TSTP Solution File: SET761+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET761+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:53 EDT 2022
% Result : Theorem 7.17s 2.27s
% Output : Proof 11.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET761+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 17:20:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.63/0.65 ____ _
% 0.63/0.65 ___ / __ \_____(_)___ ________ __________
% 0.63/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.65
% 0.63/0.65 A Theorem Prover for First-Order Logic
% 0.63/0.65 (ePrincess v.1.0)
% 0.63/0.65
% 0.63/0.65 (c) Philipp Rümmer, 2009-2015
% 0.63/0.65 (c) Peter Backeman, 2014-2015
% 0.63/0.65 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.65 Bug reports to peter@backeman.se
% 0.63/0.65
% 0.63/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.65
% 0.63/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.04/1.07 Prover 0: Preprocessing ...
% 3.23/1.42 Prover 0: Warning: ignoring some quantifiers
% 3.49/1.45 Prover 0: Constructing countermodel ...
% 4.97/1.78 Prover 0: gave up
% 4.97/1.78 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.15/1.83 Prover 1: Preprocessing ...
% 6.32/2.08 Prover 1: Constructing countermodel ...
% 7.17/2.27 Prover 1: proved (487ms)
% 7.17/2.27
% 7.17/2.27 No countermodel exists, formula is valid
% 7.17/2.27 % SZS status Theorem for theBenchmark
% 7.17/2.27
% 7.17/2.27 Generating proof ... found it (size 145)
% 10.21/3.01
% 10.21/3.01 % SZS output start Proof for theBenchmark
% 10.21/3.01 Assumed formulas after preprocessing and simplification:
% 10.21/3.01 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & image3(v0, v5, v2) = v6 & image3(v0, v4, v2) = v8 & image3(v0, v3, v2) = v7 & injective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 & intersection(v7, v8) = v9 & intersection(v3, v4) = v5 & equal_set(v6, v9) = v10 & subset(v4, v1) = 0 & subset(v3, v1) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = 0 | ~ (compose_function(v11, v12, v13, v14, v15) = v18) | ~ (apply(v18, v16, v17) = v19) | ~ (apply(v11, v20, v17) = 0) | ? [v21] : ? [v22] : ((apply(v12, v16, v20) = v22 & member(v20, v14) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))) | (member(v17, v15) = v22 & member(v16, v13) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = 0 | ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = 0) | ~ (apply(v12, v20, v18) = 0) | ~ (apply(v11, v17, v18) = v19) | ? [v21] : ? [v22] : ((apply(v13, v17, v20) = v22 & member(v20, v15) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))) | (member(v18, v16) = v22 & member(v17, v14) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (isomorphism(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v17, v19) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | (( ~ (v25 = 0) | v24 = 0) & ( ~ (v24 = 0) | v25 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (decreasing(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v19, v17) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | v25 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (increasing(v11, v12, v13, v14, v15) = 0) | ~ (apply(v11, v18, v19) = 0) | ~ (apply(v11, v16, v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v17, v19) = v25 & apply(v13, v16, v18) = v24 & member(v19, v14) = v23 & member(v18, v12) = v22 & member(v17, v14) = v21 & member(v16, v12) = v20 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | v25 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = v11 | ~ (compose_predicate(v18, v17, v16, v15, v14, v13) = v12) | ~ (compose_predicate(v18, v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (compose_function(v11, v12, v13, v14, v15) = v18) | ~ (apply(v18, v16, v17) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & apply(v12, v16, v19) = 0 & apply(v11, v19, v17) = 0 & member(v19, v14) = 0) | (member(v17, v15) = v20 & member(v16, v13) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = 0) | ~ (apply(v11, v17, v18) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & apply(v13, v17, v19) = 0 & apply(v12, v19, v18) = 0 & member(v19, v15) = 0) | (member(v18, v16) = v20 & member(v17, v14) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (equal_maps(v11, v12, v13, v14) = 0) | ~ (apply(v12, v15, v17) = 0) | ~ (apply(v11, v15, v16) = 0) | ? [v18] : ? [v19] : ? [v20] : (member(v17, v14) = v20 & member(v16, v14) = v19 & member(v15, v13) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (compose_predicate(v11, v12, v13, v14, v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v11, v18, v19) = v20 & member(v19, v16) = 0 & member(v18, v14) = 0 & ( ~ (v20 = 0) | ! [v25] : ( ~ (apply(v12, v25, v19) = 0) | ? [v26] : ? [v27] : (apply(v13, v18, v25) = v27 & member(v25, v15) = v26 & ( ~ (v27 = 0) | ~ (v26 = 0))))) & (v20 = 0 | (v24 = 0 & v23 = 0 & v22 = 0 & apply(v13, v18, v21) = 0 & apply(v12, v21, v19) = 0 & member(v21, v15) = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (inverse_image3(v11, v12, v13) = v15) | ~ (apply(v11, v14, v17) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v14, v13) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (image3(v11, v12, v13) = v15) | ~ (apply(v11, v17, v14) = 0) | ~ (member(v14, v15) = v16) | ? [v18] : (( ~ (v18 = 0) & member(v17, v12) = v18) | ( ~ (v18 = 0) & member(v14, v13) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (isomorphism(v17, v16, v15, v14, v13) = v12) | ~ (isomorphism(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (decreasing(v17, v16, v15, v14, v13) = v12) | ~ (decreasing(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (increasing(v17, v16, v15, v14, v13) = v12) | ~ (increasing(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v12 = v11 | ~ (compose_function(v17, v16, v15, v14, v13) = v12) | ~ (compose_function(v17, v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (inverse_function(v11, v12, v13) = v16) | ~ (apply(v16, v15, v14) = v17) | ? [v18] : ? [v19] : ? [v20] : (apply(v11, v14, v15) = v20 & member(v15, v13) = v19 & member(v14, v12) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v20 = 0) | v17 = 0) & ( ~ (v17 = 0) | v20 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (inverse_predicate(v11, v12, v13, v14) = 0) | ~ (apply(v11, v16, v15) = v17) | ? [v18] : ? [v19] : ? [v20] : (apply(v12, v15, v16) = v20 & member(v16, v14) = v19 & member(v15, v13) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | (( ~ (v20 = 0) | v17 = 0) & ( ~ (v17 = 0) | v20 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (maps(v11, v12, v13) = 0) | ~ (apply(v11, v14, v16) = 0) | ~ (apply(v11, v14, v15) = 0) | ? [v17] : ? [v18] : ? [v19] : (member(v16, v13) = v19 & member(v15, v13) = v18 & member(v14, v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (isomorphism(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v26 = 0 & v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & apply(v15, v18, v20) = v28 & apply(v13, v17, v19) = v27 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0 & ( ~ (v28 = 0) | ~ (v27 = 0)) & (v28 = 0 | v27 = 0)) | (one_to_one(v11, v12, v14) = v18 & maps(v11, v12, v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (decreasing(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & apply(v15, v20, v18) = v21 & apply(v13, v17, v19) = 0 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (increasing(v11, v12, v13, v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & apply(v15, v18, v20) = v21 & apply(v13, v17, v19) = 0 & apply(v11, v19, v20) = 0 & apply(v11, v17, v18) = 0 & member(v20, v14) = 0 & member(v19, v12) = 0 & member(v18, v14) = 0 & member(v17, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (injective(v11, v12, v13) = 0) | ~ (apply(v11, v15, v16) = 0) | ~ (apply(v11, v14, v16) = 0) | ? [v17] : ? [v18] : ? [v19] : (member(v16, v13) = v19 & member(v15, v12) = v18 & member(v14, v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (inverse_image2(v11, v12) = v14) | ~ (apply(v11, v13, v16) = 0) | ~ (member(v13, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (image2(v11, v12) = v14) | ~ (apply(v11, v16, v13) = 0) | ~ (member(v13, v14) = v15) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (inverse_predicate(v16, v15, v14, v13) = v12) | ~ (inverse_predicate(v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (equal_maps(v16, v15, v14, v13) = v12) | ~ (equal_maps(v16, v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (inverse_predicate(v11, v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (apply(v12, v16, v17) = v18 & apply(v11, v17, v16) = v19 & member(v17, v14) = 0 & member(v16, v13) = 0 & ( ~ (v19 = 0) | ~ (v18 = 0)) & (v19 = 0 | v18 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (equal_maps(v11, v12, v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & apply(v12, v16, v18) = 