all_10_5_10 = 0 & ~ (all_10_0_5 = 0) & apply(all_0_1_1, all_10_7_12, all_10_6_11) = 0 & apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_6_11, all_0_3_3) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0) | (all_10_4_9 = 0 & all_10_5_10 = 0 & all_10_6_11 = 0 & ~ (all_10_3_8 = 0) & apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0) | (all_10_7_12 = 0 & ~ (all_10_6_11 = 0) & apply(all_0_1_1, all_10_8_13, all_10_8_13) = all_10_6_11 & member(all_10_8_13, all_0_3_3) = 0)
% 12.47/3.47 |
% 12.47/3.47 +-Applying beta-rule and splitting (121), into two cases.
% 12.47/3.47 |-Branch one:
% 12.47/3.47 | (122) (all_10_1_6 = 0 & all_10_2_7 = 0 & all_10_3_8 = 0 & all_10_4_9 = 0 & all_10_5_10 = 0 & ~ (all_10_0_5 = 0) & apply(all_0_1_1, all_10_7_12, all_10_6_11) = 0 & apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_6_11, all_0_3_3) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0) | (all_10_4_9 = 0 & all_10_5_10 = 0 & all_10_6_11 = 0 & ~ (all_10_3_8 = 0) & apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0)
% 12.47/3.47 |
% 12.47/3.47 +-Applying beta-rule and splitting (122), into two cases.
% 12.47/3.47 |-Branch one:
% 12.47/3.47 | (123) all_10_1_6 = 0 & all_10_2_7 = 0 & all_10_3_8 = 0 & all_10_4_9 = 0 & all_10_5_10 = 0 & ~ (all_10_0_5 = 0) & apply(all_0_1_1, all_10_7_12, all_10_6_11) = 0 & apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_6_11, all_0_3_3) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0
% 12.47/3.47 |
% 12.47/3.47 | Applying alpha-rule on (123) yields:
% 12.47/3.47 | (124) apply(all_0_1_1, all_10_7_12, all_10_6_11) = 0
% 12.47/3.47 | (125) all_10_4_9 = 0
% 12.47/3.47 | (126) ~ (all_10_0_5 = 0)
% 12.47/3.47 | (127) all_10_5_10 = 0
% 12.47/3.47 | (128) apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5
% 12.47/3.47 | (129) apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0
% 12.47/3.47 | (130) all_10_3_8 = 0
% 12.47/3.47 | (131) all_10_2_7 = 0
% 12.47/3.47 | (132) member(all_10_8_13, all_0_3_3) = 0
% 12.47/3.47 | (133) member(all_10_7_12, all_0_3_3) = 0
% 12.47/3.47 | (134) member(all_10_6_11, all_0_3_3) = 0
% 12.47/3.47 | (135) all_10_1_6 = 0
% 12.47/3.47 |
% 12.47/3.47 | Instantiating formula (106) with all_10_6_11, all_10_7_12 and discharging atoms apply(all_0_1_1, all_10_7_12, all_10_6_11) = 0, yields:
% 12.47/3.47 | (136) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, all_10_6_11, v0) = 0 & apply(all_0_4_4, all_10_7_12, v0) = 0 & member(v0, all_0_2_2) = 0) | (member(all_10_6_11, all_0_3_3) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.47/3.47 |
% 12.47/3.47 | Instantiating formula (106) with all_10_7_12, all_10_8_13 and discharging atoms apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0, yields:
% 12.47/3.47 | (137) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, all_10_7_12, v0) = 0 & apply(all_0_4_4, all_10_8_13, v0) = 0 & member(v0, all_0_2_2) = 0) | (member(all_10_7_12, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.47/3.47 |
% 12.47/3.47 | Instantiating formula (23) with all_10_7_12, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.47/3.47 | (138) ? [v0] : (apply(all_0_4_4, all_10_7_12, v0) = 0 & member(v0, all_0_2_2) = 0)
% 12.47/3.47 |
% 12.47/3.47 | Instantiating formula (23) with all_10_8_13, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.47/3.47 | (139) ? [v0] : (apply(all_0_4_4, all_10_8_13, v0) = 0 & member(v0, all_0_2_2) = 0)
% 12.47/3.47 |
% 12.47/3.47 | Instantiating (139) with all_31_0_14 yields:
% 12.47/3.47 | (140) apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0 & member(all_31_0_14, all_0_2_2) = 0
% 12.47/3.47 |
% 12.47/3.47 | Applying alpha-rule on (140) yields:
% 12.47/3.47 | (141) apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0
% 12.47/3.47 | (142) member(all_31_0_14, all_0_2_2) = 0
% 12.80/3.47 |
% 12.80/3.47 | Instantiating (138) with all_33_0_15 yields:
% 12.80/3.47 | (143) apply(all_0_4_4, all_10_7_12, all_33_0_15) = 0 & member(all_33_0_15, all_0_2_2) = 0
% 12.80/3.47 |
% 12.80/3.47 | Applying alpha-rule on (143) yields:
% 12.80/3.47 | (144) apply(all_0_4_4, all_10_7_12, all_33_0_15) = 0
% 12.80/3.47 | (145) member(all_33_0_15, all_0_2_2) = 0
% 12.80/3.47 |
% 12.80/3.47 | Instantiating (137) with all_37_0_17, all_37_1_18, all_37_2_19, all_37_3_20 yields:
% 12.80/3.47 | (146) (all_37_0_17 = 0 & all_37_1_18 = 0 & all_37_2_19 = 0 & apply(all_0_4_4, all_10_7_12, all_37_3_20) = 0 & apply(all_0_4_4, all_10_8_13, all_37_3_20) = 0 & member(all_37_3_20, all_0_2_2) = 0) | (member(all_10_7_12, all_0_3_3) = all_37_2_19 & member(all_10_8_13, all_0_3_3) = all_37_3_20 & ( ~ (all_37_2_19 = 0) | ~ (all_37_3_20 = 0)))
% 12.80/3.47 |
% 12.80/3.47 | Instantiating (136) with all_38_0_21, all_38_1_22, all_38_2_23, all_38_3_24 yields:
% 12.80/3.47 | (147) (all_38_0_21 = 0 & all_38_1_22 = 0 & all_38_2_23 = 0 & apply(all_0_4_4, all_10_6_11, all_38_3_24) = 0 & apply(all_0_4_4, all_10_7_12, all_38_3_24) = 0 & member(all_38_3_24, all_0_2_2) = 0) | (member(all_10_6_11, all_0_3_3) = all_38_2_23 & member(all_10_7_12, all_0_3_3) = all_38_3_24 & ( ~ (all_38_2_23 = 0) | ~ (all_38_3_24 = 0)))
% 12.80/3.47 |
% 12.80/3.47 +-Applying beta-rule and splitting (147), into two cases.
