TSTP Solution File: SET745+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET745+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:46 EDT 2022
% Result : Theorem 10.62s 3.02s
% Output : Proof 23.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET745+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 16:02:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/0.98 Prover 0: Preprocessing ...
% 3.29/1.33 Prover 0: Warning: ignoring some quantifiers
% 3.50/1.36 Prover 0: Constructing countermodel ...
% 4.77/1.69 Prover 0: gave up
% 4.77/1.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.77/1.74 Prover 1: Preprocessing ...
% 5.80/1.97 Prover 1: Constructing countermodel ...
% 6.87/2.16 Prover 1: gave up
% 6.87/2.16 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.87/2.20 Prover 2: Preprocessing ...
% 8.10/2.48 Prover 2: Warning: ignoring some quantifiers
% 8.10/2.49 Prover 2: Constructing countermodel ...
% 10.62/3.02 Prover 2: proved (853ms)
% 10.62/3.02
% 10.62/3.02 No countermodel exists, formula is valid
% 10.62/3.02 % SZS status Theorem for theBenchmark
% 10.62/3.02
% 10.62/3.02 Generating proof ... Warning: ignoring some quantifiers
% 20.92/5.49 found it (size 1092)
% 20.92/5.49
% 20.92/5.49 % SZS output start Proof for theBenchmark
% 20.92/5.49 Assumed formulas after preprocessing and simplification:
% 20.92/5.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (maps(v2, v6, v5) = v7 & maps(v1, v4, v5) = 0 & maps(v0, v3, v5) = 0 & union(v3, v4) = v6 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v19, v22, v24) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = 0) | ~ (apply(v19, v22, v24) = v26) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v25, v23) = v26) | ~ (apply(v19, v22, v24) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v25, v23) = v26) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v25, v23) = v26) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v24, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v25, v23) = v26) | ~ (member(v24, v18) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v19, v22, v24) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v24, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (member(v24, v18) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v22, v24) = v27) | ( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_function(v17, v18, v19, v20, v21) = v24) | ~ (apply(v24, v22, v23) = v25) | ~ (apply(v18, v22, v26) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v26, v23) = v27) | ( ~ (v27 = 0) & member(v26, v20) = v27) | ( ~ (v27 = 0) & member(v23, v21) = v27) | ( ~ (v27 = 0) & member(v22, v19) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_function(v17, v18, v19, v20, v21) = v24) | ~ (apply(v24, v22, v23) = v25) | ~ (apply(v17, v26, v23) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v18, v22, v26) = v27) | ( ~ (v27 = 0) & member(v26, v20) = v27) | ( ~ (v27 = 0) & member(v23, v21) = v27) | ( ~ (v27 = 0) & member(v22, v19) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_function(v17, v18, v19, v20, v21) = v24) | ~ (apply(v24, v22, v23) = v25) | ~ (member(v26, v20) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v18, v22, v26) = v27) | ( ~ (v27 = 0) & apply(v17, v26, v23) = v27) | ( ~ (v27 = 0) & member(v23, v21) = v27) | ( ~ (v27 = 0) & member(v22, v19) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_predicate(v17, v18, v19, v20, v21, v22) = 0) | ~ (apply(v19, v23, v26) = 0) | ~ (apply(v17, v23, v24) = v25) | ? [v27] : (( ~ (v27 = 0) & apply(v18, v26, v24) = v27) | ( ~ (v27 = 0) & member(v26, v21) = v27) | ( ~ (v27 = 0) & member(v24, v22) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_predicate(v17, v18, v19, v20, v21, v22) = 0) | ~ (apply(v18, v26, v24) = 0) | ~ (apply(v17, v23, v24) = v25) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v23, v26) = v27) | ( ~ (v27 = 0) & member(v26, v21) = v27) | ( ~ (v27 = 0) & member(v24, v22) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v25 = 0 | ~ (compose_predicate(v17, v18, v19, v20, v21, v22) = 0) | ~ (apply(v17, v23, v24) = v25) | ~ (member(v26, v21) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v19, v23, v26) = v27) | ( ~ (v27 = 0) & apply(v18, v26, v24) = v27) | ( ~ (v27 = 0) & member(v24, v22) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v19, v22, v24) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v19, v22, v24) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v24, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v19, v22, v24) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v19, v22, v24) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v21, v23, v25) = v26) | ~ (member(v24, v18) = 0) | ~ (member(v22, v18) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v19, v22, v24) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v19, v22, v24) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = v26) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v25, v20) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v21, v23, v25) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = v26) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v23, v20) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v21, v23, v25) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = v26) | ~ (member(v25, v20) = 0) | ~ (member(v23, v20) = 0) | ? [v27] : (( ~ (v27 = 0) & apply(v17, v24, v25) = v27) | ( ~ (v27 = 0) & apply(v17, v22, v23) = v27) | ( ~ (v27 = 0) & member(v24, v18) = v27) | ( ~ (v27 = 0) & member(v22, v18) = v27) | (( ~ (v26 = 0) | (v27 = 0 & apply(v21, v23, v25) = 0)) & (v26 = 0 | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (apply(v17, v22, v23) = 0) | ? [v26] : ? [v27] : (( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26) | (((v27 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26)) & ((v26 = 0 & apply(v19, v22, v24) = 0) | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ? [v27] : (( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | (((v27 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26)) & ((v26 = 0 & apply(v19, v22, v24) = 0) | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ? [v26] : ? [v27] : (( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26) | (((v27 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26)) & ((v26 = 0 & apply(v19, v22, v24) = 0) | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ? [v27] : (( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | (((v27 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26)) & ((v26 = 0 & apply(v19, v22, v24) = 0) | ( ~ (v27 = 0) & apply(v21, v23, v25) = v27))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v23, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (apply(v17, v22, v23) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (decreasing(v17, v18, v19, v20, v21) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v25, v23) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v19, v22, v24) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v23, v20) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (apply(v17, v22, v23) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v24, v25) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26) | ( ~ (v26 = 0) & member(v25, v20) = v26) | ( ~ (v26 = 0) & member(v24, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (apply(v17, v22, v23) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & member(v23, v20) = v26) | ( ~ (v26 = 0) & member(v22, v18) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (increasing(v17, v18, v19, v20, v21) = 0) | ~ (member(v25, v20) = 0) | ~ (member(v24, v18) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v18) = 0) | ? [v26] : ((v26 = 0 & apply(v21, v23, v25) = 0) | ( ~ (v26 = 0) & apply(v19, v22, v24) = v26) | ( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ~ (v26 = 0) & apply(v17, v22, v23) = v26))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v18 = v17 | ~ (compose_predicate(v24, v23, v22, v21, v20, v19) = v18) | ~ (compose_predicate(v24, v23, v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (compose_function(v17, v18, v19, v20, v21) = v24) | ~ (apply(v24, v22, v23) = 0) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = 0 & v27 = 0 & v26 = 0 & apply(v18, v22, v25) = 0 & apply(v17, v25, v23) = 0 & member(v25, v20) = 0) | ( ~ (v25 = 0) & member(v23, v21) = v25) | ( ~ (v25 = 