0 & apply(v11, v16, v17) = 0 & member(v18, v14) = 0 & member(v17, v14) = 0 & member(v16, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (product(v12) = v13) | ~ (member(v11, v14) = v15) | ~ (member(v11, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & member(v14, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (difference(v13, v12) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : (member(v11, v13) = v16 & member(v11, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (union(v12, v13) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & ~ (v16 = 0) & member(v11, v13) = v17 & member(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (intersection(v12, v13) = v14) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : (member(v11, v13) = v17 & member(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (sum(v12) = v13) | ~ (member(v11, v15) = 0) | ~ (member(v11, v13) = v14) | ? [v16] : ( ~ (v16 = 0) & member(v15, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (inverse_image3(v15, v14, v13) = v12) | ~ (inverse_image3(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (image3(v15, v14, v13) = v12) | ~ (image3(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (inverse_function(v15, v14, v13) = v12) | ~ (inverse_function(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (one_to_one(v15, v14, v13) = v12) | ~ (one_to_one(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (surjective(v15, v14, v13) = v12) | ~ (surjective(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (injective(v15, v14, v13) = v12) | ~ (injective(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (maps(v15, v14, v13) = v12) | ~ (maps(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (apply(v15, v14, v13) = v12) | ~ (apply(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v11, v12, v13, v14, v15) = 0) | (one_to_one(v11, v12, v14) = 0 & maps(v11, v12, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | member(v14, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (inverse_image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v11, v14, v16) = 0 & member(v16, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | member(v14, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image3(v11, v12, v13) = v15) | ~ (member(v14, v15) = 0) | ? [v16] : (apply(v11, v16, v14) = 0 & member(v16, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (surjective(v11, v12, v13) = v14) | ? [v15] : (member(v15, v13) = 0 & ! [v16] : ( ~ (apply(v11, v16, v15) = 0) | ? [v17] : ( ~ (v17 = 0) & member(v16, v12) = v17)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (injective(v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v16 = v15) & apply(v11, v16, v17) = 0 & apply(v11, v15, v17) = 0 & member(v17, v13) = 0 & member(v16, v12) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (identity(v11, v12) = 0) | ~ (apply(v11, v13, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & member(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (maps(v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & ~ (v17 = v16) & apply(v11, v15, v17) = 0 & apply(v11, v15, v16) = 0 & member(v17, v13) = 0 & member(v16, v13) = 0 & member(v15, v12) = 0) | (v16 = 0 & member(v15, v12) = 0 & ! [v23] : ( ~ (apply(v11, v15, v23) = 0) | ? [v24] : ( ~ (v24 = 0) & member(v23, v13) = v24))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (product(v12) = v13) | ~ (member(v11, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & member(v15, v12) = 0 & member(v11, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v12, v11) = v13) | ~ (member(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (member(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (power_set(v12) = v13) | ~ (member(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | v12 = v11 | ~ (unordered_pair(v12, v13) = v14) | ~ (member(v11, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (inverse_image2(v14, v13) = v12) | ~ (inverse_image2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (image2(v14, v13) = v12) | ~ (image2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (identity(v14, v13) = v12) | ~ (identity(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (difference(v14, v13) = v12) | ~ (difference(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (union(v14, v13) = v12) | ~ (union(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (intersection(v14, v13) = v12) | ~ (intersection(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (equal_set(v14, v13) = v12) | ~ (equal_set(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (member(v14, v13) = v12) | ~ (member(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (inverse_image2(v11, v12) = v14) | ~ (member(v13, v14) = 0) | ? [v15] : (apply(v11, v13, v15) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image2(v11, v12) = v14) | ~ (member(v13, v14) = 0) | ? [v15] : (apply(v11, v15, v13) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (surjective(v11, v12, v13) = v14) | ? [v15] : ? [v16] : (one_to_one(v11, v12, v13) = v15 & injective(v11, v12, v13) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (surjective(v11, v12, v13) = 0) | ~ (member(v14, v13) = 0) | ? [v15] : (apply(v11, v15, v14) = 0 & member(v15, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (maps(v11, v12, v13) = 0) | ~ (member(v14, v12) = 0) | ? [v15] : (apply(v11, v14, v15) = 0 & member(v15, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v13, v12) = v14) | ~ (member(v11, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & member(v11, v13) = 0 & member(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v12, v13) = v14) | ~ (member(v11, v14) = 0) | ? [v15] : ? [v16] : (member(v11, v13) = v16 & member(v11, v12) = v15 & (v16 = 0 | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (intersection(v12, v13) = v14) | ~ (member(v11, v14) = 0) | (member(v11, v13) = 0 & member(v11, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (identity(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & apply(v11, v14, v14) = v15 & member(v14, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (member(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (equal_set(v11, v12) = v13) | ? [v14] : ? [v15] : (subset(v12, v11) = v15 & subset(v11, v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & member(v14, v12) = v15 & member(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (product(v13) = v12) | ~ (product(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (sum(v13) = v12) | ~ (sum(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v12) = v13) | ~ (member(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (power_set(v13) = v12) | ~ (power_set(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (surjective(v11, v12, v13) = 0) | ? [v14] : ? [v15] : (one_to_one(v11, v12, v13) = v15 & injective(v11, v12, v13) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (sum(v12) = v13) | ~ (member(v11, v13) = 0) | ? [v14] : (member(v14, v12) = 0 & member(v11, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (power_set(v12) = v13) | ~ (member(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (member(v13, v11) = 0) | member(v13, v12) = 0) & ! [v11] : ! [v12] : ( ~ (equal_set(v11, v12) = 0) | (subset(v12, v11) = 0 & subset(v11, v12) = 0)) & ! [v11] : ~ (member(v11, empty_set) = 0))
% 10.63/3.07 | 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 yields:
% 10.63/3.07 | (1) ~ (all_0_0_0 = 0) & image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4 & image3(all_0_10_10, all_0_6_6, all_0_8_8) = all_0_2_2 & image3(all_0_10_10, all_0_7_7, all_0_8_8) = all_0_3_3 & injective(all_0_10_10, all_0_9_9, all_0_8_8) = 0 & maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0 & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_5_5 & equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 & subset(all_0_6_6, all_0_9_9) = 0 & subset(all_0_7_7, all_0_9_9) = 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)
% 10.94/3.10 |
% 10.94/3.10 | Applying alpha-rule on (1) yields:
% 10.94/3.10 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v0))
% 10.94/3.10 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 10.94/3.10 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 10.94/3.10 | (5) intersection(all_0_3_3, all_0_2_2) = all_0_1_1
% 10.94/3.10 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 10.94/3.10 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v9, v7) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 10.94/3.10 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 10.94/3.10 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 10.94/3.10 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v2, v6, v8) = 0 & apply(v1, v8, v7) = 0 & member(v8, v4) = 0) | (member(v7, v5) = v9 & member(v6, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))))
