TSTP Solution File: SET708+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET708+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:21:32 EDT 2022
% Result : Theorem 6.33s 2.00s
% Output : Proof 9.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET708+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 08:15:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/0.98 Prover 0: Preprocessing ...
% 3.40/1.32 Prover 0: Warning: ignoring some quantifiers
% 3.40/1.36 Prover 0: Constructing countermodel ...
% 4.22/1.60 Prover 0: gave up
% 4.22/1.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.62/1.66 Prover 1: Preprocessing ...
% 5.53/1.90 Prover 1: Constructing countermodel ...
% 6.33/2.00 Prover 1: proved (400ms)
% 6.33/2.00
% 6.33/2.00 No countermodel exists, formula is valid
% 6.33/2.00 % SZS status Theorem for theBenchmark
% 6.33/2.00
% 6.33/2.00 Generating proof ... found it (size 98)
% 8.62/2.55
% 8.62/2.55 % SZS output start Proof for theBenchmark
% 8.62/2.55 Assumed formulas after preprocessing and simplification:
% 8.62/2.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & equal_maps(v2, v3, v4, v6) = v7 & compose_predicate(v3, v1, v0, v4, v5, v6) = 0 & compose_predicate(v2, v1, v0, v4, v5, v6) = 0 & maps(v1, v5, v6) = 0 & maps(v0, v4, v5) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = v16) | ~ (apply(v8, v17, v14) = 0) | ? [v18] : ? [v19] : ((apply(v9, v13, v17) = v19 & member(v17, v11) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))) | (member(v14, v12) = v19 & member(v13, v10) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v9, v17, v15) = 0) | ~ (apply(v8, v14, v15) = v16) | ? [v18] : ? [v19] : ((apply(v10, v14, v17) = v19 & member(v17, v12) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))) | (member(v15, v13) = v19 & member(v14, v11) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (apply(v12, v14, v16) = v22 & apply(v10, v13, v15) = v21 & member(v16, v11) = v20 & member(v15, v9) = v19 & member(v14, v11) = v18 & member(v13, v9) = v17 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | (( ~ (v22 = 0) | v21 = 0) & ( ~ (v21 = 0) | v22 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (decreasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (apply(v12, v16, v14) = v22 & apply(v10, v13, v15) = v21 & member(v16, v11) = v20 & member(v15, v9) = v19 & member(v14, v11) = v18 & member(v13, v9) = v17 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v22 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (increasing(v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v15, v16) = 0) | ~ (apply(v8, v13, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (apply(v12, v14, v16) = v22 & apply(v10, v13, v15) = v21 & member(v16, v11) = v20 & member(v15, v9) = v19 & member(v14, v11) = v18 & member(v13, v9) = v17 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v22 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v9 = v8 | ~ (compose_predicate(v15, v14, v13, v12, v11, v10) = v9) | ~ (compose_predicate(v15, v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (compose_function(v8, v9, v10, v11, v12) = v15) | ~ (apply(v15, v13, v14) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v9, v13, v16) = 0 & apply(v8, v16, v14) = 0 & member(v16, v11) = 0) | (member(v14, v12) = v17 & member(v13, v10) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = 0) | ~ (apply(v8, v14, v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v10, v14, v16) = 0 & apply(v9, v16, v15) = 0 & member(v16, v12) = 0) | (member(v15, v13) = v17 & member(v14, v11) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (equal_maps(v8, v9, v10, v11) = 0) | ~ (apply(v9, v12, v14) = 0) | ~ (apply(v8, v12, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : (member(v14, v11) = v17 & member(v13, v11) = v16 & member(v12, v10) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (compose_predicate(v8, v9, v10, v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v8, v15, v16) = v17 & member(v16, v13) = 0 & member(v15, v11) = 0 & ( ~ (v17 = 0) | ! [v22] : ( ~ (apply(v9, v22, v16) = 0) | ? [v23] : ? [v24] : (apply(v10, v15, v22) = v24 & member(v22, v12) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0))))) & (v17 = 0 | (v21 = 0 & v20 = 0 & v19 = 0 & apply(v10, v15, v18) = 0 & apply(v9, v18, v16) = 0 & member(v18, v12) = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (inverse_image3(v8, v9, v10) = v12) | ~ (apply(v8, v11, v14) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (image3(v8, v9, v10) = v12) | ~ (apply(v8, v14, v11) = 0) | ~ (member(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v11, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (isomorphism(v14, v13, v12, v11, v10) = v9) | ~ (isomorphism(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (decreasing(v14, v13, v12, v11, v10) = v9) | ~ (decreasing(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (increasing(v14, v13, v12, v11, v10) = v9) | ~ (increasing(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v9 = v8 | ~ (compose_function(v14, v13, v12, v11, v10) = v9) | ~ (compose_function(v14, v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_function(v8, v9, v10) = v13) | ~ (apply(v13, v12, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : (apply(v8, v11, v12) = v17 & member(v12, v10) = v16 & member(v11, v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | (( ~ (v17 = 0) | v14 = 0) & ( ~ (v14 = 0) | v17 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_predicate(v8, v9, v10, v11) = 0) | ~ (apply(v8, v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : (apply(v9, v12, v13) = v17 & member(v13, v11) = v16 & member(v12, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | (( ~ (v17 = 0) | v14 = 0) & ( ~ (v14 = 0) | v17 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (maps(v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v8, v11, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : (member(v13, v10) = v16 & member(v12, v10) = v15 & member(v11, v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (isomorphism(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & apply(v12, v15, v17) = v25 & apply(v10, v14, v16) = v24 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0 & ( ~ (v25 = 0) | ~ (v24 = 0)) & (v25 = 0 | v24 = 0)) | (one_to_one(v8, v9, v11) = v15 & maps(v8, v9, v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (decreasing(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & apply(v12, v17, v15) = v18 & apply(v10, v14, v16) = 0 