% 12.80/3.47 |-Branch one:
% 12.80/3.47 | (148) all_38_0_21 = 0 & all_38_1_22 = 0 & all_38_2_23 = 0 & apply(all_0_4_4, all_10_6_11, all_38_3_24) = 0 & apply(all_0_4_4, all_10_7_12, all_38_3_24) = 0 & member(all_38_3_24, all_0_2_2) = 0
% 12.80/3.47 |
% 12.80/3.47 | Applying alpha-rule on (148) yields:
% 12.80/3.47 | (149) all_38_0_21 = 0
% 12.80/3.47 | (150) member(all_38_3_24, all_0_2_2) = 0
% 12.80/3.47 | (151) all_38_2_23 = 0
% 12.80/3.47 | (152) all_38_1_22 = 0
% 12.80/3.47 | (153) apply(all_0_4_4, all_10_6_11, all_38_3_24) = 0
% 12.80/3.47 | (154) apply(all_0_4_4, all_10_7_12, all_38_3_24) = 0
% 12.80/3.47 |
% 12.80/3.47 +-Applying beta-rule and splitting (146), into two cases.
% 12.80/3.47 |-Branch one:
% 12.80/3.47 | (155) all_37_0_17 = 0 & all_37_1_18 = 0 & all_37_2_19 = 0 & apply(all_0_4_4, all_10_7_12, all_37_3_20) = 0 & apply(all_0_4_4, all_10_8_13, all_37_3_20) = 0 & member(all_37_3_20, all_0_2_2) = 0
% 12.80/3.47 |
% 12.80/3.47 | Applying alpha-rule on (155) yields:
% 12.80/3.47 | (156) all_37_0_17 = 0
% 12.80/3.47 | (157) member(all_37_3_20, all_0_2_2) = 0
% 12.80/3.47 | (158) apply(all_0_4_4, all_10_8_13, all_37_3_20) = 0
% 12.80/3.47 | (159) all_37_2_19 = 0
% 12.80/3.47 | (160) apply(all_0_4_4, all_10_7_12, all_37_3_20) = 0
% 12.80/3.48 | (161) all_37_1_18 = 0
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (29) with all_38_3_24, all_33_0_15, all_10_7_12, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, apply(all_0_4_4, all_10_7_12, all_38_3_24) = 0, apply(all_0_4_4, all_10_7_12, all_33_0_15) = 0, yields:
% 12.80/3.48 | (162) all_38_3_24 = all_33_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_38_3_24, all_0_2_2) = v2 & member(all_33_0_15, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (29) with all_37_3_20, all_33_0_15, all_10_7_12, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, apply(all_0_4_4, all_10_7_12, all_37_3_20) = 0, apply(all_0_4_4, all_10_7_12, all_33_0_15) = 0, yields:
% 12.80/3.48 | (163) all_37_3_20 = all_33_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_37_3_20, all_0_2_2) = v2 & member(all_33_0_15, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (55) with all_33_0_15, all_10_0_5, all_10_6_11, all_10_8_13 and discharging atoms apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5, yields:
% 12.80/3.48 | (164) all_10_0_5 = 0 | ~ (apply(all_0_4_4, all_10_8_13, all_33_0_15) = 0) | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_6_11, all_33_0_15) = v1 & member(all_33_0_15, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_11, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (29) with all_37_3_20, all_38_3_24, all_10_8_13, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, apply(all_0_4_4, all_10_8_13, all_37_3_20) = 0, yields:
% 12.80/3.48 | (165) all_38_3_24 = all_37_3_20 | ~ (apply(all_0_4_4, all_10_8_13, all_38_3_24) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_38_3_24, all_0_2_2) = v1 & member(all_37_3_20, all_0_2_2) = v2 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (29) with all_37_3_20, all_31_0_14, all_10_8_13, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, apply(all_0_4_4, all_10_8_13, all_37_3_20) = 0, apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0, yields:
% 12.80/3.48 | (166) all_37_3_20 = all_31_0_14 | ? [v0] : ? [v1] : ? [v2] : (member(all_37_3_20, all_0_2_2) = v2 & member(all_31_0_14, all_0_2_2) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (55) with all_31_0_14, all_10_0_5, all_10_6_11, all_10_8_13 and discharging atoms apply(all_0_1_1, all_10_8_13, all_10_6_11) = all_10_0_5, apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0, yields:
% 12.80/3.48 | (167) all_10_0_5 = 0 | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_6_11, all_31_0_14) = v1 & member(all_31_0_14, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_11, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (166), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (168) all_37_3_20 = all_31_0_14
% 12.80/3.48 |
% 12.80/3.48 | From (168) and (158) follows:
% 12.80/3.48 | (141) apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0
% 12.80/3.48 |
% 12.80/3.48 | From (168) and (157) follows:
% 12.80/3.48 | (142) member(all_31_0_14, all_0_2_2) = 0
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (167), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (171) all_10_0_5 = 0
% 12.80/3.48 |
% 12.80/3.48 | Equations (171) can reduce 126 to:
% 12.80/3.48 | (118) $false
% 12.80/3.48 |
% 12.80/3.48 |-The branch is then unsatisfiable
% 12.80/3.48 |-Branch two:
% 12.80/3.48 | (126) ~ (all_10_0_5 = 0)
% 12.80/3.48 | (174) ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_6_11, all_31_0_14) = v1 & member(all_31_0_14, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_11, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating (174) with all_69_0_25, all_69_1_26 yields:
% 12.80/3.48 | (175) (apply(all_0_4_4, all_10_6_11, all_31_0_14) = all_69_0_25 & member(all_31_0_14, all_0_2_2) = all_69_1_26 & ( ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0))) | (member(all_10_6_11, all_0_3_3) = all_69_0_25 & member(all_10_8_13, all_0_3_3) = all_69_1_26 & ( ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0)))
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (162), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (176) all_38_3_24 = all_33_0_15
% 12.80/3.48 |
% 12.80/3.48 | From (176) and (153) follows:
% 12.80/3.48 | (177) apply(all_0_4_4, all_10_6_11, all_33_0_15) = 0
% 12.80/3.48 |
% 12.80/3.48 | From (176) and (150) follows:
% 12.80/3.48 | (145) member(all_33_0_15, all_0_2_2) = 0
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (164), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (179) ~ (apply(all_0_4_4, all_10_8_13, all_33_0_15) = 0)
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (163), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (180) all_37_3_20 = all_33_0_15
% 12.80/3.48 |
% 12.80/3.48 | Combining equations (168,180) yields a new equation:
% 12.80/3.48 | (181) all_33_0_15 = all_31_0_14
% 12.80/3.48 |
% 12.80/3.48 | From (181) and (179) follows:
