TSTP Solution File: SET710+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET710+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 00:21:33 EDT 2022
% Result : Theorem 7.12s 2.24s
% Output : Proof 13.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET710+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jul 11 03:05:52 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/1.00 Prover 0: Preprocessing ...
% 3.21/1.34 Prover 0: Warning: ignoring some quantifiers
% 3.21/1.37 Prover 0: Constructing countermodel ...
% 4.48/1.71 Prover 0: gave up
% 4.48/1.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.95/1.76 Prover 1: Preprocessing ...
% 5.71/1.98 Prover 1: Constructing countermodel ...
% 7.12/2.23 Prover 1: proved (528ms)
% 7.12/2.23
% 7.12/2.23 No countermodel exists, formula is valid
% 7.12/2.24 % SZS status Theorem for theBenchmark
% 7.12/2.24
% 7.12/2.24 Generating proof ... found it (size 200)
% 12.69/3.50
% 12.69/3.50 % SZS output start Proof for theBenchmark
% 12.69/3.50 Assumed formulas after preprocessing and simplification:
% 12.69/3.50 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & equal_maps(v8, v10, v3, v6) = v11 & compose_function(v9, v0, v3, v4, v6) = v10 & compose_function(v2, v7, v3, v5, v6) = v8 & compose_function(v2, v1, v4, v5, v6) = v9 & compose_function(v1, v0, v3, v4, v5) = v7 & maps(v2, v5, v6) = 0 & maps(v1, v4, v5) = 0 & maps(v0, v3, v4) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (compose_function(v12, v13, v14, v15, v16) = v19) | ~ (apply(v19, v17, v18) = v20) | ~ (apply(v12, v21, v18) = 0) | ? [v22] : ? [v23] : ((apply(v13, v17, v21) = v23 & member(v21, v15) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))) | (member(v18, v16) = v23 & member(v17, v14) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (compose_predicate(v12, v13, v14, v15, v16, v17) = 0) | ~ (apply(v13, v21, v19) = 0) | ~ (apply(v12, v18, v19) = v20) | ? [v22] : ? [v23] : ((apply(v14, v18, v21) = v23 & member(v21, v16) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))) | (member(v19, v17) = v23 & member(v18, v15) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (isomorphism(v12, v13, v14, v15, v16) = 0) | ~ (apply(v12, v19, v20) = 0) | ~ (apply(v12, v17, v18) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (apply(v16, v18, v20) = v26 & apply(v14, v17, v19) = v25 & member(v20, v15) = v24 & member(v19, v13) = v23 & member(v18, v15) = v22 & member(v17, v13) = v21 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | (( ~ (v26 = 0) | v25 = 0) & ( ~ (v25 = 0) | v26 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (decreasing(v12, v13, v14, v15, v16) = 0) | ~ (apply(v12, v19, v20) = 0) | ~ (apply(v12, v17, v18) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (apply(v16, v20, v18) = v26 & apply(v14, v17, v19) = v25 & member(v20, v15) = v24 & member(v19, v13) = v23 & member(v18, v15) = v22 & member(v17, v13) = v21 & ( ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | v26 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (increasing(v12, v13, v14, v15, v16) = 0) | ~ (apply(v12, v19, v20) = 0) | ~ (apply(v12, v17, v18) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (apply(v16, v18, v20) = v26 & apply(v14, v17, v19) = v25 & member(v20, v15) = v24 & member(v19, v13) = v23 & member(v18, v15) = v22 & member(v17, v13) = v21 & ( ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | v26 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = v12 | ~ (compose_predicate(v19, v18, v17, v16, v15, v14) = v13) | ~ (compose_predicate(v19, v18, v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (compose_function(v12, v13, v14, v15, v16) = v19) | ~ (apply(v19, v17, v18) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & v21 = 0 & apply(v13, v17, v20) = 0 & apply(v12, v20, v18) = 0 & member(v20, v15) = 0) | (member(v18, v16) = v21 & member(v17, v14) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (compose_predicate(v12, v13, v14, v15, v16, v17) = 0) | ~ (apply(v12, v18, v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & v21 = 0 & apply(v14, v18, v20) = 0 & apply(v13, v20, v19) = 0 & member(v20, v16) = 0) | (member(v19, v17) = v21 & member(v18, v15) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (equal_maps(v12, v13, v14, v15) = 0) | ~ (apply(v13, v16, v18) = 0) | ~ (apply(v12, v16, v17) = 0) | ? [v19] : ? [v20] : ? [v21] : (member(v18, v15) = v21 & member(v17, v15) = v20 & member(v16, v14) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (compose_predicate(v12, v13, v14, v15, v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v12, v19, v20) = v21 & member(v20, v17) = 0 & member(v19, v15) = 0 & ( ~ (v21 = 0) | ! [v26] : ( ~ (apply(v13, v26, v20) = 0) | ? [v27] : ? [v28] : (apply(v14, v19, v26) = v28 & member(v26, v16) = v27 & ( ~ (v28 = 0) | ~ (v27 = 0))))) & (v21 = 0 | (v25 = 0 & v24 = 0 & v23 = 0 & apply(v14, v19, v22) = 0 & apply(v13, v22, v20) = 0 & member(v22, v16) = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (inverse_image3(v12, v13, v14) = v16) | ~ (apply(v12, v15, v18) = 0) | ~ (member(v15, v16) = v17) | ? [v19] : (( ~ (v19 = 0) & member(v18, v13) = v19) | ( ~ (v19 = 0) & member(v15, v14) = v19))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = 0 | ~ (image3(v12, v13, v14) = v16) | ~ (apply(v12, v18, v15) = 0) | ~ (member(v15, v16) = v17) | ? [v19] : (( ~ (v19 = 0) & member(v18, v13) = v19) | ( ~ (v19 = 0) & member(v15, v14) = v19))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v13 = v12 | ~ (isomorphism(v18, v17, v16, v15, v14) = v13) | ~ (isomorphism(v18, v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v13 = v12 | ~ (decreasing(v18, v17, v16, v15, v14) = v13) | ~ (decreasing(v18, v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v13 = v12 | ~ (increasing(v18, v17, v16, v15, v14) = v13) | ~ (increasing(v18, v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v13 = v12 | ~ (compose_function(v18, v17, v16, v15, v14) = v13) | ~ (compose_function(v18, v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (inverse_function(v12, v13, v14) = v17) | ~ (apply(v17, v16, v15) = v18) | ? [v19] : ? [v20] : ? [v21] : (apply(v12, v15, v16) = v21 & member(v16, v14) = v20 & member(v15, v13) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | (( ~ (v21 = 0) | v18 = 0) & ( ~ (v18 = 0) | v21 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (inverse_predicate(v12, v13, v14, v15) = 0) | ~ (apply(v12, v17, v16) = v18) | ? [v19] : ? [v20] : ? [v21] : (apply(v13, v16, v17) = v21 & member(v17, v15) = v20 & member(v16, v14) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | (( ~ (v21 = 0) | v18 = 0) & ( ~ (v18 = 0) | v21 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (maps(v12, v13, v14) = 0) | ~ (apply(v12, v15, v17) = 0) | ~ (apply(v12, v15, v16) = 0) | ? [v18] : ? [v19] : ? [v20] : (member(v17, v14) = v20 & member(v16, v14) = v19 & member(v15, v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (isomorphism(v12, v13, v14, v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ((v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & apply(v16, v19, v21) = v29 & apply(v14, v18, v20) = v28 & apply(v12, v20, v21) = 0 & apply(v12, v18, v19) = 0 & member(v21, v15) = 0 & member(v20, v13) = 0 & member(v19, v15) = 0 & member(v18, v13) = 0 & ( ~ (v29 = 0) | ~ (v28 = 0)) & (v29 = 0 | v28 = 0)) | (one_to_one(v12, v13, v15) = v19 & maps(v12, v13, v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (decreasing(v12, v13, v14, v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = 0) & apply(v16, v21, v19) = v22 & apply(v14, v18, v20) = 0 & apply(v12, v20, v21) = 0 & apply(v12, v18, v19) = 0 & member(v21, v15) = 0 & member(v20, v13) = 0 & member(v19, v15) = 0 & member(v18, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (increasing(v12, v13, v14, v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = 0) & apply(v16, v19, v21) = v22 & apply(v14, v18, v20) = 0 & apply(v12, v20, v21) = 0 & apply(v12, v18, v19) = 0 & member(v21, v15) = 0 & member(v20, v13) = 0 & member(v19, v15) = 0 & member(v18, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (injective(v12, v13, v14) = 0) | ~ (apply(v12, v16, v17) = 0) | ~ (apply(v12, v15, v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (member(v17, v14) = v20 & member(v16, v13) = v19 & member(v15, v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (inverse_image2(v12, v13) = v15) | ~ (apply(v12, v14, v17) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : ( ~ (v18 = 0) & member(v17, v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (image2(v12, v13) = v15) | ~ (apply(v12, v17, v14) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : ( ~ (v18 = 0) & member(v17, v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (inverse_predicate(v17, v16, v15, v14) = v13) | ~ (inverse_predicate(v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (equal_maps(v17, v16, v15, v14) = v13) | ~ (equal_maps(v17, v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (inverse_predicate(v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v13, v17, v18) = v19 & apply(v12, v18, v17) = v20 & member(v18, v15) = 0 & member(v17, v14) = 0 & ( ~ (v20 = 0) | ~ (v19 = 0)) & (v20 = 0 | v19 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (equal_maps(v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ( ~ (v19 = v18) & apply(v13, v17, v19) = 0 & apply(v12, v17, v18) = 0 & member(v19, v15) = 0 & member(v18, v15) = 0 & member(v17, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (product(v13) = v14) | ~ (member(v12, v15) = v16) | ~ (member(v12, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & member(v15, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (difference(v14, v13) = v15) | ~ (member(v12, v15) = v16) | ? [v17] : ? [v18] : (member(v12, v14) = v17 & member(v12, v13) = v18 & ( ~ (v17 = 0) | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (union(v13, v14) = v15) | ~ (member(v12, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & ~ (v17 = 0) & member(v12, v14) = v18 & member(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (intersection(v13, v14) = v15) | ~ (member(v12, v15) = v16) | ? [v17] : ? [v18] : (member(v12, v14) = v18 & member(v12, v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (sum(v13) = v14) | ~ (member(v12, v16) = 0) | ~ (member(v12, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & member(v16, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (inverse_image3(v16, v15, v14) = v13) | ~ (inverse_image3(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (image3(v16, v15, v14) = v13) | ~ (image3(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (inverse_function(v16, v15, v14) = v13) | ~ (inverse_function(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (one_to_one(v16, v15, v14) = v13) | ~ (one_to_one(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (surjective(v16, v15, v14) = v13) | ~ (surjective(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (injective(v16, v15, v14) = v13) | ~ (injective(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (maps(v16, v15, v14) = v13) | ~ (maps(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (apply(v16, v15, v14) = v13) | ~ (apply(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (isomorphism(v12, v13, v14, v15, v16) = 0) | (one_to_one(v12, v13, v15) = 0 & maps(v12, v13, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (inverse_image3(v12, v13, v14) = v16) | ~ (member(v15, v16) = 0) | member(v15, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (inverse_image3(v12, v13, v14) = v16) | ~ (member(v15, v16) = 0) | ? [v17] : (apply(v12, v15, v17) = 0 & member(v17, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image3(v12, v13, v14) = v16) | ~ (member(v15, v16) = 0) | member(v15, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image3(v12, v13, v14) = v16) | ~ (member(v15, v16) = 0) | ? [v17] : (apply(v12, v17, v15) = 0 & member(v17, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (surjective(v12, v13, v14) = v15) | ? [v16] : (member(v16, v14) = 0 & ! [v17] : ( ~ (apply(v12, v17, v16) = 0) | ? [v18] : ( ~ (v18 = 0) & member(v17, v13) = v18)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (injective(v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v17 = v16) & apply(v12, v17, v18) = 0 & apply(v12, v16, v18) = 0 & member(v18, v14) = 0 & member(v17, v13) = 0 & member(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (identity(v12, v13) = 0) | ~ (apply(v12, v14, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & member(v14, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (maps(v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & ~ (v18 = v17) & apply(v12, v16, v18) = 0 & apply(v12, v16, v17) = 0 & member(v18, v14) = 0 & member(v17, v14) = 0 & member(v16, v13) = 0) | (v17 = 0 & member(v16, v13) = 0 & ! [v24] : ( ~ (apply(v12, v16, v24) = 0) | ? [v25] : ( ~ (v25 = 0) & member(v24, v14) = v25))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (product(v13) = v14) | ~ (member(v12, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & member(v16, v13) = 0 & member(v12, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (unordered_pair(v13, v12) = v14) | ~ (member(v12, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (unordered_pair(v12, v13) = v14) | ~ (member(v12, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (power_set(v13) = v14) | ~ (member(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v12 | v13 = v12 | ~ (unordered_pair(v13, v14) = v15) | ~ (member(v12, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (inverse_image2(v15, v14) = v13) | ~ (inverse_image2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (image2(v15, v14) = v13) | ~ (image2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (identity(v15, v14) = v13) | ~ (identity(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (difference(v15, v14) = v13) | ~ (difference(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (union(v15, v14) = v13) | ~ (union(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (intersection(v15, v14) = v13) | ~ (intersection(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (equal_set(v15, v14) = v13) | ~ (equal_set(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (member(v15, v14) = v13) | ~ (member(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_image2(v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v12, v14, v16) = 0 & member(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image2(v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v12, v16, v14) = 0 & member(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (surjective(v12, v13, v14) = v15) | ? [v16] : ? [v17] : (one_to_one(v12, v13, v14) = v16 & injective(v12, v13, v14) = v17 & ( ~ (v16 = 0) | (v17 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (surjective(v12, v13, v14) = 0) | ~ (member(v15, v14) = 0) | ? [v16] : (apply(v12, v16, v15) = 0 & member(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (maps(v12, v13, v14) = 0) | ~ (member(v15, v13) = 0) | ? [v16] : (apply(v12, v15, v16) = 0 & member(v16, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (difference(v14, v13) = v15) | ~ (member(v12, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v12, v14) = 0 & member(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (union(v13, v14) = v15) | ~ (member(v12, v15) = 0) | ? [v16] : ? [v17] : (member(v12, v14) = v17 & member(v12, v13) = v16 & (v17 = 0 | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (intersection(v13, v14) = v15) | ~ (member(v12, v15) = 0) | (member(v12, v14) = 0 & member(v12, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (identity(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v12, v15, v15) = v16 & member(v15, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v12) = v13) | ~ (member(v12, v13) = v14)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (equal_set(v12, v13) = v14) | ? [v15] : ? [v16] : (subset(v13, v12) = v16 & subset(v12, v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & member(v15, v13) = v16 & member(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (product(v14) = v13) | ~ (product(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (sum(v14) = v13) | ~ (sum(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v13) = v14) | ~ (member(v12, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (power_set(v14) = v13) | ~ (power_set(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (surjective(v12, v13, v14) = 0) | ? [v15] : ? [v16] : (one_to_one(v12, v13, v14) = v16 & injective(v12, v13, v14) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (sum(v13) = v14) | ~ (member(v12, v14) = 0) | ? [v15] : (member(v15, v13) = 0 & member(v12, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (power_set(v13) = v14) | ~ (member(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (member(v14, v12) = 0) | member(v14, v13) = 0) & ! [v12] : ! [v13] : ( ~ (equal_set(v12, v13) = 0) | (subset(v13, v12) = 0 & subset(v12, v13) = 0)) & ! [v12] : ~ (member(v12, empty_set) = 0))
% 12.85/3.57 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 12.85/3.57 | (1) ~ (all_0_0_0 = 0) & equal_maps(all_0_3_3, all_0_1_1, all_0_8_8, all_0_5_5) = all_0_0_0 & compose_function(all_0_2_2, all_0_11_11, all_0_8_8, all_0_7_7, all_0_5_5) = all_0_1_1 & compose_function(all_0_9_9, all_0_4_4, all_0_8_8, all_0_6_6, all_0_5_5) = all_0_3_3 & compose_function(all_0_9_9, all_0_10_10, all_0_7_7, all_0_6_6, all_0_5_5) = all_0_2_2 & compose_function(all_0_10_10, all_0_11_11, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4 & maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0 & maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0 & maps(all_0_11_11, all_0_8_8, all_0_7_7) = 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)
% 13.21/3.60 |
% 13.21/3.60 | Applying alpha-rule on (1) yields:
% 13.21/3.60 | (2) ! [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))))
% 13.21/3.60 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 13.21/3.61 | (4) ! [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)))
% 13.21/3.61 | (5) ! [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)))))
% 13.21/3.61 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 13.21/3.61 | (7) compose_function(all_0_2_2, all_0_11_11, all_0_8_8, all_0_7_7, all_0_5_5) = all_0_1_1
% 13.21/3.61 | (8) maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0
% 13.21/3.61 | (9) ! [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))
% 13.21/3.61 | (10) ! [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))
% 13.21/3.61 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 13.21/3.61 | (12) ~ (all_0_0_0 = 0)
% 13.21/3.61 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 13.21/3.61 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 13.21/3.61 | (15) ! [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)))))
% 13.21/3.61 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 13.21/3.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 13.21/3.61 | (18) ! [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)))))
% 13.21/3.61 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 13.21/3.61 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 13.21/3.61 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 13.21/3.61 | (22) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.21/3.61 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 13.21/3.61 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 13.21/3.61 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 13.21/3.61 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 13.21/3.61 | (27) ! [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))
