TSTP Solution File: SET759+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET759+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 00:21:53 EDT 2022
% Result : Theorem 6.59s 2.21s
% Output : Proof 9.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET759+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % 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 00:09:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.57 ____ _
% 0.56/0.57 ___ / __ \_____(_)___ ________ __________
% 0.56/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.57
% 0.56/0.57 A Theorem Prover for First-Order Logic
% 0.56/0.57 (ePrincess v.1.0)
% 0.56/0.57
% 0.56/0.57 (c) Philipp Rümmer, 2009-2015
% 0.56/0.57 (c) Peter Backeman, 2014-2015
% 0.56/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.57 Bug reports to peter@backeman.se
% 0.56/0.57
% 0.56/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.57
% 0.56/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/0.97 Prover 0: Preprocessing ...
% 3.34/1.33 Prover 0: Warning: ignoring some quantifiers
% 3.52/1.39 Prover 0: Constructing countermodel ...
% 4.50/1.76 Prover 0: gave up
% 4.50/1.76 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.05/1.81 Prover 1: Preprocessing ...
% 6.23/2.07 Prover 1: Constructing countermodel ...
% 6.59/2.21 Prover 1: proved (453ms)
% 6.59/2.21
% 6.59/2.21 No countermodel exists, formula is valid
% 6.59/2.21 % SZS status Theorem for theBenchmark
% 6.59/2.21
% 6.59/2.21 Generating proof ... found it (size 117)
% 9.08/2.75
% 9.08/2.75 % SZS output start Proof for theBenchmark
% 9.08/2.75 Assumed formulas after preprocessing and simplification:
% 9.08/2.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & inverse_image3(v0, v4, v1) = v5 & image3(v0, v3, v2) = v4 & injective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & equal_set(v5, v3) = v6 & subset(v3, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = v15) | ~ (apply(v7, v16, v13) = 0) | ? [v17] : ? [v18] : ((apply(v8, v12, v16) = v18 & member(v16, v10) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))) | (member(v13, v11) = v18 & member(v12, v9) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v8, v16, v14) = 0) | ~ (apply(v7, v13, v14) = v15) | ? [v17] : ? [v18] : ((apply(v9, v13, v16) = v18 & member(v16, v11) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))) | (member(v14, v12) = v18 & member(v13, v10) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v11, v13, v15) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | (( ~ (v21 = 0) | v20 = 0) & ( ~ (v20 = 0) | v21 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (decreasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v11, v15, v13) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | v21 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (increasing(v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v14, v15) = 0) | ~ (apply(v7, v12, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v11, v13, v15) = v21 & apply(v9, v12, v14) = v20 & member(v15, v10) = v19 & member(v14, v8) = v18 & member(v13, v10) = v17 & member(v12, v8) = v16 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | v21 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v8 = v7 | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v8) | ~ (compose_predicate(v14, v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_function(v7, v8, v9, v10, v11) = v14) | ~ (apply(v14, v12, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v8, v12, v15) = 0 & apply(v7, v15, v13) = 0 & member(v15, v10) = 0) | (member(v13, v11) = v16 & member(v12, v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = 0) | ~ (apply(v7, v13, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & apply(v9, v13, v15) = 0 & apply(v8, v15, v14) = 0 & member(v15, v11) = 0) | (member(v14, v12) = v16 & member(v13, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (equal_maps(v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v7, v11, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : (member(v13, v10) = v16 & member(v12, v10) = v15 & member(v11, v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (compose_predicate(v7, v8, v9, v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v7, v14, v15) = v16 & member(v15, v12) = 0 & member(v14, v10) = 0 & ( ~ (v16 = 0) | ! [v21] : ( ~ (apply(v8, v21, v15) = 0) | ? [v22] : ? [v23] : (apply(v9, v14, v21) = v23 & member(v21, v11) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & (v16 = 0 | (v20 = 0 & v19 = 0 & v18 = 0 & apply(v9, v14, v17) = 0 & apply(v8, v17, v15) = 0 & member(v17, v11) = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (inverse_image3(v7, v8, v9) = v11) | ~ (apply(v7, v10, v13) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (image3(v7, v8, v9) = v11) | ~ (apply(v7, v13, v10) = 0) | ~ (member(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & member(v13, v8) = v14) | ( ~ (v14 = 0) & member(v10, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (isomorphism(v13, v12, v11, v10, v9) = v8) | ~ (isomorphism(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (decreasing(v13, v12, v11, v10, v9) = v8) | ~ (decreasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (increasing(v13, v12, v11, v10, v9) = v8) | ~ (increasing(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v8 = v7 | ~ (compose_function(v13, v12, v11, v10, v9) = v8) | ~ (compose_function(v13, v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_function(v7, v8, v9) = v12) | ~ (apply(v12, v11, v10) = v13) | ? [v14] : ? [v15] : ? [v16] : (apply(v7, v10, v11) = v16 & member(v11, v9) = v15 & member(v10, v8) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | (( ~ (v16 = 0) | v13 = 0) & ( ~ (v13 = 0) | v16 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (inverse_predicate(v7, v8, v9, v10) = 0) | ~ (apply(v7, v12, v11) = v13) | ? [v14] : ? [v15] : ? [v16] : (apply(v8, v11, v12) = v16 & member(v12, v10) = v15 & member(v11, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | (( ~ (v16 = 0) | v13 = 0) & ( ~ (v13 = 0) | v16 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (maps(v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v7, v10, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : (member(v12, v9) = v15 & member(v11, v9) = v14 & member(v10, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (isomorphism(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & apply(v11, v14, v16) = v24 & apply(v9, v13, v15) = v23 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0 & ( ~ (v24 = 0) | ~ (v23 = 0)) & (v24 = 0 | v23 = 0)) | (one_to_one(v7, v8, v10) = v14 & maps(v7, v8, v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (decreasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v16, v14) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (increasing(v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & apply(v11, v14, v16) = v17 & apply(v9, v13, v15) = 0 & apply(v7, v15, v16) = 0 & apply(v7, v13, v14) = 0 & member(v16, v10) = 0 & member(v15, v8) = 0 & member(v14, v10) = 0 & member(v13, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (injective(v7, v8, v9) = 0) | ~ (apply(v7, v11, v12) = 0) | ~ (apply(v7, v10, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : (member(v12, v9) = v15 & member(v11, v8) = v14 & member(v10, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image2(v7, v8) = v10) | ~ (apply(v7, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image2(v7, v8) = v10) | ~ (apply(v7, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (inverse_predicate(v12, v11, v10, v9) = v8) | ~ (inverse_predicate(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (equal_maps(v12, v11, v10, v9) = v8) | ~ (equal_maps(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (inverse_predicate(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apply(v8, v12, v13) = v14 & apply(v7, v13, v12) = v15 & member(v13, v10) = 0 & member(v12, v9) = 0 & ( ~ (v15 = 0) | ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equal_maps(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v8, v12, v14) = 0 & apply(v7, v12, v13) = 0 & member(v14, v10) = 0 & member(v13, v10) = 0 & member(v12, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_image3(v11, v10, v9) = v8) | ~ (inverse_image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (image3(v11, v10, v9) = v8) | ~ (image3(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (inverse_function(v11, v10, v9) = v8) | ~ (inverse_function(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (one_to_one(v11, v10, v9) = v8) | ~ (one_to_one(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (surjective(v11, v10, v9) = v8) | ~ (surjective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (injective(v11, v10, v9) = v8) | ~ (injective(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (maps(v11, v10, v9) = v8) | ~ (maps(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (apply(v11, v10, v9) = v8) | ~ (apply(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (isomorphism(v7, v8, v9, v10, v11) = 0) | (one_to_one(v7, v8, v10) = 0 & maps(v7, v8, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (inverse_image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v10, v12) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | member(v10, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image3(v7, v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : (apply(v7, v12, v10) = 0 & member(v12, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (surjective(v7, v8, v9) = v10) | ? [v11] : (member(v11, v9) = 0 & ! [v12] : ( ~ (apply(v7, v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v8) = v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (injective(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v12 = v11) & apply(v7, v12, v13) = 0 & apply(v7, v11, v13) = 0 & member(v13, v9) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (identity(v7, v8) = 0) | ~ (apply(v7, v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (maps(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v7, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0) | (v12 = 0 & member(v11, v8) = 0 & ! [v19] : ( ~ (apply(v7, v11, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & member(v19, v9) = v20))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (inverse_image2(v10, v9) = v8) | ~ (inverse_image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (image2(v10, v9) = v8) | ~ (image2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (identity(v10, v9) = v8) | ~ (identity(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v9, v11) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image2(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v7, v11, v9) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = v10) | ? [v11] : ? [v12] : (one_to_one(v7, v8, v9) = v11 & injective(v7, v8, v9) = v12 & ( ~ (v11 = 0) | (v12 = 0 & v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (surjective(v7, v8, v9) = 0) | ~ (member(v10, v9) = 0) | ? [v11] : (apply(v7, v11, v10) = 0 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (maps(v7, v8, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v11] : (apply(v7, v10, v11) = 0 & member(v11, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & apply(v7, v10, v10) = v11 & member(v10, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v7, v8, v9) = 0) | ? [v10] : ? [v11] : (one_to_one(v7, v8, v9) = v11 & injective(v7, v8, v9) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ~ (member(v7, empty_set) = 0))
% 9.39/2.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 9.39/2.81 | (1) ~ (all_0_0_0 = 0) & inverse_image3(all_0_6_6, all_0_2_2, all_0_5_5) = all_0_1_1 & image3(all_0_6_6, all_0_3_3, all_0_4_4) = all_0_2_2 & injective(all_0_6_6, all_0_5_5, all_0_4_4) = 0 & maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0 & equal_set(all_0_1_1, all_0_3_3) = all_0_0_0 & subset(all_0_3_3, all_0_5_5) = 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)
% 9.39/2.83 |
% 9.39/2.83 | Applying alpha-rule on (1) yields:
% 9.39/2.83 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 9.39/2.83 | (3) ! [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))
% 9.39/2.83 | (4) ! [v0] : ~ (member(v0, empty_set) = 0)
% 9.39/2.83 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 9.39/2.83 | (6) ! [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)))))
% 9.39/2.83 | (7) ! [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)))))
% 9.39/2.84 | (8) ! [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)))
% 9.39/2.84 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.39/2.84 | (10) ! [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))))
% 9.39/2.84 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 9.39/2.84 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 9.39/2.84 | (13) ~ (all_0_0_0 = 0)