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (increasing(v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & apply(v12, v15, v17) = v18 & apply(v10, v14, v16) = 0 & apply(v8, v16, v17) = 0 & apply(v8, v14, v15) = 0 & member(v17, v11) = 0 & member(v16, v9) = 0 & member(v15, v11) = 0 & member(v14, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (injective(v8, v9, v10) = 0) | ~ (apply(v8, v12, v13) = 0) | ~ (apply(v8, v11, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (member(v13, v10) = v16 & member(v12, v9) = v15 & member(v11, v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image2(v8, v9) = v11) | ~ (apply(v8, v10, v13) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image2(v8, v9) = v11) | ~ (apply(v8, v13, v10) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (inverse_predicate(v13, v12, v11, v10) = v9) | ~ (inverse_predicate(v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (equal_maps(v13, v12, v11, v10) = v9) | ~ (equal_maps(v13, v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (inverse_predicate(v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (apply(v9, v13, v14) = v15 & apply(v8, v14, v13) = v16 & member(v14, v11) = 0 & member(v13, v10) = 0 & ( ~ (v16 = 0) | ~ (v15 = 0)) & (v16 = 0 | v15 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (equal_maps(v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v14) & apply(v9, v13, v15) = 0 & apply(v8, v13, v14) = 0 & member(v15, v11) = 0 & member(v14, v11) = 0 & member(v13, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (inverse_image3(v12, v11, v10) = v9) | ~ (inverse_image3(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (image3(v12, v11, v10) = v9) | ~ (image3(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (inverse_function(v12, v11, v10) = v9) | ~ (inverse_function(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (one_to_one(v12, v11, v10) = v9) | ~ (one_to_one(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (surjective(v12, v11, v10) = v9) | ~ (surjective(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (injective(v12, v11, v10) = v9) | ~ (injective(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (maps(v12, v11, v10) = v9) | ~ (maps(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (apply(v12, v11, v10) = v9) | ~ (apply(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (isomorphism(v8, v9, v10, v11, v12) = 0) | (one_to_one(v8, v9, v11) = 0 & maps(v8, v9, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | member(v11, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v8, v11, v13) = 0 & member(v13, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | member(v11, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image3(v8, v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : (apply(v8, v13, v11) = 0 & member(v13, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (surjective(v8, v9, v10) = v11) | ? [v12] : (member(v12, v10) = 0 & ! [v13] : ( ~ (apply(v8, v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & member(v13, v9) = v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (injective(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v13 = v12) & apply(v8, v13, v14) = 0 & apply(v8, v12, v14) = 0 & member(v14, v10) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (identity(v8, v9) = 0) | ~ (apply(v8, v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (maps(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v8, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0) | (v13 = 0 & member(v12, v9) = 0 & ! [v20] : ( ~ (apply(v8, v12, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & member(v20, v10) = v21))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (inverse_image2(v11, v10) = v9) | ~ (inverse_image2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (image2(v11, v10) = v9) | ~ (image2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (identity(v11, v10) = v9) | ~ (identity(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image2(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v8, v10, v12) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image2(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v8, v12, v10) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (surjective(v8, v9, v10) = v11) | ? [v12] : ? [v13] : (one_to_one(v8, v9, v10) = v12 & injective(v8, v9, v10) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (surjective(v8, v9, v10) = 0) | ~ (member(v11, v10) = 0) | ? [v12] : (apply(v8, v12, v11) = 0 & member(v12, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (maps(v8, v9, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v12] : (apply(v8, v11, v12) = 0 & member(v12, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (identity(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & apply(v8, v11, v11) = v12 & member(v11, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v8, v9, v10) = 0) | ? [v11] : ? [v12] : (one_to_one(v8, v9, v10) = v12 & injective(v8, v9, v10) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0))
% 9.11/2.62 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 9.11/2.62 | (1) ~ (all_0_0_0 = 0) & equal_maps(all_0_5_5, all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0 & compose_predicate(all_0_4_4, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0 & compose_predicate(all_0_5_5, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0 & maps(all_0_6_6, all_0_2_2, all_0_1_1) = 0 & maps(all_0_7_7, 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 | ~ (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 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (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] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ? [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 | ~ (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] : ( ~ (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] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 9.11/2.65 |
% 9.11/2.65 | Applying alpha-rule on (1) yields:
% 9.11/2.65 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 9.11/2.65 | (3) ! [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))
% 9.11/2.65 | (4) ! [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))
% 9.11/2.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 9.11/2.65 | (6) ! [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)))
% 9.11/2.65 | (7) ! [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))
% 9.11/2.65 | (8) ! [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)))))
% 9.11/2.65 | (9) compose_predicate(all_0_4_4, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0