% 10.94/3.10 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 10.94/3.10 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 10.94/3.10 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 10.94/3.10 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 10.94/3.10 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 10.94/3.10 | (16) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0
% 10.94/3.10 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 10.94/3.10 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.94/3.10 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 10.94/3.10 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 10.94/3.11 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.94/3.11 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v8, v6) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 10.94/3.11 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 10.94/3.11 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ? [v10] : ? [v11] : ((apply(v1, v5, v9) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))
% 10.94/3.11 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 10.94/3.11 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 10.94/3.11 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 10.94/3.11 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 10.94/3.11 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 10.94/3.11 | (30) image3(all_0_10_10, all_0_6_6, all_0_8_8) = all_0_2_2
% 10.94/3.11 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 10.94/3.11 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 10.94/3.11 | (33) ~ (all_0_0_0 = 0)
% 10.94/3.11 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 10.94/3.11 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 10.94/3.11 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 10.94/3.11 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 10.94/3.11 | (38) subset(all_0_6_6, all_0_9_9) = 0
% 10.94/3.11 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v4, v7, v9) = v10 & apply(v2, v6, v8) = 0 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0))
% 10.94/3.11 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 10.94/3.11 | (41) intersection(all_0_7_7, all_0_6_6) = all_0_5_5
% 10.94/3.11 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 10.94/3.11 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 10.94/3.11 | (44) ! [v0] : ~ (member(v0, empty_set) = 0)
% 10.94/3.12 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 10.94/3.12 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | (( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0)))))
% 10.94/3.12 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 10.94/3.12 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 10.94/3.12 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (apply(v0, v2, v5) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 10.94/3.12 | (50) ! [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)))
% 10.94/3.12 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.94/3.12 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = 0) | (v5 = 0 & member(v4, v1) = 0 & ! [v12] : ( ~ (apply(v0, v4, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v2) = v13)))))
% 10.94/3.12 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.94/3.12 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 10.94/3.12 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0))
% 10.94/3.12 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v1, v5, v6) = v7 & apply(v0, v6, v5) = v8 & member(v6, v3) = 0 & member(v5, v2) = 0 & ( ~ (v8 = 0) | ~ (v7 = 0)) & (v8 = 0 | v7 = 0)))
% 10.94/3.12 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 10.94/3.12 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & apply(v1, v5, v8) = 0 & apply(v0, v8, v6) = 0 & member(v8, v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))))
% 10.94/3.12 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 10.94/3.12 | (60) maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0
% 10.94/3.12 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 10.94/3.12 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 10.94/3.12 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (injective(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0))
% 10.94/3.12 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v1, v9, v7) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : ? [v11] : ((apply(v2, v6, v9) = v11 & member(v9, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v7, v5) = v11 & member(v6, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))))
% 10.94/3.13 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 10.94/3.13 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ (compose_function(v6, v5, v4, v3, v2) = v0))
% 10.94/3.13 | (67) ! [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))))
% 10.94/3.13 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 10.94/3.13 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v4, v6, v8) = v14 & apply(v2, v5, v7) = v13 & member(v8, v3) = v12 & member(v7, v1) = v11 & member(v6, v3) = v10 & member(v5, v1) = v9 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v14 = 0)))
% 10.94/3.13 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 10.94/3.13 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 10.94/3.13 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (apply(v0, v3, v6) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 10.94/3.13 | (73) image3(all_0_10_10, all_0_7_7, all_0_8_8) = all_0_3_3
% 10.94/3.13 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 10.94/3.13 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 10.94/3.13 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 10.94/3.13 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : (member(v6, v3) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0))))
% 10.94/3.13 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 10.94/3.13 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 10.94/3.13 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 10.94/3.13 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 10.94/3.13 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 10.94/3.13 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 10.94/3.13 | (84) subset(all_0_7_7, all_0_9_9) = 0
% 10.94/3.13 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v0, v7, v8) = v9 & member(v8, v5) = 0 & member(v7, v3) = 0 & ( ~ (v9 = 0) | ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : ? [v16] : (apply(v2, v7, v14) = v16 & member(v14, v4) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & (v9 = 0 | (v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0))))
% 10.94/3.13 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 10.94/3.13 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 10.94/3.13 | (88) image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4
% 10.94/3.13 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 10.94/3.14 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & apply(v4, v7, v9) = v17 & apply(v2, v6, v8) = v16 & apply(v0, v8, v9) = 0 & apply(v0, v6, v7) = 0 & member(v9, v3) = 0 & member(v8, v1) = 0 & member(v7, v3) = 0 & member(v6, v1) = 0 & ( ~ (v17 = 0) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0)) | (one_to_one(v0, v1, v3) = v7 & maps(v0, v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 10.94/3.14 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0))
% 10.94/3.14 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 10.94/3.14 | (93) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.94/3.14 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 10.94/3.14 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 10.94/3.14 | (96) injective(all_0_10_10, all_0_9_9, all_0_8_8) = 0
% 10.94/3.14 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.94/3.14 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 10.94/3.14 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 10.94/3.14 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (surjective(v0, v1, v2) = v3) | ? [v4] : (member(v4, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5, v4) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v1) = v6))))
% 10.94/3.14 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (apply(v1, v4, v5) = v9 & member(v5, v3) = v8 & member(v4, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 10.94/3.14 |
% 10.94/3.14 | Instantiating formula (78) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 10.94/3.14 | (102) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.94/3.14 |
% 10.94/3.14 +-Applying beta-rule and splitting (102), into two cases.