% 9.39/2.84 | (14) ! [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))
% 9.39/2.84 | (15) ! [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))))
% 9.39/2.84 | (16) ! [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)))))
% 9.39/2.84 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 9.39/2.84 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 9.39/2.84 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 9.39/2.84 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 9.39/2.84 | (21) equal_set(all_0_1_1, all_0_3_3) = all_0_0_0
% 9.39/2.84 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 9.39/2.84 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 9.39/2.84 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 9.39/2.84 | (25) ! [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))
% 9.39/2.84 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 9.39/2.84 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 9.39/2.84 | (28) ! [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))
% 9.39/2.84 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 9.39/2.84 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 9.39/2.84 | (31) subset(all_0_3_3, all_0_5_5) = 0
% 9.39/2.84 | (32) maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0
% 9.39/2.84 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 9.39/2.84 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 9.39/2.84 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0))))
% 9.39/2.84 | (36) ! [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)))
% 9.39/2.84 | (37) ! [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)))
% 9.39/2.84 | (38) ! [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)))))
% 9.39/2.84 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 9.39/2.84 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 9.39/2.84 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 9.39/2.84 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 9.39/2.84 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 9.39/2.85 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 9.39/2.85 | (45) ! [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)))
% 9.39/2.85 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 9.39/2.85 | (47) ! [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))
% 9.39/2.85 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 9.39/2.85 | (49) ! [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))
% 9.39/2.85 | (50) ! [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)))))
% 9.39/2.85 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 9.39/2.85 | (52) image3(all_0_6_6, all_0_3_3, all_0_4_4) = all_0_2_2
% 9.39/2.85 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 9.39/2.85 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 9.39/2.85 | (55) ! [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))
% 9.39/2.85 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 9.39/2.85 | (57) ! [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)))))
% 9.39/2.85 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 9.39/2.85 | (59) ! [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))
% 9.39/2.85 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 9.39/2.85 | (61) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.39/2.85 | (62) ! [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))))
% 9.39/2.85 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.39/2.85 | (64) ! [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)))
% 9.39/2.85 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 9.39/2.85 | (66) ! [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)))
% 9.39/2.85 | (67) ! [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))
% 9.39/2.85 | (68) ! [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))
% 9.39/2.85 | (69) ! [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)))
% 9.39/2.85 | (70) ! [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)))))
% 9.39/2.85 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 9.39/2.86 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 9.39/2.86 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 9.39/2.86 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 9.39/2.86 | (75) ! [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))
% 9.39/2.86 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 9.39/2.86 | (77) inverse_image3(all_0_6_6, all_0_2_2, all_0_5_5) = all_0_1_1
% 9.39/2.86 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.39/2.86 | (79) ! [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)))))
% 9.39/2.86 | (80) injective(all_0_6_6, all_0_5_5, all_0_4_4) = 0
% 9.39/2.86 | (81) ! [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)))))
% 9.39/2.86 | (82) ! [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))))
% 9.39/2.86 | (83) ! [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)))
% 9.39/2.86 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 9.39/2.86 | (85) ! [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))
% 9.39/2.86 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 9.39/2.86 | (87) ! [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))))
% 9.39/2.86 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 9.39/2.86 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 9.39/2.86 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 9.39/2.86 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.39/2.86 | (92) ! [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))))
% 9.39/2.86 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 9.39/2.86 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 9.39/2.86 | (95) ! [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))
% 9.39/2.86 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 9.39/2.86 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 9.39/2.86 |
% 9.39/2.86 | Instantiating formula (51) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms equal_set(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 9.39/2.86 | (98) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v0 & subset(all_0_3_3, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.39/2.86 |
% 9.39/2.86 +-Applying beta-rule and splitting (98), into two cases.
% 9.39/2.86 |-Branch one:
% 9.39/2.86 | (99) all_0_0_0 = 0
