TSTP Solution File: SET760+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET760+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 6.31s 2.02s
% Output : Proof 10.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET760+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 01:43:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/0.96 Prover 0: Preprocessing ...
% 3.04/1.29 Prover 0: Warning: ignoring some quantifiers
% 3.32/1.33 Prover 0: Constructing countermodel ...
% 4.29/1.58 Prover 0: gave up
% 4.29/1.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.65/1.63 Prover 1: Preprocessing ...
% 5.60/1.87 Prover 1: Constructing countermodel ...
% 6.31/2.02 Prover 1: proved (441ms)
% 6.31/2.02
% 6.31/2.02 No countermodel exists, formula is valid
% 6.31/2.02 % SZS status Theorem for theBenchmark
% 6.31/2.02
% 6.31/2.02 Generating proof ... found it (size 125)
% 9.36/2.70
% 9.36/2.70 % SZS output start Proof for theBenchmark
% 9.36/2.70 Assumed formulas after preprocessing and simplification:
% 9.36/2.70 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & inverse_image3(v0, v3, v1) = v4 & image3(v0, v4, v2) = v5 & surjective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & equal_set(v5, v3) = v6 & subset(v3, v2) = 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 | ~ (one_to_one(v7, v8, v9) = v10) | ? [v11] : ? [v12] : (surjective(v7, v8, v9) = v12 & injective(v7, v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 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) = 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] : ( ~ (one_to_one(v7, v8, v9) = 0) | (surjective(v7, v8, v9) = 0 & injective(v7, v8, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(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))
% 9.83/2.78 | 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:
% 9.83/2.78 | (1) ~ (all_0_0_0 = 0) & inverse_image3(all_0_6_6, all_0_3_3, all_0_5_5) = all_0_2_2 & image3(all_0_6_6, all_0_2_2, all_0_4_4) = all_0_1_1 & surjective(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_4_4) = 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] : ( ~ (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)
% 10.03/2.81 |
% 10.03/2.81 | Applying alpha-rule on (1) yields:
% 10.03/2.81 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 10.03/2.81 | (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))
% 10.03/2.81 | (4) ! [v0] : ~ (member(v0, empty_set) = 0)
% 10.03/2.81 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 10.03/2.81 | (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)))))
% 10.03/2.81 | (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)))))
% 10.03/2.81 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.03/2.81 | (9) ! [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))))
% 10.03/2.81 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 10.03/2.81 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 10.03/2.82 | (12) ~ (all_0_0_0 = 0)
% 10.03/2.82 | (13) ! [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))
% 10.03/2.82 | (14) ! [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)))))
% 10.03/2.82 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 10.03/2.82 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 10.03/2.82 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.03/2.82 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 10.03/2.82 | (19) equal_set(all_0_1_1, all_0_3_3) = all_0_0_0
% 10.03/2.82 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 10.03/2.82 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 10.03/2.82 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 10.03/2.82 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 10.03/2.82 | (24) ! [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))
% 10.03/2.82 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 10.03/2.82 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 10.03/2.82 | (27) ! [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))
% 10.03/2.82 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 10.03/2.82 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 10.03/2.82 | (30) maps(all_0_6_6, all_0_5_5, all_0_4_4) = 0
% 10.03/2.82 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 10.03/2.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 10.03/2.82 | (33) ! [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))))
% 10.03/2.82 | (34) ! [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)))
% 10.03/2.82 | (35) ! [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)))
% 10.03/2.83 | (36) ! [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)))))
% 10.03/2.83 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 10.03/2.83 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 10.03/2.83 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 10.03/2.83 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 10.03/2.83 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 10.03/2.83 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 10.03/2.83 | (43) ! [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)))