% 10.94/3.14 |-Branch one:
% 10.94/3.14 | (103) all_0_0_0 = 0
% 10.94/3.14 |
% 10.94/3.14 | Equations (103) can reduce 33 to:
% 10.94/3.14 | (104) $false
% 10.94/3.14 |
% 10.94/3.14 |-The branch is then unsatisfiable
% 10.94/3.14 |-Branch two:
% 10.94/3.14 | (33) ~ (all_0_0_0 = 0)
% 10.94/3.14 | (106) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.94/3.14 |
% 10.94/3.14 | Instantiating (106) with all_14_0_11, all_14_1_12 yields:
% 10.94/3.14 | (107) subset(all_0_1_1, all_0_4_4) = all_14_0_11 & subset(all_0_4_4, all_0_1_1) = all_14_1_12 & ( ~ (all_14_0_11 = 0) | ~ (all_14_1_12 = 0))
% 10.94/3.14 |
% 10.94/3.14 | Applying alpha-rule on (107) yields:
% 10.94/3.14 | (108) subset(all_0_1_1, all_0_4_4) = all_14_0_11
% 10.94/3.14 | (109) subset(all_0_4_4, all_0_1_1) = all_14_1_12
% 10.94/3.14 | (110) ~ (all_14_0_11 = 0) | ~ (all_14_1_12 = 0)
% 10.94/3.14 |
% 10.94/3.14 | Instantiating formula (61) with all_14_0_11, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_0_11, yields:
% 10.94/3.14 | (111) all_14_0_11 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 10.94/3.14 |
% 10.94/3.14 | Instantiating formula (61) with all_14_1_12, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_1_12, yields:
% 10.94/3.14 | (112) all_14_1_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 10.94/3.14 |
% 10.94/3.14 +-Applying beta-rule and splitting (110), into two cases.
% 10.94/3.14 |-Branch one:
% 10.94/3.14 | (113) ~ (all_14_0_11 = 0)
% 10.94/3.14 |
% 10.94/3.14 +-Applying beta-rule and splitting (111), into two cases.
% 10.94/3.14 |-Branch one:
% 10.94/3.14 | (114) all_14_0_11 = 0
% 10.94/3.14 |
% 10.94/3.14 | Equations (114) can reduce 113 to:
% 10.94/3.14 | (104) $false
% 10.94/3.14 |
% 10.94/3.14 |-The branch is then unsatisfiable
% 10.94/3.14 |-Branch two:
% 10.94/3.14 | (113) ~ (all_14_0_11 = 0)
% 10.94/3.14 | (117) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 10.94/3.14 |
% 10.94/3.14 | Instantiating (117) with all_53_0_13, all_53_1_14 yields:
% 10.94/3.15 | (118) ~ (all_53_0_13 = 0) & member(all_53_1_14, all_0_1_1) = 0 & member(all_53_1_14, all_0_4_4) = all_53_0_13
% 10.94/3.15 |
% 10.94/3.15 | Applying alpha-rule on (118) yields:
% 10.94/3.15 | (119) ~ (all_53_0_13 = 0)
% 10.94/3.15 | (120) member(all_53_1_14, all_0_1_1) = 0
% 10.94/3.15 | (121) member(all_53_1_14, all_0_4_4) = all_53_0_13
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (86) with all_0_2_2, all_53_1_14, all_0_8_8, all_0_6_6, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_6_6, all_0_8_8) = all_0_2_2, yields:
% 10.94/3.15 | (122) ~ (member(all_53_1_14, all_0_2_2) = 0) | ? [v0] : (apply(all_0_10_10, v0, all_53_1_14) = 0 & member(v0, all_0_6_6) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (14) with all_0_3_3, all_53_1_14, all_0_8_8, all_0_7_7, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_7_7, all_0_8_8) = all_0_3_3, yields:
% 10.94/3.15 | (123) ~ (member(all_53_1_14, all_0_3_3) = 0) | member(all_53_1_14, all_0_8_8) = 0
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (86) with all_0_3_3, all_53_1_14, all_0_8_8, all_0_7_7, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_7_7, all_0_8_8) = all_0_3_3, yields:
% 10.94/3.15 | (124) ~ (member(all_53_1_14, all_0_3_3) = 0) | ? [v0] : (apply(all_0_10_10, v0, all_53_1_14) = 0 & member(v0, all_0_7_7) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (37) with all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_14 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_14, all_0_1_1) = 0, yields:
% 10.94/3.15 | (125) member(all_53_1_14, all_0_2_2) = 0 & member(all_53_1_14, all_0_3_3) = 0
% 10.94/3.15 |
% 10.94/3.15 | Applying alpha-rule on (125) yields:
% 10.94/3.15 | (126) member(all_53_1_14, all_0_2_2) = 0
% 10.94/3.15 | (127) member(all_53_1_14, all_0_3_3) = 0
% 10.94/3.15 |
% 10.94/3.15 +-Applying beta-rule and splitting (123), into two cases.
% 10.94/3.15 |-Branch one:
% 10.94/3.15 | (128) ~ (member(all_53_1_14, all_0_3_3) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Using (127) and (128) yields:
% 10.94/3.15 | (129) $false
% 10.94/3.15 |
% 10.94/3.15 |-The branch is then unsatisfiable
% 10.94/3.15 |-Branch two:
% 10.94/3.15 | (127) member(all_53_1_14, all_0_3_3) = 0
% 10.94/3.15 | (131) member(all_53_1_14, all_0_8_8) = 0
% 10.94/3.15 |
% 10.94/3.15 +-Applying beta-rule and splitting (124), into two cases.
% 10.94/3.15 |-Branch one:
% 10.94/3.15 | (128) ~ (member(all_53_1_14, all_0_3_3) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Using (127) and (128) yields:
% 10.94/3.15 | (129) $false
% 10.94/3.15 |
% 10.94/3.15 |-The branch is then unsatisfiable
% 10.94/3.15 |-Branch two:
% 10.94/3.15 | (127) member(all_53_1_14, all_0_3_3) = 0
% 10.94/3.15 | (135) ? [v0] : (apply(all_0_10_10, v0, all_53_1_14) = 0 & member(v0, all_0_7_7) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating (135) with all_81_0_15 yields:
% 10.94/3.15 | (136) apply(all_0_10_10, all_81_0_15, all_53_1_14) = 0 & member(all_81_0_15, all_0_7_7) = 0
% 10.94/3.15 |
% 10.94/3.15 | Applying alpha-rule on (136) yields:
% 10.94/3.15 | (137) apply(all_0_10_10, all_81_0_15, all_53_1_14) = 0
% 10.94/3.15 | (138) member(all_81_0_15, all_0_7_7) = 0
% 10.94/3.15 |
% 10.94/3.15 +-Applying beta-rule and splitting (122), into two cases.