% 9.39/2.86 |
% 9.87/2.86 | Equations (99) can reduce 13 to:
% 9.87/2.86 | (100) $false
% 9.87/2.86 |
% 9.87/2.86 |-The branch is then unsatisfiable
% 9.87/2.86 |-Branch two:
% 9.87/2.86 | (13) ~ (all_0_0_0 = 0)
% 9.87/2.86 | (102) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v0 & subset(all_0_3_3, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.87 |
% 9.87/2.87 | Instantiating (102) with all_10_0_7, all_10_1_8 yields:
% 9.87/2.87 | (103) subset(all_0_1_1, all_0_3_3) = all_10_1_8 & subset(all_0_3_3, all_0_1_1) = all_10_0_7 & ( ~ (all_10_0_7 = 0) | ~ (all_10_1_8 = 0))
% 9.87/2.87 |
% 9.87/2.87 | Applying alpha-rule on (103) yields:
% 9.87/2.87 | (104) subset(all_0_1_1, all_0_3_3) = all_10_1_8
% 9.87/2.87 | (105) subset(all_0_3_3, all_0_1_1) = all_10_0_7
% 9.87/2.87 | (106) ~ (all_10_0_7 = 0) | ~ (all_10_1_8 = 0)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (91) with all_0_3_3, all_0_5_5, all_10_0_7, 0 and discharging atoms subset(all_0_3_3, all_0_5_5) = 0, yields:
% 9.87/2.87 | (107) all_10_0_7 = 0 | ~ (subset(all_0_3_3, all_0_5_5) = all_10_0_7)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (24) with all_10_1_8, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_10_1_8, yields:
% 9.87/2.87 | (108) all_10_1_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (24) with all_10_0_7, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_10_0_7, yields:
% 9.87/2.87 | (109) all_10_0_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (107), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (110) ~ (subset(all_0_3_3, all_0_5_5) = all_10_0_7)
% 9.87/2.87 |
% 9.87/2.87 | Using (31) and (110) yields:
% 9.87/2.87 | (111) ~ (all_10_0_7 = 0)
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (109), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (112) all_10_0_7 = 0
% 9.87/2.87 |
% 9.87/2.87 | Equations (112) can reduce 111 to:
% 9.87/2.87 | (100) $false
% 9.87/2.87 |
% 9.87/2.87 |-The branch is then unsatisfiable
% 9.87/2.87 |-Branch two:
% 9.87/2.87 | (111) ~ (all_10_0_7 = 0)
% 9.87/2.87 | (115) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating (115) with all_27_0_9, all_27_1_10 yields:
% 9.87/2.87 | (116) ~ (all_27_0_9 = 0) & member(all_27_1_10, all_0_1_1) = all_27_0_9 & member(all_27_1_10, all_0_3_3) = 0
% 9.87/2.87 |
% 9.87/2.87 | Applying alpha-rule on (116) yields:
% 9.87/2.87 | (117) ~ (all_27_0_9 = 0)
% 9.87/2.87 | (118) member(all_27_1_10, all_0_1_1) = all_27_0_9
% 9.87/2.87 | (119) member(all_27_1_10, all_0_3_3) = 0
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (84) with all_27_1_10, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 9.87/2.87 | (120) ~ (member(all_27_1_10, all_0_5_5) = 0) | ? [v0] : (apply(all_0_6_6, all_27_1_10, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (97) with all_27_1_10, all_0_5_5, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_5_5) = 0, member(all_27_1_10, all_0_3_3) = 0, yields:
% 9.87/2.87 | (121) member(all_27_1_10, all_0_5_5) = 0
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (120), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (122) ~ (member(all_27_1_10, all_0_5_5) = 0)
% 9.87/2.87 |
% 9.87/2.87 | Using (121) and (122) yields:
% 9.87/2.87 | (123) $false
% 9.87/2.87 |
% 9.87/2.87 |-The branch is then unsatisfiable
% 9.87/2.87 |-Branch two:
% 9.87/2.87 | (121) member(all_27_1_10, all_0_5_5) = 0
% 9.87/2.87 | (125) ? [v0] : (apply(all_0_6_6, all_27_1_10, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.87 |
% 9.87/2.87 | Instantiating (125) with all_47_0_11 yields:
% 9.87/2.87 | (126) apply(all_0_6_6, all_27_1_10, all_47_0_11) = 0 & member(all_47_0_11, all_0_4_4) = 0
% 9.87/2.87 |
% 9.87/2.87 | Applying alpha-rule on (126) yields:
% 9.87/2.87 | (127) apply(all_0_6_6, all_27_1_10, all_47_0_11) = 0
% 9.87/2.87 | (128) member(all_47_0_11, all_0_4_4) = 0
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (64) with all_47_0_11, all_27_0_9, all_0_1_1, all_27_1_10, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_2_2, all_0_5_5) = all_0_1_1, apply(all_0_6_6, all_27_1_10, all_47_0_11) = 0, member(all_27_1_10, all_0_1_1) = all_27_0_9, yields:
% 9.87/2.87 | (129) all_27_0_9 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_5_5) = v0))
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (129), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (130) all_27_0_9 = 0
% 9.87/2.87 |
% 9.87/2.87 | Equations (130) can reduce 117 to:
% 9.87/2.87 | (100) $false
% 9.87/2.87 |
% 9.87/2.87 |-The branch is then unsatisfiable
% 9.87/2.87 |-Branch two:
% 9.87/2.87 | (117) ~ (all_27_0_9 = 0)
% 9.87/2.87 | (133) ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_5_5) = v0))
% 9.87/2.87 |
% 9.87/2.87 | Instantiating (133) with all_68_0_12 yields:
% 9.87/2.87 | (134) ( ~ (all_68_0_12 = 0) & member(all_47_0_11, all_0_2_2) = all_68_0_12) | ( ~ (all_68_0_12 = 0) & member(all_27_1_10, all_0_5_5) = all_68_0_12)
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (134), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (135) ~ (all_68_0_12 = 0) & member(all_47_0_11, all_0_2_2) = all_68_0_12
% 9.87/2.87 |
% 9.87/2.87 | Applying alpha-rule on (135) yields:
% 9.87/2.87 | (136) ~ (all_68_0_12 = 0)
% 9.87/2.87 | (137) member(all_47_0_11, all_0_2_2) = all_68_0_12
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (36) with all_27_1_10, all_68_0_12, all_0_2_2, all_47_0_11, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_3_3, all_0_4_4) = all_0_2_2, apply(all_0_6_6, all_27_1_10, all_47_0_11) = 0, member(all_47_0_11, all_0_2_2) = all_68_0_12, yields:
% 9.87/2.87 | (138) all_68_0_12 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_3_3) = v0))
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (138), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (139) all_68_0_12 = 0
% 9.87/2.87 |
% 9.87/2.87 | Equations (139) can reduce 136 to:
% 9.87/2.87 | (100) $false
% 9.87/2.87 |
% 9.87/2.87 |-The branch is then unsatisfiable
% 9.87/2.87 |-Branch two:
% 9.87/2.87 | (136) ~ (all_68_0_12 = 0)
% 9.87/2.87 | (142) ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_3_3) = v0))
% 9.87/2.87 |
% 9.87/2.87 | Instantiating (142) with all_84_0_13 yields:
% 9.87/2.87 | (143) ( ~ (all_84_0_13 = 0) & member(all_47_0_11, all_0_4_4) = all_84_0_13) | ( ~ (all_84_0_13 = 0) & member(all_27_1_10, all_0_3_3) = all_84_0_13)
% 9.87/2.87 |
% 9.87/2.87 +-Applying beta-rule and splitting (143), into two cases.