% 10.03/2.83 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 10.03/2.83 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 10.03/2.83 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 10.03/2.83 | (47) ! [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))
% 10.03/2.83 | (48) ! [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)))))
% 10.03/2.83 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 10.03/2.83 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 10.03/2.83 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 10.03/2.83 | (52) ! [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))
% 10.03/2.83 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 10.03/2.83 | (54) ! [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)))))
% 10.03/2.83 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 10.03/2.83 | (56) ! [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))
% 10.03/2.83 | (57) surjective(all_0_6_6, all_0_5_5, all_0_4_4) = 0
% 10.03/2.83 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 10.03/2.83 | (59) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.03/2.83 | (60) ! [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))))
% 10.03/2.84 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.03/2.84 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 10.03/2.84 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 10.03/2.84 | (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)))
% 10.03/2.84 | (65) ! [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))
% 10.03/2.84 | (66) ! [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))
% 10.03/2.84 | (67) ! [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)))
% 10.03/2.84 | (68) ! [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)))))
% 10.03/2.84 | (69) image3(all_0_6_6, all_0_2_2, all_0_4_4) = all_0_1_1
% 10.03/2.84 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 10.03/2.84 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 10.03/2.84 | (72) subset(all_0_3_3, all_0_4_4) = 0
% 10.03/2.84 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 10.03/2.84 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 10.03/2.84 | (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))
% 10.03/2.84 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 10.03/2.84 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.03/2.84 | (78) ! [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)))))
% 10.22/2.84 | (79) ! [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))))
% 10.22/2.84 | (80) ! [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)))))
% 10.22/2.84 | (81) ! [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))))
% 10.22/2.84 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 10.23/2.85 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 10.23/2.85 | (84) ! [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))
% 10.23/2.85 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 10.23/2.85 | (86) ! [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))))
% 10.23/2.85 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 10.23/2.85 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 10.23/2.85 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 10.23/2.85 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.23/2.85 | (91) ! [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))))
% 10.23/2.85 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 10.23/2.85 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 10.23/2.85 | (94) ! [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))
% 10.23/2.85 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 10.23/2.85 | (96) inverse_image3(all_0_6_6, all_0_3_3, all_0_5_5) = all_0_2_2
% 10.23/2.85 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 10.23/2.85 |
% 10.23/2.85 | Instantiating formula (49) 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:
% 10.23/2.85 | (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)))
% 10.23/2.85 |
% 10.23/2.85 +-Applying beta-rule and splitting (98), into two cases.
% 10.23/2.85 |-Branch one:
% 10.23/2.85 | (99) all_0_0_0 = 0
% 10.23/2.85 |
% 10.23/2.85 | Equations (99) can reduce 12 to:
% 10.23/2.85 | (100) $false
% 10.23/2.85 |
% 10.23/2.85 |-The branch is then unsatisfiable
% 10.23/2.85 |-Branch two:
% 10.23/2.85 | (12) ~ (all_0_0_0 = 0)
% 10.23/2.85 | (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)))
% 10.23/2.85 |
% 10.23/2.85 | Instantiating (102) with all_10_0_7, all_10_1_8 yields:
% 10.23/2.85 | (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))
% 10.23/2.85 |
% 10.23/2.85 | Applying alpha-rule on (103) yields:
% 10.23/2.85 | (104) subset(all_0_1_1, all_0_3_3) = all_10_1_8
% 10.23/2.85 | (105) subset(all_0_3_3, all_0_1_1) = all_10_0_7
% 10.23/2.85 | (106) ~ (all_10_0_7 = 0) | ~ (all_10_1_8 = 0)
% 10.23/2.85 |
% 10.23/2.85 | Instantiating formula (90) with all_0_3_3, all_0_4_4, all_10_0_7, 0 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, yields:
% 10.23/2.85 | (107) all_10_0_7 = 0 | ~ (subset(all_0_3_3, all_0_4_4) = all_10_0_7)
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (23) 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:
% 10.23/2.86 | (108) all_10_1_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (23) 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:
% 10.23/2.86 | (109) all_10_0_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (107), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (110) ~ (subset(all_0_3_3, all_0_4_4) = all_10_0_7)
% 10.23/2.86 |
% 10.23/2.86 | Using (72) and (110) yields:
% 10.23/2.86 | (111) ~ (all_10_0_7 = 0)
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (109), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (112) all_10_0_7 = 0
% 10.23/2.86 |
% 10.23/2.86 | Equations (112) can reduce 111 to:
% 10.23/2.86 | (100) $false
% 10.23/2.86 |
% 10.23/2.86 |-The branch is then unsatisfiable
% 10.23/2.86 |-Branch two:
% 10.23/2.86 | (111) ~ (all_10_0_7 = 0)
% 10.23/2.86 | (115) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 10.23/2.86 |
% 10.23/2.86 | Instantiating (115) with all_27_0_9, all_27_1_10 yields:
% 10.23/2.86 | (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
% 10.23/2.86 |
% 10.23/2.86 | Applying alpha-rule on (116) yields:
% 10.23/2.86 | (117) ~ (all_27_0_9 = 0)
% 10.23/2.86 | (118) member(all_27_1_10, all_0_1_1) = all_27_0_9
% 10.23/2.86 | (119) member(all_27_1_10, all_0_3_3) = 0
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (74) with all_27_1_10, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms surjective(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 10.23/2.86 | (120) ~ (member(all_27_1_10, all_0_4_4) = 0) | ? [v0] : (apply(all_0_6_6, v0, all_27_1_10) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (97) with all_27_1_10, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, member(all_27_1_10, all_0_3_3) = 0, yields:
% 10.23/2.86 | (121) member(all_27_1_10, all_0_4_4) = 0
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (120), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (122) ~ (member(all_27_1_10, all_0_4_4) = 0)
% 10.23/2.86 |
% 10.23/2.86 | Using (121) and (122) yields:
% 10.23/2.86 | (123) $false
% 10.23/2.86 |
% 10.23/2.86 |-The branch is then unsatisfiable
% 10.23/2.86 |-Branch two:
% 10.23/2.86 | (121) member(all_27_1_10, all_0_4_4) = 0
% 10.23/2.86 | (125) ? [v0] : (apply(all_0_6_6, v0, all_27_1_10) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.86 |
% 10.23/2.86 | Instantiating (125) with all_47_0_11 yields:
% 10.23/2.86 | (126) apply(all_0_6_6, all_47_0_11, all_27_1_10) = 0 & member(all_47_0_11, all_0_5_5) = 0
% 10.23/2.86 |
% 10.23/2.86 | Applying alpha-rule on (126) yields:
% 10.23/2.86 | (127) apply(all_0_6_6, all_47_0_11, all_27_1_10) = 0
% 10.23/2.86 | (128) member(all_47_0_11, all_0_5_5) = 0
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (34) with all_47_0_11, all_27_0_9, all_0_1_1, all_27_1_10, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_2_2, all_0_4_4) = all_0_1_1, apply(all_0_6_6, all_47_0_11, all_27_1_10) = 0, member(all_27_1_10, all_0_1_1) = all_27_0_9, yields:
% 10.23/2.86 | (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_4_4) = v0))
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (129), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (130) all_27_0_9 = 0
% 10.23/2.86 |
% 10.23/2.86 | Equations (130) can reduce 117 to:
% 10.23/2.86 | (100) $false
% 10.23/2.86 |
% 10.23/2.86 |-The branch is then unsatisfiable
% 10.23/2.86 |-Branch two:
% 10.23/2.86 | (117) ~ (all_27_0_9 = 0)
% 10.23/2.86 | (133) ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_4_4) = v0))
% 10.23/2.86 |
% 10.23/2.86 | Instantiating (133) with all_68_0_13 yields:
% 10.23/2.86 | (134) ( ~ (all_68_0_13 = 0) & member(all_47_0_11, all_0_2_2) = all_68_0_13) | ( ~ (all_68_0_13 = 0) & member(all_27_1_10, all_0_4_4) = all_68_0_13)
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (134), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (135) ~ (all_68_0_13 = 0) & member(all_47_0_11, all_0_2_2) = all_68_0_13
% 10.23/2.86 |
% 10.23/2.86 | Applying alpha-rule on (135) yields:
% 10.23/2.86 | (136) ~ (all_68_0_13 = 0)
% 10.23/2.86 | (137) member(all_47_0_11, all_0_2_2) = all_68_0_13
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (62) with all_27_1_10, all_68_0_13, all_0_2_2, all_47_0_11, all_0_5_5, all_0_3_3, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_3_3, all_0_5_5) = all_0_2_2, apply(all_0_6_6, all_47_0_11, all_27_1_10) = 0, member(all_47_0_11, all_0_2_2) = all_68_0_13, yields:
% 10.23/2.86 | (138) all_68_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_3_3) = v0))
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (138), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (139) all_68_0_13 = 0
% 10.23/2.86 |
% 10.23/2.86 | Equations (139) can reduce 136 to:
% 10.23/2.86 | (100) $false
% 10.23/2.86 |
% 10.23/2.86 |-The branch is then unsatisfiable
% 10.23/2.86 |-Branch two:
% 10.23/2.86 | (136) ~ (all_68_0_13 = 0)
% 10.23/2.86 | (142) ? [v0] : (( ~ (v0 = 0) & member(all_47_0_11, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_27_1_10, all_0_3_3) = v0))
% 10.23/2.86 |
% 10.23/2.86 | Instantiating (142) with all_84_0_15 yields:
% 10.23/2.86 | (143) ( ~ (all_84_0_15 = 0) & member(all_47_0_11, all_0_5_5) = all_84_0_15) | ( ~ (all_84_0_15 = 0) & member(all_27_1_10, all_0_3_3) = all_84_0_15)
% 10.23/2.86 |
% 10.23/2.86 +-Applying beta-rule and splitting (143), into two cases.