% 9.11/2.65 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 9.11/2.65 | (11) ! [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))
% 9.11/2.66 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 9.11/2.66 | (13) ! [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))))
% 9.11/2.66 | (14) ! [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)))))
% 9.11/2.66 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 9.11/2.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 9.11/2.66 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 9.11/2.66 | (18) equal_maps(all_0_5_5, all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0
% 9.11/2.66 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 9.11/2.66 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 9.11/2.66 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 9.11/2.66 | (22) ! [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)))))
% 9.11/2.66 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 9.11/2.66 | (24) ! [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))))
% 9.11/2.66 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 9.11/2.66 | (26) ~ (all_0_0_0 = 0)
% 9.11/2.66 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 9.11/2.66 | (28) ! [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))))
% 9.11/2.66 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 9.11/2.66 | (30) ! [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))))
% 9.11/2.66 | (31) ! [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)))))
% 9.11/2.66 | (32) ! [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))
% 9.11/2.66 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.11/2.66 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 9.11/2.66 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 9.11/2.66 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.11/2.66 | (37) ! [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)))))
% 9.11/2.66 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 9.11/2.66 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 9.11/2.67 | (40) maps(all_0_7_7, all_0_3_3, all_0_2_2) = 0
% 9.11/2.67 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 9.11/2.67 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 9.11/2.67 | (43) ! [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))
% 9.11/2.67 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 9.11/2.67 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 9.11/2.67 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 9.11/2.67 | (47) ! [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)))
% 9.11/2.67 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 9.11/2.67 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 9.11/2.67 | (50) ! [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))))
% 9.11/2.67 | (51) ! [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)))
% 9.11/2.67 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 9.11/2.67 | (53) ! [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)))))
% 9.11/2.67 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 9.11/2.67 | (55) ! [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)))
% 9.11/2.67 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 9.11/2.67 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 9.11/2.67 | (58) maps(all_0_6_6, all_0_2_2, all_0_1_1) = 0
% 9.11/2.67 | (59) ! [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))))
% 9.11/2.67 | (60) ! [v0] : ~ (member(v0, empty_set) = 0)
% 9.11/2.67 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 9.11/2.67 | (62) ! [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))
% 9.11/2.67 | (63) ! [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)))))
% 9.11/2.67 | (64) ! [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))
% 9.11/2.67 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 9.11/2.67 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 9.11/2.67 | (67) ! [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))
% 9.11/2.67 | (68) ! [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))
% 9.11/2.67 | (69) ! [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))))
% 9.11/2.67 | (70) ! [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)))
% 9.11/2.67 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 9.11/2.67 | (72) ! [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))
% 9.11/2.67 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 9.11/2.67 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 9.11/2.67 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 9.11/2.67 | (76) ! [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)))))
% 9.11/2.67 | (77) ! [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))
% 9.11/2.67 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 9.11/2.67 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 9.11/2.67 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.11/2.68 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 9.11/2.68 | (82) ! [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)))
% 9.11/2.68 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 9.11/2.68 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 9.11/2.68 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.11/2.68 | (86) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.11/2.68 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 9.11/2.68 | (88) compose_predicate(all_0_5_5, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0
% 9.11/2.68 | (89) ! [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)))
% 9.11/2.68 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 9.11/2.68 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 9.11/2.68 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 9.11/2.68 | (93) ! [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))
% 9.11/2.68 | (94) ! [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)))))
% 9.11/2.68 | (95) ! [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)))
% 9.11/2.68 | (96) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 9.11/2.68 |
% 9.11/2.68 | Instantiating formula (11) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms equal_maps(all_0_5_5, all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 9.11/2.68 | (97) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_4_4, v0, v2) = 0 & apply(all_0_5_5, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_3_3) = 0)
% 9.11/2.68 |
% 9.11/2.68 +-Applying beta-rule and splitting (97), into two cases.