% 10.94/3.15 |-Branch one:
% 10.94/3.15 | (139) ~ (member(all_53_1_14, all_0_2_2) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Using (126) and (139) yields:
% 10.94/3.15 | (129) $false
% 10.94/3.15 |
% 10.94/3.15 |-The branch is then unsatisfiable
% 10.94/3.15 |-Branch two:
% 10.94/3.15 | (126) member(all_53_1_14, all_0_2_2) = 0
% 10.94/3.15 | (142) ? [v0] : (apply(all_0_10_10, v0, all_53_1_14) = 0 & member(v0, all_0_6_6) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating (142) with all_86_0_16 yields:
% 10.94/3.15 | (143) apply(all_0_10_10, all_86_0_16, all_53_1_14) = 0 & member(all_86_0_16, all_0_6_6) = 0
% 10.94/3.15 |
% 10.94/3.15 | Applying alpha-rule on (143) yields:
% 10.94/3.15 | (144) apply(all_0_10_10, all_86_0_16, all_53_1_14) = 0
% 10.94/3.15 | (145) member(all_86_0_16, all_0_6_6) = 0
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (42) with all_86_0_16, all_53_0_13, all_0_4_4, all_53_1_14, all_0_8_8, all_0_5_5, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4, apply(all_0_10_10, all_86_0_16, all_53_1_14) = 0, member(all_53_1_14, all_0_4_4) = all_53_0_13, yields:
% 10.94/3.15 | (146) all_53_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_86_0_16, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_8_8) = v0))
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (42) with all_81_0_15, all_53_0_13, all_0_4_4, all_53_1_14, all_0_8_8, all_0_5_5, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4, apply(all_0_10_10, all_81_0_15, all_53_1_14) = 0, member(all_53_1_14, all_0_4_4) = all_53_0_13, yields:
% 10.94/3.15 | (147) all_53_0_13 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_81_0_15, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_8_8) = v0))
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (25) with all_53_1_14, all_86_0_16, all_81_0_15, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms injective(all_0_10_10, all_0_9_9, all_0_8_8) = 0, apply(all_0_10_10, all_86_0_16, all_53_1_14) = 0, apply(all_0_10_10, all_81_0_15, all_53_1_14) = 0, yields:
% 10.94/3.15 | (148) all_86_0_16 = all_81_0_15 | ? [v0] : ? [v1] : ? [v2] : (member(all_86_0_16, all_0_9_9) = v1 & member(all_81_0_15, all_0_9_9) = v0 & member(all_53_1_14, all_0_8_8) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (75) with all_86_0_16, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, yields:
% 10.94/3.15 | (149) ~ (member(all_86_0_16, all_0_9_9) = 0) | ? [v0] : (apply(all_0_10_10, all_86_0_16, v0) = 0 & member(v0, all_0_8_8) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (80) with all_86_0_16, all_0_9_9, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_9_9) = 0, member(all_86_0_16, all_0_6_6) = 0, yields:
% 10.94/3.15 | (150) member(all_86_0_16, all_0_9_9) = 0
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (75) with all_81_0_15, all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms maps(all_0_10_10, all_0_9_9, all_0_8_8) = 0, yields:
% 10.94/3.15 | (151) ~ (member(all_81_0_15, all_0_9_9) = 0) | ? [v0] : (apply(all_0_10_10, all_81_0_15, v0) = 0 & member(v0, all_0_8_8) = 0)
% 10.94/3.15 |
% 10.94/3.15 | Instantiating formula (80) with all_81_0_15, all_0_9_9, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_9_9) = 0, member(all_81_0_15, all_0_7_7) = 0, yields:
% 10.94/3.15 | (152) member(all_81_0_15, all_0_9_9) = 0
% 10.94/3.15 |
% 10.94/3.15 +-Applying beta-rule and splitting (148), into two cases.
% 10.94/3.15 |-Branch one:
% 10.94/3.15 | (153) all_86_0_16 = all_81_0_15
% 10.94/3.15 |
% 10.94/3.15 | From (153) and (145) follows:
% 10.94/3.15 | (154) member(all_81_0_15, all_0_6_6) = 0
% 10.94/3.15 |
% 10.94/3.16 +-Applying beta-rule and splitting (146), into two cases.
% 10.94/3.16 |-Branch one:
% 10.94/3.16 | (155) all_53_0_13 = 0
% 10.94/3.16 |
% 10.94/3.16 | Equations (155) can reduce 119 to:
% 10.94/3.16 | (104) $false
% 10.94/3.16 |
% 10.94/3.16 |-The branch is then unsatisfiable
% 10.94/3.16 |-Branch two:
% 10.94/3.16 | (119) ~ (all_53_0_13 = 0)
% 10.94/3.16 | (158) ? [v0] : (( ~ (v0 = 0) & member(all_86_0_16, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_8_8) = v0))
% 10.94/3.16 |
% 10.94/3.16 | Instantiating (158) with all_120_0_19 yields:
% 10.94/3.16 | (159) ( ~ (all_120_0_19 = 0) & member(all_86_0_16, all_0_5_5) = all_120_0_19) | ( ~ (all_120_0_19 = 0) & member(all_53_1_14, all_0_8_8) = all_120_0_19)
% 10.94/3.16 |
% 10.94/3.16 +-Applying beta-rule and splitting (147), into two cases.
% 10.94/3.16 |-Branch one:
% 10.94/3.16 | (155) all_53_0_13 = 0
% 10.94/3.16 |
% 10.94/3.16 | Equations (155) can reduce 119 to:
% 10.94/3.16 | (104) $false
% 10.94/3.16 |
% 10.94/3.16 |-The branch is then unsatisfiable
% 10.94/3.16 |-Branch two:
% 10.94/3.16 | (119) ~ (all_53_0_13 = 0)
% 10.94/3.16 | (163) ? [v0] : (( ~ (v0 = 0) & member(all_81_0_15, all_0_5_5) = v0) | ( ~ (v0 = 0) & member(all_53_1_14, all_0_8_8) = v0))
% 10.94/3.16 |
% 10.94/3.16 | Instantiating (163) with all_124_0_20 yields:
% 10.94/3.16 | (164) ( ~ (all_124_0_20 = 0) & member(all_81_0_15, all_0_5_5) = all_124_0_20) | ( ~ (all_124_0_20 = 0) & member(all_53_1_14, all_0_8_8) = all_124_0_20)
% 10.94/3.16 |
% 10.94/3.16 +-Applying beta-rule and splitting (159), into two cases.
% 10.94/3.16 |-Branch one:
% 10.94/3.16 | (165) ~ (all_120_0_19 = 0) & member(all_86_0_16, all_0_5_5) = all_120_0_19
% 10.94/3.16 |
% 10.94/3.16 | Applying alpha-rule on (165) yields:
% 10.94/3.16 | (166) ~ (all_120_0_19 = 0)
% 10.94/3.16 | (167) member(all_86_0_16, all_0_5_5) = all_120_0_19
% 10.94/3.16 |
% 10.94/3.16 | From (153) and (167) follows:
% 10.94/3.16 | (168) member(all_81_0_15, all_0_5_5) = all_120_0_19
% 10.94/3.16 |
% 10.94/3.16 +-Applying beta-rule and splitting (164), into two cases.
% 10.94/3.16 |-Branch one:
% 10.94/3.16 | (169) ~ (all_124_0_20 = 0) & member(all_81_0_15, all_0_5_5) = all_124_0_20
% 10.94/3.16 |
% 10.94/3.16 | Applying alpha-rule on (169) yields:
% 10.94/3.16 | (170) ~ (all_124_0_20 = 0)
% 11.27/3.16 | (171) member(all_81_0_15, all_0_5_5) = all_124_0_20
% 11.27/3.16 |
% 11.27/3.16 | Instantiating formula (31) with all_81_0_15, all_0_5_5, all_120_0_19, all_124_0_20 and discharging atoms member(all_81_0_15, all_0_5_5) = all_124_0_20, member(all_81_0_15, all_0_5_5) = all_120_0_19, yields:
% 11.27/3.16 | (172) all_124_0_20 = all_120_0_19
% 11.27/3.16 |
% 11.27/3.16 | Equations (172) can reduce 170 to:
% 11.27/3.16 | (166) ~ (all_120_0_19 = 0)
% 11.27/3.16 |
% 11.27/3.16 | From (172) and (171) follows:
% 11.27/3.16 | (168) member(all_81_0_15, all_0_5_5) = all_120_0_19
% 11.27/3.16 |
% 11.27/3.16 | Instantiating formula (74) with all_120_0_19, all_0_5_5, all_0_6_6, all_0_7_7, all_81_0_15 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_81_0_15, all_0_5_5) = all_120_0_19, yields:
% 11.27/3.16 | (175) all_120_0_19 = 0 | ? [v0] : ? [v1] : (member(all_81_0_15, all_0_6_6) = v1 & member(all_81_0_15, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.27/3.16 |
% 11.27/3.16 +-Applying beta-rule and splitting (175), into two cases.
