TSTP Solution File: SET731+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET731+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:42 EDT 2022
% Result : Theorem 6.28s 1.99s
% Output : Proof 8.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET731+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 22:06:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.57 ____ _
% 0.50/0.57 ___ / __ \_____(_)___ ________ __________
% 0.50/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.57
% 0.50/0.57 A Theorem Prover for First-Order Logic
% 0.50/0.57 (ePrincess v.1.0)
% 0.50/0.57
% 0.50/0.57 (c) Philipp Rümmer, 2009-2015
% 0.50/0.57 (c) Peter Backeman, 2014-2015
% 0.50/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.57 Bug reports to peter@backeman.se
% 0.50/0.57
% 0.50/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.57
% 0.50/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/0.98 Prover 0: Preprocessing ...
% 3.39/1.35 Prover 0: Warning: ignoring some quantifiers
% 3.46/1.38 Prover 0: Constructing countermodel ...
% 4.39/1.62 Prover 0: gave up
% 4.39/1.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.75/1.67 Prover 1: Preprocessing ...
% 5.72/1.90 Prover 1: Constructing countermodel ...
% 6.28/1.99 Prover 1: proved (371ms)
% 6.28/1.99
% 6.28/1.99 No countermodel exists, formula is valid
% 6.28/1.99 % SZS status Theorem for theBenchmark
% 6.28/1.99
% 6.28/1.99 Generating proof ... found it (size 33)
% 7.74/2.30
% 7.74/2.30 % SZS output start Proof for theBenchmark
% 7.74/2.30 Assumed formulas after preprocessing and simplification:
% 7.74/2.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & image2(v0, v2) = v4 & surjective(v1, v2, v4) = v5 & maps(v0, v2, v3) = 0 & subset(v4, v3) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (apply(v6, v15, v12) = 0) | ? [v16] : ? [v17] : ((apply(v7, v11, v15) = v17 & member(v15, v9) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))) | (member(v12, v10) = v17 & member(v11, v8) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v15, v13) = 0) | ~ (apply(v6, v12, v13) = v14) | ? [v16] : ? [v17] : ((apply(v8, v12, v15) = v17 & member(v15, v10) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))) | (member(v13, v11) = v17 & member(v12, v9) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v10, v12, v14) = v20 & apply(v8, v11, v13) = v19 & member(v14, v9) = v18 & member(v13, v7) = v17 & member(v12, v9) = v16 & member(v11, v7) = v15 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | (( ~ (v20 = 0) | v19 = 0) & ( ~ (v19 = 0) | v20 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v10, v14, v12) = v20 & apply(v8, v11, v13) = v19 & member(v14, v9) = v18 & member(v13, v7) = v17 & member(v12, v9) = v16 & member(v11, v7) = v15 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | v20 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v10, v12, v14) = v20 & apply(v8, v11, v13) = v19 & member(v14, v9) = v18 & member(v13, v7) = v17 & member(v12, v9) = v16 & member(v11, v7) = v15 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | v20 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v7 = v6 | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v7) | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v7, v11, v14) = 0 & apply(v6, v14, v12) = 0 & member(v14, v9) = 0) | (member(v12, v10) = v15 & member(v11, v8) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v6, v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v8, v12, v14) = 0 & apply(v7, v14, v13) = 0 & member(v14, v10) = 0) | (member(v13, v11) = v15 & member(v12, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v6, v10, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : (member(v12, v9) = v15 & member(v11, v9) = v14 & member(v10, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v6, v13, v14) = v15 & member(v14, v11) = 0 & member(v13, v9) = 0 & ( ~ (v15 = 0) | ! [v20] : ( ~ (apply(v7, v20, v14) = 0) | ? [v21] : ? [v22] : (apply(v8, v13, v20) = v22 & member(v20, v10) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & (v15 = 0 | (v19 = 0 & v18 = 0 & v17 = 0 & apply(v8, v13, v16) = 0 & apply(v7, v16, v14) = 0 & member(v16, v10) = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image3(v6, v7, v8) = v10) | ~ (apply(v6, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image3(v6, v7, v8) = v10) | ~ (apply(v6, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (isomorphism(v12, v11, v10, v9, v8) = v7) | ~ (isomorphism(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (decreasing(v12, v11, v10, v9, v8) = v7) | ~ (decreasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (increasing(v12, v11, v10, v9, v8) = v7) | ~ (increasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (compose_function(v12, v11, v10, v9, v8) = v7) | ~ (compose_function(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_function(v6, v7, v8) = v11) | ~ (apply(v11, v10, v9) = v12) | ? [v13] : ? [v14] : ? [v15] : (apply(v6, v9, v10) = v15 & member(v10, v8) = v14 & member(v9, v7) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | (( ~ (v15 = 0) | v12 = 0) & ( ~ (v12 = 0) | v15 