% 9.11/2.68 |-Branch one:
% 9.11/2.68 | (98) all_0_0_0 = 0
% 9.11/2.68 |
% 9.11/2.68 | Equations (98) can reduce 26 to:
% 9.11/2.68 | (99) $false
% 9.11/2.68 |
% 9.11/2.68 |-The branch is then unsatisfiable
% 9.11/2.68 |-Branch two:
% 9.11/2.68 | (26) ~ (all_0_0_0 = 0)
% 9.11/2.68 | (101) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_4_4, v0, v2) = 0 & apply(all_0_5_5, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_3_3) = 0)
% 9.11/2.68 |
% 9.11/2.68 | Instantiating (101) with all_10_0_8, all_10_1_9, all_10_2_10 yields:
% 9.11/2.68 | (102) ~ (all_10_0_8 = all_10_1_9) & apply(all_0_4_4, all_10_2_10, all_10_0_8) = 0 & apply(all_0_5_5, all_10_2_10, all_10_1_9) = 0 & member(all_10_0_8, all_0_1_1) = 0 & member(all_10_1_9, all_0_1_1) = 0 & member(all_10_2_10, all_0_3_3) = 0
% 9.11/2.68 |
% 9.11/2.68 | Applying alpha-rule on (102) yields:
% 9.11/2.68 | (103) member(all_10_1_9, all_0_1_1) = 0
% 9.11/2.68 | (104) apply(all_0_4_4, all_10_2_10, all_10_0_8) = 0
% 9.11/2.68 | (105) apply(all_0_5_5, all_10_2_10, all_10_1_9) = 0
% 9.11/2.68 | (106) member(all_10_2_10, all_0_3_3) = 0
% 9.11/2.68 | (107) member(all_10_0_8, all_0_1_1) = 0
% 9.11/2.68 | (108) ~ (all_10_0_8 = all_10_1_9)
% 9.11/2.68 |
% 9.11/2.68 | Instantiating formula (8) with all_10_0_8, all_10_2_10, all_0_1_1, all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6, all_0_4_4 and discharging atoms compose_predicate(all_0_4_4, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0, apply(all_0_4_4, all_10_2_10, all_10_0_8) = 0, yields:
% 9.11/2.68 | (109) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_6_6, v0, all_10_0_8) = 0 & apply(all_0_7_7, all_10_2_10, v0) = 0 & member(v0, all_0_2_2) = 0) | (member(all_10_0_8, all_0_1_1) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 9.11/2.68 |
% 9.11/2.68 | Instantiating formula (8) with all_10_1_9, all_10_2_10, all_0_1_1, all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6, all_0_5_5 and discharging atoms compose_predicate(all_0_5_5, all_0_6_6, all_0_7_7, all_0_3_3, all_0_2_2, all_0_1_1) = 0, apply(all_0_5_5, all_10_2_10, all_10_1_9) = 0, yields:
% 9.11/2.68 | (110) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_6_6, v0, all_10_1_9) = 0 & apply(all_0_7_7, all_10_2_10, v0) = 0 & member(v0, all_0_2_2) = 0) | (member(all_10_1_9, all_0_1_1) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 9.11/2.68 |
% 9.11/2.68 | Instantiating formula (78) with all_10_2_10, all_0_2_2, all_0_3_3, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_3_3, all_0_2_2) = 0, member(all_10_2_10, all_0_3_3) = 0, yields:
% 9.11/2.68 | (111) ? [v0] : (apply(all_0_7_7, all_10_2_10, v0) = 0 & member(v0, all_0_2_2) = 0)
% 9.11/2.68 |
% 9.11/2.68 | Instantiating (111) with all_25_0_11 yields:
% 9.11/2.68 | (112) apply(all_0_7_7, all_10_2_10, all_25_0_11) = 0 & member(all_25_0_11, all_0_2_2) = 0
% 9.11/2.68 |
% 9.11/2.68 | Applying alpha-rule on (112) yields:
% 9.11/2.68 | (113) apply(all_0_7_7, all_10_2_10, all_25_0_11) = 0
% 9.11/2.69 | (114) member(all_25_0_11, all_0_2_2) = 0
% 9.11/2.69 |
% 9.11/2.69 | Instantiating (110) with all_27_0_12, all_27_1_13, all_27_2_14, all_27_3_15 yields:
% 9.11/2.69 | (115) (all_27_0_12 = 0 & all_27_1_13 = 0 & all_27_2_14 = 0 & apply(all_0_6_6, all_27_3_15, all_10_1_9) = 0 & apply(all_0_7_7, all_10_2_10, all_27_3_15) = 0 & member(all_27_3_15, all_0_2_2) = 0) | (member(all_10_1_9, all_0_1_1) = all_27_2_14 & member(all_10_2_10, all_0_3_3) = all_27_3_15 & ( ~ (all_27_2_14 = 0) | ~ (all_27_3_15 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | Instantiating (109) with all_28_0_16, all_28_1_17, all_28_2_18, all_28_3_19 yields:
% 9.11/2.69 | (116) (all_28_0_16 = 0 & all_28_1_17 = 0 & all_28_2_18 = 0 & apply(all_0_6_6, all_28_3_19, all_10_0_8) = 0 & apply(all_0_7_7, all_10_2_10, all_28_3_19) = 0 & member(all_28_3_19, all_0_2_2) = 0) | (member(all_10_0_8, all_0_1_1) = all_28_2_18 & member(all_10_2_10, all_0_3_3) = all_28_3_19 & ( ~ (all_28_2_18 = 0) | ~ (all_28_3_19 = 0)))
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (115), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (117) all_27_0_12 = 0 & all_27_1_13 = 0 & all_27_2_14 = 0 & apply(all_0_6_6, all_27_3_15, all_10_1_9) = 0 & apply(all_0_7_7, all_10_2_10, all_27_3_15) = 0 & member(all_27_3_15, all_0_2_2) = 0
% 9.11/2.69 |
% 9.11/2.69 | Applying alpha-rule on (117) yields:
% 9.11/2.69 | (118) all_27_1_13 = 0
% 9.11/2.69 | (119) apply(all_0_7_7, all_10_2_10, all_27_3_15) = 0
% 9.11/2.69 | (120) member(all_27_3_15, all_0_2_2) = 0
% 9.11/2.69 | (121) all_27_0_12 = 0
% 9.11/2.69 | (122) all_27_2_14 = 0
% 9.11/2.69 | (123) apply(all_0_6_6, all_27_3_15, all_10_1_9) = 0