% 10.23/2.86 |-Branch one:
% 10.23/2.86 | (144) ~ (all_84_0_15 = 0) & member(all_47_0_11, all_0_5_5) = all_84_0_15
% 10.23/2.86 |
% 10.23/2.86 | Applying alpha-rule on (144) yields:
% 10.23/2.86 | (145) ~ (all_84_0_15 = 0)
% 10.23/2.86 | (146) member(all_47_0_11, all_0_5_5) = all_84_0_15
% 10.23/2.86 |
% 10.23/2.86 | Instantiating formula (40) with all_47_0_11, all_0_5_5, all_84_0_15, 0 and discharging atoms member(all_47_0_11, all_0_5_5) = all_84_0_15, member(all_47_0_11, all_0_5_5) = 0, yields:
% 10.23/2.86 | (147) all_84_0_15 = 0
% 10.23/2.86 |
% 10.23/2.86 | Equations (147) can reduce 145 to:
% 10.23/2.87 | (100) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (149) ~ (all_84_0_15 = 0) & member(all_27_1_10, all_0_3_3) = all_84_0_15
% 10.23/2.87 |
% 10.23/2.87 | Applying alpha-rule on (149) yields:
% 10.23/2.87 | (145) ~ (all_84_0_15 = 0)
% 10.23/2.87 | (151) member(all_27_1_10, all_0_3_3) = all_84_0_15
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (40) with all_27_1_10, all_0_3_3, all_84_0_15, 0 and discharging atoms member(all_27_1_10, all_0_3_3) = all_84_0_15, member(all_27_1_10, all_0_3_3) = 0, yields:
% 10.23/2.87 | (147) all_84_0_15 = 0
% 10.23/2.87 |
% 10.23/2.87 | Equations (147) can reduce 145 to:
% 10.23/2.87 | (100) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (154) ~ (all_68_0_13 = 0) & member(all_27_1_10, all_0_4_4) = all_68_0_13
% 10.23/2.87 |
% 10.23/2.87 | Applying alpha-rule on (154) yields:
% 10.23/2.87 | (136) ~ (all_68_0_13 = 0)
% 10.23/2.87 | (156) member(all_27_1_10, all_0_4_4) = all_68_0_13
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (40) with all_27_1_10, all_0_4_4, all_68_0_13, 0 and discharging atoms member(all_27_1_10, all_0_4_4) = all_68_0_13, member(all_27_1_10, all_0_4_4) = 0, yields:
% 10.23/2.87 | (139) all_68_0_13 = 0
% 10.23/2.87 |
% 10.23/2.87 | Equations (139) can reduce 136 to:
% 10.23/2.87 | (100) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (159) subset(all_0_3_3, all_0_4_4) = all_10_0_7
% 10.23/2.87 | (112) all_10_0_7 = 0
% 10.23/2.87 |
% 10.23/2.87 | From (112) and (159) follows:
% 10.23/2.87 | (72) subset(all_0_3_3, all_0_4_4) = 0
% 10.23/2.87 |
% 10.23/2.87 +-Applying beta-rule and splitting (106), into two cases.
% 10.23/2.87 |-Branch one:
% 10.23/2.87 | (111) ~ (all_10_0_7 = 0)
% 10.23/2.87 |
% 10.23/2.87 | Equations (112) can reduce 111 to:
% 10.23/2.87 | (100) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (112) all_10_0_7 = 0
% 10.23/2.87 | (165) ~ (all_10_1_8 = 0)
% 10.23/2.87 |
% 10.23/2.87 +-Applying beta-rule and splitting (108), into two cases.