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_predicate(v6, v7, v8, v9) = 0) | ~ (apply(v6, v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : (apply(v7, v10, v11) = v15 & member(v11, v9) = v14 & member(v10, v8) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | (( ~ (v15 = 0) | v12 = 0) & ( ~ (v12 = 0) | v15 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (apply(v6, v9, v10) = 0) | ? [v12] : ? [v13] : ? [v14] : (member(v11, v8) = v14 & member(v10, v8) = v13 & member(v9, v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & apply(v10, v13, v15) = v23 & apply(v8, v12, v14) = v22 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0 & ( ~ (v23 = 0) | ~ (v22 = 0)) & (v23 = 0 | v22 = 0)) | (one_to_one(v6, v7, v9) = v13 & maps(v6, v7, v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v15, v13) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v13, v15) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (apply(v6, v9, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (member(v11, v8) = v14 & member(v10, v7) = v13 & member(v9, v7) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image2(v6, v7) = v9) | ~ (apply(v6, v8, v11) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image2(v6, v7) = v9) | ~ (apply(v6, v11, v8) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (inverse_predicate(v11, v10, v9, v8) = v7) | ~ (inverse_predicate(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (equal_maps(v11, v10, v9, v8) = v7) | ~ (equal_maps(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (inverse_predicate(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v7, v11, v12) = v13 & apply(v6, v12, v11) = v14 & member(v12, v9) = 0 & member(v11, v8) = 0 & ( ~ (v14 = 0) | ~ (v13 = 0)) & (v14 = 0 | v13 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_maps(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v6, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v9) = v10) | ~ (member(v6, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ? [v12] : (member(v6, v8) = v11 & member(v6, v7) = v12 & ( ~ (v11 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ~ (v11 = 0) & member(v6, v8) = v12 & member(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ? [v12] : (member(v6, v8) = v12 & member(v6, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sum(v7) = v8) | ~ (member(v6, v10) = 0) | ~ (member(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_image3(v10, v9, v8) = v7) | ~ (inverse_image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (image3(v10, v9, v8) = v7) | ~ (image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_function(v10, v9, v8) = v7) | ~ (inverse_function(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (one_to_one(v10, v9, v8) = v7) | ~ (one_to_one(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (surjective(v10, v9, v8) = v7) | ~ (surjective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (injective(v10, v9, v8) = v7) | ~ (injective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (maps(v10, v9, v8) = v7) | ~ (maps(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (apply(v10, v9, v8) = v7) | ~ (apply(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | (one_to_one(v6, v7, v9) = 0 & maps(v6, v7, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v9, v11) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v11, v9) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (one_to_one(v6, v7, v8) = v9) | ? [v10] : ? [v11] : (surjective(v6, v7, v8) = v11 & injective(v6, v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (surjective(v6, v7, v8) = v9) | ? [v10] : (member(v10, v8) = 0 & ! [v11] : ( ~ (apply(v6, v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (injective(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v11 = v10) & apply(v6, v11, v12) = 0 & apply(v6, v10, v12) = 0 & member(v12, v8) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v6, v7) = 0) | ~ (apply(v6, v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (maps(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v12 = v11) & apply(v6, v10, v12) = 0 & apply(v6, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v7) = 0) | (v11 = 0 & member(v10, v7) = 0 & ! [v18] : ( ~ (apply(v6, v10, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & member(v18, v8) = v19))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = 0 & member(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v7, v6) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (power_set(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v6 | v7 = v6 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (inverse_image2(v9, v8) = v7) | ~ (inverse_image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (image2(v9, v8) = v7) | ~ (image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (identity(v9, v8) = v7) | ~ (identity(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unordered_pair(v9, v8) = v7) | ~ (unordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_set(v9, v8) = v7) | ~ (equal_set(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v8, v10) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v10, v8) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v6, v7, v8) = 