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (116), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (124) all_28_0_16 = 0 & all_28_1_17 = 0 & all_28_2_18 = 0 & apply(all_0_6_6, all_28_3_19, all_10_0_8) = 0 & apply(all_0_7_7, all_10_2_10, all_28_3_19) = 0 & member(all_28_3_19, all_0_2_2) = 0
% 9.11/2.69 |
% 9.11/2.69 | Applying alpha-rule on (124) yields:
% 9.11/2.69 | (125) member(all_28_3_19, all_0_2_2) = 0
% 9.11/2.69 | (126) all_28_0_16 = 0
% 9.11/2.69 | (127) all_28_1_17 = 0
% 9.11/2.69 | (128) apply(all_0_7_7, all_10_2_10, all_28_3_19) = 0
% 9.11/2.69 | (129) all_28_2_18 = 0
% 9.11/2.69 | (130) apply(all_0_6_6, all_28_3_19, all_10_0_8) = 0
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (13) with all_10_1_9, all_10_0_8, all_27_3_15, all_0_1_1, all_0_2_2, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_2_2, all_0_1_1) = 0, apply(all_0_6_6, all_27_3_15, all_10_1_9) = 0, yields:
% 9.11/2.69 | (131) all_10_0_8 = all_10_1_9 | ~ (apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v0 & member(all_10_0_8, all_0_1_1) = v1 & member(all_10_1_9, all_0_1_1) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (13) with all_10_0_8, all_10_1_9, all_27_3_15, all_0_1_1, all_0_2_2, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_2_2, all_0_1_1) = 0, apply(all_0_6_6, all_27_3_15, all_10_1_9) = 0, yields:
% 9.11/2.69 | (132) all_10_0_8 = all_10_1_9 | ~ (apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v0 & member(all_10_0_8, all_0_1_1) = v2 & member(all_10_1_9, all_0_1_1) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (13) with all_28_3_19, all_27_3_15, all_10_2_10, all_0_2_2, all_0_3_3, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_3_3, all_0_2_2) = 0, apply(all_0_7_7, all_10_2_10, all_28_3_19) = 0, apply(all_0_7_7, all_10_2_10, all_27_3_15) = 0, yields:
% 9.11/2.69 | (133) all_28_3_19 = all_27_3_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_28_3_19, all_0_2_2) = v2 & member(all_27_3_15, all_0_2_2) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (13) with all_27_3_15, all_25_0_11, all_10_2_10, all_0_2_2, all_0_3_3, all_0_7_7 and discharging atoms maps(all_0_7_7, all_0_3_3, all_0_2_2) = 0, apply(all_0_7_7, all_10_2_10, all_27_3_15) = 0, apply(all_0_7_7, all_10_2_10, all_25_0_11) = 0, yields:
% 9.11/2.69 | (134) all_27_3_15 = all_25_0_11 | ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v2 & member(all_25_0_11, all_0_2_2) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (134), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (135) all_27_3_15 = all_25_0_11
% 9.11/2.69 |
% 9.11/2.69 | From (135) and (120) follows:
% 9.11/2.69 | (114) member(all_25_0_11, all_0_2_2) = 0
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (133), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (137) all_28_3_19 = all_27_3_15
% 9.11/2.69 |
% 9.11/2.69 | Combining equations (135,137) yields a new equation:
% 9.11/2.69 | (138) all_28_3_19 = all_25_0_11
% 9.11/2.69 |
% 9.11/2.69 | From (138) and (130) follows:
% 9.11/2.69 | (139) apply(all_0_6_6, all_25_0_11, all_10_0_8) = 0
% 9.11/2.69 |
% 9.11/2.69 | From (138) and (125) follows:
% 9.11/2.69 | (114) member(all_25_0_11, all_0_2_2) = 0
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (132), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (141) ~ (apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0)
% 9.11/2.69 |
% 9.11/2.69 | From (135) and (141) follows:
% 9.11/2.69 | (142) ~ (apply(all_0_6_6, all_25_0_11, all_10_0_8) = 0)
% 9.11/2.69 |
% 9.11/2.69 | Using (139) and (142) yields:
% 9.11/2.69 | (143) $false
% 9.11/2.69 |
% 9.11/2.69 |-The branch is then unsatisfiable
% 9.11/2.69 |-Branch two:
% 9.11/2.69 | (144) apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0
% 9.11/2.69 | (145) all_10_0_8 = all_10_1_9 | ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v0 & member(all_10_0_8, all_0_1_1) = v2 & member(all_10_1_9, all_0_1_1) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | From (135) and (144) follows:
% 9.11/2.69 | (139) apply(all_0_6_6, all_25_0_11, all_10_0_8) = 0
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (131), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (141) ~ (apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0)
% 9.11/2.69 |
% 9.11/2.69 | From (135) and (141) follows:
% 9.11/2.69 | (142) ~ (apply(all_0_6_6, all_25_0_11, all_10_0_8) = 0)
% 9.11/2.69 |
% 9.11/2.69 | Using (139) and (142) yields:
% 9.11/2.69 | (143) $false
% 9.11/2.69 |
% 9.11/2.69 |-The branch is then unsatisfiable
% 9.11/2.69 |-Branch two:
% 9.11/2.69 | (144) apply(all_0_6_6, all_27_3_15, all_10_0_8) = 0
% 9.11/2.69 | (151) all_10_0_8 = all_10_1_9 | ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v0 & member(all_10_0_8, all_0_1_1) = v1 & member(all_10_1_9, all_0_1_1) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 +-Applying beta-rule and splitting (151), into two cases.