% 10.23/2.87 |-Branch one:
% 10.23/2.87 | (166) all_10_1_8 = 0
% 10.23/2.87 |
% 10.23/2.87 | Equations (166) can reduce 165 to:
% 10.23/2.87 | (100) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (165) ~ (all_10_1_8 = 0)
% 10.23/2.87 | (169) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating (169) with all_27_0_20, all_27_1_21 yields:
% 10.23/2.87 | (170) ~ (all_27_0_20 = 0) & member(all_27_1_21, all_0_1_1) = 0 & member(all_27_1_21, all_0_3_3) = all_27_0_20
% 10.23/2.87 |
% 10.23/2.87 | Applying alpha-rule on (170) yields:
% 10.23/2.87 | (171) ~ (all_27_0_20 = 0)
% 10.23/2.87 | (172) member(all_27_1_21, all_0_1_1) = 0
% 10.23/2.87 | (173) member(all_27_1_21, all_0_3_3) = all_27_0_20
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (40) with all_27_1_21, all_0_3_3, all_27_0_20, 0 and discharging atoms member(all_27_1_21, all_0_3_3) = all_27_0_20, yields:
% 10.23/2.87 | (174) all_27_0_20 = 0 | ~ (member(all_27_1_21, all_0_3_3) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (55) with all_0_1_1, all_27_1_21, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_2_2, all_0_4_4) = all_0_1_1, member(all_27_1_21, all_0_1_1) = 0, yields:
% 10.23/2.87 | (175) member(all_27_1_21, all_0_4_4) = 0
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (46) with all_0_1_1, all_27_1_21, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms image3(all_0_6_6, all_0_2_2, all_0_4_4) = all_0_1_1, member(all_27_1_21, all_0_1_1) = 0, yields:
% 10.23/2.87 | (176) ? [v0] : (apply(all_0_6_6, v0, all_27_1_21) = 0 & member(v0, all_0_2_2) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (74) with all_27_1_21, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms surjective(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 10.23/2.87 | (177) ~ (member(all_27_1_21, all_0_4_4) = 0) | ? [v0] : (apply(all_0_6_6, v0, all_27_1_21) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating (176) with all_43_0_22 yields:
% 10.23/2.87 | (178) apply(all_0_6_6, all_43_0_22, all_27_1_21) = 0 & member(all_43_0_22, all_0_2_2) = 0
% 10.23/2.87 |
% 10.23/2.87 | Applying alpha-rule on (178) yields:
% 10.23/2.87 | (179) apply(all_0_6_6, all_43_0_22, all_27_1_21) = 0
% 10.23/2.87 | (180) member(all_43_0_22, all_0_2_2) = 0
% 10.23/2.87 |
% 10.23/2.87 +-Applying beta-rule and splitting (177), into two cases.
% 10.23/2.87 |-Branch one:
% 10.23/2.87 | (181) ~ (member(all_27_1_21, all_0_4_4) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Using (175) and (181) yields:
% 10.23/2.87 | (123) $false
% 10.23/2.87 |
% 10.23/2.87 |-The branch is then unsatisfiable
% 10.23/2.87 |-Branch two:
% 10.23/2.87 | (175) member(all_27_1_21, all_0_4_4) = 0
% 10.23/2.87 | (184) ? [v0] : (apply(all_0_6_6, v0, all_27_1_21) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (95) with all_0_2_2, all_43_0_22, all_0_5_5, all_0_3_3, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_3_3, all_0_5_5) = all_0_2_2, member(all_43_0_22, all_0_2_2) = 0, yields:
% 10.23/2.87 | (185) member(all_43_0_22, all_0_5_5) = 0
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (94) with all_0_2_2, all_43_0_22, all_0_5_5, all_0_3_3, all_0_6_6 and discharging atoms inverse_image3(all_0_6_6, all_0_3_3, all_0_5_5) = all_0_2_2, member(all_43_0_22, all_0_2_2) = 0, yields:
% 10.23/2.87 | (186) ? [v0] : (apply(all_0_6_6, all_43_0_22, v0) = 0 & member(v0, all_0_3_3) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating formula (83) with all_43_0_22, 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:
% 10.23/2.87 | (187) ~ (member(all_43_0_22, all_0_5_5) = 0) | ? [v0] : (apply(all_0_6_6, all_43_0_22, v0) = 0 & member(v0, all_0_4_4) = 0)
% 10.23/2.87 |
% 10.23/2.87 | Instantiating (186) with all_67_0_25 yields:
% 10.23/2.87 | (188) apply(all_0_6_6, all_43_0_22, all_67_0_25) = 0 & member(all_67_0_25, all_0_3_3) = 0
% 10.23/2.88 |
% 10.23/2.88 | Applying alpha-rule on (188) yields:
% 10.23/2.88 | (189) apply(all_0_6_6, all_43_0_22, all_67_0_25) = 0
% 10.23/2.88 | (190) member(all_67_0_25, all_0_3_3) = 0
% 10.23/2.88 |
% 10.23/2.88 +-Applying beta-rule and splitting (187), into two cases.