% 13.21/3.61 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 13.21/3.61 | (29) ! [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)))
% 13.21/3.61 | (30) ! [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))
% 13.21/3.62 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 13.21/3.62 | (32) ! [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)))))
% 13.21/3.62 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 13.21/3.62 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 13.21/3.62 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 13.21/3.62 | (36) ! [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)))))
% 13.21/3.62 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 13.21/3.62 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 13.21/3.62 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))))
% 13.21/3.62 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 13.21/3.62 | (41) equal_maps(all_0_3_3, all_0_1_1, all_0_8_8, all_0_5_5) = all_0_0_0
% 13.21/3.62 | (42) ! [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)))
% 13.21/3.62 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 13.21/3.62 | (44) maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0
% 13.21/3.62 | (45) ! [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)))
% 13.21/3.62 | (46) ! [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))
% 13.21/3.62 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 13.21/3.62 | (48) ! [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))))
% 13.21/3.62 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 13.21/3.62 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 13.21/3.62 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 13.21/3.62 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 13.21/3.62 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 13.21/3.62 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 13.21/3.62 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 13.21/3.62 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 13.21/3.62 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 13.21/3.62 | (58) ! [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))
% 13.21/3.62 | (59) ! [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))
% 13.21/3.62 | (60) ! [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))
% 13.21/3.62 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 13.21/3.63 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 13.21/3.63 | (63) ! [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)))
% 13.21/3.63 | (64) ! [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))))
% 13.21/3.63 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 13.21/3.63 | (66) ! [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))))
% 13.21/3.63 | (67) ! [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))))
% 13.21/3.63 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 13.21/3.63 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 13.21/3.63 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 13.21/3.63 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 13.21/3.63 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 13.21/3.63 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 13.21/3.63 | (74) ! [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)))))
% 13.21/3.63 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 13.21/3.63 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 13.21/3.63 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 13.21/3.63 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 13.21/3.63 | (79) ! [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)))))
% 13.21/3.63 | (80) compose_function(all_0_9_9, all_0_10_10, all_0_7_7, all_0_6_6, all_0_5_5) = all_0_2_2
% 13.21/3.63 | (81) ! [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))
% 13.21/3.63 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 13.21/3.63 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 13.21/3.63 | (84) maps(all_0_11_11, all_0_8_8, all_0_7_7) = 0
% 13.21/3.63 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 13.21/3.63 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 13.21/3.63 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13)))))
% 13.21/3.63 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 13.21/3.63 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 13.21/3.63 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 13.21/3.64 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 13.21/3.64 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 13.21/3.64 | (93) compose_function(all_0_10_10, all_0_11_11, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4
% 13.21/3.64 | (94) compose_function(all_0_9_9, all_0_4_4, all_0_8_8, all_0_6_6, all_0_5_5) = all_0_3_3
% 13.21/3.64 | (95) ! [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))
% 13.21/3.64 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 13.21/3.64 | (97) ! [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))))
% 13.21/3.64 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 13.21/3.64 | (99) ! [v0] : ~ (member(v0, empty_set) = 0)
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (81) with all_0_0_0, all_0_5_5, all_0_8_8, all_0_1_1, all_0_3_3 and discharging atoms equal_maps(all_0_3_3, all_0_1_1, all_0_8_8, all_0_5_5) = all_0_0_0, yields:
% 13.21/3.64 | (100) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & apply(all_0_3_3, v0, v1) = 0 & member(v2, all_0_5_5) = 0 & member(v1, all_0_5_5) = 0 & member(v0, all_0_8_8) = 0)
% 13.21/3.64 |
% 13.21/3.64 +-Applying beta-rule and splitting (100), into two cases.
% 13.21/3.64 |-Branch one:
% 13.21/3.64 | (101) all_0_0_0 = 0
% 13.21/3.64 |
% 13.21/3.64 | Equations (101) can reduce 12 to:
% 13.21/3.64 | (102) $false
% 13.21/3.64 |
% 13.21/3.64 |-The branch is then unsatisfiable
% 13.21/3.64 |-Branch two:
% 13.21/3.64 | (12) ~ (all_0_0_0 = 0)
% 13.21/3.64 | (104) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_1_1, v0, v2) = 0 & apply(all_0_3_3, v0, v1) = 0 & member(v2, all_0_5_5) = 0 & member(v1, all_0_5_5) = 0 & member(v0, all_0_8_8) = 0)
% 13.21/3.64 |
% 13.21/3.64 | Instantiating (104) with all_10_0_12, all_10_1_13, all_10_2_14 yields:
% 13.21/3.64 | (105) ~ (all_10_0_12 = all_10_1_13) & apply(all_0_1_1, all_10_2_14, all_10_0_12) = 0 & apply(all_0_3_3, all_10_2_14, all_10_1_13) = 0 & member(all_10_0_12, all_0_5_5) = 0 & member(all_10_1_13, all_0_5_5) = 0 & member(all_10_2_14, all_0_8_8) = 0
% 13.21/3.64 |
% 13.21/3.64 | Applying alpha-rule on (105) yields:
% 13.21/3.64 | (106) member(all_10_1_13, all_0_5_5) = 0
% 13.21/3.64 | (107) apply(all_0_3_3, all_10_2_14, all_10_1_13) = 0
% 13.21/3.64 | (108) ~ (all_10_0_12 = all_10_1_13)
% 13.21/3.64 | (109) member(all_10_0_12, all_0_5_5) = 0
% 13.21/3.64 | (110) member(all_10_2_14, all_0_8_8) = 0
% 13.21/3.64 | (111) apply(all_0_1_1, all_10_2_14, all_10_0_12) = 0
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (32) with all_0_1_1, all_10_0_12, all_10_2_14, all_0_5_5, all_0_7_7, all_0_8_8, all_0_11_11, all_0_2_2 and discharging atoms compose_function(all_0_2_2, all_0_11_11, all_0_8_8, all_0_7_7, all_0_5_5) = all_0_1_1, apply(all_0_1_1, all_10_2_14, all_10_0_12) = 0, yields:
% 13.21/3.64 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_2_2, v0, all_10_0_12) = 0 & apply(all_0_11_11, all_10_2_14, v0) = 0 & member(v0, all_0_7_7) = 0) | (member(all_10_0_12, all_0_5_5) = v1 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (32) with all_0_3_3, all_10_1_13, all_10_2_14, all_0_5_5, all_0_6_6, all_0_8_8, all_0_4_4, all_0_9_9 and discharging atoms compose_function(all_0_9_9, all_0_4_4, all_0_8_8, all_0_6_6, all_0_5_5) = all_0_3_3, apply(all_0_3_3, all_10_2_14, all_10_1_13) = 0, yields:
% 13.21/3.64 | (113) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_4_4, all_10_2_14, v0) = 0 & apply(all_0_9_9, v0, all_10_1_13) = 0 & member(v0, all_0_6_6) = 0) | (member(all_10_1_13, all_0_5_5) = v1 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (35) with all_10_2_14, all_0_7_7, all_0_8_8, all_0_11_11 and discharging atoms maps(all_0_11_11, all_0_8_8, all_0_7_7) = 0, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.21/3.64 | (114) ? [v0] : (apply(all_0_11_11, all_10_2_14, v0) = 0 & member(v0, all_0_7_7) = 0)
% 13.21/3.64 |
% 13.21/3.64 | Instantiating (114) with all_25_0_15 yields:
% 13.21/3.64 | (115) apply(all_0_11_11, all_10_2_14, all_25_0_15) = 0 & member(all_25_0_15, all_0_7_7) = 0
% 13.21/3.64 |
% 13.21/3.64 | Applying alpha-rule on (115) yields:
% 13.21/3.64 | (116) apply(all_0_11_11, all_10_2_14, all_25_0_15) = 0
% 13.21/3.64 | (117) member(all_25_0_15, all_0_7_7) = 0
% 13.21/3.64 |
% 13.21/3.64 | Instantiating (113) with all_27_0_16, all_27_1_17, all_27_2_18, all_27_3_19 yields:
% 13.21/3.64 | (118) (all_27_0_16 = 0 & all_27_1_17 = 0 & all_27_2_18 = 0 & apply(all_0_4_4, all_10_2_14, all_27_3_19) = 0 & apply(all_0_9_9, all_27_3_19, all_10_1_13) = 0 & member(all_27_3_19, all_0_6_6) = 0) | (member(all_10_1_13, all_0_5_5) = all_27_2_18 & member(all_10_2_14, all_0_8_8) = all_27_3_19 & ( ~ (all_27_2_18 = 0) | ~ (all_27_3_19 = 0)))
% 13.21/3.64 |
% 13.21/3.64 | Instantiating (112) with all_28_0_20, all_28_1_21, all_28_2_22, all_28_3_23 yields:
% 13.21/3.64 | (119) (all_28_0_20 = 0 & all_28_1_21 = 0 & all_28_2_22 = 0 & apply(all_0_2_2, all_28_3_23, all_10_0_12) = 0 & apply(all_0_11_11, all_10_2_14, all_28_3_23) = 0 & member(all_28_3_23, all_0_7_7) = 0) | (member(all_10_0_12, all_0_5_5) = all_28_2_22 & member(all_10_2_14, all_0_8_8) = all_28_3_23 & ( ~ (all_28_2_22 = 0) | ~ (all_28_3_23 = 0)))
% 13.21/3.64 |
% 13.21/3.64 +-Applying beta-rule and splitting (118), into two cases.