% 9.11/2.69 |-Branch one:
% 9.11/2.69 | (152) all_10_0_8 = all_10_1_9
% 9.11/2.69 |
% 9.11/2.69 | Equations (152) can reduce 108 to:
% 9.11/2.69 | (99) $false
% 9.11/2.69 |
% 9.11/2.69 |-The branch is then unsatisfiable
% 9.11/2.69 |-Branch two:
% 9.11/2.69 | (108) ~ (all_10_0_8 = all_10_1_9)
% 9.11/2.69 | (155) ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v0 & member(all_10_0_8, all_0_1_1) = v1 & member(all_10_1_9, all_0_1_1) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.69 |
% 9.11/2.69 | Instantiating (155) with all_76_0_23, all_76_1_24, all_76_2_25 yields:
% 9.11/2.69 | (156) member(all_27_3_15, all_0_2_2) = all_76_2_25 & member(all_10_0_8, all_0_1_1) = all_76_1_24 & member(all_10_1_9, all_0_1_1) = all_76_0_23 & ( ~ (all_76_0_23 = 0) | ~ (all_76_1_24 = 0) | ~ (all_76_2_25 = 0))
% 9.11/2.69 |
% 9.11/2.69 | Applying alpha-rule on (156) yields:
% 9.11/2.69 | (157) member(all_27_3_15, all_0_2_2) = all_76_2_25
% 9.11/2.69 | (158) member(all_10_0_8, all_0_1_1) = all_76_1_24
% 9.11/2.69 | (159) member(all_10_1_9, all_0_1_1) = all_76_0_23
% 9.11/2.69 | (160) ~ (all_76_0_23 = 0) | ~ (all_76_1_24 = 0) | ~ (all_76_2_25 = 0)
% 9.11/2.69 |
% 9.11/2.69 | From (135) and (157) follows:
% 9.11/2.69 | (161) member(all_25_0_11, all_0_2_2) = all_76_2_25
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (12) with all_25_0_11, all_0_2_2, all_76_2_25, 0 and discharging atoms member(all_25_0_11, all_0_2_2) = all_76_2_25, member(all_25_0_11, all_0_2_2) = 0, yields:
% 9.11/2.69 | (162) all_76_2_25 = 0
% 9.11/2.69 |
% 9.11/2.69 | Instantiating formula (12) with all_10_0_8, all_0_1_1, all_76_1_24, 0 and discharging atoms member(all_10_0_8, all_0_1_1) = all_76_1_24, member(all_10_0_8, all_0_1_1) = 0, yields:
% 9.11/2.70 | (163) all_76_1_24 = 0
% 9.11/2.70 |
% 9.11/2.70 | Instantiating formula (12) with all_10_1_9, all_0_1_1, all_76_0_23, 0 and discharging atoms member(all_10_1_9, all_0_1_1) = all_76_0_23, member(all_10_1_9, all_0_1_1) = 0, yields:
% 9.11/2.70 | (164) all_76_0_23 = 0
% 9.11/2.70 |
% 9.11/2.70 +-Applying beta-rule and splitting (160), into two cases.
% 9.11/2.70 |-Branch one:
% 9.11/2.70 | (165) ~ (all_76_0_23 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (164) can reduce 165 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (164) all_76_0_23 = 0
% 9.11/2.70 | (168) ~ (all_76_1_24 = 0) | ~ (all_76_2_25 = 0)
% 9.11/2.70 |
% 9.11/2.70 +-Applying beta-rule and splitting (168), into two cases.