% 9.87/2.87 |-Branch one:
% 9.87/2.87 | (144) ~ (all_84_0_13 = 0) & member(all_47_0_11, all_0_4_4) = all_84_0_13
% 9.87/2.87 |
% 9.87/2.87 | Applying alpha-rule on (144) yields:
% 9.87/2.87 | (145) ~ (all_84_0_13 = 0)
% 9.87/2.87 | (146) member(all_47_0_11, all_0_4_4) = all_84_0_13
% 9.87/2.87 |
% 9.87/2.87 | Instantiating formula (42) with all_47_0_11, all_0_4_4, all_84_0_13, 0 and discharging atoms member(all_47_0_11, all_0_4_4) = all_84_0_13, member(all_47_0_11, all_0_4_4) = 0, yields:
% 9.87/2.87 | (147) all_84_0_13 = 0
% 9.87/2.87 |
% 9.87/2.87 | Equations (147) can reduce 145 to:
% 9.87/2.87 | (100) $false
% 9.87/2.87 |
% 9.87/2.87 |-The branch is then unsatisfiable
% 9.87/2.87 |-Branch two:
% 9.87/2.87 | (149) ~ (all_84_0_13 = 0) & member(all_27_1_10, all_0_3_3) = all_84_0_13
% 9.87/2.87 |
% 9.87/2.88 | Applying alpha-rule on (149) yields:
% 9.87/2.88 | (145) ~ (all_84_0_13 = 0)
% 9.87/2.88 | (151) member(all_27_1_10, all_0_3_3) = all_84_0_13
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (42) with all_27_1_10, all_0_3_3, all_84_0_13, 0 and discharging atoms member(all_27_1_10, all_0_3_3) = all_84_0_13, member(all_27_1_10, all_0_3_3) = 0, yields:
% 9.87/2.88 | (147) all_84_0_13 = 0
% 9.87/2.88 |
% 9.87/2.88 | Equations (147) can reduce 145 to:
% 9.87/2.88 | (100) $false
% 9.87/2.88 |
% 9.87/2.88 |-The branch is then unsatisfiable
% 9.87/2.88 |-Branch two:
% 9.87/2.88 | (154) ~ (all_68_0_12 = 0) & member(all_27_1_10, all_0_5_5) = all_68_0_12
% 9.87/2.88 |
% 9.87/2.88 | Applying alpha-rule on (154) yields:
% 9.87/2.88 | (136) ~ (all_68_0_12 = 0)
% 9.87/2.88 | (156) member(all_27_1_10, all_0_5_5) = all_68_0_12
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (42) with all_27_1_10, all_0_5_5, all_68_0_12, 0 and discharging atoms member(all_27_1_10, all_0_5_5) = all_68_0_12, member(all_27_1_10, all_0_5_5) = 0, yields:
% 9.87/2.88 | (139) all_68_0_12 = 0
% 9.87/2.88 |
% 9.87/2.88 | Equations (139) can reduce 136 to:
% 9.87/2.88 | (100) $false
% 9.87/2.88 |
% 9.87/2.88 |-The branch is then unsatisfiable
% 9.87/2.88 |-Branch two:
% 9.87/2.88 | (159) subset(all_0_3_3, all_0_5_5) = all_10_0_7
% 9.87/2.88 | (112) all_10_0_7 = 0
% 9.87/2.88 |
% 9.87/2.88 | From (112) and (159) follows:
% 9.87/2.88 | (31) subset(all_0_3_3, all_0_5_5) = 0
% 9.87/2.88 |
% 9.87/2.88 +-Applying beta-rule and splitting (106), into two cases.
% 9.87/2.88 |-Branch one:
% 9.87/2.88 | (111) ~ (all_10_0_7 = 0)
% 9.87/2.88 |
% 9.87/2.88 | Equations (112) can reduce 111 to:
% 9.87/2.88 | (100) $false
% 9.87/2.88 |
% 9.87/2.88 |-The branch is then unsatisfiable
% 9.87/2.88 |-Branch two:
% 9.87/2.88 | (112) all_10_0_7 = 0
% 9.87/2.88 | (165) ~ (all_10_1_8 = 0)
% 9.87/2.88 |
% 9.87/2.88 +-Applying beta-rule and splitting (108), into two cases.