% 12.80/3.48 | (182) ~ (apply(all_0_4_4, all_10_8_13, all_31_0_14) = 0)
% 12.80/3.48 |
% 12.80/3.48 | Using (141) and (182) yields:
% 12.80/3.48 | (183) $false
% 12.80/3.48 |
% 12.80/3.48 |-The branch is then unsatisfiable
% 12.80/3.48 |-Branch two:
% 12.80/3.48 | (184) ~ (all_37_3_20 = all_33_0_15)
% 12.80/3.48 | (185) ? [v0] : ? [v1] : ? [v2] : (member(all_37_3_20, all_0_2_2) = v2 & member(all_33_0_15, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.48 |
% 12.80/3.48 | Instantiating (185) with all_82_0_27, all_82_1_28, all_82_2_29 yields:
% 12.80/3.48 | (186) member(all_37_3_20, all_0_2_2) = all_82_0_27 & member(all_33_0_15, all_0_2_2) = all_82_1_28 & member(all_10_7_12, all_0_3_3) = all_82_2_29 & ( ~ (all_82_0_27 = 0) | ~ (all_82_1_28 = 0) | ~ (all_82_2_29 = 0))
% 12.80/3.48 |
% 12.80/3.48 | Applying alpha-rule on (186) yields:
% 12.80/3.48 | (187) member(all_37_3_20, all_0_2_2) = all_82_0_27
% 12.80/3.48 | (188) member(all_33_0_15, all_0_2_2) = all_82_1_28
% 12.80/3.48 | (189) member(all_10_7_12, all_0_3_3) = all_82_2_29
% 12.80/3.48 | (190) ~ (all_82_0_27 = 0) | ~ (all_82_1_28 = 0) | ~ (all_82_2_29 = 0)
% 12.80/3.48 |
% 12.80/3.48 | From (168) and (187) follows:
% 12.80/3.48 | (191) member(all_31_0_14, all_0_2_2) = all_82_0_27
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (68) with all_33_0_15, all_0_2_2, all_82_1_28, 0 and discharging atoms member(all_33_0_15, all_0_2_2) = all_82_1_28, member(all_33_0_15, all_0_2_2) = 0, yields:
% 12.80/3.48 | (192) all_82_1_28 = 0
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (68) with all_31_0_14, all_0_2_2, all_82_0_27, 0 and discharging atoms member(all_31_0_14, all_0_2_2) = all_82_0_27, member(all_31_0_14, all_0_2_2) = 0, yields:
% 12.80/3.48 | (193) all_82_0_27 = 0
% 12.80/3.48 |
% 12.80/3.48 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_82_2_29, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_82_2_29, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.48 | (194) all_82_2_29 = 0
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (190), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (195) ~ (all_82_0_27 = 0)
% 12.80/3.48 |
% 12.80/3.48 | Equations (193) can reduce 195 to:
% 12.80/3.48 | (118) $false
% 12.80/3.48 |
% 12.80/3.48 |-The branch is then unsatisfiable
% 12.80/3.48 |-Branch two:
% 12.80/3.48 | (193) all_82_0_27 = 0
% 12.80/3.48 | (198) ~ (all_82_1_28 = 0) | ~ (all_82_2_29 = 0)
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (198), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (199) ~ (all_82_1_28 = 0)
% 12.80/3.48 |
% 12.80/3.48 | Equations (192) can reduce 199 to:
% 12.80/3.48 | (118) $false
% 12.80/3.48 |
% 12.80/3.48 |-The branch is then unsatisfiable
% 12.80/3.48 |-Branch two:
% 12.80/3.48 | (192) all_82_1_28 = 0
% 12.80/3.48 | (202) ~ (all_82_2_29 = 0)
% 12.80/3.48 |
% 12.80/3.48 | Equations (194) can reduce 202 to:
% 12.80/3.48 | (118) $false
% 12.80/3.48 |
% 12.80/3.48 |-The branch is then unsatisfiable
% 12.80/3.48 |-Branch two:
% 12.80/3.48 | (204) apply(all_0_4_4, all_10_8_13, all_33_0_15) = 0
% 12.80/3.48 | (205) all_10_0_5 = 0 | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_6_11, all_33_0_15) = v1 & member(all_33_0_15, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_11, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.48 |
% 12.80/3.48 +-Applying beta-rule and splitting (165), into two cases.
% 12.80/3.48 |-Branch one:
% 12.80/3.48 | (206) ~ (apply(all_0_4_4, all_10_8_13, all_38_3_24) = 0)
% 12.80/3.48 |
% 12.80/3.48 | From (176) and (206) follows:
% 12.80/3.48 | (179) ~ (apply(all_0_4_4, all_10_8_13, all_33_0_15) = 0)
% 12.80/3.48 |
% 12.80/3.49 | Using (204) and (179) yields:
% 12.80/3.49 | (183) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (209) apply(all_0_4_4, all_10_8_13, all_38_3_24) = 0
% 12.80/3.49 | (210) all_38_3_24 = all_37_3_20 | ? [v0] : ? [v1] : ? [v2] : (member(all_38_3_24, all_0_2_2) = v1 & member(all_37_3_20, all_0_2_2) = v2 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (210), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (211) all_38_3_24 = all_37_3_20
% 12.80/3.49 |
% 12.80/3.49 | Combining equations (211,176) yields a new equation:
% 12.80/3.49 | (212) all_37_3_20 = all_33_0_15
% 12.80/3.49 |
% 12.80/3.49 | Simplifying 212 yields:
% 12.80/3.49 | (180) all_37_3_20 = all_33_0_15
% 12.80/3.49 |
% 12.80/3.49 | Combining equations (180,168) yields a new equation:
% 12.80/3.49 | (214) all_33_0_15 = all_31_0_14
% 12.80/3.49 |
% 12.80/3.49 | Simplifying 214 yields:
% 12.80/3.49 | (181) all_33_0_15 = all_31_0_14
% 12.80/3.49 |
% 12.80/3.49 | From (181) and (177) follows:
% 12.80/3.49 | (216) apply(all_0_4_4, all_10_6_11, all_31_0_14) = 0
% 12.80/3.49 |
% 12.80/3.49 | From (181) and (145) follows:
% 12.80/3.49 | (142) member(all_31_0_14, all_0_2_2) = 0
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (175), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (218) apply(all_0_4_4, all_10_6_11, all_31_0_14) = all_69_0_25 & member(all_31_0_14, all_0_2_2) = all_69_1_26 & ( ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0))
% 12.80/3.49 |
% 12.80/3.49 | Applying alpha-rule on (218) yields:
% 12.80/3.49 | (219) apply(all_0_4_4, all_10_6_11, all_31_0_14) = all_69_0_25
% 12.80/3.49 | (220) member(all_31_0_14, all_0_2_2) = all_69_1_26
% 12.80/3.49 | (221) ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (67) with all_0_4_4, all_10_6_11, all_31_0_14, all_69_0_25, 0 and discharging atoms apply(all_0_4_4, all_10_6_11, all_31_0_14) = all_69_0_25, apply(all_0_4_4, all_10_6_11, all_31_0_14) = 0, yields:
% 12.80/3.49 | (222) all_69_0_25 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_31_0_14, all_0_2_2, all_69_1_26, 0 and discharging atoms member(all_31_0_14, all_0_2_2) = all_69_1_26, member(all_31_0_14, all_0_2_2) = 0, yields:
% 12.80/3.49 | (223) all_69_1_26 = 0
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (221), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (224) ~ (all_69_0_25 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (222) can reduce 224 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (222) all_69_0_25 = 0