% 9.11/2.70 |-Branch one:
% 9.11/2.70 | (169) ~ (all_76_1_24 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (163) can reduce 169 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (163) all_76_1_24 = 0
% 9.11/2.70 | (172) ~ (all_76_2_25 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (162) can reduce 172 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (174) ~ (all_28_3_19 = all_27_3_15)
% 9.11/2.70 | (175) ? [v0] : ? [v1] : ? [v2] : (member(all_28_3_19, all_0_2_2) = v2 & member(all_27_3_15, all_0_2_2) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.70 |
% 9.11/2.70 | Instantiating (175) with all_64_0_26, all_64_1_27, all_64_2_28 yields:
% 9.11/2.70 | (176) member(all_28_3_19, all_0_2_2) = all_64_0_26 & member(all_27_3_15, all_0_2_2) = all_64_1_27 & member(all_10_2_10, all_0_3_3) = all_64_2_28 & ( ~ (all_64_0_26 = 0) | ~ (all_64_1_27 = 0) | ~ (all_64_2_28 = 0))
% 9.11/2.70 |
% 9.11/2.70 | Applying alpha-rule on (176) yields:
% 9.11/2.70 | (177) member(all_28_3_19, all_0_2_2) = all_64_0_26
% 9.11/2.70 | (178) member(all_27_3_15, all_0_2_2) = all_64_1_27
% 9.11/2.70 | (179) member(all_10_2_10, all_0_3_3) = all_64_2_28
% 9.11/2.70 | (180) ~ (all_64_0_26 = 0) | ~ (all_64_1_27 = 0) | ~ (all_64_2_28 = 0)
% 9.11/2.70 |
% 9.11/2.70 | From (135) and (178) follows:
% 9.11/2.70 | (181) member(all_25_0_11, all_0_2_2) = all_64_1_27
% 9.11/2.70 |
% 9.11/2.70 | Instantiating formula (12) with all_28_3_19, all_0_2_2, all_64_0_26, 0 and discharging atoms member(all_28_3_19, all_0_2_2) = all_64_0_26, member(all_28_3_19, all_0_2_2) = 0, yields:
% 9.11/2.70 | (182) all_64_0_26 = 0
% 9.11/2.70 |
% 9.11/2.70 | Instantiating formula (12) with all_25_0_11, all_0_2_2, all_64_1_27, 0 and discharging atoms member(all_25_0_11, all_0_2_2) = all_64_1_27, member(all_25_0_11, all_0_2_2) = 0, yields:
% 9.11/2.70 | (183) all_64_1_27 = 0
% 9.11/2.70 |
% 9.11/2.70 | Instantiating formula (12) with all_10_2_10, all_0_3_3, all_64_2_28, 0 and discharging atoms member(all_10_2_10, all_0_3_3) = all_64_2_28, member(all_10_2_10, all_0_3_3) = 0, yields:
% 9.11/2.70 | (184) all_64_2_28 = 0
% 9.11/2.70 |
% 9.11/2.70 +-Applying beta-rule and splitting (180), into two cases.
% 9.11/2.70 |-Branch one:
% 9.11/2.70 | (185) ~ (all_64_0_26 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (182) can reduce 185 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (182) all_64_0_26 = 0
% 9.11/2.70 | (188) ~ (all_64_1_27 = 0) | ~ (all_64_2_28 = 0)
% 9.11/2.70 |
% 9.11/2.70 +-Applying beta-rule and splitting (188), into two cases.
% 9.11/2.70 |-Branch one:
% 9.11/2.70 | (189) ~ (all_64_1_27 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (183) can reduce 189 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (183) all_64_1_27 = 0
% 9.11/2.70 | (192) ~ (all_64_2_28 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Equations (184) can reduce 192 to:
% 9.11/2.70 | (99) $false
% 9.11/2.70 |
% 9.11/2.70 |-The branch is then unsatisfiable
% 9.11/2.70 |-Branch two:
% 9.11/2.70 | (194) ~ (all_27_3_15 = all_25_0_11)
% 9.11/2.70 | (195) ? [v0] : ? [v1] : ? [v2] : (member(all_27_3_15, all_0_2_2) = v2 & member(all_25_0_11, all_0_2_2) = v1 & member(all_10_2_10, all_0_3_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.11/2.70 |
% 9.11/2.70 | Instantiating (195) with all_60_0_29, all_60_1_30, all_60_2_31 yields:
% 9.11/2.70 | (196) member(all_27_3_15, all_0_2_2) = all_60_0_29 & member(all_25_0_11, all_0_2_2) = all_60_1_30 & member(all_10_2_10, all_0_3_3) = all_60_2_31 & ( ~ (all_60_0_29 = 0) | ~ (all_60_1_30 = 0) | ~ (all_60_2_31 = 0))
% 9.11/2.70 |
% 9.11/2.70 | Applying alpha-rule on (196) yields:
% 9.11/2.70 | (197) member(all_27_3_15, all_0_2_2) = all_60_0_29
% 9.11/2.70 | (198) member(all_25_0_11, all_0_2_2) = all_60_1_30
% 9.11/2.70 | (199) member(all_10_2_10, all_0_3_3) = all_60_2_31
% 9.11/2.70 | (200) ~ (all_60_0_29 = 0) | ~ (all_60_1_30 = 0) | ~ (all_60_2_31 = 0)
% 9.11/2.70 |
% 9.11/2.70 | Instantiating formula (12) with all_27_3_15, all_0_2_2, all_60_0_29, 0 and discharging atoms member(all_27_3_15, all_0_2_2) = all_60_0_29, member(all_27_3_15, all_0_2_2) = 0, yields:
% 9.60/2.70 | (201) all_60_0_29 = 0
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_25_0_11, all_0_2_2, all_60_1_30, 0 and discharging atoms member(all_25_0_11, all_0_2_2) = all_60_1_30, member(all_25_0_11, all_0_2_2) = 0, yields:
% 9.60/2.70 | (202) all_60_1_30 = 0
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_10_2_10, all_0_3_3, all_60_2_31, 0 and discharging atoms member(all_10_2_10, all_0_3_3) = all_60_2_31, member(all_10_2_10, all_0_3_3) = 0, yields:
% 9.60/2.70 | (203) all_60_2_31 = 0
% 9.60/2.70 |
% 9.60/2.70 +-Applying beta-rule and splitting (200), into two cases.