% 10.23/2.88 |-Branch one:
% 10.23/2.88 | (191) ~ (member(all_43_0_22, all_0_5_5) = 0)
% 10.23/2.88 |
% 10.23/2.88 | Using (185) and (191) yields:
% 10.23/2.88 | (123) $false
% 10.23/2.88 |
% 10.23/2.88 |-The branch is then unsatisfiable
% 10.23/2.88 |-Branch two:
% 10.23/2.88 | (185) member(all_43_0_22, all_0_5_5) = 0
% 10.23/2.88 | (194) ? [v0] : (apply(all_0_6_6, all_43_0_22, v0) = 0 & member(v0, all_0_4_4) = 0)
% 10.23/2.88 |
% 10.23/2.88 | Instantiating (194) with all_76_0_26 yields:
% 10.23/2.88 | (195) apply(all_0_6_6, all_43_0_22, all_76_0_26) = 0 & member(all_76_0_26, all_0_4_4) = 0
% 10.23/2.88 |
% 10.23/2.88 | Applying alpha-rule on (195) yields:
% 10.23/2.88 | (196) apply(all_0_6_6, all_43_0_22, all_76_0_26) = 0
% 10.23/2.88 | (197) member(all_76_0_26, all_0_4_4) = 0
% 10.23/2.88 |
% 10.23/2.88 | Instantiating formula (91) with all_27_1_21, all_76_0_26, all_43_0_22, 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_43_0_22, all_76_0_26) = 0, apply(all_0_6_6, all_43_0_22, all_27_1_21) = 0, yields:
% 10.23/2.88 | (198) all_76_0_26 = all_27_1_21 | ? [v0] : ? [v1] : ? [v2] : (member(all_76_0_26, all_0_4_4) = v1 & member(all_43_0_22, all_0_5_5) = v0 & member(all_27_1_21, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 10.23/2.88 |
% 10.23/2.88 | Instantiating formula (91) with all_76_0_26, all_67_0_25, all_43_0_22, 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_43_0_22, all_76_0_26) = 0, apply(all_0_6_6, all_43_0_22, all_67_0_25) = 0, yields:
% 10.23/2.88 | (199) all_76_0_26 = all_67_0_25 | ? [v0] : ? [v1] : ? [v2] : (member(all_76_0_26, all_0_4_4) = v2 & member(all_67_0_25, all_0_4_4) = v1 & member(all_43_0_22, all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 10.23/2.88 |
% 10.23/2.88 | Instantiating formula (74) with all_67_0_25, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms surjective(all_0_6_6, all_0_5_5, all_0_4_4) = 0, yields:
% 10.23/2.88 | (200) ~ (member(all_67_0_25, all_0_4_4) = 0) | ? [v0] : (apply(all_0_6_6, v0, all_67_0_25) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.88 |
% 10.23/2.88 | Instantiating formula (97) with all_67_0_25, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = 0, member(all_67_0_25, all_0_3_3) = 0, yields:
% 10.23/2.88 | (201) member(all_67_0_25, all_0_4_4) = 0
% 10.23/2.88 |
% 10.23/2.88 +-Applying beta-rule and splitting (199), into two cases.
% 10.23/2.88 |-Branch one:
% 10.23/2.88 | (202) all_76_0_26 = all_67_0_25
% 10.23/2.88 |
% 10.23/2.88 | From (202) and (197) follows:
% 10.23/2.88 | (201) member(all_67_0_25, all_0_4_4) = 0
% 10.23/2.88 |
% 10.23/2.88 +-Applying beta-rule and splitting (198), into two cases.
% 10.23/2.88 |-Branch one:
% 10.23/2.88 | (204) all_76_0_26 = all_27_1_21
% 10.23/2.88 |
% 10.23/2.88 | Combining equations (204,202) yields a new equation:
% 10.23/2.88 | (205) all_67_0_25 = all_27_1_21
% 10.23/2.88 |
% 10.23/2.88 | From (205) and (190) follows:
% 10.23/2.88 | (206) member(all_27_1_21, all_0_3_3) = 0
% 10.23/2.88 |
% 10.23/2.88 +-Applying beta-rule and splitting (174), into two cases.