% 12.80/3.49 | (227) ~ (all_69_1_26 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (223) can reduce 227 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (229) member(all_10_6_11, all_0_3_3) = all_69_0_25 & member(all_10_8_13, all_0_3_3) = all_69_1_26 & ( ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0))
% 12.80/3.49 |
% 12.80/3.49 | Applying alpha-rule on (229) yields:
% 12.80/3.49 | (230) member(all_10_6_11, all_0_3_3) = all_69_0_25
% 12.80/3.49 | (231) member(all_10_8_13, all_0_3_3) = all_69_1_26
% 12.80/3.49 | (221) ~ (all_69_0_25 = 0) | ~ (all_69_1_26 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_10_6_11, all_0_3_3, all_69_0_25, 0 and discharging atoms member(all_10_6_11, all_0_3_3) = all_69_0_25, member(all_10_6_11, all_0_3_3) = 0, yields:
% 12.80/3.49 | (222) all_69_0_25 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_69_1_26, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_69_1_26, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.49 | (223) all_69_1_26 = 0
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (221), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (224) ~ (all_69_0_25 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (222) can reduce 224 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (222) all_69_0_25 = 0
% 12.80/3.49 | (227) ~ (all_69_1_26 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (223) can reduce 227 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (240) ~ (all_38_3_24 = all_37_3_20)
% 12.80/3.49 | (241) ? [v0] : ? [v1] : ? [v2] : (member(all_38_3_24, all_0_2_2) = v1 & member(all_37_3_20, all_0_2_2) = v2 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.49 |
% 12.80/3.49 | Instantiating (241) with all_86_0_37, all_86_1_38, all_86_2_39 yields:
% 12.80/3.49 | (242) member(all_38_3_24, all_0_2_2) = all_86_1_38 & member(all_37_3_20, all_0_2_2) = all_86_0_37 & member(all_10_8_13, all_0_3_3) = all_86_2_39 & ( ~ (all_86_0_37 = 0) | ~ (all_86_1_38 = 0) | ~ (all_86_2_39 = 0))
% 12.80/3.49 |
% 12.80/3.49 | Applying alpha-rule on (242) yields:
% 12.80/3.49 | (243) member(all_38_3_24, all_0_2_2) = all_86_1_38
% 12.80/3.49 | (244) member(all_37_3_20, all_0_2_2) = all_86_0_37
% 12.80/3.49 | (245) member(all_10_8_13, all_0_3_3) = all_86_2_39
% 12.80/3.49 | (246) ~ (all_86_0_37 = 0) | ~ (all_86_1_38 = 0) | ~ (all_86_2_39 = 0)
% 12.80/3.49 |
% 12.80/3.49 | From (176) and (243) follows:
% 12.80/3.49 | (247) member(all_33_0_15, all_0_2_2) = all_86_1_38
% 12.80/3.49 |
% 12.80/3.49 | From (168) and (244) follows:
% 12.80/3.49 | (248) member(all_31_0_14, all_0_2_2) = all_86_0_37
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_33_0_15, all_0_2_2, all_86_1_38, 0 and discharging atoms member(all_33_0_15, all_0_2_2) = all_86_1_38, member(all_33_0_15, all_0_2_2) = 0, yields:
% 12.80/3.49 | (249) all_86_1_38 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_31_0_14, all_0_2_2, all_86_0_37, 0 and discharging atoms member(all_31_0_14, all_0_2_2) = all_86_0_37, member(all_31_0_14, all_0_2_2) = 0, yields:
% 12.80/3.49 | (250) all_86_0_37 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_86_2_39, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_86_2_39, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.49 | (251) all_86_2_39 = 0
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (246), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (252) ~ (all_86_0_37 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (250) can reduce 252 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (250) all_86_0_37 = 0
% 12.80/3.49 | (255) ~ (all_86_1_38 = 0) | ~ (all_86_2_39 = 0)
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (255), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (256) ~ (all_86_1_38 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (249) can reduce 256 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (249) all_86_1_38 = 0
% 12.80/3.49 | (259) ~ (all_86_2_39 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (251) can reduce 259 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (261) ~ (all_38_3_24 = all_33_0_15)
% 12.80/3.49 | (262) ? [v0] : ? [v1] : ? [v2] : (member(all_38_3_24, all_0_2_2) = v2 & member(all_33_0_15, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.49 |
% 12.80/3.49 | Instantiating (262) with all_74_0_49, all_74_1_50, all_74_2_51 yields:
% 12.80/3.49 | (263) member(all_38_3_24, all_0_2_2) = all_74_0_49 & member(all_33_0_15, all_0_2_2) = all_74_1_50 & member(all_10_7_12, all_0_3_3) = all_74_2_51 & ( ~ (all_74_0_49 = 0) | ~ (all_74_1_50 = 0) | ~ (all_74_2_51 = 0))
% 12.80/3.49 |
% 12.80/3.49 | Applying alpha-rule on (263) yields:
% 12.80/3.49 | (264) member(all_38_3_24, all_0_2_2) = all_74_0_49
% 12.80/3.49 | (265) member(all_33_0_15, all_0_2_2) = all_74_1_50
% 12.80/3.49 | (266) member(all_10_7_12, all_0_3_3) = all_74_2_51
% 12.80/3.49 | (267) ~ (all_74_0_49 = 0) | ~ (all_74_1_50 = 0) | ~ (all_74_2_51 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_38_3_24, all_0_2_2, all_74_0_49, 0 and discharging atoms member(all_38_3_24, all_0_2_2) = all_74_0_49, member(all_38_3_24, all_0_2_2) = 0, yields:
% 12.80/3.49 | (268) all_74_0_49 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_33_0_15, all_0_2_2, all_74_1_50, 0 and discharging atoms member(all_33_0_15, all_0_2_2) = all_74_1_50, member(all_33_0_15, all_0_2_2) = 0, yields:
% 12.80/3.49 | (269) all_74_1_50 = 0
% 12.80/3.49 |
% 12.80/3.49 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_74_2_51, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_74_2_51, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.49 | (270) all_74_2_51 = 0
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (267), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (271) ~ (all_74_0_49 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (268) can reduce 271 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (268) all_74_0_49 = 0
% 12.80/3.49 | (274) ~ (all_74_1_50 = 0) | ~ (all_74_2_51 = 0)
% 12.80/3.49 |
% 12.80/3.49 +-Applying beta-rule and splitting (274), into two cases.