% 9.60/2.70 |-Branch one:
% 9.60/2.70 | (204) ~ (all_60_0_29 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (201) can reduce 204 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (201) all_60_0_29 = 0
% 9.60/2.70 | (207) ~ (all_60_1_30 = 0) | ~ (all_60_2_31 = 0)
% 9.60/2.70 |
% 9.60/2.70 +-Applying beta-rule and splitting (207), into two cases.
% 9.60/2.70 |-Branch one:
% 9.60/2.70 | (208) ~ (all_60_1_30 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (202) can reduce 208 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (202) all_60_1_30 = 0
% 9.60/2.70 | (211) ~ (all_60_2_31 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (203) can reduce 211 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (213) member(all_10_0_8, all_0_1_1) = all_28_2_18 & member(all_10_2_10, all_0_3_3) = all_28_3_19 & ( ~ (all_28_2_18 = 0) | ~ (all_28_3_19 = 0))
% 9.60/2.70 |
% 9.60/2.70 | Applying alpha-rule on (213) yields:
% 9.60/2.70 | (214) member(all_10_0_8, all_0_1_1) = all_28_2_18
% 9.60/2.70 | (215) member(all_10_2_10, all_0_3_3) = all_28_3_19
% 9.60/2.70 | (216) ~ (all_28_2_18 = 0) | ~ (all_28_3_19 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_10_0_8, all_0_1_1, all_28_2_18, 0 and discharging atoms member(all_10_0_8, all_0_1_1) = all_28_2_18, member(all_10_0_8, all_0_1_1) = 0, yields:
% 9.60/2.70 | (129) all_28_2_18 = 0
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_10_2_10, all_0_3_3, all_28_3_19, 0 and discharging atoms member(all_10_2_10, all_0_3_3) = all_28_3_19, member(all_10_2_10, all_0_3_3) = 0, yields:
% 9.60/2.70 | (218) all_28_3_19 = 0
% 9.60/2.70 |
% 9.60/2.70 +-Applying beta-rule and splitting (216), into two cases.
% 9.60/2.70 |-Branch one:
% 9.60/2.70 | (219) ~ (all_28_2_18 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (129) can reduce 219 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (129) all_28_2_18 = 0
% 9.60/2.70 | (222) ~ (all_28_3_19 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (218) can reduce 222 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (224) member(all_10_1_9, all_0_1_1) = all_27_2_14 & member(all_10_2_10, all_0_3_3) = all_27_3_15 & ( ~ (all_27_2_14 = 0) | ~ (all_27_3_15 = 0))
% 9.60/2.70 |
% 9.60/2.70 | Applying alpha-rule on (224) yields:
% 9.60/2.70 | (225) member(all_10_1_9, all_0_1_1) = all_27_2_14
% 9.60/2.70 | (226) member(all_10_2_10, all_0_3_3) = all_27_3_15
% 9.60/2.70 | (227) ~ (all_27_2_14 = 0) | ~ (all_27_3_15 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_10_1_9, all_0_1_1, all_27_2_14, 0 and discharging atoms member(all_10_1_9, all_0_1_1) = all_27_2_14, member(all_10_1_9, all_0_1_1) = 0, yields:
% 9.60/2.70 | (122) all_27_2_14 = 0
% 9.60/2.70 |
% 9.60/2.70 | Instantiating formula (12) with all_10_2_10, all_0_3_3, all_27_3_15, 0 and discharging atoms member(all_10_2_10, all_0_3_3) = all_27_3_15, member(all_10_2_10, all_0_3_3) = 0, yields:
% 9.60/2.70 | (229) all_27_3_15 = 0
% 9.60/2.70 |
% 9.60/2.70 +-Applying beta-rule and splitting (227), into two cases.
% 9.60/2.70 |-Branch one:
% 9.60/2.70 | (230) ~ (all_27_2_14 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (122) can reduce 230 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 |-Branch two:
% 9.60/2.70 | (122) all_27_2_14 = 0
% 9.60/2.70 | (233) ~ (all_27_3_15 = 0)
% 9.60/2.70 |
% 9.60/2.70 | Equations (229) can reduce 233 to:
% 9.60/2.70 | (99) $false
% 9.60/2.70 |
% 9.60/2.70 |-The branch is then unsatisfiable
% 9.60/2.70 % SZS output end Proof for theBenchmark
% 9.60/2.70
% 9.60/2.70 2114ms
%------------------------------------------------------------------------------