0) | ~ (member(v9, v8) = 0) | ? [v10] : (apply(v6, v10, v9) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (maps(v6, v7, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v10] : (apply(v6, v9, v10) = 0 & member(v10, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v6, v8) = 0 & member(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ? [v11] : (member(v6, v8) = v11 & member(v6, v7) = v10 & (v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = 0) | (member(v6, v8) = 0 & member(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (identity(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v6, v9, v9) = v10 & member(v9, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v6) = v7) | ~ (member(v6, v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_set(v6, v7) = v8) | ? [v9] : ? [v10] : (subset(v7, v6) = v10 & subset(v6, v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (product(v8) = v7) | ~ (product(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sum(v8) = v7) | ~ (sum(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v7) = v8) | ~ (member(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (power_set(v8) = v7) | ~ (power_set(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (one_to_one(v6, v7, v8) = 0) | (surjective(v6, v7, v8) = 0 & injective(v6, v7, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v0, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (apply(v1, v6, v7) = v11 & member(v7, v4) = v10 & member(v6, v2) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v11 = 0) | v8 = 0) & ( ~ (v8 = 0) | v11 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sum(v7) = v8) | ~ (member(v6, v8) = 0) | ? [v9] : (member(v9, v7) = 0 & member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (power_set(v7) = v8) | ~ (member(v6, v8) = 0) | subset(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ( ~ (equal_set(v6, v7) = 0) | (subset(v7, v6) = 0 & subset(v6, v7) = 0)) & ! [v6] : ~ (member(v6, empty_set) = 0))
% 7.91/2.37 | 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 yields:
% 7.91/2.37 | (1) ~ (all_0_0_0 = 0) & image2(all_0_5_5, all_0_3_3) = all_0_1_1 & surjective(all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0 & maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & subset(all_0_1_1, 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 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 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) = 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] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_5_5, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_4_4, v0, v1) = v5 & member(v1, all_0_1_1) = v4 & member(v0, all_0_3_3) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 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)
% 8.24/2.40 |
% 8.24/2.40 | Applying alpha-rule on (1) yields:
% 8.24/2.40 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 8.24/2.40 | (3) ! [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))))
% 8.24/2.40 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 8.24/2.40 | (5) surjective(all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0
% 8.24/2.40 | (6) ! [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)))))
% 8.24/2.40 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 8.24/2.40 | (8) ! [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))
% 8.24/2.41 | (9) ! [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))
% 8.24/2.41 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 8.24/2.41 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 8.24/2.41 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 8.24/2.41 | (13) ! [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)))))
% 8.24/2.41 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 8.24/2.41 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 8.24/2.41 | (16) ! [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)))))
% 8.24/2.41 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 8.24/2.41 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 8.24/2.41 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 8.24/2.41 | (20) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.24/2.41 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 8.24/2.41 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 8.24/2.41 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 8.24/2.41 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 8.24/2.41 | (25) ! [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))
% 8.24/2.41 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 8.24/2.41 | (27) ! [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)))
% 8.24/2.41 | (28) ! [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))
% 8.24/2.41 | (29) ~ (all_0_0_0 = 0)
% 8.24/2.41 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 8.24/2.41 | (31) ! [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)))))