% 12.80/3.49 |-Branch one:
% 12.80/3.49 | (275) ~ (all_74_1_50 = 0)
% 12.80/3.49 |
% 12.80/3.49 | Equations (269) can reduce 275 to:
% 12.80/3.49 | (118) $false
% 12.80/3.49 |
% 12.80/3.49 |-The branch is then unsatisfiable
% 12.80/3.49 |-Branch two:
% 12.80/3.49 | (269) all_74_1_50 = 0
% 12.80/3.49 | (278) ~ (all_74_2_51 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (270) can reduce 278 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (280) ~ (all_37_3_20 = all_31_0_14)
% 12.80/3.50 | (281) ? [v0] : ? [v1] : ? [v2] : (member(all_37_3_20, all_0_2_2) = v2 & member(all_31_0_14, all_0_2_2) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.50 |
% 12.80/3.50 | Instantiating (281) with all_66_0_54, all_66_1_55, all_66_2_56 yields:
% 12.80/3.50 | (282) member(all_37_3_20, all_0_2_2) = all_66_0_54 & member(all_31_0_14, all_0_2_2) = all_66_1_55 & member(all_10_8_13, all_0_3_3) = all_66_2_56 & ( ~ (all_66_0_54 = 0) | ~ (all_66_1_55 = 0) | ~ (all_66_2_56 = 0))
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (282) yields:
% 12.80/3.50 | (283) member(all_37_3_20, all_0_2_2) = all_66_0_54
% 12.80/3.50 | (284) member(all_31_0_14, all_0_2_2) = all_66_1_55
% 12.80/3.50 | (285) member(all_10_8_13, all_0_3_3) = all_66_2_56
% 12.80/3.50 | (286) ~ (all_66_0_54 = 0) | ~ (all_66_1_55 = 0) | ~ (all_66_2_56 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_37_3_20, all_0_2_2, all_66_0_54, 0 and discharging atoms member(all_37_3_20, all_0_2_2) = all_66_0_54, member(all_37_3_20, all_0_2_2) = 0, yields:
% 12.80/3.50 | (287) all_66_0_54 = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_31_0_14, all_0_2_2, all_66_1_55, 0 and discharging atoms member(all_31_0_14, all_0_2_2) = all_66_1_55, member(all_31_0_14, all_0_2_2) = 0, yields:
% 12.80/3.50 | (288) all_66_1_55 = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_66_2_56, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_66_2_56, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.50 | (289) all_66_2_56 = 0
% 12.80/3.50 |
% 12.80/3.50 +-Applying beta-rule and splitting (286), into two cases.
% 12.80/3.50 |-Branch one:
% 12.80/3.50 | (290) ~ (all_66_0_54 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (287) can reduce 290 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (287) all_66_0_54 = 0
% 12.80/3.50 | (293) ~ (all_66_1_55 = 0) | ~ (all_66_2_56 = 0)
% 12.80/3.50 |
% 12.80/3.50 +-Applying beta-rule and splitting (293), into two cases.
% 12.80/3.50 |-Branch one:
% 12.80/3.50 | (294) ~ (all_66_1_55 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (288) can reduce 294 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (288) all_66_1_55 = 0
% 12.80/3.50 | (297) ~ (all_66_2_56 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (289) can reduce 297 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (299) member(all_10_7_12, all_0_3_3) = all_37_2_19 & member(all_10_8_13, all_0_3_3) = all_37_3_20 & ( ~ (all_37_2_19 = 0) | ~ (all_37_3_20 = 0))
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (299) yields:
% 12.80/3.50 | (300) member(all_10_7_12, all_0_3_3) = all_37_2_19
% 12.80/3.50 | (301) member(all_10_8_13, all_0_3_3) = all_37_3_20
% 12.80/3.50 | (302) ~ (all_37_2_19 = 0) | ~ (all_37_3_20 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_37_2_19, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_37_2_19, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.50 | (159) all_37_2_19 = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_37_3_20, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_37_3_20, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.50 | (304) all_37_3_20 = 0
% 12.80/3.50 |
% 12.80/3.50 +-Applying beta-rule and splitting (302), into two cases.
% 12.80/3.50 |-Branch one:
% 12.80/3.50 | (305) ~ (all_37_2_19 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (159) can reduce 305 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (159) all_37_2_19 = 0
% 12.80/3.50 | (308) ~ (all_37_3_20 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (304) can reduce 308 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (310) member(all_10_6_11, all_0_3_3) = all_38_2_23 & member(all_10_7_12, all_0_3_3) = all_38_3_24 & ( ~ (all_38_2_23 = 0) | ~ (all_38_3_24 = 0))
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (310) yields:
% 12.80/3.50 | (311) member(all_10_6_11, all_0_3_3) = all_38_2_23
% 12.80/3.50 | (312) member(all_10_7_12, all_0_3_3) = all_38_3_24
% 12.80/3.50 | (313) ~ (all_38_2_23 = 0) | ~ (all_38_3_24 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_10_6_11, all_0_3_3, all_38_2_23, 0 and discharging atoms member(all_10_6_11, all_0_3_3) = all_38_2_23, member(all_10_6_11, all_0_3_3) = 0, yields:
% 12.80/3.50 | (151) all_38_2_23 = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_38_3_24, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_38_3_24, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.50 | (315) all_38_3_24 = 0
% 12.80/3.50 |
% 12.80/3.50 +-Applying beta-rule and splitting (313), into two cases.