% 13.21/3.64 |-Branch one:
% 13.21/3.64 | (120) all_27_0_16 = 0 & all_27_1_17 = 0 & all_27_2_18 = 0 & apply(all_0_4_4, all_10_2_14, all_27_3_19) = 0 & apply(all_0_9_9, all_27_3_19, all_10_1_13) = 0 & member(all_27_3_19, all_0_6_6) = 0
% 13.21/3.64 |
% 13.21/3.64 | Applying alpha-rule on (120) yields:
% 13.21/3.64 | (121) all_27_0_16 = 0
% 13.21/3.64 | (122) member(all_27_3_19, all_0_6_6) = 0
% 13.21/3.64 | (123) all_27_2_18 = 0
% 13.21/3.64 | (124) apply(all_0_9_9, all_27_3_19, all_10_1_13) = 0
% 13.21/3.64 | (125) all_27_1_17 = 0
% 13.21/3.64 | (126) apply(all_0_4_4, all_10_2_14, all_27_3_19) = 0
% 13.21/3.64 |
% 13.21/3.64 +-Applying beta-rule and splitting (119), into two cases.
% 13.21/3.64 |-Branch one:
% 13.21/3.64 | (127) all_28_0_20 = 0 & all_28_1_21 = 0 & all_28_2_22 = 0 & apply(all_0_2_2, all_28_3_23, all_10_0_12) = 0 & apply(all_0_11_11, all_10_2_14, all_28_3_23) = 0 & member(all_28_3_23, all_0_7_7) = 0
% 13.21/3.64 |
% 13.21/3.64 | Applying alpha-rule on (127) yields:
% 13.21/3.64 | (128) all_28_2_22 = 0
% 13.21/3.64 | (129) member(all_28_3_23, all_0_7_7) = 0
% 13.21/3.64 | (130) all_28_1_21 = 0
% 13.21/3.64 | (131) apply(all_0_2_2, all_28_3_23, all_10_0_12) = 0
% 13.21/3.64 | (132) apply(all_0_11_11, all_10_2_14, all_28_3_23) = 0
% 13.21/3.64 | (133) all_28_0_20 = 0
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (32) with all_0_2_2, all_10_0_12, all_28_3_23, all_0_5_5, all_0_6_6, all_0_7_7, all_0_10_10, all_0_9_9 and discharging atoms compose_function(all_0_9_9, all_0_10_10, all_0_7_7, all_0_6_6, all_0_5_5) = all_0_2_2, apply(all_0_2_2, all_28_3_23, all_10_0_12) = 0, yields:
% 13.21/3.64 | (134) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_9_9, v0, all_10_0_12) = 0 & apply(all_0_10_10, all_28_3_23, v0) = 0 & member(v0, all_0_6_6) = 0) | (member(all_28_3_23, all_0_7_7) = v0 & member(all_10_0_12, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.21/3.64 |
% 13.21/3.64 | Instantiating formula (32) with all_0_4_4, all_27_3_19, all_10_2_14, all_0_6_6, all_0_7_7, all_0_8_8, all_0_11_11, all_0_10_10 and discharging atoms compose_function(all_0_10_10, all_0_11_11, all_0_8_8, all_0_7_7, all_0_6_6) = all_0_4_4, apply(all_0_4_4, all_10_2_14, all_27_3_19) = 0, yields:
% 13.21/3.64 | (135) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_10_10, v0, all_27_3_19) = 0 & apply(all_0_11_11, all_10_2_14, v0) = 0 & member(v0, all_0_7_7) = 0) | (member(all_27_3_19, all_0_6_6) = v1 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_28_3_23, all_25_0_15, all_10_2_14, all_0_7_7, all_0_8_8, all_0_11_11 and discharging atoms maps(all_0_11_11, all_0_8_8, all_0_7_7) = 0, apply(all_0_11_11, all_10_2_14, all_28_3_23) = 0, apply(all_0_11_11, all_10_2_14, all_25_0_15) = 0, yields:
% 13.21/3.65 | (136) all_28_3_23 = all_25_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_28_3_23, all_0_7_7) = v2 & member(all_25_0_15, all_0_7_7) = v1 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (35) with all_28_3_23, all_0_6_6, all_0_7_7, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0, member(all_28_3_23, all_0_7_7) = 0, yields:
% 13.21/3.65 | (137) ? [v0] : (apply(all_0_10_10, all_28_3_23, v0) = 0 & member(v0, all_0_6_6) = 0)
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (35) with all_27_3_19, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0, member(all_27_3_19, all_0_6_6) = 0, yields:
% 13.21/3.65 | (138) ? [v0] : (apply(all_0_9_9, all_27_3_19, v0) = 0 & member(v0, all_0_5_5) = 0)
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (35) with all_25_0_15, all_0_6_6, all_0_7_7, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.21/3.65 | (139) ? [v0] : (apply(all_0_10_10, all_25_0_15, v0) = 0 & member(v0, all_0_6_6) = 0)
% 13.21/3.65 |
% 13.21/3.65 | Instantiating (139) with all_50_0_24 yields:
% 13.21/3.65 | (140) apply(all_0_10_10, all_25_0_15, all_50_0_24) = 0 & member(all_50_0_24, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 | Applying alpha-rule on (140) yields:
% 13.21/3.65 | (141) apply(all_0_10_10, all_25_0_15, all_50_0_24) = 0
% 13.21/3.65 | (142) member(all_50_0_24, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 | Instantiating (138) with all_52_0_25 yields:
% 13.21/3.65 | (143) apply(all_0_9_9, all_27_3_19, all_52_0_25) = 0 & member(all_52_0_25, all_0_5_5) = 0
% 13.21/3.65 |
% 13.21/3.65 | Applying alpha-rule on (143) yields:
% 13.21/3.65 | (144) apply(all_0_9_9, all_27_3_19, all_52_0_25) = 0
% 13.21/3.65 | (145) member(all_52_0_25, all_0_5_5) = 0
% 13.21/3.65 |
% 13.21/3.65 | Instantiating (135) with all_54_0_26, all_54_1_27, all_54_2_28, all_54_3_29 yields:
% 13.21/3.65 | (146) (all_54_0_26 = 0 & all_54_1_27 = 0 & all_54_2_28 = 0 & apply(all_0_10_10, all_54_3_29, all_27_3_19) = 0 & apply(all_0_11_11, all_10_2_14, all_54_3_29) = 0 & member(all_54_3_29, all_0_7_7) = 0) | (member(all_27_3_19, all_0_6_6) = all_54_2_28 & member(all_10_2_14, all_0_8_8) = all_54_3_29 & ( ~ (all_54_2_28 = 0) | ~ (all_54_3_29 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating (134) with all_55_0_30, all_55_1_31, all_55_2_32, all_55_3_33 yields:
% 13.21/3.65 | (147) (all_55_0_30 = 0 & all_55_1_31 = 0 & all_55_2_32 = 0 & apply(all_0_9_9, all_55_3_33, all_10_0_12) = 0 & apply(all_0_10_10, all_28_3_23, all_55_3_33) = 0 & member(all_55_3_33, all_0_6_6) = 0) | (member(all_28_3_23, all_0_7_7) = all_55_3_33 & member(all_10_0_12, all_0_5_5) = all_55_2_32 & ( ~ (all_55_2_32 = 0) | ~ (all_55_3_33 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating (137) with all_56_0_34 yields:
% 13.21/3.65 | (148) apply(all_0_10_10, all_28_3_23, all_56_0_34) = 0 & member(all_56_0_34, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 | Applying alpha-rule on (148) yields:
% 13.21/3.65 | (149) apply(all_0_10_10, all_28_3_23, all_56_0_34) = 0
% 13.21/3.65 | (150) member(all_56_0_34, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (136), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (151) all_28_3_23 = all_25_0_15
% 13.21/3.65 |
% 13.21/3.65 | From (151) and (149) follows:
% 13.21/3.65 | (152) apply(all_0_10_10, all_25_0_15, all_56_0_34) = 0
% 13.21/3.65 |
% 13.21/3.65 | From (151) and (132) follows:
% 13.21/3.65 | (116) apply(all_0_11_11, all_10_2_14, all_25_0_15) = 0
% 13.21/3.65 |
% 13.21/3.65 | From (151) and (129) follows:
% 13.21/3.65 | (117) member(all_25_0_15, all_0_7_7) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (147), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (155) all_55_0_30 = 0 & all_55_1_31 = 0 & all_55_2_32 = 0 & apply(all_0_9_9, all_55_3_33, all_10_0_12) = 0 & apply(all_0_10_10, all_28_3_23, all_55_3_33) = 0 & member(all_55_3_33, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 | Applying alpha-rule on (155) yields:
% 13.21/3.65 | (156) apply(all_0_9_9, all_55_3_33, all_10_0_12) = 0
% 13.21/3.65 | (157) all_55_1_31 = 0
% 13.21/3.65 | (158) apply(all_0_10_10, all_28_3_23, all_55_3_33) = 0
% 13.21/3.65 | (159) all_55_0_30 = 0
% 13.21/3.65 | (160) all_55_2_32 = 0
% 13.21/3.65 | (161) member(all_55_3_33, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 | From (151) and (158) follows:
% 13.21/3.65 | (162) apply(all_0_10_10, all_25_0_15, all_55_3_33) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (146), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (163) all_54_0_26 = 0 & all_54_1_27 = 0 & all_54_2_28 = 0 & apply(all_0_10_10, all_54_3_29, all_27_3_19) = 0 & apply(all_0_11_11, all_10_2_14, all_54_3_29) = 0 & member(all_54_3_29, all_0_7_7) = 0
% 13.21/3.65 |
% 13.21/3.65 | Applying alpha-rule on (163) yields:
% 13.21/3.65 | (164) apply(all_0_10_10, all_54_3_29, all_27_3_19) = 0
% 13.21/3.65 | (165) all_54_0_26 = 0
% 13.21/3.65 | (166) apply(all_0_11_11, all_10_2_14, all_54_3_29) = 0
% 13.21/3.65 | (167) all_54_2_28 = 0
% 13.21/3.65 | (168) member(all_54_3_29, all_0_7_7) = 0
% 13.21/3.65 | (169) all_54_1_27 = 0