0) & member(v22, v19) = v25))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (compose_predicate(v17, v18, v19, v20, v21, v22) = 0) | ~ (apply(v17, v23, v24) = 0) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = 0 & v27 = 0 & v26 = 0 & apply(v19, v23, v25) = 0 & apply(v18, v25, v24) = 0 & member(v25, v21) = 0) | ( ~ (v25 = 0) & member(v24, v22) = v25) | ( ~ (v25 = 0) & member(v23, v20) = v25))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (equal_maps(v17, v18, v19, v20) = 0) | ~ (apply(v18, v21, v23) = 0) | ~ (apply(v17, v21, v22) = 0) | ? [v24] : (( ~ (v24 = 0) & member(v23, v20) = v24) | ( ~ (v24 = 0) & member(v22, v20) = v24) | ( ~ (v24 = 0) & member(v21, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (equal_maps(v17, v18, v19, v20) = 0) | ~ (apply(v18, v21, v23) = 0) | ~ (member(v22, v20) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v17, v21, v22) = v24) | ( ~ (v24 = 0) & member(v23, v20) = v24) | ( ~ (v24 = 0) & member(v21, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (equal_maps(v17, v18, v19, v20) = 0) | ~ (apply(v17, v21, v22) = 0) | ~ (member(v23, v20) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v18, v21, v23) = v24) | ( ~ (v24 = 0) & member(v22, v20) = v24) | ( ~ (v24 = 0) & member(v21, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (equal_maps(v17, v18, v19, v20) = 0) | ~ (member(v23, v20) = 0) | ~ (member(v22, v20) = 0) | ~ (member(v21, v19) = 0) | ? [v24] : (( ~ (v24 = 0) & apply(v18, v21, v23) = v24) | ( ~ (v24 = 0) & apply(v17, v21, v22) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (compose_predicate(v17, v18, v19, v20, v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (member(v25, v22) = 0 & member(v24, v20) = 0 & ((v30 = 0 & v29 = 0 & v28 = 0 & apply(v19, v24, v27) = 0 & apply(v18, v27, v25) = 0 & member(v27, v21) = 0) | (v26 = 0 & apply(v17, v24, v25) = 0)) & (( ~ (v26 = 0) & apply(v17, v24, v25) = v26) | ( ! [v31] : ( ~ (apply(v19, v24, v31) = 0) | ? [v32] : (( ~ (v32 = 0) & apply(v18, v31, v25) = v32) | ( ~ (v32 = 0) & member(v31, v21) = v32))) & ! [v31] : ( ~ (apply(v18, v31, v25) = 0) | ? [v32] : (( ~ (v32 = 0) & apply(v19, v24, v31) = v32) | ( ~ (v32 = 0) & member(v31, v21) = v32))) & ! [v31] : ( ~ (member(v31, v21) = 0) | ? [v32] : (( ~ (v32 = 0) & apply(v19, v24, v31) = v32) | ( ~ (v32 = 0) & apply(v18, v31, v25) = v32))))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = 0 | ~ (inverse_image3(v17, v18, v19) = v21) | ~ (apply(v17, v20, v23) = 0) | ~ (member(v20, v21) = v22) | ? [v24] : (( ~ (v24 = 0) & member(v23, v18) = v24) | ( ~ (v24 = 0) & member(v20, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = 0 | ~ (inverse_image3(v17, v18, v19) = v21) | ~ (member(v23, v18) = 0) | ~ (member(v20, v21) = v22) | ? [v24] : (( ~ (v24 = 0) & apply(v17, v20, v23) = v24) | ( ~ (v24 = 0) & member(v20, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = 0 | ~ (image3(v17, v18, v19) = v21) | ~ (apply(v17, v23, v20) = 0) | ~ (member(v20, v21) = v22) | ? [v24] : (( ~ (v24 = 0) & member(v23, v18) = v24) | ( ~ (v24 = 0) & member(v20, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = 0 | ~ (image3(v17, v18, v19) = v21) | ~ (member(v23, v18) = 0) | ~ (member(v20, v21) = v22) | ? [v24] : (( ~ (v24 = 0) & apply(v17, v23, v20) = v24) | ( ~ (v24 = 0) & member(v20, v19) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v18 = v17 | ~ (isomorphism(v23, v22, v21, v20, v19) = v18) | ~ (isomorphism(v23, v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v18 = v17 | ~ (decreasing(v23, v22, v21, v20, v19) = v18) | ~ (decreasing(v23, v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v18 = v17 | ~ (increasing(v23, v22, v21, v20, v19) = v18) | ~ (increasing(v23, v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v18 = v17 | ~ (compose_function(v23, v22, v21, v20, v19) = v18) | ~ (compose_function(v23, v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (inverse_function(v17, v18, v19) = v22) | ~ (apply(v22, v21, v20) = v23) | ? [v24] : (( ~ (v24 = 0) & member(v21, v19) = v24) | ( ~ (v24 = 0) & member(v20, v18) = v24) | (( ~ (v23 = 0) | (v24 = 0 & apply(v17, v20, v21) = 0)) & (v23 = 0 | ( ~ (v24 = 0) & apply(v17, v20, v21) = v24))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (inverse_predicate(v17, v18, v19, v20) = 