% 11.27/3.16 |-Branch one:
% 11.27/3.16 | (176) all_120_0_19 = 0
% 11.27/3.16 |
% 11.27/3.16 | Equations (176) can reduce 166 to:
% 11.27/3.16 | (104) $false
% 11.27/3.16 |
% 11.27/3.16 |-The branch is then unsatisfiable
% 11.27/3.16 |-Branch two:
% 11.27/3.16 | (166) ~ (all_120_0_19 = 0)
% 11.27/3.16 | (179) ? [v0] : ? [v1] : (member(all_81_0_15, all_0_6_6) = v1 & member(all_81_0_15, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.27/3.16 |
% 11.27/3.16 | Instantiating (179) with all_148_0_21, all_148_1_22 yields:
% 11.27/3.16 | (180) member(all_81_0_15, all_0_6_6) = all_148_0_21 & member(all_81_0_15, all_0_7_7) = all_148_1_22 & ( ~ (all_148_0_21 = 0) | ~ (all_148_1_22 = 0))
% 11.27/3.16 |
% 11.27/3.16 | Applying alpha-rule on (180) yields:
% 11.27/3.16 | (181) member(all_81_0_15, all_0_6_6) = all_148_0_21
% 11.27/3.16 | (182) member(all_81_0_15, all_0_7_7) = all_148_1_22
% 11.27/3.16 | (183) ~ (all_148_0_21 = 0) | ~ (all_148_1_22 = 0)
% 11.27/3.16 |
% 11.27/3.16 | Instantiating formula (31) with all_81_0_15, all_0_6_6, all_148_0_21, 0 and discharging atoms member(all_81_0_15, all_0_6_6) = all_148_0_21, member(all_81_0_15, all_0_6_6) = 0, yields:
% 11.27/3.16 | (184) all_148_0_21 = 0
% 11.27/3.16 |
% 11.27/3.16 | Instantiating formula (31) with all_81_0_15, all_0_7_7, all_148_1_22, 0 and discharging atoms member(all_81_0_15, all_0_7_7) = all_148_1_22, member(all_81_0_15, all_0_7_7) = 0, yields:
% 11.27/3.16 | (185) all_148_1_22 = 0
% 11.27/3.16 |
% 11.27/3.16 +-Applying beta-rule and splitting (183), into two cases.
% 11.27/3.16 |-Branch one:
% 11.27/3.16 | (186) ~ (all_148_0_21 = 0)
% 11.27/3.16 |
% 11.27/3.16 | Equations (184) can reduce 186 to:
% 11.27/3.16 | (104) $false
% 11.27/3.16 |
% 11.27/3.16 |-The branch is then unsatisfiable
% 11.27/3.16 |-Branch two:
% 11.27/3.16 | (184) all_148_0_21 = 0
% 11.27/3.16 | (189) ~ (all_148_1_22 = 0)
% 11.27/3.16 |
% 11.27/3.16 | Equations (185) can reduce 189 to:
% 11.27/3.16 | (104) $false
% 11.27/3.16 |
% 11.27/3.16 |-The branch is then unsatisfiable
% 11.27/3.16 |-Branch two:
% 11.27/3.16 | (191) ~ (all_124_0_20 = 0) & member(all_53_1_14, all_0_8_8) = all_124_0_20
% 11.27/3.16 |
% 11.27/3.16 | Applying alpha-rule on (191) yields:
% 11.27/3.16 | (170) ~ (all_124_0_20 = 0)
% 11.27/3.16 | (193) member(all_53_1_14, all_0_8_8) = all_124_0_20
% 11.27/3.16 |
% 11.27/3.16 | Instantiating formula (31) with all_53_1_14, all_0_8_8, all_124_0_20, 0 and discharging atoms member(all_53_1_14, all_0_8_8) = all_124_0_20, member(all_53_1_14, all_0_8_8) = 0, yields:
% 11.29/3.16 | (194) all_124_0_20 = 0
% 11.29/3.16 |
% 11.29/3.16 | Equations (194) can reduce 170 to:
% 11.29/3.16 | (104) $false
% 11.29/3.16 |
% 11.29/3.16 |-The branch is then unsatisfiable
% 11.29/3.16 |-Branch two:
% 11.29/3.16 | (196) ~ (all_120_0_19 = 0) & member(all_53_1_14, all_0_8_8) = all_120_0_19
% 11.29/3.16 |
% 11.29/3.16 | Applying alpha-rule on (196) yields:
% 11.29/3.16 | (166) ~ (all_120_0_19 = 0)
% 11.29/3.16 | (198) member(all_53_1_14, all_0_8_8) = all_120_0_19
% 11.29/3.16 |
% 11.29/3.16 | Instantiating formula (31) with all_53_1_14, all_0_8_8, all_120_0_19, 0 and discharging atoms member(all_53_1_14, all_0_8_8) = all_120_0_19, member(all_53_1_14, all_0_8_8) = 0, yields:
% 11.29/3.16 | (176) all_120_0_19 = 0
% 11.29/3.16 |
% 11.29/3.17 | Equations (176) can reduce 166 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (201) ~ (all_86_0_16 = all_81_0_15)
% 11.29/3.17 | (202) ? [v0] : ? [v1] : ? [v2] : (member(all_86_0_16, all_0_9_9) = v1 & member(all_81_0_15, all_0_9_9) = v0 & member(all_53_1_14, all_0_8_8) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 11.29/3.17 |
% 11.29/3.17 | Instantiating (202) with all_106_0_23, all_106_1_24, all_106_2_25 yields:
% 11.29/3.17 | (203) member(all_86_0_16, all_0_9_9) = all_106_1_24 & member(all_81_0_15, all_0_9_9) = all_106_2_25 & member(all_53_1_14, all_0_8_8) = all_106_0_23 & ( ~ (all_106_0_23 = 0) | ~ (all_106_1_24 = 0) | ~ (all_106_2_25 = 0))
% 11.29/3.17 |
% 11.29/3.17 | Applying alpha-rule on (203) yields:
% 11.29/3.17 | (204) member(all_86_0_16, all_0_9_9) = all_106_1_24
% 11.29/3.17 | (205) member(all_81_0_15, all_0_9_9) = all_106_2_25
% 11.29/3.17 | (206) member(all_53_1_14, all_0_8_8) = all_106_0_23
% 11.29/3.17 | (207) ~ (all_106_0_23 = 0) | ~ (all_106_1_24 = 0) | ~ (all_106_2_25 = 0)
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (151), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (208) ~ (member(all_81_0_15, all_0_9_9) = 0)
% 11.29/3.17 |
% 11.29/3.17 | Using (152) and (208) yields:
% 11.29/3.17 | (129) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (152) member(all_81_0_15, all_0_9_9) = 0
% 11.29/3.17 | (211) ? [v0] : (apply(all_0_10_10, all_81_0_15, v0) = 0 & member(v0, all_0_8_8) = 0)
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (149), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (212) ~ (member(all_86_0_16, all_0_9_9) = 0)
% 11.29/3.17 |
% 11.29/3.17 | Using (150) and (212) yields:
% 11.29/3.17 | (129) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (150) member(all_86_0_16, all_0_9_9) = 0
% 11.29/3.17 | (215) ? [v0] : (apply(all_0_10_10, all_86_0_16, v0) = 0 & member(v0, all_0_8_8) = 0)
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (31) with all_86_0_16, all_0_9_9, all_106_1_24, 0 and discharging atoms member(all_86_0_16, all_0_9_9) = all_106_1_24, member(all_86_0_16, all_0_9_9) = 0, yields:
% 11.29/3.17 | (216) all_106_1_24 = 0
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (31) with all_81_0_15, all_0_9_9, all_106_2_25, 0 and discharging atoms member(all_81_0_15, all_0_9_9) = all_106_2_25, member(all_81_0_15, all_0_9_9) = 0, yields:
% 11.29/3.17 | (217) all_106_2_25 = 0