% 10.23/2.88 |-Branch one:
% 10.23/2.88 | (207) ~ (member(all_27_1_21, all_0_3_3) = 0)
% 10.23/2.88 |
% 10.23/2.88 | Using (206) and (207) yields:
% 10.23/2.88 | (123) $false
% 10.23/2.88 |
% 10.23/2.88 |-The branch is then unsatisfiable
% 10.23/2.88 |-Branch two:
% 10.23/2.88 | (206) member(all_27_1_21, all_0_3_3) = 0
% 10.23/2.88 | (210) all_27_0_20 = 0
% 10.23/2.88 |
% 10.23/2.88 | Equations (210) can reduce 171 to:
% 10.23/2.88 | (100) $false
% 10.23/2.88 |
% 10.23/2.88 |-The branch is then unsatisfiable
% 10.23/2.88 |-Branch two:
% 10.23/2.88 | (212) ~ (all_76_0_26 = all_27_1_21)
% 10.23/2.88 | (213) ? [v0] : ? [v1] : ? [v2] : (member(all_76_0_26, all_0_4_4) = v1 & member(all_43_0_22, all_0_5_5) = v0 & member(all_27_1_21, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 10.23/2.88 |
% 10.23/2.88 | Instantiating (213) with all_104_0_29, all_104_1_30, all_104_2_31 yields:
% 10.23/2.88 | (214) member(all_76_0_26, all_0_4_4) = all_104_1_30 & member(all_43_0_22, all_0_5_5) = all_104_2_31 & member(all_27_1_21, all_0_4_4) = all_104_0_29 & ( ~ (all_104_0_29 = 0) | ~ (all_104_1_30 = 0) | ~ (all_104_2_31 = 0))
% 10.23/2.88 |
% 10.23/2.88 | Applying alpha-rule on (214) yields:
% 10.23/2.88 | (215) member(all_76_0_26, all_0_4_4) = all_104_1_30
% 10.23/2.88 | (216) member(all_43_0_22, all_0_5_5) = all_104_2_31
% 10.23/2.88 | (217) member(all_27_1_21, all_0_4_4) = all_104_0_29
% 10.23/2.88 | (218) ~ (all_104_0_29 = 0) | ~ (all_104_1_30 = 0) | ~ (all_104_2_31 = 0)
% 10.23/2.88 |
% 10.23/2.88 | From (202) and (215) follows:
% 10.23/2.88 | (219) member(all_67_0_25, all_0_4_4) = all_104_1_30
% 10.23/2.88 |
% 10.23/2.88 +-Applying beta-rule and splitting (200), into two cases.
% 10.23/2.88 |-Branch one:
% 10.23/2.88 | (220) ~ (member(all_67_0_25, all_0_4_4) = 0)
% 10.23/2.88 |
% 10.23/2.88 | Using (201) and (220) yields:
% 10.23/2.88 | (123) $false
% 10.23/2.88 |
% 10.23/2.88 |-The branch is then unsatisfiable
% 10.23/2.88 |-Branch two:
% 10.23/2.88 | (201) member(all_67_0_25, all_0_4_4) = 0
% 10.23/2.88 | (223) ? [v0] : (apply(all_0_6_6, v0, all_67_0_25) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_67_0_25, all_0_4_4, all_104_1_30, 0 and discharging atoms member(all_67_0_25, all_0_4_4) = all_104_1_30, member(all_67_0_25, all_0_4_4) = 0, yields:
% 10.23/2.89 | (224) all_104_1_30 = 0
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_43_0_22, all_0_5_5, all_104_2_31, 0 and discharging atoms member(all_43_0_22, all_0_5_5) = all_104_2_31, member(all_43_0_22, all_0_5_5) = 0, yields:
% 10.23/2.89 | (225) all_104_2_31 = 0
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_27_1_21, all_0_4_4, all_104_0_29, 0 and discharging atoms member(all_27_1_21, all_0_4_4) = all_104_0_29, member(all_27_1_21, all_0_4_4) = 0, yields:
% 10.23/2.89 | (226) all_104_0_29 = 0
% 10.23/2.89 |
% 10.23/2.89 +-Applying beta-rule and splitting (218), into two cases.
% 10.23/2.89 |-Branch one:
% 10.23/2.89 | (227) ~ (all_104_0_29 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (226) can reduce 227 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (226) all_104_0_29 = 0
% 10.23/2.89 | (230) ~ (all_104_1_30 = 0) | ~ (all_104_2_31 = 0)
% 10.23/2.89 |
% 10.23/2.89 +-Applying beta-rule and splitting (230), into two cases.