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_10_1_13, all_52_0_25, all_27_3_19, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0, apply(all_0_9_9, all_27_3_19, all_52_0_25) = 0, apply(all_0_9_9, all_27_3_19, all_10_1_13) = 0, yields:
% 13.21/3.65 | (170) all_52_0_25 = all_10_1_13 | ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v1 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_1_13, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_52_0_25, all_10_0_12, all_27_3_19, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0, apply(all_0_9_9, all_27_3_19, all_52_0_25) = 0, yields:
% 13.21/3.65 | (171) all_52_0_25 = all_10_0_12 | ~ (apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v2 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_0_12, all_0_5_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_10_0_12, all_52_0_25, all_27_3_19, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms maps(all_0_9_9, all_0_6_6, all_0_5_5) = 0, apply(all_0_9_9, all_27_3_19, all_52_0_25) = 0, yields:
% 13.21/3.65 | (172) all_52_0_25 = all_10_0_12 | ~ (apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v1 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_0_12, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_27_3_19, all_50_0_24, all_25_0_15, all_0_6_6, all_0_7_7, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0, apply(all_0_10_10, all_25_0_15, all_50_0_24) = 0, yields:
% 13.21/3.65 | (173) all_50_0_24 = all_27_3_19 | ~ (apply(all_0_10_10, all_25_0_15, all_27_3_19) = 0) | ? [v0] : ? [v1] : ? [v2] : (member(all_50_0_24, all_0_6_6) = v1 & member(all_27_3_19, all_0_6_6) = v2 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_56_0_34, all_50_0_24, all_25_0_15, all_0_6_6, all_0_7_7, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0, apply(all_0_10_10, all_25_0_15, all_56_0_34) = 0, apply(all_0_10_10, all_25_0_15, all_50_0_24) = 0, yields:
% 13.21/3.65 | (174) all_56_0_34 = all_50_0_24 | ? [v0] : ? [v1] : ? [v2] : (member(all_56_0_34, all_0_6_6) = v2 & member(all_50_0_24, all_0_6_6) = v1 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_55_3_33, all_50_0_24, all_25_0_15, all_0_6_6, all_0_7_7, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_7_7, all_0_6_6) = 0, apply(all_0_10_10, all_25_0_15, all_55_3_33) = 0, apply(all_0_10_10, all_25_0_15, all_50_0_24) = 0, yields:
% 13.21/3.65 | (175) all_55_3_33 = all_50_0_24 | ? [v0] : ? [v1] : ? [v2] : (member(all_55_3_33, all_0_6_6) = v2 & member(all_50_0_24, all_0_6_6) = v1 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 | Instantiating formula (40) with all_25_0_15, all_54_3_29, all_10_2_14, all_0_7_7, all_0_8_8, all_0_11_11 and discharging atoms maps(all_0_11_11, all_0_8_8, all_0_7_7) = 0, apply(all_0_11_11, all_10_2_14, all_54_3_29) = 0, apply(all_0_11_11, all_10_2_14, all_25_0_15) = 0, yields:
% 13.21/3.65 | (176) all_54_3_29 = all_25_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_54_3_29, all_0_7_7) = v1 & member(all_25_0_15, all_0_7_7) = v2 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (174), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (177) all_56_0_34 = all_50_0_24
% 13.21/3.65 |
% 13.21/3.65 | From (177) and (150) follows:
% 13.21/3.65 | (142) member(all_50_0_24, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (175), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (179) all_55_3_33 = all_50_0_24
% 13.21/3.65 |
% 13.21/3.65 | From (179) and (156) follows:
% 13.21/3.65 | (180) apply(all_0_9_9, all_50_0_24, all_10_0_12) = 0
% 13.21/3.65 |
% 13.21/3.65 | From (179) and (161) follows:
% 13.21/3.65 | (142) member(all_50_0_24, all_0_6_6) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (170), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (182) all_52_0_25 = all_10_1_13
% 13.21/3.65 |
% 13.21/3.65 | From (182) and (145) follows:
% 13.21/3.65 | (106) member(all_10_1_13, all_0_5_5) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (176), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (184) all_54_3_29 = all_25_0_15
% 13.21/3.65 |
% 13.21/3.65 | From (184) and (164) follows:
% 13.21/3.65 | (185) apply(all_0_10_10, all_25_0_15, all_27_3_19) = 0
% 13.21/3.65 |
% 13.21/3.65 | From (184) and (168) follows:
% 13.21/3.65 | (117) member(all_25_0_15, all_0_7_7) = 0
% 13.21/3.65 |
% 13.21/3.65 +-Applying beta-rule and splitting (173), into two cases.
% 13.21/3.65 |-Branch one:
% 13.21/3.65 | (187) ~ (apply(all_0_10_10, all_25_0_15, all_27_3_19) = 0)
% 13.21/3.65 |
% 13.21/3.66 | Using (185) and (187) yields:
% 13.21/3.66 | (188) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (185) apply(all_0_10_10, all_25_0_15, all_27_3_19) = 0
% 13.21/3.66 | (190) all_50_0_24 = all_27_3_19 | ? [v0] : ? [v1] : ? [v2] : (member(all_50_0_24, all_0_6_6) = v1 & member(all_27_3_19, all_0_6_6) = v2 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (190), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (191) all_50_0_24 = all_27_3_19
% 13.21/3.66 |
% 13.21/3.66 | From (191) and (180) follows:
% 13.21/3.66 | (192) apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0
% 13.21/3.66 |
% 13.21/3.66 | From (191) and (142) follows:
% 13.21/3.66 | (122) member(all_27_3_19, all_0_6_6) = 0
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (172), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (194) ~ (apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0)
% 13.21/3.66 |
% 13.21/3.66 | Using (192) and (194) yields:
% 13.21/3.66 | (188) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (192) apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0
% 13.21/3.66 | (197) all_52_0_25 = all_10_0_12 | ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v1 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_0_12, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (171), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (194) ~ (apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0)
% 13.21/3.66 |
% 13.21/3.66 | Using (192) and (194) yields:
% 13.21/3.66 | (188) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (192) apply(all_0_9_9, all_27_3_19, all_10_0_12) = 0
% 13.21/3.66 | (201) all_52_0_25 = all_10_0_12 | ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v2 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_0_12, all_0_5_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (201), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (202) all_52_0_25 = all_10_0_12
% 13.21/3.66 |
% 13.21/3.66 | Combining equations (182,202) yields a new equation:
% 13.21/3.66 | (203) all_10_0_12 = all_10_1_13
% 13.21/3.66 |
% 13.21/3.66 | Equations (203) can reduce 108 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (205) ~ (all_52_0_25 = all_10_0_12)
% 13.21/3.66 | (206) ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v2 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_0_12, all_0_5_5) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 | Instantiating (206) with all_119_0_39, all_119_1_40, all_119_2_41 yields:
% 13.21/3.66 | (207) member(all_52_0_25, all_0_5_5) = all_119_0_39 & member(all_27_3_19, all_0_6_6) = all_119_2_41 & member(all_10_0_12, all_0_5_5) = all_119_1_40 & ( ~ (all_119_0_39 = 0) | ~ (all_119_1_40 = 0) | ~ (all_119_2_41 = 0))
% 13.21/3.66 |
% 13.21/3.66 | Applying alpha-rule on (207) yields:
% 13.21/3.66 | (208) member(all_52_0_25, all_0_5_5) = all_119_0_39
% 13.21/3.66 | (209) member(all_27_3_19, all_0_6_6) = all_119_2_41
% 13.21/3.66 | (210) member(all_10_0_12, all_0_5_5) = all_119_1_40
% 13.21/3.66 | (211) ~ (all_119_0_39 = 0) | ~ (all_119_1_40 = 0) | ~ (all_119_2_41 = 0)
% 13.21/3.66 |
% 13.21/3.66 | From (182) and (208) follows:
% 13.21/3.66 | (212) member(all_10_1_13, all_0_5_5) = all_119_0_39
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_27_3_19, all_0_6_6, all_119_2_41, 0 and discharging atoms member(all_27_3_19, all_0_6_6) = all_119_2_41, member(all_27_3_19, all_0_6_6) = 0, yields:
% 13.21/3.66 | (213) all_119_2_41 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_10_0_12, all_0_5_5, all_119_1_40, 0 and discharging atoms member(all_10_0_12, all_0_5_5) = all_119_1_40, member(all_10_0_12, all_0_5_5) = 0, yields:
% 13.21/3.66 | (214) all_119_1_40 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_10_1_13, all_0_5_5, all_119_0_39, 0 and discharging atoms member(all_10_1_13, all_0_5_5) = all_119_0_39, member(all_10_1_13, all_0_5_5) = 0, yields:
% 13.21/3.66 | (215) all_119_0_39 = 0
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (211), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (216) ~ (all_119_0_39 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (215) can reduce 216 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (215) all_119_0_39 = 0
% 13.21/3.66 | (219) ~ (all_119_1_40 = 0) | ~ (all_119_2_41 = 0)
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (219), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (220) ~ (all_119_1_40 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (214) can reduce 220 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (214) all_119_1_40 = 0
% 13.21/3.66 | (223) ~ (all_119_2_41 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (213) can reduce 223 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (225) ~ (all_50_0_24 = all_27_3_19)
% 13.21/3.66 | (226) ? [v0] : ? [v1] : ? [v2] : (member(all_50_0_24, all_0_6_6) = v1 & member(all_27_3_19, all_0_6_6) = v2 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 | Instantiating (226) with all_107_0_42, all_107_1_43, all_107_2_44 yields:
% 13.21/3.66 | (227) member(all_50_0_24, all_0_6_6) = all_107_1_43 & member(all_27_3_19, all_0_6_6) = all_107_0_42 & member(all_25_0_15, all_0_7_7) = all_107_2_44 & ( ~ (all_107_0_42 = 0) | ~ (all_107_1_43 = 0) | ~ (all_107_2_44 = 0))
% 13.21/3.66 |
% 13.21/3.66 | Applying alpha-rule on (227) yields:
% 13.21/3.66 | (228) member(all_50_0_24, all_0_6_6) = all_107_1_43
% 13.21/3.66 | (229) member(all_27_3_19, all_0_6_6) = all_107_0_42
% 13.21/3.66 | (230) member(all_25_0_15, all_0_7_7) = all_107_2_44
% 13.21/3.66 | (231) ~ (all_107_0_42 = 0) | ~ (all_107_1_43 = 0) | ~ (all_107_2_44 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_50_0_24, all_0_6_6, all_107_1_43, 0 and discharging atoms member(all_50_0_24, all_0_6_6) = all_107_1_43, member(all_50_0_24, all_0_6_6) = 0, yields:
% 13.21/3.66 | (232) all_107_1_43 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_27_3_19, all_0_6_6, all_107_0_42, 0 and discharging atoms member(all_27_3_19, all_0_6_6) = all_107_0_42, member(all_27_3_19, all_0_6_6) = 0, yields:
% 13.21/3.66 | (233) all_107_0_42 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_107_2_44, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_107_2_44, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.21/3.66 | (234) all_107_2_44 = 0
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (231), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (235) ~ (all_107_0_42 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (233) can reduce 235 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (233) all_107_0_42 = 0
% 13.21/3.66 | (238) ~ (all_107_1_43 = 0) | ~ (all_107_2_44 = 0)
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (238), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (239) ~ (all_107_1_43 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (232) can reduce 239 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (232) all_107_1_43 = 0
% 13.21/3.66 | (242) ~ (all_107_2_44 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (234) can reduce 242 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (244) ~ (all_54_3_29 = all_25_0_15)
% 13.21/3.66 | (245) ? [v0] : ? [v1] : ? [v2] : (member(all_54_3_29, all_0_7_7) = v1 & member(all_25_0_15, all_0_7_7) = v2 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.66 |
% 13.21/3.66 | Instantiating (245) with all_99_0_48, all_99_1_49, all_99_2_50 yields:
% 13.21/3.66 | (246) member(all_54_3_29, all_0_7_7) = all_99_1_49 & member(all_25_0_15, all_0_7_7) = all_99_0_48 & member(all_10_2_14, all_0_8_8) = all_99_2_50 & ( ~ (all_99_0_48 = 0) | ~ (all_99_1_49 = 0) | ~ (all_99_2_50 = 0))
% 13.21/3.66 |
% 13.21/3.66 | Applying alpha-rule on (246) yields:
% 13.21/3.66 | (247) member(all_54_3_29, all_0_7_7) = all_99_1_49
% 13.21/3.66 | (248) member(all_25_0_15, all_0_7_7) = all_99_0_48
% 13.21/3.66 | (249) member(all_10_2_14, all_0_8_8) = all_99_2_50
% 13.21/3.66 | (250) ~ (all_99_0_48 = 0) | ~ (all_99_1_49 = 0) | ~ (all_99_2_50 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_54_3_29, all_0_7_7, all_99_1_49, 0 and discharging atoms member(all_54_3_29, all_0_7_7) = all_99_1_49, member(all_54_3_29, all_0_7_7) = 0, yields:
% 13.21/3.66 | (251) all_99_1_49 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_99_0_48, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_99_0_48, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.21/3.66 | (252) all_99_0_48 = 0
% 13.21/3.66 |
% 13.21/3.66 | Instantiating formula (76) with all_10_2_14, all_0_8_8, all_99_2_50, 0 and discharging atoms member(all_10_2_14, all_0_8_8) = all_99_2_50, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.21/3.66 | (253) all_99_2_50 = 0
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (250), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (254) ~ (all_99_0_48 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (252) can reduce 254 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (252) all_99_0_48 = 0
% 13.21/3.66 | (257) ~ (all_99_1_49 = 0) | ~ (all_99_2_50 = 0)
% 13.21/3.66 |
% 13.21/3.66 +-Applying beta-rule and splitting (257), into two cases.
% 13.21/3.66 |-Branch one:
% 13.21/3.66 | (258) ~ (all_99_1_49 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (251) can reduce 258 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.66 |-The branch is then unsatisfiable
% 13.21/3.66 |-Branch two:
% 13.21/3.66 | (251) all_99_1_49 = 0
% 13.21/3.66 | (261) ~ (all_99_2_50 = 0)
% 13.21/3.66 |
% 13.21/3.66 | Equations (253) can reduce 261 to:
% 13.21/3.66 | (102) $false
% 13.21/3.66 |
% 13.21/3.67 |-The branch is then unsatisfiable
% 13.21/3.67 |-Branch two:
% 13.21/3.67 | (263) ~ (all_52_0_25 = all_10_1_13)
% 13.21/3.67 | (264) ? [v0] : ? [v1] : ? [v2] : (member(all_52_0_25, all_0_5_5) = v1 & member(all_27_3_19, all_0_6_6) = v0 & member(all_10_1_13, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.67 |
% 13.21/3.67 | Instantiating (264) with all_95_0_54, all_95_1_55, all_95_2_56 yields:
% 13.21/3.67 | (265) member(all_52_0_25, all_0_5_5) = all_95_1_55 & member(all_27_3_19, all_0_6_6) = all_95_2_56 & member(all_10_1_13, all_0_5_5) = all_95_0_54 & ( ~ (all_95_0_54 = 0) | ~ (all_95_1_55 = 0) | ~ (all_95_2_56 = 0))
% 13.21/3.67 |
% 13.21/3.67 | Applying alpha-rule on (265) yields:
% 13.21/3.67 | (266) member(all_52_0_25, all_0_5_5) = all_95_1_55
% 13.21/3.67 | (267) member(all_27_3_19, all_0_6_6) = all_95_2_56
% 13.21/3.67 | (268) member(all_10_1_13, all_0_5_5) = all_95_0_54
% 13.21/3.67 | (269) ~ (all_95_0_54 = 0) | ~ (all_95_1_55 = 0) | ~ (all_95_2_56 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_52_0_25, all_0_5_5, all_95_1_55, 0 and discharging atoms member(all_52_0_25, all_0_5_5) = all_95_1_55, member(all_52_0_25, all_0_5_5) = 0, yields:
% 13.21/3.67 | (270) all_95_1_55 = 0
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_27_3_19, all_0_6_6, all_95_2_56, 0 and discharging atoms member(all_27_3_19, all_0_6_6) = all_95_2_56, member(all_27_3_19, all_0_6_6) = 0, yields:
% 13.21/3.67 | (271) all_95_2_56 = 0
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_10_1_13, all_0_5_5, all_95_0_54, 0 and discharging atoms member(all_10_1_13, all_0_5_5) = all_95_0_54, member(all_10_1_13, all_0_5_5) = 0, yields:
% 13.21/3.67 | (272) all_95_0_54 = 0
% 13.21/3.67 |
% 13.21/3.67 +-Applying beta-rule and splitting (269), into two cases.