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (31) with all_53_1_14, all_0_8_8, all_106_0_23, 0 and discharging atoms member(all_53_1_14, all_0_8_8) = all_106_0_23, member(all_53_1_14, all_0_8_8) = 0, yields:
% 11.29/3.17 | (218) all_106_0_23 = 0
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (207), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (219) ~ (all_106_0_23 = 0)
% 11.29/3.17 |
% 11.29/3.17 | Equations (218) can reduce 219 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (218) all_106_0_23 = 0
% 11.29/3.17 | (222) ~ (all_106_1_24 = 0) | ~ (all_106_2_25 = 0)
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (222), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (223) ~ (all_106_1_24 = 0)
% 11.29/3.17 |
% 11.29/3.17 | Equations (216) can reduce 223 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (216) all_106_1_24 = 0
% 11.29/3.17 | (226) ~ (all_106_2_25 = 0)
% 11.29/3.17 |
% 11.29/3.17 | Equations (217) can reduce 226 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (114) all_14_0_11 = 0
% 11.29/3.17 | (229) ~ (all_14_1_12 = 0)
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (112), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (230) all_14_1_12 = 0
% 11.29/3.17 |
% 11.29/3.17 | Equations (230) can reduce 229 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (229) ~ (all_14_1_12 = 0)
% 11.29/3.17 | (233) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 11.29/3.17 |
% 11.29/3.17 | Instantiating (233) with all_53_0_30, all_53_1_31 yields:
% 11.29/3.17 | (234) ~ (all_53_0_30 = 0) & member(all_53_1_31, all_0_1_1) = all_53_0_30 & member(all_53_1_31, all_0_4_4) = 0
% 11.29/3.17 |
% 11.29/3.17 | Applying alpha-rule on (234) yields:
% 11.29/3.17 | (235) ~ (all_53_0_30 = 0)
% 11.29/3.17 | (236) member(all_53_1_31, all_0_1_1) = all_53_0_30
% 11.29/3.17 | (237) member(all_53_1_31, all_0_4_4) = 0
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (74) with all_53_0_30, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_31 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_31, all_0_1_1) = all_53_0_30, yields:
% 11.29/3.17 | (238) all_53_0_30 = 0 | ? [v0] : ? [v1] : (member(all_53_1_31, all_0_2_2) = v1 & member(all_53_1_31, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (14) with all_0_4_4, all_53_1_31, all_0_8_8, all_0_5_5, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4, member(all_53_1_31, all_0_4_4) = 0, yields:
% 11.29/3.17 | (239) member(all_53_1_31, all_0_8_8) = 0
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (86) with all_0_4_4, all_53_1_31, all_0_8_8, all_0_5_5, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_5_5, all_0_8_8) = all_0_4_4, member(all_53_1_31, all_0_4_4) = 0, yields:
% 11.29/3.17 | (240) ? [v0] : (apply(all_0_10_10, v0, all_53_1_31) = 0 & member(v0, all_0_5_5) = 0)
% 11.29/3.17 |
% 11.29/3.17 | Instantiating (240) with all_69_0_32 yields:
% 11.29/3.17 | (241) apply(all_0_10_10, all_69_0_32, all_53_1_31) = 0 & member(all_69_0_32, all_0_5_5) = 0
% 11.29/3.17 |
% 11.29/3.17 | Applying alpha-rule on (241) yields:
% 11.29/3.17 | (242) apply(all_0_10_10, all_69_0_32, all_53_1_31) = 0
% 11.29/3.17 | (243) member(all_69_0_32, all_0_5_5) = 0
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (238), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (244) all_53_0_30 = 0
% 11.29/3.17 |
% 11.29/3.17 | Equations (244) can reduce 235 to:
% 11.29/3.17 | (104) $false
% 11.29/3.17 |
% 11.29/3.17 |-The branch is then unsatisfiable
% 11.29/3.17 |-Branch two:
% 11.29/3.17 | (235) ~ (all_53_0_30 = 0)
% 11.29/3.17 | (247) ? [v0] : ? [v1] : (member(all_53_1_31, all_0_2_2) = v1 & member(all_53_1_31, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.29/3.17 |
% 11.29/3.17 | Instantiating (247) with all_75_0_33, all_75_1_34 yields:
% 11.29/3.17 | (248) member(all_53_1_31, all_0_2_2) = all_75_0_33 & member(all_53_1_31, all_0_3_3) = all_75_1_34 & ( ~ (all_75_0_33 = 0) | ~ (all_75_1_34 = 0))
% 11.29/3.17 |
% 11.29/3.17 | Applying alpha-rule on (248) yields:
% 11.29/3.17 | (249) member(all_53_1_31, all_0_2_2) = all_75_0_33
% 11.29/3.17 | (250) member(all_53_1_31, all_0_3_3) = all_75_1_34
% 11.29/3.17 | (251) ~ (all_75_0_33 = 0) | ~ (all_75_1_34 = 0)
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (37) with all_0_5_5, all_0_6_6, all_0_7_7, all_69_0_32 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_69_0_32, all_0_5_5) = 0, yields:
% 11.29/3.17 | (252) member(all_69_0_32, all_0_6_6) = 0 & member(all_69_0_32, all_0_7_7) = 0
% 11.29/3.17 |
% 11.29/3.17 | Applying alpha-rule on (252) yields:
% 11.29/3.17 | (253) member(all_69_0_32, all_0_6_6) = 0
% 11.29/3.17 | (254) member(all_69_0_32, all_0_7_7) = 0
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (42) with all_69_0_32, all_75_0_33, all_0_2_2, all_53_1_31, all_0_8_8, all_0_6_6, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_6_6, all_0_8_8) = all_0_2_2, apply(all_0_10_10, all_69_0_32, all_53_1_31) = 0, member(all_53_1_31, all_0_2_2) = all_75_0_33, yields:
% 11.29/3.17 | (255) all_75_0_33 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_69_0_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_53_1_31, all_0_8_8) = v0))
% 11.29/3.17 |
% 11.29/3.17 | Instantiating formula (42) with all_69_0_32, all_75_1_34, all_0_3_3, all_53_1_31, all_0_8_8, all_0_7_7, all_0_10_10 and discharging atoms image3(all_0_10_10, all_0_7_7, all_0_8_8) = all_0_3_3, apply(all_0_10_10, all_69_0_32, all_53_1_31) = 0, member(all_53_1_31, all_0_3_3) = all_75_1_34, yields:
% 11.29/3.17 | (256) all_75_1_34 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_69_0_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_53_1_31, all_0_8_8) = v0))
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (255), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.17 | (257) all_75_0_33 = 0
% 11.29/3.17 |
% 11.29/3.17 +-Applying beta-rule and splitting (251), into two cases.