% 9.87/2.88 |-Branch one:
% 9.87/2.88 | (166) all_10_1_8 = 0
% 9.87/2.88 |
% 9.87/2.88 | Equations (166) can reduce 165 to:
% 9.87/2.88 | (100) $false
% 9.87/2.88 |
% 9.87/2.88 |-The branch is then unsatisfiable
% 9.87/2.88 |-Branch two:
% 9.87/2.88 | (165) ~ (all_10_1_8 = 0)
% 9.87/2.88 | (169) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 9.87/2.88 |
% 9.87/2.88 | Instantiating (169) with all_27_0_14, all_27_1_15 yields:
% 9.87/2.88 | (170) ~ (all_27_0_14 = 0) & member(all_27_1_15, all_0_1_1) = 0 & member(all_27_1_15, all_0_3_3) = all_27_0_14
% 9.87/2.88 |
% 9.87/2.88 | Applying alpha-rule on (170) yields:
% 9.87/2.88 | (171) ~ (all_27_0_14 = 0)
% 9.87/2.88 | (172) member(all_27_1_15, all_0_1_1) = 0
% 9.87/2.88 | (173) member(all_27_1_15, all_0_3_3) = all_27_0_14
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (42) with all_27_1_15, all_0_3_3, all_27_0_14, 0 and discharging atoms member(all_27_1_15, all_0_3_3) = all_27_0_14, yields:
% 9.87/2.88 | (174) all_27_0_14 = 0 | ~ (member(all_27_1_15, all_0_3_3) = 0)
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (96) with all_0_1_1, all_27_1_15, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_2_2, all_0_5_5) = all_0_1_1, member(all_27_1_15, all_0_1_1) = 0, yields:
% 9.87/2.88 | (175) member(all_27_1_15, all_0_5_5) = 0
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (95) with all_0_1_1, all_27_1_15, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_2_2, all_0_5_5) = all_0_1_1, member(all_27_1_15, all_0_1_1) = 0, yields:
% 9.87/2.88 | (176) ? [v0] : (apply(all_0_6_6, all_27_1_15, v0) = 0 & member(v0, all_0_2_2) = 0)
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (84) with all_27_1_15, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 9.87/2.88 | (177) ~ (member(all_27_1_15, all_0_5_5) = 0) | ? [v0] : (apply(all_0_6_6, all_27_1_15, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.88 |
% 9.87/2.88 | Instantiating (176) with all_43_0_16 yields:
% 9.87/2.88 | (178) apply(all_0_6_6, all_27_1_15, all_43_0_16) = 0 & member(all_43_0_16, all_0_2_2) = 0
% 9.87/2.88 |
% 9.87/2.88 | Applying alpha-rule on (178) yields:
% 9.87/2.88 | (179) apply(all_0_6_6, all_27_1_15, all_43_0_16) = 0
% 9.87/2.88 | (180) member(all_43_0_16, all_0_2_2) = 0
% 9.87/2.88 |
% 9.87/2.88 +-Applying beta-rule and splitting (177), into two cases.
% 9.87/2.88 |-Branch one:
% 9.87/2.88 | (181) ~ (member(all_27_1_15, all_0_5_5) = 0)
% 9.87/2.88 |
% 9.87/2.88 | Using (175) and (181) yields:
% 9.87/2.88 | (123) $false
% 9.87/2.88 |
% 9.87/2.88 |-The branch is then unsatisfiable
% 9.87/2.88 |-Branch two:
% 9.87/2.88 | (175) member(all_27_1_15, all_0_5_5) = 0
% 9.87/2.88 | (184) ? [v0] : (apply(all_0_6_6, all_27_1_15, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.88 |
% 9.87/2.88 | Instantiating (184) with all_49_0_17 yields:
% 9.87/2.88 | (185) apply(all_0_6_6, all_27_1_15, all_49_0_17) = 0 & member(all_49_0_17, all_0_4_4) = 0
% 9.87/2.88 |
% 9.87/2.88 | Applying alpha-rule on (185) yields:
% 9.87/2.88 | (186) apply(all_0_6_6, all_27_1_15, all_49_0_17) = 0
% 9.87/2.88 | (187) member(all_49_0_17, all_0_4_4) = 0
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (92) with all_49_0_17, all_43_0_16, all_27_1_15, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, apply(all_0_6_6, all_27_1_15, all_49_0_17) = 0, apply(all_0_6_6, all_27_1_15, all_43_0_16) = 0, yields:
% 9.87/2.88 | (188) all_49_0_17 = all_43_0_16 | ? [v0] : ? [v1] : ? [v2] : (member(all_49_0_17, all_0_4_4) = v2 & member(all_43_0_16, all_0_4_4) = v1 & member(all_27_1_15, all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (58) with all_0_2_2, all_43_0_16, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_3_3, all_0_4_4) = all_0_2_2, member(all_43_0_16, all_0_2_2) = 0, yields:
% 9.87/2.88 | (189) member(all_43_0_16, all_0_4_4) = 0
% 9.87/2.88 |
% 9.87/2.88 | Instantiating formula (48) with all_0_2_2, all_43_0_16, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_3_3, all_0_4_4) = all_0_2_2, member(all_43_0_16, all_0_2_2) = 0, yields:
% 9.87/2.88 | (190) ? [v0] : (apply(all_0_6_6, v0, all_43_0_16) = 0 & member(v0, all_0_3_3) = 0)
% 9.87/2.88 |
% 9.87/2.89 | Instantiating (190) with all_65_0_18 yields:
% 9.87/2.89 | (191) apply(all_0_6_6, all_65_0_18, all_43_0_16) = 0 & member(all_65_0_18, all_0_3_3) = 0
% 9.87/2.89 |
% 9.87/2.89 | Applying alpha-rule on (191) yields:
% 9.87/2.89 | (192) apply(all_0_6_6, all_65_0_18, all_43_0_16) = 0
% 9.87/2.89 | (193) member(all_65_0_18, all_0_3_3) = 0