% 13.21/3.67 |-Branch one:
% 13.21/3.67 | (273) ~ (all_95_0_54 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Equations (272) can reduce 273 to:
% 13.21/3.67 | (102) $false
% 13.21/3.67 |
% 13.21/3.67 |-The branch is then unsatisfiable
% 13.21/3.67 |-Branch two:
% 13.21/3.67 | (272) all_95_0_54 = 0
% 13.21/3.67 | (276) ~ (all_95_1_55 = 0) | ~ (all_95_2_56 = 0)
% 13.21/3.67 |
% 13.21/3.67 +-Applying beta-rule and splitting (276), into two cases.
% 13.21/3.67 |-Branch one:
% 13.21/3.67 | (277) ~ (all_95_1_55 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Equations (270) can reduce 277 to:
% 13.21/3.67 | (102) $false
% 13.21/3.67 |
% 13.21/3.67 |-The branch is then unsatisfiable
% 13.21/3.67 |-Branch two:
% 13.21/3.67 | (270) all_95_1_55 = 0
% 13.21/3.67 | (280) ~ (all_95_2_56 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Equations (271) can reduce 280 to:
% 13.21/3.67 | (102) $false
% 13.21/3.67 |
% 13.21/3.67 |-The branch is then unsatisfiable
% 13.21/3.67 |-Branch two:
% 13.21/3.67 | (282) ~ (all_55_3_33 = all_50_0_24)
% 13.21/3.67 | (283) ? [v0] : ? [v1] : ? [v2] : (member(all_55_3_33, all_0_6_6) = v2 & member(all_50_0_24, all_0_6_6) = v1 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.21/3.67 |
% 13.21/3.67 | Instantiating (283) with all_91_0_60, all_91_1_61, all_91_2_62 yields:
% 13.21/3.67 | (284) member(all_55_3_33, all_0_6_6) = all_91_0_60 & member(all_50_0_24, all_0_6_6) = all_91_1_61 & member(all_25_0_15, all_0_7_7) = all_91_2_62 & ( ~ (all_91_0_60 = 0) | ~ (all_91_1_61 = 0) | ~ (all_91_2_62 = 0))
% 13.21/3.67 |
% 13.21/3.67 | Applying alpha-rule on (284) yields:
% 13.21/3.67 | (285) member(all_55_3_33, all_0_6_6) = all_91_0_60
% 13.21/3.67 | (286) member(all_50_0_24, all_0_6_6) = all_91_1_61
% 13.21/3.67 | (287) member(all_25_0_15, all_0_7_7) = all_91_2_62
% 13.21/3.67 | (288) ~ (all_91_0_60 = 0) | ~ (all_91_1_61 = 0) | ~ (all_91_2_62 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_55_3_33, all_0_6_6, all_91_0_60, 0 and discharging atoms member(all_55_3_33, all_0_6_6) = all_91_0_60, member(all_55_3_33, all_0_6_6) = 0, yields:
% 13.21/3.67 | (289) all_91_0_60 = 0
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_50_0_24, all_0_6_6, all_91_1_61, 0 and discharging atoms member(all_50_0_24, all_0_6_6) = all_91_1_61, member(all_50_0_24, all_0_6_6) = 0, yields:
% 13.21/3.67 | (290) all_91_1_61 = 0
% 13.21/3.67 |
% 13.21/3.67 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_91_2_62, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_91_2_62, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.21/3.67 | (291) all_91_2_62 = 0
% 13.21/3.67 |
% 13.21/3.67 +-Applying beta-rule and splitting (288), into two cases.
% 13.21/3.67 |-Branch one:
% 13.21/3.67 | (292) ~ (all_91_0_60 = 0)
% 13.21/3.67 |
% 13.21/3.67 | Equations (289) can reduce 292 to:
% 13.21/3.67 | (102) $false
% 13.21/3.67 |
% 13.21/3.67 |-The branch is then unsatisfiable
% 13.21/3.67 |-Branch two:
% 13.21/3.67 | (289) all_91_0_60 = 0
% 13.21/3.67 | (295) ~ (all_91_1_61 = 0) | ~ (all_91_2_62 = 0)
% 13.21/3.67 |
% 13.21/3.67 +-Applying beta-rule and splitting (295), into two cases.
% 13.21/3.67 |-Branch one:
% 13.21/3.67 | (296) ~ (all_91_1_61 = 0)
% 13.21/3.67 |
% 13.53/3.67 | Equations (290) can reduce 296 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (290) all_91_1_61 = 0
% 13.53/3.67 | (299) ~ (all_91_2_62 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (291) can reduce 299 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (301) ~ (all_56_0_34 = all_50_0_24)
% 13.53/3.67 | (302) ? [v0] : ? [v1] : ? [v2] : (member(all_56_0_34, all_0_6_6) = v2 & member(all_50_0_24, all_0_6_6) = v1 & member(all_25_0_15, all_0_7_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.53/3.67 |
% 13.53/3.67 | Instantiating (302) with all_87_0_66, all_87_1_67, all_87_2_68 yields:
% 13.53/3.67 | (303) member(all_56_0_34, all_0_6_6) = all_87_0_66 & member(all_50_0_24, all_0_6_6) = all_87_1_67 & member(all_25_0_15, all_0_7_7) = all_87_2_68 & ( ~ (all_87_0_66 = 0) | ~ (all_87_1_67 = 0) | ~ (all_87_2_68 = 0))
% 13.53/3.67 |
% 13.53/3.67 | Applying alpha-rule on (303) yields:
% 13.53/3.67 | (304) member(all_56_0_34, all_0_6_6) = all_87_0_66
% 13.53/3.67 | (305) member(all_50_0_24, all_0_6_6) = all_87_1_67
% 13.53/3.67 | (306) member(all_25_0_15, all_0_7_7) = all_87_2_68
% 13.53/3.67 | (307) ~ (all_87_0_66 = 0) | ~ (all_87_1_67 = 0) | ~ (all_87_2_68 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_56_0_34, all_0_6_6, all_87_0_66, 0 and discharging atoms member(all_56_0_34, all_0_6_6) = all_87_0_66, member(all_56_0_34, all_0_6_6) = 0, yields:
% 13.53/3.67 | (308) all_87_0_66 = 0
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_50_0_24, all_0_6_6, all_87_1_67, 0 and discharging atoms member(all_50_0_24, all_0_6_6) = all_87_1_67, member(all_50_0_24, all_0_6_6) = 0, yields:
% 13.53/3.67 | (309) all_87_1_67 = 0
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_87_2_68, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_87_2_68, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.53/3.67 | (310) all_87_2_68 = 0
% 13.53/3.67 |
% 13.53/3.67 +-Applying beta-rule and splitting (307), into two cases.
% 13.53/3.67 |-Branch one:
% 13.53/3.67 | (311) ~ (all_87_0_66 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (308) can reduce 311 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (308) all_87_0_66 = 0
% 13.53/3.67 | (314) ~ (all_87_1_67 = 0) | ~ (all_87_2_68 = 0)
% 13.53/3.67 |
% 13.53/3.67 +-Applying beta-rule and splitting (314), into two cases.
% 13.53/3.67 |-Branch one:
% 13.53/3.67 | (315) ~ (all_87_1_67 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (309) can reduce 315 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (309) all_87_1_67 = 0
% 13.53/3.67 | (318) ~ (all_87_2_68 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (310) can reduce 318 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (320) member(all_27_3_19, all_0_6_6) = all_54_2_28 & member(all_10_2_14, all_0_8_8) = all_54_3_29 & ( ~ (all_54_2_28 = 0) | ~ (all_54_3_29 = 0))
% 13.53/3.67 |
% 13.53/3.67 | Applying alpha-rule on (320) yields:
% 13.53/3.67 | (321) member(all_27_3_19, all_0_6_6) = all_54_2_28
% 13.53/3.67 | (322) member(all_10_2_14, all_0_8_8) = all_54_3_29
% 13.53/3.67 | (323) ~ (all_54_2_28 = 0) | ~ (all_54_3_29 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_27_3_19, all_0_6_6, all_54_2_28, 0 and discharging atoms member(all_27_3_19, all_0_6_6) = all_54_2_28, member(all_27_3_19, all_0_6_6) = 0, yields:
% 13.53/3.67 | (167) all_54_2_28 = 0
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_10_2_14, all_0_8_8, all_54_3_29, 0 and discharging atoms member(all_10_2_14, all_0_8_8) = all_54_3_29, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.53/3.67 | (325) all_54_3_29 = 0
% 13.53/3.67 |
% 13.53/3.67 +-Applying beta-rule and splitting (323), into two cases.