% 12.80/3.50 |-Branch one:
% 12.80/3.50 | (316) ~ (all_38_2_23 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (151) can reduce 316 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (151) all_38_2_23 = 0
% 12.80/3.50 | (319) ~ (all_38_3_24 = 0)
% 12.80/3.50 |
% 12.80/3.50 | Equations (315) can reduce 319 to:
% 12.80/3.50 | (118) $false
% 12.80/3.50 |
% 12.80/3.50 |-The branch is then unsatisfiable
% 12.80/3.50 |-Branch two:
% 12.80/3.50 | (321) all_10_4_9 = 0 & all_10_5_10 = 0 & all_10_6_11 = 0 & ~ (all_10_3_8 = 0) & apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8 & apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0 & member(all_10_7_12, all_0_3_3) = 0 & member(all_10_8_13, all_0_3_3) = 0
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (321) yields:
% 12.80/3.50 | (322) all_10_6_11 = 0
% 12.80/3.50 | (125) all_10_4_9 = 0
% 12.80/3.50 | (324) apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8
% 12.80/3.50 | (127) all_10_5_10 = 0
% 12.80/3.50 | (129) apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0
% 12.80/3.50 | (327) ~ (all_10_3_8 = 0)
% 12.80/3.50 | (132) member(all_10_8_13, all_0_3_3) = 0
% 12.80/3.50 | (133) member(all_10_7_12, all_0_3_3) = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (106) with all_10_7_12, all_10_8_13 and discharging atoms apply(all_0_1_1, all_10_8_13, all_10_7_12) = 0, yields:
% 12.80/3.50 | (137) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, all_10_7_12, v0) = 0 & apply(all_0_4_4, all_10_8_13, v0) = 0 & member(v0, all_0_2_2) = 0) | (member(all_10_7_12, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (23) with all_10_7_12, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.50 | (138) ? [v0] : (apply(all_0_4_4, all_10_7_12, v0) = 0 & member(v0, all_0_2_2) = 0)
% 12.80/3.50 |
% 12.80/3.50 | Instantiating (138) with all_33_0_65 yields:
% 12.80/3.50 | (332) apply(all_0_4_4, all_10_7_12, all_33_0_65) = 0 & member(all_33_0_65, all_0_2_2) = 0
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (332) yields:
% 12.80/3.50 | (333) apply(all_0_4_4, all_10_7_12, all_33_0_65) = 0
% 12.80/3.50 | (334) member(all_33_0_65, all_0_2_2) = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating (137) with all_35_0_66, all_35_1_67, all_35_2_68, all_35_3_69 yields:
% 12.80/3.50 | (335) (all_35_0_66 = 0 & all_35_1_67 = 0 & all_35_2_68 = 0 & apply(all_0_4_4, all_10_7_12, all_35_3_69) = 0 & apply(all_0_4_4, all_10_8_13, all_35_3_69) = 0 & member(all_35_3_69, all_0_2_2) = 0) | (member(all_10_7_12, all_0_3_3) = all_35_2_68 & member(all_10_8_13, all_0_3_3) = all_35_3_69 & ( ~ (all_35_2_68 = 0) | ~ (all_35_3_69 = 0)))
% 12.80/3.50 |
% 12.80/3.50 +-Applying beta-rule and splitting (335), into two cases.
% 12.80/3.50 |-Branch one:
% 12.80/3.50 | (336) all_35_0_66 = 0 & all_35_1_67 = 0 & all_35_2_68 = 0 & apply(all_0_4_4, all_10_7_12, all_35_3_69) = 0 & apply(all_0_4_4, all_10_8_13, all_35_3_69) = 0 & member(all_35_3_69, all_0_2_2) = 0
% 12.80/3.50 |
% 12.80/3.50 | Applying alpha-rule on (336) yields:
% 12.80/3.50 | (337) apply(all_0_4_4, all_10_7_12, all_35_3_69) = 0
% 12.80/3.50 | (338) all_35_2_68 = 0
% 12.80/3.50 | (339) apply(all_0_4_4, all_10_8_13, all_35_3_69) = 0
% 12.80/3.50 | (340) all_35_1_67 = 0
% 12.80/3.50 | (341) member(all_35_3_69, all_0_2_2) = 0
% 12.80/3.50 | (342) all_35_0_66 = 0
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (55) with all_35_3_69, all_10_3_8, all_10_8_13, all_10_7_12 and discharging atoms apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8, apply(all_0_4_4, all_10_7_12, all_35_3_69) = 0, yields:
% 12.80/3.50 | (343) all_10_3_8 = 0 | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_35_3_69) = v1 & member(all_35_3_69, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_12, all_0_3_3) = v0 & member(all_10_8_13, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.50 |
% 12.80/3.50 | Instantiating formula (29) with all_35_3_69, all_33_0_65, all_10_7_12, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, apply(all_0_4_4, all_10_7_12, all_35_3_69) = 0, apply(all_0_4_4, all_10_7_12, all_33_0_65) = 0, yields:
% 12.80/3.50 | (344) all_35_3_69 = all_33_0_65 | ? [v0] : ? [v1] : ? [v2] : (member(all_35_3_69, all_0_2_2) = v2 & member(all_33_0_65, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.50 |
% 12.80/3.51 | Instantiating formula (55) with all_33_0_65, all_10_3_8, all_10_8_13, all_10_7_12 and discharging atoms apply(all_0_1_1, all_10_7_12, all_10_8_13) = all_10_3_8, apply(all_0_4_4, all_10_7_12, all_33_0_65) = 0, yields:
% 12.80/3.51 | (345) all_10_3_8 = 0 | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_33_0_65) = v1 & member(all_33_0_65, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_12, all_0_3_3) = v0 & member(all_10_8_13, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (343), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (130) all_10_3_8 = 0
% 12.80/3.51 |
% 12.80/3.51 | Equations (130) can reduce 327 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (327) ~ (all_10_3_8 = 0)
% 12.80/3.51 | (349) ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_35_3_69) = v1 & member(all_35_3_69, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_12, all_0_3_3) = v0 & member(all_10_8_13, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (345), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (130) all_10_3_8 = 0
% 12.80/3.51 |
% 12.80/3.51 | Equations (130) can reduce 327 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (327) ~ (all_10_3_8 = 0)
% 12.80/3.51 | (353) ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_33_0_65) = v1 & member(all_33_0_65, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_12, all_0_3_3) = v0 & member(all_10_8_13, all_0_3_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.51 |
% 12.80/3.51 | Instantiating (353) with all_63_0_72, all_63_1_73 yields:
% 12.80/3.51 | (354) (apply(all_0_4_4, all_10_8_13, all_33_0_65) = all_63_0_72 & member(all_33_0_65, all_0_2_2) = all_63_1_73 & ( ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0))) | (member(all_10_7_12, all_0_3_3) = all_63_1_73 & member(all_10_8_13, all_0_3_3) = all_63_0_72 & ( ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0)))
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (344), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (355) all_35_3_69 = all_33_0_65
% 12.80/3.51 |
% 12.80/3.51 | From (355) and (339) follows:
% 12.80/3.51 | (356) apply(all_0_4_4, all_10_8_13, all_33_0_65) = 0
% 12.80/3.51 |
% 12.80/3.51 | From (355) and (341) follows:
% 12.80/3.51 | (334) member(all_33_0_65, all_0_2_2) = 0
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (354), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (358) apply(all_0_4_4, all_10_8_13, all_33_0_65) = all_63_0_72 & member(all_33_0_65, all_0_2_2) = all_63_1_73 & ( ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0))
% 12.80/3.51 |
% 12.80/3.51 | Applying alpha-rule on (358) yields:
% 12.80/3.51 | (359) apply(all_0_4_4, all_10_8_13, all_33_0_65) = all_63_0_72
% 12.80/3.51 | (360) member(all_33_0_65, all_0_2_2) = all_63_1_73
% 12.80/3.51 | (361) ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (67) with all_0_4_4, all_10_8_13, all_33_0_65, all_63_0_72, 0 and discharging atoms apply(all_0_4_4, all_10_8_13, all_33_0_65) = all_63_0_72, apply(all_0_4_4, all_10_8_13, all_33_0_65) = 0, yields:
% 12.80/3.51 | (362) all_63_0_72 = 0
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_33_0_65, all_0_2_2, all_63_1_73, 0 and discharging atoms member(all_33_0_65, all_0_2_2) = all_63_1_73, member(all_33_0_65, all_0_2_2) = 0, yields:
% 12.80/3.51 | (363) all_63_1_73 = 0
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (361), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (364) ~ (all_63_0_72 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (362) can reduce 364 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (362) all_63_0_72 = 0
% 12.80/3.51 | (367) ~ (all_63_1_73 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (363) can reduce 367 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (369) member(all_10_7_12, all_0_3_3) = all_63_1_73 & member(all_10_8_13, all_0_3_3) = all_63_0_72 & ( ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0))
% 12.80/3.51 |
% 12.80/3.51 | Applying alpha-rule on (369) yields:
% 12.80/3.51 | (370) member(all_10_7_12, all_0_3_3) = all_63_1_73
% 12.80/3.51 | (371) member(all_10_8_13, all_0_3_3) = all_63_0_72
% 12.80/3.51 | (361) ~ (all_63_0_72 = 0) | ~ (all_63_1_73 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_63_1_73, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_63_1_73, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.51 | (363) all_63_1_73 = 0
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_63_0_72, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_63_0_72, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.51 | (362) all_63_0_72 = 0
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (361), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (364) ~ (all_63_0_72 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (362) can reduce 364 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (362) all_63_0_72 = 0
% 12.80/3.51 | (367) ~ (all_63_1_73 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (363) can reduce 367 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (380) ~ (all_35_3_69 = all_33_0_65)
% 12.80/3.51 | (381) ? [v0] : ? [v1] : ? [v2] : (member(all_35_3_69, all_0_2_2) = v2 & member(all_33_0_65, all_0_2_2) = v1 & member(all_10_7_12, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 12.80/3.51 |
% 12.80/3.51 | Instantiating (381) with all_68_0_74, all_68_1_75, all_68_2_76 yields:
% 12.80/3.51 | (382) member(all_35_3_69, all_0_2_2) = all_68_0_74 & member(all_33_0_65, all_0_2_2) = all_68_1_75 & member(all_10_7_12, all_0_3_3) = all_68_2_76 & ( ~ (all_68_0_74 = 0) | ~ (all_68_1_75 = 0) | ~ (all_68_2_76 = 0))
% 12.80/3.51 |
% 12.80/3.51 | Applying alpha-rule on (382) yields:
% 12.80/3.51 | (383) member(all_35_3_69, all_0_2_2) = all_68_0_74
% 12.80/3.51 | (384) member(all_33_0_65, all_0_2_2) = all_68_1_75
% 12.80/3.51 | (385) member(all_10_7_12, all_0_3_3) = all_68_2_76
% 12.80/3.51 | (386) ~ (all_68_0_74 = 0) | ~ (all_68_1_75 = 0) | ~ (all_68_2_76 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_35_3_69, all_0_2_2, all_68_0_74, 0 and discharging atoms member(all_35_3_69, all_0_2_2) = all_68_0_74, member(all_35_3_69, all_0_2_2) = 0, yields:
% 12.80/3.51 | (387) all_68_0_74 = 0
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_33_0_65, all_0_2_2, all_68_1_75, 0 and discharging atoms member(all_33_0_65, all_0_2_2) = all_68_1_75, member(all_33_0_65, all_0_2_2) = 0, yields:
% 12.80/3.51 | (388) all_68_1_75 = 0
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_68_2_76, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_68_2_76, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.51 | (389) all_68_2_76 = 0
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (386), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (390) ~ (all_68_0_74 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (387) can reduce 390 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (387) all_68_0_74 = 0
% 12.80/3.51 | (393) ~ (all_68_1_75 = 0) | ~ (all_68_2_76 = 0)
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (393), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (394) ~ (all_68_1_75 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (388) can reduce 394 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (388) all_68_1_75 = 0
% 12.80/3.51 | (397) ~ (all_68_2_76 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Equations (389) can reduce 397 to:
% 12.80/3.51 | (118) $false
% 12.80/3.51 |
% 12.80/3.51 |-The branch is then unsatisfiable
% 12.80/3.51 |-Branch two:
% 12.80/3.51 | (399) member(all_10_7_12, all_0_3_3) = all_35_2_68 & member(all_10_8_13, all_0_3_3) = all_35_3_69 & ( ~ (all_35_2_68 = 0) | ~ (all_35_3_69 = 0))
% 12.80/3.51 |
% 12.80/3.51 | Applying alpha-rule on (399) yields:
% 12.80/3.51 | (400) member(all_10_7_12, all_0_3_3) = all_35_2_68
% 12.80/3.51 | (401) member(all_10_8_13, all_0_3_3) = all_35_3_69
% 12.80/3.51 | (402) ~ (all_35_2_68 = 0) | ~ (all_35_3_69 = 0)
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_10_7_12, all_0_3_3, all_35_2_68, 0 and discharging atoms member(all_10_7_12, all_0_3_3) = all_35_2_68, member(all_10_7_12, all_0_3_3) = 0, yields:
% 12.80/3.51 | (338) all_35_2_68 = 0
% 12.80/3.51 |
% 12.80/3.51 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_35_3_69, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_35_3_69, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.51 | (404) all_35_3_69 = 0
% 12.80/3.51 |
% 12.80/3.51 +-Applying beta-rule and splitting (402), into two cases.