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (188), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (194) all_49_0_17 = all_43_0_16
% 9.87/2.89 |
% 9.87/2.89 | From (194) and (186) follows:
% 9.87/2.89 | (179) apply(all_0_6_6, all_27_1_15, all_43_0_16) = 0
% 9.87/2.89 |
% 9.87/2.89 | From (194) and (187) follows:
% 9.87/2.89 | (189) member(all_43_0_16, all_0_4_4) = 0
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (10) with all_43_0_16, all_27_1_15, all_65_0_18, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms injective(all_0_6_6, all_0_5_5, all_0_4_4) = 0, apply(all_0_6_6, all_65_0_18, all_43_0_16) = 0, apply(all_0_6_6, all_27_1_15, all_43_0_16) = 0, yields:
% 9.87/2.89 | (197) all_65_0_18 = all_27_1_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_65_0_18, all_0_5_5) = v0 & member(all_43_0_16, all_0_4_4) = v2 & member(all_27_1_15, all_0_5_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (84) with all_65_0_18, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 9.87/2.89 | (198) ~ (member(all_65_0_18, all_0_5_5) = 0) | ? [v0] : (apply(all_0_6_6, all_65_0_18, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (97) with all_65_0_18, all_0_5_5, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_5_5) = 0, member(all_65_0_18, all_0_3_3) = 0, yields:
% 9.87/2.89 | (199) member(all_65_0_18, all_0_5_5) = 0
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (197), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (200) all_65_0_18 = all_27_1_15
% 9.87/2.89 |
% 9.87/2.89 | From (200) and (193) follows:
% 9.87/2.89 | (201) member(all_27_1_15, all_0_3_3) = 0
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (174), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (202) ~ (member(all_27_1_15, all_0_3_3) = 0)
% 9.87/2.89 |
% 9.87/2.89 | Using (201) and (202) yields:
% 9.87/2.89 | (123) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (201) member(all_27_1_15, all_0_3_3) = 0
% 9.87/2.89 | (205) all_27_0_14 = 0
% 9.87/2.89 |
% 9.87/2.89 | Equations (205) can reduce 171 to:
% 9.87/2.89 | (100) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (207) ~ (all_65_0_18 = all_27_1_15)
% 9.87/2.89 | (208) ? [v0] : ? [v1] : ? [v2] : (member(all_65_0_18, all_0_5_5) = v0 & member(all_43_0_16, all_0_4_4) = v2 & member(all_27_1_15, all_0_5_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.89 |
% 9.87/2.89 | Instantiating (208) with all_93_0_19, all_93_1_20, all_93_2_21 yields:
% 9.87/2.89 | (209) member(all_65_0_18, all_0_5_5) = all_93_2_21 & member(all_43_0_16, all_0_4_4) = all_93_0_19 & member(all_27_1_15, all_0_5_5) = all_93_1_20 & ( ~ (all_93_0_19 = 0) | ~ (all_93_1_20 = 0) | ~ (all_93_2_21 = 0))
% 9.87/2.89 |
% 9.87/2.89 | Applying alpha-rule on (209) yields:
% 9.87/2.89 | (210) member(all_65_0_18, all_0_5_5) = all_93_2_21
% 9.87/2.89 | (211) member(all_43_0_16, all_0_4_4) = all_93_0_19
% 9.87/2.89 | (212) member(all_27_1_15, all_0_5_5) = all_93_1_20
% 9.87/2.89 | (213) ~ (all_93_0_19 = 0) | ~ (all_93_1_20 = 0) | ~ (all_93_2_21 = 0)
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (198), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (214) ~ (member(all_65_0_18, all_0_5_5) = 0)
% 9.87/2.89 |
% 9.87/2.89 | Using (199) and (214) yields:
% 9.87/2.89 | (123) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (199) member(all_65_0_18, all_0_5_5) = 0
% 9.87/2.89 | (217) ? [v0] : (apply(all_0_6_6, all_65_0_18, v0) = 0 & member(v0, all_0_4_4) = 0)
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (42) with all_65_0_18, all_0_5_5, all_93_2_21, 0 and discharging atoms member(all_65_0_18, all_0_5_5) = all_93_2_21, member(all_65_0_18, all_0_5_5) = 0, yields:
% 9.87/2.89 | (218) all_93_2_21 = 0
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (42) with all_43_0_16, all_0_4_4, all_93_0_19, 0 and discharging atoms member(all_43_0_16, all_0_4_4) = all_93_0_19, member(all_43_0_16, all_0_4_4) = 0, yields:
% 9.87/2.89 | (219) all_93_0_19 = 0
% 9.87/2.89 |
% 9.87/2.89 | Instantiating formula (42) with all_27_1_15, all_0_5_5, all_93_1_20, 0 and discharging atoms member(all_27_1_15, all_0_5_5) = all_93_1_20, member(all_27_1_15, all_0_5_5) = 0, yields:
% 9.87/2.89 | (220) all_93_1_20 = 0
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (213), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (221) ~ (all_93_0_19 = 0)
% 9.87/2.89 |
% 9.87/2.89 | Equations (219) can reduce 221 to:
% 9.87/2.89 | (100) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (219) all_93_0_19 = 0
% 9.87/2.89 | (224) ~ (all_93_1_20 = 0) | ~ (all_93_2_21 = 0)
% 9.87/2.89 |
% 9.87/2.89 +-Applying beta-rule and splitting (224), into two cases.