% 13.53/3.67 |-Branch one:
% 13.53/3.67 | (326) ~ (all_54_2_28 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (167) can reduce 326 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (167) all_54_2_28 = 0
% 13.53/3.67 | (329) ~ (all_54_3_29 = 0)
% 13.53/3.67 |
% 13.53/3.67 | Equations (325) can reduce 329 to:
% 13.53/3.67 | (102) $false
% 13.53/3.67 |
% 13.53/3.67 |-The branch is then unsatisfiable
% 13.53/3.67 |-Branch two:
% 13.53/3.67 | (331) member(all_28_3_23, all_0_7_7) = all_55_3_33 & member(all_10_0_12, all_0_5_5) = all_55_2_32 & ( ~ (all_55_2_32 = 0) | ~ (all_55_3_33 = 0))
% 13.53/3.67 |
% 13.53/3.67 | Applying alpha-rule on (331) yields:
% 13.53/3.67 | (332) member(all_28_3_23, all_0_7_7) = all_55_3_33
% 13.53/3.67 | (333) member(all_10_0_12, all_0_5_5) = all_55_2_32
% 13.53/3.67 | (334) ~ (all_55_2_32 = 0) | ~ (all_55_3_33 = 0)
% 13.53/3.67 |
% 13.53/3.67 | From (151) and (332) follows:
% 13.53/3.67 | (335) member(all_25_0_15, all_0_7_7) = all_55_3_33
% 13.53/3.67 |
% 13.53/3.67 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_55_3_33, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_55_3_33, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.53/3.67 | (336) all_55_3_33 = 0
% 13.53/3.67 |
% 13.53/3.68 | Instantiating formula (76) with all_10_0_12, all_0_5_5, all_55_2_32, 0 and discharging atoms member(all_10_0_12, all_0_5_5) = all_55_2_32, member(all_10_0_12, all_0_5_5) = 0, yields:
% 13.53/3.68 | (160) all_55_2_32 = 0
% 13.53/3.68 |
% 13.53/3.68 +-Applying beta-rule and splitting (334), into two cases.
% 13.53/3.68 |-Branch one:
% 13.53/3.68 | (338) ~ (all_55_2_32 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (160) can reduce 338 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (160) all_55_2_32 = 0
% 13.53/3.68 | (341) ~ (all_55_3_33 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (336) can reduce 341 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (343) ~ (all_28_3_23 = all_25_0_15)
% 13.53/3.68 | (344) ? [v0] : ? [v1] : ? [v2] : (member(all_28_3_23, all_0_7_7) = v2 & member(all_25_0_15, all_0_7_7) = v1 & member(all_10_2_14, all_0_8_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.53/3.68 |
% 13.53/3.68 | Instantiating (344) with all_62_0_75, all_62_1_76, all_62_2_77 yields:
% 13.53/3.68 | (345) member(all_28_3_23, all_0_7_7) = all_62_0_75 & member(all_25_0_15, all_0_7_7) = all_62_1_76 & member(all_10_2_14, all_0_8_8) = all_62_2_77 & ( ~ (all_62_0_75 = 0) | ~ (all_62_1_76 = 0) | ~ (all_62_2_77 = 0))
% 13.53/3.68 |
% 13.53/3.68 | Applying alpha-rule on (345) yields:
% 13.53/3.68 | (346) member(all_28_3_23, all_0_7_7) = all_62_0_75
% 13.53/3.68 | (347) member(all_25_0_15, all_0_7_7) = all_62_1_76
% 13.53/3.68 | (348) member(all_10_2_14, all_0_8_8) = all_62_2_77
% 13.53/3.68 | (349) ~ (all_62_0_75 = 0) | ~ (all_62_1_76 = 0) | ~ (all_62_2_77 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_28_3_23, all_0_7_7, all_62_0_75, 0 and discharging atoms member(all_28_3_23, all_0_7_7) = all_62_0_75, member(all_28_3_23, all_0_7_7) = 0, yields:
% 13.53/3.68 | (350) all_62_0_75 = 0
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_25_0_15, all_0_7_7, all_62_1_76, 0 and discharging atoms member(all_25_0_15, all_0_7_7) = all_62_1_76, member(all_25_0_15, all_0_7_7) = 0, yields:
% 13.53/3.68 | (351) all_62_1_76 = 0
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_10_2_14, all_0_8_8, all_62_2_77, 0 and discharging atoms member(all_10_2_14, all_0_8_8) = all_62_2_77, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.53/3.68 | (352) all_62_2_77 = 0
% 13.53/3.68 |
% 13.53/3.68 +-Applying beta-rule and splitting (349), into two cases.
% 13.53/3.68 |-Branch one:
% 13.53/3.68 | (353) ~ (all_62_0_75 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (350) can reduce 353 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (350) all_62_0_75 = 0
% 13.53/3.68 | (356) ~ (all_62_1_76 = 0) | ~ (all_62_2_77 = 0)
% 13.53/3.68 |
% 13.53/3.68 +-Applying beta-rule and splitting (356), into two cases.
% 13.53/3.68 |-Branch one:
% 13.53/3.68 | (357) ~ (all_62_1_76 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (351) can reduce 357 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (351) all_62_1_76 = 0
% 13.53/3.68 | (360) ~ (all_62_2_77 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (352) can reduce 360 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (362) member(all_10_0_12, all_0_5_5) = all_28_2_22 & member(all_10_2_14, all_0_8_8) = all_28_3_23 & ( ~ (all_28_2_22 = 0) | ~ (all_28_3_23 = 0))
% 13.53/3.68 |
% 13.53/3.68 | Applying alpha-rule on (362) yields:
% 13.53/3.68 | (363) member(all_10_0_12, all_0_5_5) = all_28_2_22
% 13.53/3.68 | (364) member(all_10_2_14, all_0_8_8) = all_28_3_23
% 13.53/3.68 | (365) ~ (all_28_2_22 = 0) | ~ (all_28_3_23 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_10_0_12, all_0_5_5, all_28_2_22, 0 and discharging atoms member(all_10_0_12, all_0_5_5) = all_28_2_22, member(all_10_0_12, all_0_5_5) = 0, yields:
% 13.53/3.68 | (128) all_28_2_22 = 0
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_10_2_14, all_0_8_8, all_28_3_23, 0 and discharging atoms member(all_10_2_14, all_0_8_8) = all_28_3_23, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.53/3.68 | (367) all_28_3_23 = 0
% 13.53/3.68 |
% 13.53/3.68 +-Applying beta-rule and splitting (365), into two cases.
% 13.53/3.68 |-Branch one:
% 13.53/3.68 | (368) ~ (all_28_2_22 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (128) can reduce 368 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (128) all_28_2_22 = 0
% 13.53/3.68 | (371) ~ (all_28_3_23 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (367) can reduce 371 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (373) member(all_10_1_13, all_0_5_5) = all_27_2_18 & member(all_10_2_14, all_0_8_8) = all_27_3_19 & ( ~ (all_27_2_18 = 0) | ~ (all_27_3_19 = 0))
% 13.53/3.68 |
% 13.53/3.68 | Applying alpha-rule on (373) yields:
% 13.53/3.68 | (374) member(all_10_1_13, all_0_5_5) = all_27_2_18
% 13.53/3.68 | (375) member(all_10_2_14, all_0_8_8) = all_27_3_19
% 13.53/3.68 | (376) ~ (all_27_2_18 = 0) | ~ (all_27_3_19 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_10_1_13, all_0_5_5, all_27_2_18, 0 and discharging atoms member(all_10_1_13, all_0_5_5) = all_27_2_18, member(all_10_1_13, all_0_5_5) = 0, yields:
% 13.53/3.68 | (123) all_27_2_18 = 0
% 13.53/3.68 |
% 13.53/3.68 | Instantiating formula (76) with all_10_2_14, all_0_8_8, all_27_3_19, 0 and discharging atoms member(all_10_2_14, all_0_8_8) = all_27_3_19, member(all_10_2_14, all_0_8_8) = 0, yields:
% 13.53/3.68 | (378) all_27_3_19 = 0
% 13.53/3.68 |
% 13.53/3.68 +-Applying beta-rule and splitting (376), into two cases.
% 13.53/3.68 |-Branch one:
% 13.53/3.68 | (379) ~ (all_27_2_18 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (123) can reduce 379 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 |-Branch two:
% 13.53/3.68 | (123) all_27_2_18 = 0
% 13.53/3.68 | (382) ~ (all_27_3_19 = 0)
% 13.53/3.68 |
% 13.53/3.68 | Equations (378) can reduce 382 to:
% 13.53/3.68 | (102) $false
% 13.53/3.68 |
% 13.53/3.68 |-The branch is then unsatisfiable
% 13.53/3.68 % SZS output end Proof for theBenchmark
% 13.53/3.68
% 13.53/3.68 3070ms
%------------------------------------------------------------------------------