% 10.23/2.89 |-Branch one:
% 10.23/2.89 | (231) ~ (all_104_1_30 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (224) can reduce 231 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (224) all_104_1_30 = 0
% 10.23/2.89 | (234) ~ (all_104_2_31 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (225) can reduce 234 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (236) ~ (all_76_0_26 = all_67_0_25)
% 10.23/2.89 | (237) ? [v0] : ? [v1] : ? [v2] : (member(all_76_0_26, all_0_4_4) = v2 & member(all_67_0_25, all_0_4_4) = v1 & member(all_43_0_22, all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 10.23/2.89 |
% 10.23/2.89 | Instantiating (237) with all_100_0_36, all_100_1_37, all_100_2_38 yields:
% 10.23/2.89 | (238) member(all_76_0_26, all_0_4_4) = all_100_0_36 & member(all_67_0_25, all_0_4_4) = all_100_1_37 & member(all_43_0_22, all_0_5_5) = all_100_2_38 & ( ~ (all_100_0_36 = 0) | ~ (all_100_1_37 = 0) | ~ (all_100_2_38 = 0))
% 10.23/2.89 |
% 10.23/2.89 | Applying alpha-rule on (238) yields:
% 10.23/2.89 | (239) member(all_76_0_26, all_0_4_4) = all_100_0_36
% 10.23/2.89 | (240) member(all_67_0_25, all_0_4_4) = all_100_1_37
% 10.23/2.89 | (241) member(all_43_0_22, all_0_5_5) = all_100_2_38
% 10.23/2.89 | (242) ~ (all_100_0_36 = 0) | ~ (all_100_1_37 = 0) | ~ (all_100_2_38 = 0)
% 10.23/2.89 |
% 10.23/2.89 +-Applying beta-rule and splitting (200), into two cases.
% 10.23/2.89 |-Branch one:
% 10.23/2.89 | (220) ~ (member(all_67_0_25, all_0_4_4) = 0)
% 10.23/2.89 |
% 10.23/2.89 | Using (201) and (220) yields:
% 10.23/2.89 | (123) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (201) member(all_67_0_25, all_0_4_4) = 0
% 10.23/2.89 | (223) ? [v0] : (apply(all_0_6_6, v0, all_67_0_25) = 0 & member(v0, all_0_5_5) = 0)
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_76_0_26, all_0_4_4, all_100_0_36, 0 and discharging atoms member(all_76_0_26, all_0_4_4) = all_100_0_36, member(all_76_0_26, all_0_4_4) = 0, yields:
% 10.23/2.89 | (247) all_100_0_36 = 0
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_67_0_25, all_0_4_4, all_100_1_37, 0 and discharging atoms member(all_67_0_25, all_0_4_4) = all_100_1_37, member(all_67_0_25, all_0_4_4) = 0, yields:
% 10.23/2.89 | (248) all_100_1_37 = 0
% 10.23/2.89 |
% 10.23/2.89 | Instantiating formula (40) with all_43_0_22, all_0_5_5, all_100_2_38, 0 and discharging atoms member(all_43_0_22, all_0_5_5) = all_100_2_38, member(all_43_0_22, all_0_5_5) = 0, yields:
% 10.23/2.89 | (249) all_100_2_38 = 0
% 10.23/2.89 |
% 10.23/2.89 +-Applying beta-rule and splitting (242), into two cases.
% 10.23/2.89 |-Branch one:
% 10.23/2.89 | (250) ~ (all_100_0_36 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (247) can reduce 250 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (247) all_100_0_36 = 0
% 10.23/2.89 | (253) ~ (all_100_1_37 = 0) | ~ (all_100_2_38 = 0)
% 10.23/2.89 |
% 10.23/2.89 +-Applying beta-rule and splitting (253), into two cases.
% 10.23/2.89 |-Branch one:
% 10.23/2.89 | (254) ~ (all_100_1_37 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (248) can reduce 254 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 |-Branch two:
% 10.23/2.89 | (248) all_100_1_37 = 0
% 10.23/2.89 | (257) ~ (all_100_2_38 = 0)
% 10.23/2.89 |
% 10.23/2.89 | Equations (249) can reduce 257 to:
% 10.23/2.89 | (100) $false
% 10.23/2.89 |
% 10.23/2.89 |-The branch is then unsatisfiable
% 10.23/2.89 % SZS output end Proof for theBenchmark
% 10.23/2.89
% 10.23/2.89 2302ms
%------------------------------------------------------------------------------