% 9.87/2.89 |-Branch one:
% 9.87/2.89 | (225) ~ (all_93_1_20 = 0)
% 9.87/2.89 |
% 9.87/2.89 | Equations (220) can reduce 225 to:
% 9.87/2.89 | (100) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (220) all_93_1_20 = 0
% 9.87/2.89 | (228) ~ (all_93_2_21 = 0)
% 9.87/2.89 |
% 9.87/2.89 | Equations (218) can reduce 228 to:
% 9.87/2.89 | (100) $false
% 9.87/2.89 |
% 9.87/2.89 |-The branch is then unsatisfiable
% 9.87/2.89 |-Branch two:
% 9.87/2.89 | (230) ~ (all_49_0_17 = all_43_0_16)
% 9.87/2.89 | (231) ? [v0] : ? [v1] : ? [v2] : (member(all_49_0_17, all_0_4_4) = v2 & member(all_43_0_16, all_0_4_4) = v1 & member(all_27_1_15, all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 9.87/2.89 |
% 9.87/2.89 | Instantiating (231) with all_71_0_26, all_71_1_27, all_71_2_28 yields:
% 9.87/2.89 | (232) member(all_49_0_17, all_0_4_4) = all_71_0_26 & member(all_43_0_16, all_0_4_4) = all_71_1_27 & member(all_27_1_15, all_0_5_5) = all_71_2_28 & ( ~ (all_71_0_26 = 0) | ~ (all_71_1_27 = 0) | ~ (all_71_2_28 = 0))
% 9.87/2.89 |
% 9.87/2.90 | Applying alpha-rule on (232) yields:
% 9.87/2.90 | (233) member(all_49_0_17, all_0_4_4) = all_71_0_26
% 9.87/2.90 | (234) member(all_43_0_16, all_0_4_4) = all_71_1_27
% 9.87/2.90 | (235) member(all_27_1_15, all_0_5_5) = all_71_2_28
% 9.87/2.90 | (236) ~ (all_71_0_26 = 0) | ~ (all_71_1_27 = 0) | ~ (all_71_2_28 = 0)
% 9.87/2.90 |
% 9.87/2.90 | Instantiating formula (42) with all_49_0_17, all_0_4_4, all_71_0_26, 0 and discharging atoms member(all_49_0_17, all_0_4_4) = all_71_0_26, member(all_49_0_17, all_0_4_4) = 0, yields:
% 9.87/2.90 | (237) all_71_0_26 = 0
% 9.87/2.90 |
% 9.87/2.90 | Instantiating formula (42) with all_43_0_16, all_0_4_4, all_71_1_27, 0 and discharging atoms member(all_43_0_16, all_0_4_4) = all_71_1_27, member(all_43_0_16, all_0_4_4) = 0, yields:
% 9.87/2.90 | (238) all_71_1_27 = 0
% 9.87/2.90 |
% 9.87/2.90 | Instantiating formula (42) with all_27_1_15, all_0_5_5, all_71_2_28, 0 and discharging atoms member(all_27_1_15, all_0_5_5) = all_71_2_28, member(all_27_1_15, all_0_5_5) = 0, yields:
% 9.87/2.90 | (239) all_71_2_28 = 0
% 9.87/2.90 |
% 9.87/2.90 +-Applying beta-rule and splitting (236), into two cases.
% 9.87/2.90 |-Branch one:
% 9.87/2.90 | (240) ~ (all_71_0_26 = 0)
% 9.87/2.90 |
% 9.87/2.90 | Equations (237) can reduce 240 to:
% 9.87/2.90 | (100) $false
% 9.87/2.90 |
% 9.87/2.90 |-The branch is then unsatisfiable
% 9.87/2.90 |-Branch two:
% 9.87/2.90 | (237) all_71_0_26 = 0
% 9.87/2.90 | (243) ~ (all_71_1_27 = 0) | ~ (all_71_2_28 = 0)
% 9.87/2.90 |
% 9.87/2.90 +-Applying beta-rule and splitting (243), into two cases.
% 9.87/2.90 |-Branch one:
% 9.87/2.90 | (244) ~ (all_71_1_27 = 0)
% 9.87/2.90 |
% 9.87/2.90 | Equations (238) can reduce 244 to:
% 9.87/2.90 | (100) $false
% 9.87/2.90 |
% 9.87/2.90 |-The branch is then unsatisfiable
% 9.87/2.90 |-Branch two:
% 9.87/2.90 | (238) all_71_1_27 = 0
% 9.87/2.90 | (247) ~ (all_71_2_28 = 0)
% 9.87/2.90 |
% 9.87/2.90 | Equations (239) can reduce 247 to:
% 9.87/2.90 | (100) $false
% 9.87/2.90 |
% 9.87/2.90 |-The branch is then unsatisfiable
% 9.87/2.90 % SZS output end Proof for theBenchmark
% 9.87/2.90
% 9.87/2.90 2315ms
%------------------------------------------------------------------------------