% 8.24/2.42 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 8.24/2.42 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 8.24/2.42 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 8.24/2.42 | (35) ! [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)))))
% 8.24/2.42 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_5_5, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_4_4, v0, v1) = v5 & member(v1, all_0_1_1) = v4 & member(v0, all_0_3_3) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0)))))
% 8.24/2.42 | (37) ! [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))
% 8.24/2.42 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 8.24/2.42 | (39) ! [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)))))
% 8.24/2.42 | (40) ! [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))))
% 8.24/2.42 | (41) ! [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)))
% 8.24/2.42 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 8.24/2.42 | (43) ! [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)))
% 8.24/2.42 | (44) image2(all_0_5_5, all_0_3_3) = all_0_1_1
% 8.24/2.42 | (45) ! [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))
% 8.24/2.42 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.24/2.42 | (47) ! [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))))
% 8.24/2.42 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.24/2.42 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 8.24/2.42 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.24/2.42 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 8.24/2.42 | (52) maps(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 8.24/2.42 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 8.24/2.42 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 8.24/2.42 | (55) subset(all_0_1_1, all_0_2_2) = 0
% 8.24/2.42 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 8.24/2.42 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 8.24/2.42 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 8.24/2.42 | (59) ! [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))
% 8.24/2.42 | (60) ! [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))
% 8.24/2.42 | (61) ! [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))
% 8.24/2.43 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 8.24/2.43 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 8.24/2.43 | (64) ! [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)))
% 8.24/2.43 | (65) ! [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))))
% 8.24/2.43 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 8.24/2.43 | (67) ! [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))))
% 8.24/2.43 | (68) ! [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))))
% 8.24/2.43 | (69) ! [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))
% 8.24/2.43 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.24/2.43 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 8.24/2.43 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.24/2.43 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 8.24/2.43 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 8.24/2.43 | (75) ! [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)))))
% 8.24/2.43 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 8.24/2.43 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 8.24/2.43 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 8.24/2.43 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 8.24/2.43 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 8.24/2.43 | (81) ! [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)))))
% 8.24/2.43 | (82) ! [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))
% 8.24/2.43 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 8.24/2.43 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 8.24/2.43 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 8.24/2.43 | (86) ! [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))
% 8.24/2.43 | (87) ! [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)))))
% 8.24/2.43 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 8.24/2.43 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 8.24/2.43 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [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)))
% 8.24/2.43 | (91) ! [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)))
% 8.24/2.44 | (92) ! [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)))
% 8.24/2.44 | (93) ! [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))
% 8.24/2.44 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 8.24/2.44 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 8.24/2.44 | (96) ! [v0] : ~ (member(v0, empty_set) = 0)
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (68) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms surjective(all_0_4_4, all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 8.24/2.44 | (97) all_0_0_0 = 0 | ? [v0] : (member(v0, all_0_1_1) = 0 & ! [v1] : ( ~ (apply(all_0_4_4, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_3_3) = v2)))
% 8.24/2.44 |
% 8.24/2.44 +-Applying beta-rule and splitting (97), into two cases.