% 12.80/3.51 |-Branch one:
% 12.80/3.51 | (405) ~ (all_35_2_68 = 0)
% 12.80/3.51 |
% 12.80/3.52 | Equations (338) can reduce 405 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (338) all_35_2_68 = 0
% 12.80/3.52 | (408) ~ (all_35_3_69 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Equations (404) can reduce 408 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (410) all_10_7_12 = 0 & ~ (all_10_6_11 = 0) & apply(all_0_1_1, all_10_8_13, all_10_8_13) = all_10_6_11 & member(all_10_8_13, all_0_3_3) = 0
% 12.80/3.52 |
% 12.80/3.52 | Applying alpha-rule on (410) yields:
% 12.80/3.52 | (411) all_10_7_12 = 0
% 12.80/3.52 | (412) ~ (all_10_6_11 = 0)
% 12.80/3.52 | (413) apply(all_0_1_1, all_10_8_13, all_10_8_13) = all_10_6_11
% 12.80/3.52 | (132) member(all_10_8_13, all_0_3_3) = 0
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (23) with all_10_8_13, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms maps(all_0_4_4, all_0_3_3, all_0_2_2) = 0, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.52 | (139) ? [v0] : (apply(all_0_4_4, all_10_8_13, v0) = 0 & member(v0, all_0_2_2) = 0)
% 12.80/3.52 |
% 12.80/3.52 | Instantiating (139) with all_31_0_77 yields:
% 12.80/3.52 | (416) apply(all_0_4_4, all_10_8_13, all_31_0_77) = 0 & member(all_31_0_77, all_0_2_2) = 0
% 12.80/3.52 |
% 12.80/3.52 | Applying alpha-rule on (416) yields:
% 12.80/3.52 | (417) apply(all_0_4_4, all_10_8_13, all_31_0_77) = 0
% 12.80/3.52 | (418) member(all_31_0_77, all_0_2_2) = 0
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (55) with all_31_0_77, all_10_6_11, all_10_8_13, all_10_8_13 and discharging atoms apply(all_0_1_1, all_10_8_13, all_10_8_13) = all_10_6_11, apply(all_0_4_4, all_10_8_13, all_31_0_77) = 0, yields:
% 12.80/3.52 | (419) all_10_6_11 = 0 | ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_31_0_77) = v1 & member(all_31_0_77, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_13, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.52 |
% 12.80/3.52 +-Applying beta-rule and splitting (419), into two cases.
% 12.80/3.52 |-Branch one:
% 12.80/3.52 | (322) all_10_6_11 = 0
% 12.80/3.52 |
% 12.80/3.52 | Equations (322) can reduce 412 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (412) ~ (all_10_6_11 = 0)
% 12.80/3.52 | (423) ? [v0] : ? [v1] : ((apply(all_0_4_4, all_10_8_13, all_31_0_77) = v1 & member(all_31_0_77, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_13, all_0_3_3) = v1 & member(all_10_8_13, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.80/3.52 |
% 12.80/3.52 | Instantiating (423) with all_52_0_78, all_52_1_79 yields:
% 12.80/3.52 | (424) (apply(all_0_4_4, all_10_8_13, all_31_0_77) = all_52_0_78 & member(all_31_0_77, all_0_2_2) = all_52_1_79 & ( ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0))) | (member(all_10_8_13, all_0_3_3) = all_52_0_78 & member(all_10_8_13, all_0_3_3) = all_52_1_79 & ( ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0)))
% 12.80/3.52 |
% 12.80/3.52 +-Applying beta-rule and splitting (424), into two cases.
% 12.80/3.52 |-Branch one:
% 12.80/3.52 | (425) apply(all_0_4_4, all_10_8_13, all_31_0_77) = all_52_0_78 & member(all_31_0_77, all_0_2_2) = all_52_1_79 & ( ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0))
% 12.80/3.52 |
% 12.80/3.52 | Applying alpha-rule on (425) yields:
% 12.80/3.52 | (426) apply(all_0_4_4, all_10_8_13, all_31_0_77) = all_52_0_78
% 12.80/3.52 | (427) member(all_31_0_77, all_0_2_2) = all_52_1_79
% 12.80/3.52 | (428) ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (67) with all_0_4_4, all_10_8_13, all_31_0_77, all_52_0_78, 0 and discharging atoms apply(all_0_4_4, all_10_8_13, all_31_0_77) = all_52_0_78, apply(all_0_4_4, all_10_8_13, all_31_0_77) = 0, yields:
% 12.80/3.52 | (429) all_52_0_78 = 0
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (68) with all_31_0_77, all_0_2_2, all_52_1_79, 0 and discharging atoms member(all_31_0_77, all_0_2_2) = all_52_1_79, member(all_31_0_77, all_0_2_2) = 0, yields:
% 12.80/3.52 | (430) all_52_1_79 = 0
% 12.80/3.52 |
% 12.80/3.52 +-Applying beta-rule and splitting (428), into two cases.
% 12.80/3.52 |-Branch one:
% 12.80/3.52 | (431) ~ (all_52_0_78 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Equations (429) can reduce 431 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (429) all_52_0_78 = 0
% 12.80/3.52 | (434) ~ (all_52_1_79 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Equations (430) can reduce 434 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (436) member(all_10_8_13, all_0_3_3) = all_52_0_78 & member(all_10_8_13, all_0_3_3) = all_52_1_79 & ( ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0))
% 12.80/3.52 |
% 12.80/3.52 | Applying alpha-rule on (436) yields:
% 12.80/3.52 | (437) member(all_10_8_13, all_0_3_3) = all_52_0_78
% 12.80/3.52 | (438) member(all_10_8_13, all_0_3_3) = all_52_1_79
% 12.80/3.52 | (428) ~ (all_52_0_78 = 0) | ~ (all_52_1_79 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_52_0_78, 0 and discharging atoms member(all_10_8_13, all_0_3_3) = all_52_0_78, member(all_10_8_13, all_0_3_3) = 0, yields:
% 12.80/3.52 | (429) all_52_0_78 = 0
% 12.80/3.52 |
% 12.80/3.52 | Instantiating formula (68) with all_10_8_13, all_0_3_3, all_52_1_79, all_52_0_78 and discharging atoms member(all_10_8_13, all_0_3_3) = all_52_0_78, member(all_10_8_13, all_0_3_3) = all_52_1_79, yields:
% 12.80/3.52 | (441) all_52_0_78 = all_52_1_79
% 12.80/3.52 |
% 12.80/3.52 | Combining equations (429,441) yields a new equation:
% 12.80/3.52 | (430) all_52_1_79 = 0
% 12.80/3.52 |
% 12.80/3.52 | Combining equations (430,441) yields a new equation:
% 12.80/3.52 | (429) all_52_0_78 = 0
% 12.80/3.52 |
% 12.80/3.52 +-Applying beta-rule and splitting (428), into two cases.
% 12.80/3.52 |-Branch one:
% 12.80/3.52 | (431) ~ (all_52_0_78 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Equations (429) can reduce 431 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 |-Branch two:
% 12.80/3.52 | (429) all_52_0_78 = 0
% 12.80/3.52 | (434) ~ (all_52_1_79 = 0)
% 12.80/3.52 |
% 12.80/3.52 | Equations (430) can reduce 434 to:
% 12.80/3.52 | (118) $false
% 12.80/3.52 |
% 12.80/3.52 |-The branch is then unsatisfiable
% 12.80/3.52 % SZS output end Proof for theBenchmark
% 12.80/3.52
% 12.80/3.52 2916ms
%------------------------------------------------------------------------------