% 11.29/3.17 |-Branch one:
% 11.29/3.18 | (258) ~ (all_75_0_33 = 0)
% 11.29/3.18 |
% 11.29/3.18 | Equations (257) can reduce 258 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 |-Branch two:
% 11.29/3.18 | (257) all_75_0_33 = 0
% 11.29/3.18 | (261) ~ (all_75_1_34 = 0)
% 11.29/3.18 |
% 11.29/3.18 +-Applying beta-rule and splitting (256), into two cases.
% 11.29/3.18 |-Branch one:
% 11.29/3.18 | (262) all_75_1_34 = 0
% 11.29/3.18 |
% 11.29/3.18 | Equations (262) can reduce 261 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 |-Branch two:
% 11.29/3.18 | (261) ~ (all_75_1_34 = 0)
% 11.29/3.18 | (265) ? [v0] : (( ~ (v0 = 0) & member(all_69_0_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_53_1_31, all_0_8_8) = v0))
% 11.29/3.18 |
% 11.29/3.18 | Instantiating (265) with all_120_0_36 yields:
% 11.29/3.18 | (266) ( ~ (all_120_0_36 = 0) & member(all_69_0_32, all_0_7_7) = all_120_0_36) | ( ~ (all_120_0_36 = 0) & member(all_53_1_31, all_0_8_8) = all_120_0_36)
% 11.29/3.18 |
% 11.29/3.18 +-Applying beta-rule and splitting (266), into two cases.
% 11.29/3.18 |-Branch one:
% 11.29/3.18 | (267) ~ (all_120_0_36 = 0) & member(all_69_0_32, all_0_7_7) = all_120_0_36
% 11.29/3.18 |
% 11.29/3.18 | Applying alpha-rule on (267) yields:
% 11.29/3.18 | (268) ~ (all_120_0_36 = 0)
% 11.29/3.18 | (269) member(all_69_0_32, all_0_7_7) = all_120_0_36
% 11.29/3.18 |
% 11.29/3.18 | Instantiating formula (31) with all_69_0_32, all_0_7_7, 0, all_120_0_36 and discharging atoms member(all_69_0_32, all_0_7_7) = all_120_0_36, member(all_69_0_32, all_0_7_7) = 0, yields:
% 11.29/3.18 | (270) all_120_0_36 = 0
% 11.29/3.18 |
% 11.29/3.18 | Equations (270) can reduce 268 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 |-Branch two:
% 11.29/3.18 | (272) ~ (all_120_0_36 = 0) & member(all_53_1_31, all_0_8_8) = all_120_0_36
% 11.29/3.18 |
% 11.29/3.18 | Applying alpha-rule on (272) yields:
% 11.29/3.18 | (268) ~ (all_120_0_36 = 0)
% 11.29/3.18 | (274) member(all_53_1_31, all_0_8_8) = all_120_0_36
% 11.29/3.18 |
% 11.29/3.18 | Instantiating formula (31) with all_53_1_31, all_0_8_8, all_120_0_36, 0 and discharging atoms member(all_53_1_31, all_0_8_8) = all_120_0_36, member(all_53_1_31, all_0_8_8) = 0, yields:
% 11.29/3.18 | (270) all_120_0_36 = 0
% 11.29/3.18 |
% 11.29/3.18 | Equations (270) can reduce 268 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 |-Branch two:
% 11.29/3.18 | (258) ~ (all_75_0_33 = 0)
% 11.29/3.18 | (278) ? [v0] : (( ~ (v0 = 0) & member(all_69_0_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_53_1_31, all_0_8_8) = v0))
% 11.29/3.18 |
% 11.29/3.18 | Instantiating (278) with all_95_0_37 yields:
% 11.29/3.18 | (279) ( ~ (all_95_0_37 = 0) & member(all_69_0_32, all_0_6_6) = all_95_0_37) | ( ~ (all_95_0_37 = 0) & member(all_53_1_31, all_0_8_8) = all_95_0_37)
% 11.29/3.18 |
% 11.29/3.18 +-Applying beta-rule and splitting (279), into two cases.
% 11.29/3.18 |-Branch one:
% 11.29/3.18 | (280) ~ (all_95_0_37 = 0) & member(all_69_0_32, all_0_6_6) = all_95_0_37
% 11.29/3.18 |
% 11.29/3.18 | Applying alpha-rule on (280) yields:
% 11.29/3.18 | (281) ~ (all_95_0_37 = 0)
% 11.29/3.18 | (282) member(all_69_0_32, all_0_6_6) = all_95_0_37
% 11.29/3.18 |
% 11.29/3.18 | Instantiating formula (31) with all_69_0_32, all_0_6_6, 0, all_95_0_37 and discharging atoms member(all_69_0_32, all_0_6_6) = all_95_0_37, member(all_69_0_32, all_0_6_6) = 0, yields:
% 11.29/3.18 | (283) all_95_0_37 = 0
% 11.29/3.18 |
% 11.29/3.18 | Equations (283) can reduce 281 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 |-Branch two:
% 11.29/3.18 | (285) ~ (all_95_0_37 = 0) & member(all_53_1_31, all_0_8_8) = all_95_0_37
% 11.29/3.18 |
% 11.29/3.18 | Applying alpha-rule on (285) yields:
% 11.29/3.18 | (281) ~ (all_95_0_37 = 0)
% 11.29/3.18 | (287) member(all_53_1_31, all_0_8_8) = all_95_0_37
% 11.29/3.18 |
% 11.29/3.18 | Instantiating formula (31) with all_53_1_31, all_0_8_8, all_95_0_37, 0 and discharging atoms member(all_53_1_31, all_0_8_8) = all_95_0_37, member(all_53_1_31, all_0_8_8) = 0, yields:
% 11.29/3.18 | (283) all_95_0_37 = 0
% 11.29/3.18 |
% 11.29/3.18 | Equations (283) can reduce 281 to:
% 11.29/3.18 | (104) $false
% 11.29/3.18 |
% 11.29/3.18 |-The branch is then unsatisfiable
% 11.29/3.18 % SZS output end Proof for theBenchmark
% 11.29/3.18
% 11.29/3.18 2516ms
%------------------------------------------------------------------------------