% 8.24/2.44 |-Branch one:
% 8.24/2.44 | (98) all_0_0_0 = 0
% 8.24/2.44 |
% 8.24/2.44 | Equations (98) can reduce 29 to:
% 8.24/2.44 | (99) $false
% 8.24/2.44 |
% 8.24/2.44 |-The branch is then unsatisfiable
% 8.24/2.44 |-Branch two:
% 8.24/2.44 | (29) ~ (all_0_0_0 = 0)
% 8.24/2.44 | (101) ? [v0] : (member(v0, all_0_1_1) = 0 & ! [v1] : ( ~ (apply(all_0_4_4, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_3_3) = v2)))
% 8.24/2.44 |
% 8.24/2.44 | Instantiating (101) with all_10_0_6 yields:
% 8.24/2.44 | (102) member(all_10_0_6, all_0_1_1) = 0 & ! [v0] : ( ~ (apply(all_0_4_4, v0, all_10_0_6) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1))
% 8.24/2.44 |
% 8.24/2.44 | Applying alpha-rule on (102) yields:
% 8.24/2.44 | (103) member(all_10_0_6, all_0_1_1) = 0
% 8.24/2.44 | (104) ! [v0] : ( ~ (apply(all_0_4_4, v0, all_10_0_6) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1))
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (76) with all_0_1_1, all_10_0_6, all_0_3_3, all_0_5_5 and discharging atoms image2(all_0_5_5, all_0_3_3) = all_0_1_1, member(all_10_0_6, all_0_1_1) = 0, yields:
% 8.24/2.44 | (105) ? [v0] : (apply(all_0_5_5, v0, all_10_0_6) = 0 & member(v0, all_0_3_3) = 0)
% 8.24/2.44 |
% 8.24/2.44 | Instantiating (105) with all_27_0_7 yields:
% 8.24/2.44 | (106) apply(all_0_5_5, all_27_0_7, all_10_0_6) = 0 & member(all_27_0_7, all_0_3_3) = 0
% 8.24/2.44 |
% 8.24/2.44 | Applying alpha-rule on (106) yields:
% 8.24/2.44 | (107) apply(all_0_5_5, all_27_0_7, all_10_0_6) = 0
% 8.24/2.44 | (108) member(all_27_0_7, all_0_3_3) = 0
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (104) with all_27_0_7 yields:
% 8.24/2.44 | (109) ~ (apply(all_0_4_4, all_27_0_7, all_10_0_6) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_27_0_7, all_0_3_3) = v0)
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (36) with 0, all_10_0_6, all_27_0_7 and discharging atoms apply(all_0_5_5, all_27_0_7, all_10_0_6) = 0, yields:
% 8.24/2.44 | (110) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_4_4, all_27_0_7, all_10_0_6) = v2 & member(all_27_0_7, all_0_3_3) = v0 & member(all_10_0_6, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 8.24/2.44 |
% 8.24/2.44 | Instantiating (110) with all_44_0_9, all_44_1_10, all_44_2_11 yields:
% 8.24/2.44 | (111) apply(all_0_4_4, all_27_0_7, all_10_0_6) = all_44_0_9 & member(all_27_0_7, all_0_3_3) = all_44_2_11 & member(all_10_0_6, all_0_1_1) = all_44_1_10 & ( ~ (all_44_1_10 = 0) | ~ (all_44_2_11 = 0) | all_44_0_9 = 0)
% 8.24/2.44 |
% 8.24/2.44 | Applying alpha-rule on (111) yields:
% 8.24/2.44 | (112) apply(all_0_4_4, all_27_0_7, all_10_0_6) = all_44_0_9
% 8.24/2.44 | (113) member(all_27_0_7, all_0_3_3) = all_44_2_11
% 8.24/2.44 | (114) member(all_10_0_6, all_0_1_1) = all_44_1_10
% 8.24/2.44 | (115) ~ (all_44_1_10 = 0) | ~ (all_44_2_11 = 0) | all_44_0_9 = 0
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (77) with all_27_0_7, all_0_3_3, all_44_2_11, 0 and discharging atoms member(all_27_0_7, all_0_3_3) = all_44_2_11, member(all_27_0_7, all_0_3_3) = 0, yields:
% 8.24/2.44 | (116) all_44_2_11 = 0
% 8.24/2.44 |
% 8.24/2.44 | Instantiating formula (77) with all_10_0_6, all_0_1_1, all_44_1_10, 0 and discharging atoms member(all_10_0_6, all_0_1_1) = all_44_1_10, member(all_10_0_6, all_0_1_1) = 0, yields:
% 8.24/2.44 | (117) all_44_1_10 = 0
% 8.24/2.44 |
% 8.24/2.44 | From (116) and (113) follows:
% 8.24/2.44 | (108) member(all_27_0_7, all_0_3_3) = 0
% 8.24/2.44 |
% 8.24/2.44 +-Applying beta-rule and splitting (109), into two cases.
% 8.24/2.44 |-Branch one:
% 8.24/2.44 | (119) ~ (apply(all_0_4_4, all_27_0_7, all_10_0_6) = 0)
% 8.24/2.44 |
% 8.24/2.44 +-Applying beta-rule and splitting (115), into two cases.
% 8.24/2.44 |-Branch one:
% 8.24/2.44 | (120) ~ (all_44_1_10 = 0)
% 8.24/2.44 |
% 8.24/2.44 | Equations (117) can reduce 120 to:
% 8.24/2.44 | (99) $false
% 8.24/2.44 |
% 8.24/2.44 |-The branch is then unsatisfiable
% 8.24/2.44 |-Branch two:
% 8.24/2.44 | (117) all_44_1_10 = 0
% 8.24/2.44 | (123) ~ (all_44_2_11 = 0) | all_44_0_9 = 0
% 8.24/2.44 |
% 8.24/2.44 +-Applying beta-rule and splitting (123), into two cases.
% 8.24/2.44 |-Branch one:
% 8.24/2.45 | (124) ~ (all_44_2_11 = 0)
% 8.24/2.45 |
% 8.24/2.45 | Equations (116) can reduce 124 to:
% 8.24/2.45 | (99) $false
% 8.24/2.45 |
% 8.24/2.45 |-The branch is then unsatisfiable
% 8.24/2.45 |-Branch two:
% 8.24/2.45 | (116) all_44_2_11 = 0
% 8.24/2.45 | (127) all_44_0_9 = 0
% 8.24/2.45 |
% 8.24/2.45 | From (127) and (112) follows:
% 8.24/2.45 | (128) apply(all_0_4_4, all_27_0_7, all_10_0_6) = 0
% 8.24/2.45 |
% 8.24/2.45 | Using (128) and (119) yields:
% 8.24/2.45 | (129) $false
% 8.24/2.45 |
% 8.24/2.45 |-The branch is then unsatisfiable
% 8.24/2.45 |-Branch two:
% 8.24/2.45 | (128) apply(all_0_4_4, all_27_0_7, all_10_0_6) = 0
% 8.24/2.45 | (131) ? [v0] : ( ~ (v0 = 0) & member(all_27_0_7, all_0_3_3) = v0)
% 8.24/2.45 |
% 8.24/2.45 | Instantiating (131) with all_54_0_12 yields:
% 8.24/2.45 | (132) ~ (all_54_0_12 = 0) & member(all_27_0_7, all_0_3_3) = all_54_0_12
% 8.24/2.45 |
% 8.24/2.45 | Applying alpha-rule on (132) yields:
% 8.24/2.45 | (133) ~ (all_54_0_12 = 0)
% 8.24/2.45 | (134) member(all_27_0_7, all_0_3_3) = all_54_0_12
% 8.24/2.45 |
% 8.24/2.45 | Instantiating formula (77) with all_27_0_7, all_0_3_3, all_54_0_12, 0 and discharging atoms member(all_27_0_7, all_0_3_3) = all_54_0_12, member(all_27_0_7, all_0_3_3) = 0, yields:
% 8.24/2.45 | (135) all_54_0_12 = 0
% 8.24/2.45 |
% 8.24/2.45 | Equations (135) can reduce 133 to:
% 8.24/2.45 | (99) $false
% 8.24/2.45 |
% 8.24/2.45 |-The branch is then unsatisfiable
% 8.24/2.45 % SZS output end Proof for theBenchmark
% 8.24/2.45
% 8.24/2.45 1867ms
%------------------------------------------------------------------------------