0) | ~ (apply(v18, v21, v22) = v23) | ? [v24] : (( ~ (v24 = 0) & member(v22, v20) = v24) | ( ~ (v24 = 0) & member(v21, v19) = v24) | (( ~ (v23 = 0) | (v24 = 0 & apply(v17, v22, v21) = 0)) & (v23 = 0 | ( ~ (v24 = 0) & apply(v17, v22, v21) = v24))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (inverse_predicate(v17, v18, v19, v20) = 0) | ~ (apply(v17, v22, v21) = v23) | ? [v24] : (( ~ (v24 = 0) & member(v22, v20) = v24) | ( ~ (v24 = 0) & member(v21, v19) = v24) | (( ~ (v23 = 0) | (v24 = 0 & apply(v18, v21, v22) = 0)) & (v23 = 0 | ( ~ (v24 = 0) & apply(v18, v21, v22) = v24))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (maps(v17, v18, v19) = 0) | ~ (apply(v17, v20, v22) = 0) | ~ (apply(v17, v20, v21) = 0) | ? [v23] : (( ~ (v23 = 0) & member(v22, v19) = v23) | ( ~ (v23 = 0) & member(v21, v19) = v23) | ( ~ (v23 = 0) & member(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (maps(v17, v18, v19) = 0) | ~ (apply(v17, v20, v22) = 0) | ~ (member(v21, v19) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v20, v21) = v23) | ( ~ (v23 = 0) & member(v22, v19) = v23) | ( ~ (v23 = 0) & member(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (maps(v17, v18, v19) = 0) | ~ (apply(v17, v20, v21) = 0) | ~ (member(v22, v19) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v20, v22) = v23) | ( ~ (v23 = 0) & member(v21, v19) = v23) | ( ~ (v23 = 0) & member(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (maps(v17, v18, v19) = 0) | ~ (member(v22, v19) = 0) | ~ (member(v21, v19) = 0) | ~ (member(v20, v18) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v20, v22) = v23) | ( ~ (v23 = 0) & apply(v17, v20, v21) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (isomorphism(v17, v18, v19, v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ((v32 = 0 & v31 = 0 & v30 = 0 & v29 = 0 & v28 = 0 & v27 = 0 & apply(v17, v25, v26) = 0 & apply(v17, v23, v24) = 0 & member(v26, v20) = 0 & member(v25, v18) = 0 & member(v24, v20) = 0 & member(v23, v18) = 0 & ((v34 = 0 & apply(v21, v24, v26) = 0) | (v33 = 0 & apply(v19, v23, v25) = 0)) & (( ~ (v34 = 0) & apply(v21, v24, v26) = v34) | ( ~ (v33 = 0) & apply(v19, v23, v25) = v33))) | ( ~ (v23 = 0) & one_to_one(v17, v18, v20) = v23) | ( ~ (v23 = 0) & maps(v17, v18, v20) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (decreasing(v17, v18, v19, v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ( ~ (v27 = 0) & apply(v21, v26, v24) = v27 & apply(v19, v23, v25) = 0 & apply(v17, v25, v26) = 0 & apply(v17, v23, v24) = 0 & member(v26, v20) = 0 & member(v25, v18) = 0 & member(v24, v20) = 0 & member(v23, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (increasing(v17, v18, v19, v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ( ~ (v27 = 0) & apply(v21, v24, v26) = v27 & apply(v19, v23, v25) = 0 & apply(v17, v25, v26) = 0 & apply(v17, v23, v24) = 0 & member(v26, v20) = 0 & member(v25, v18) = 0 & member(v24, v20) = 0 & member(v23, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (injective(v17, v18, v19) = 0) | ~ (apply(v17, v21, v22) = 0) | ~ (apply(v17, v20, v22) = 0) | ? [v23] : (( ~ (v23 = 0) & member(v22, v19) = v23) | ( ~ (v23 = 0) & member(v21, v18) = v23) | ( ~ (v23 = 0) & member(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (injective(v17, v18, v19) = 0) | ~ (apply(v17, v21, v22) = 0) | ~ (member(v20, v18) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v20, v22) = v23) | ( ~ (v23 = 0) & member(v22, v19) = v23) | ( ~ (v23 = 0) & member(v21, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (injective(v17, v18, v19) = 0) | ~ (apply(v17, v20, v22) = 0) | ~ (member(v21, v18) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v21, v22) = v23) | ( ~ (v23 = 0) & member(v22, v19) = v23) | ( ~ (v23 = 0) & member(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (injective(v17, v18, v19) = 0) | ~ (member(v22, v19) = 0) | ~ (member(v21, v18) = 0) | ~ (member(v20, v18) = 0) | ? [v23] : (( ~ (v23 = 0) & apply(v17, v21, v22) = v23) | ( ~ (v23 = 0) & apply(v17, v20, v22) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (inverse_image2(v17, v18) = v20) | ~ (apply(v17, v19, v22) = 0) | ~ (member(v19, v20) = v21) | ? [v23] : ( ~ (v23 = 0) & member(v22, v18) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (inverse_image2(v17, v18) = v20) | ~ (member(v22, v18) = 0) | ~ (member(v19, v20) = v21) | ? [v23] : ( ~ (v23 = 0) & apply(v17, v19, v22) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (image2(v17, v18) = v20) | ~ (apply(v17, v22, v19) = 0) | ~ (member(v19, v20) = v21) | ? [v23] : ( ~ (v23 = 0) & member(v22, v18) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (image2(v17, v18) = v20) | ~ (member(v22, v18) = 0) | ~ (member(v19, v20) = v21) | ? [v23] : ( ~ (v23 = 0) & apply(v17, v22, v19) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v18 = v17 | ~ (inverse_predicate(v22, v21, v20, v19) = v18) | ~ (inverse_predicate(v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v18 = v17 | ~ (equal_maps(v22, v21, v20, v19) = v18) | ~ (equal_maps(v22, v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (inverse_predicate(v17, v18, v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (member(v23, v20) = 0 & member(v22, v19) = 0 & ((v25 = 0 & apply(v17, v23, v22) = 0) | (v24 = 0 & apply(v18, v22, v23) = 0)) & (( ~ (v25 = 0) & apply(v17, v23, v22) = v25) | ( ~ (v24 = 0) & apply(v18, v22, v23) = v24)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (equal_maps(v17, v18, v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ( ~ (v24 = v23) & apply(v18, v22, v24) = 0 & apply(v17, v22, v23) = 0 & member(v24, v20) = 0 & member(v23, v20) = 0 & member(v22, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (product(v18) = v19) | ~ (member(v17, v20) = v21) | ~ (member(v17, v19) = 0) | ? [v22] : ( ~ (v22 = 0) & member(v20, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (difference(v19, v18) = v20) | ~ (member(v17, v20) = v21) | ? [v22] : ((v22 = 0 & member(v17, v18) = 0) | ( ~ (v22 = 0) & member(v17, v19) = v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (union(v18, v19) = v20) | ~ (member(v17, v20) = v21) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & ~ (v22 = 0) & member(v17, v19) = v23 & member(v17, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (intersection(v18, v19) = v20) | ~ (member(v17, v20) = v21) | ? [v22] : (( ~ (v22 = 0) & member(v17, v19) = v22) | ( ~ (v22 = 0) & member(v17, v18) = v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (sum(v18) = v19) | ~ (member(v21, v18) = 0) | ~ (member(v17, v19) = v20) | ? [v22] : ( ~ (v22 = 0) & member(v17, v21) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (sum(v18) = v19) | ~ (member(v17, v21) = 0) | ~ (member(v17, v19) = v20) | ? [v22] : ( ~ (v22 = 0) & member(v21, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (inverse_image3(v21, v20, v19) = v18) | ~ (inverse_image3(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (image3(v21, v20, v19) = v18) | ~ (image3(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (inverse_function(v21, v20, v19) = v18) | ~ (inverse_function(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (one_to_one(v21, v20, v19) = v18) | ~ (one_to_one(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (surjective(v21, v20, v19) = v18) | ~ (surjective(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (injective(v21, v20, v19) = v18) | ~ (injective(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (maps(v21, v20, v19) = v18) | ~ (maps(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (apply(v21, v20, v19) = v18) | ~ (apply(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (isomorphism(v17, v18, v19, v20, v21) = 0) | (one_to_one(v17, v18, v20) = 0 & maps(v17, v18, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (inverse_image3(v17, v18, v19) = v21) | ~ (member(v20, v21) = 0) | member(v20, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (inverse_image3(v17, v18, v19) = v21) | ~ (member(v20, v21) = 0) | ? [v22] : (apply(v17, v20, v22) = 0 & member(v22, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (image3(v17, v18, v19) = v21) | ~ (member(v20, v21) = 0) | member(v20, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (image3(v17, v18, v19) = v21) | ~ (member(v20, v21) = 0) | ? [v22] : (apply(v17, v22, v20) = 0 & member(v22, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (one_to_one(v17, v18, v19) = v20) | ? [v21] : (( ~ (v21 = 0) & surjective(v17, v18, v19) = v21) | ( ~ (v21 = 0) & injective(v17, v18, v19) = v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (surjective(v17, v18, v19) = v20) | ? [v21] : (member(v21, v19) = 0 & ! [v22] : ( ~ (apply(v17, v22, v21) = 0) | ? [v23] : ( ~ (v23 = 0) & member(v22, v18) = v23)) & ! [v22] : ( ~ (member(v22, v18) = 0) | ? [v23] : ( ~ (v23 = 0) & apply(v17, v22, v21) = v23)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (injective(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ( ~ (v22 = v21) & apply(v17, v22, v23) = 0 & apply(v17, v21, v23) = 0 & member(v23, v19) = 0 & member(v22, v18) = 0 & member(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (identity(v17, v18) = 0) | ~ (apply(v17, v19, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & member(v19, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (maps(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = 0 & v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v23 = v22) & apply(v17, v21, v23) = 0 & apply(v17, v21, v22) = 0 & member(v23, v19) = 0 & member(v22, v19) = 0 & member(v21, v18) = 0) | (v22 = 0 & member(v21, v18) = 0 & ! [v29] : ( ~ (apply(v17, v21, v29) = 0) | ? [v30] : ( ~ (v30 = 0) & member(v29, v19) = v30)) & ! [v29] : ( ~ (member(v29, v19) = 0) | ? [v30] : ( ~ (v30 = 0) & apply(v17, v21, v29) = v30))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (product(v18) = v19) | ~ (member(v17, v19) = v20) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & member(v21, v18) = 0 & member(v17, v21) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (unordered_pair(v18, v17) = v19) | ~ (member(v17, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (unordered_pair(v17, v18) = v19) | ~ (member(v17, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (power_set(v18) = v19) | ~ (member(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v17, v18) = 0) | ~ (member(v19, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & member(v19, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v17 | v18 = v17 | ~ (unordered_pair(v18, v19) = v20) | ~ (member(v17, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (inverse_image2(v20, v19) = v18) | ~ (inverse_image2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (image2(v20, v19) = v18) | ~ (image2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (identity(v20, v19) = v18) | ~ (identity(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (unordered_pair(v20, v19) = v18) | ~ (unordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (difference(v20, v19) = v18) | ~ (difference(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (union(v20, v19) = v18) | ~ (union(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (intersection(v20, v19) = v18) | ~ (intersection(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (equal_set(v20, v19) = v18) | ~ (equal_set(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset(v20, v19) = v18) | ~ (subset(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (member(v20, v19) = v18) | ~ (member(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (inverse_image2(v17, v18) = v20) | ~ (member(v19, v20) = 0) | ? [v21] : (apply(v17, v19, v21) = 0 & member(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (image2(v17, v18) = v20) | ~ (member(v19, v20) = 0) | ? [v21] : (apply(v17, v21, v19) = 0 & member(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (surjective(v17, v18, v19) = v20) | ? [v21] : ((v21 = 0 & v20 = 0 & injective(v17, v18, v19) = 0) | ( ~ (v21 = 0) & one_to_one(v17, v18, v19) = v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (surjective(v17, v18, v19) = 0) | ~ (member(v20, v19) = 0) | ? [v21] : (apply(v17, v21, v20) = 0 & member(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (injective(v17, v18, v19) = v20) | ? [v21] : ((v21 = 0 & v20 = 0 & surjective(v17, v18, v19) = 0) | ( ~ (v21 = 0) & one_to_one(v17, v18, v19) = v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (maps(v17, v18, v19) = 0) | ~ (member(v20, v18) = 0) | ? [v21] : (apply(v17, v20, v21) = 0 & member(v21, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (product(v18) = v19) | ~ (member(v20, v18) = 0) | ~ (member(v17, v19) = 0) | member(v17, v20) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (difference(v19, v18) = v20) | ~ (member(v17, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & member(v17, v19) = 0 & member(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (union(v18, v19) = v20) | ~ (member(v17, v20) = 0) | ? [v21] : ((v21 = 0 & member(v17, v19) = 0) | (v21 = 0 & member(v17, v18) = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (intersection(v18, v19) = v20) | ~ (member(v17, v20) = 0) | (member(v17, v19) = 0 & member(v17, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (identity(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & apply(v17, v20, v20) = v21 & member(v20, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (singleton(v17) = v18) | ~ (member(v17, v18) = v19)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (equal_set(v17, v18) = v19) | ? [v20] : (( ~ (v20 = 0) & subset(v18, v17) = v20) | ( ~ (v20 = 0) & subset(v17, v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & power_set(v18) = v20 & member(v17, v20) = v21)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & member(v20, v18) = v21 & member(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (product(v19) = v18) | ~ (product(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (sum(v19) = v18) | ~ (sum(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v19) = v18) | ~ (singleton(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v18) = v19) | ~ (member(v17, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (power_set(v19) = v18) | ~ (power_set(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (one_to_one(v17, v18, v19) = 0) | (surjective(v17, v18, v19) = 0 & injective(v17, v18, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (surjective(v17, v18, v19) = 0) | ? [v20] : ((v20 = 0 & one_to_one(v17, v18, v19) = 0) | ( ~ (v20 = 0) & injective(v17, v18, v19) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (injective(v17, v18, v19) = 0) | ? [v20] : ((v20 = 0 & one_to_one(v17, v18, v19) = 0) | ( ~ (v20 = 0) & surjective(v17, v18, v19) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (identity(v17, v18) = 0) | ~ (member(v19, v18) = 0) | apply(v17, v19, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v2, v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ (v20 = 0) & member(v18, v5) = v20) | ( ~ (v20 = 0) & member(v17, v6) = v20) | (( ~ (v19 = 0) | (v23 = 0 & v22 = 0 & apply(v1, v17, v18) = 0 & member(v17, v4) = 0) | (v21 = 0 & v20 = 0 & apply(v0, v17, v18) = 0 & member(v17, v3) = 0)) & (v19 = 0 | ((( ~ (v23 = 0) & apply(v1, v17, v18) = v23) | ( ~ (v22 = 0) & member(v17, v4) = v22)) & (( ~ (v21 = 0) & apply(v0, v17, v18) = v21) | ( ~ (v20 = 0) & member(v17, v3) = v20))))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v1, v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ (v20 = 0) & member(v18, v5) = v20) | ( ~ (v20 = 0) & member(v17, v6) = v20) | (((v23 = 0 & v19 = 0 & member(v17, v4) = 0) | (v22 = 0 & v21 = 0 & apply(v0, v17, v18) = 0 & member(v17, v3) = 0) | ( ~ (v20 = 0) & apply(v2, v17, v18) = v20)) & ((v20 = 0 & apply(v2, v17, v18) = 0) | (( ~ (v19 = 0) | ( ~ (v23 = 0) & member(v17, v4) = v23)) & (( ~ (v22 = 0) & apply(v0, v17, v18) = v22) | ( ~ (v21 = 0) & member(v17, v3) = v21))))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v0, v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ (v20 = 0) & member(v18, v5) = v20) | ( ~ (v20 = 0) & member(v17, v6) = v20) | (((v23 = 0 & v22 = 0 & apply(v1, v17, v18) = 0 & member(v17, v4) = 0) | (v21 = 0 & v19 = 0 & member(v17, v3) = 0) | ( ~ (v20 = 0) & apply(v2, v17, v18) = v20)) & ((v20 = 0 & apply(v2, v17, v18) = 0) | (( ~ (v19 = 0) | ( ~ (v21 = 0) & member(v17, v3) = v21)) & (( ~ (v23 = 0) & apply(v1, v17, v18) = v23) | ( ~ (v22 = 0) & member(v17, v4) = v22))))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (sum(v18) = v19) | ~ (member(v17, v19) = 0) | ? [v20] : (member(v20, v18) = 0 & member(v17, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (power_set(v18) = v19) | ~ (member(v17, v19) = 0) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v18, v17) = v19) | ? [v20] : ((v20 = 0 & v19 = 0 & subset(v17, v18) = 0) | ( ~ (v20 = 0) & equal_set(v17, v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v17, v18) = v19) | ? [v20] : ((v20 = 0 & v19 = 0 & subset(v18, v17) = 0) | ( ~ (v20 = 0) & equal_set(v17, v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v17, v18) = 0) | ~ (member(v19, v17) = 0) | member(v19, v18) = 0) & ! [v17] : ! [v18] : ( ~ (equal_set(v17, v18) = 0) | (subset(v18, v17) = 0 & subset(v17, v18) = 0)) & ! [v17] : ! [v18] : ( ~ (subset(v18, v17) = 0) | ? [v19] : ((v19 = 0 & equal_set(v17, v18) = 0) | ( ~ (v19 = 0) & subset(v17, v18) = v19))) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : (power_set(v18) = v19 & member(v17, v19) = 0)) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : ((v19 = 0 & equal_set(v17, v18) = 0) | ( ~ (v19 = 0) & subset(v18, v17) = v19))) & ! [v17] : ~ (member(v17, empty_set) = 0) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : compose_predicate(v22, v21, v20, v19, v18, v17) = v23 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : isomorphism(v21, v20, v19, v18, v17) = v22 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : decreasing(v21, v20, v19, v18, v17) = v22 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : increasing(v21, v20, v19, v18, v17) = v22 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : compose_function(v21, v20, v19, v18, v17) = v22 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : inverse_predicate(v20, v19, v18, v17) = v21 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : equal_maps(v20, v19, v18, v17) = v21 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : inverse_image3(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : image3(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : inverse_function(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : one_to_one(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : surjective(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : injective(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : maps(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : ? [v20] : apply(v19, v18, v17) = v20 & ? [v17] : ? [v18] : ? [v19] : inverse_image2(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : image2(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : identity(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : unordered_pair(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : difference(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : union(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : intersection(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : equal_set(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : subset(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : member(v18, v17) = v19 & ? [v17] : ? [v18] : product(v17) = v18 & ? [v17] : ? [v18] : sum(v17) = v18 & ? [v17] : ? [v18] : singleton(v17) = v18 & ? [v17] : ? [v18] : power_set(v17) = v18 & ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v7 = 0 & ~ (v10 = v9) & apply(v1, v8, v10) = 0 & apply(v0, v8, v9) = 0 & member(v10, v5) = 0 & member(v9, v5) = 0 & member(v8, v4) = 0 & member(v8, v3) = 0) | ( ~ (v7 = 0) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (apply(v1, v17, v19) = 0) | ~ (apply(v0, v17, v18) = 0) | ? [v20] : (( ~ (v20 = 0) & member(v19, v5) = v20) | ( ~ (v20 = 0) & member(v18, v5) = v20) | ( ~ (v20 = 0) & member(v17, v4) = v20) | ( ~ (v20 = 0) & member(v17, v3) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (apply(v1, v17, v19) = 0) | ~ (member(v18, v5) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v0, v17, v18) = v20) | ( ~ (v20 = 0) & member(v19, v5) = v20) | ( ~ (v20 = 0) & member(v17, v4) = v20) | ( ~ (v20 = 0) & member(v17, v3) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (apply(v0, v17, v18) = 0) | ~ (member(v19, v5) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v1, v17, v19) = v20) | ( ~ (v20 = 0) & member(v18, v5) = v20) | ( ~ (v20 = 0) & member(v17, v4) = v20) | ( ~ (v20 = 0) & member(v17, v3) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (member(v19, v5) = 0) | ~ (member(v18, v5) = 0) | ~ (member(v17, v4) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v1, v17, v19) = v20) | ( ~ (v20 = 0) & apply(v0, v17, v18) = v20) | ( ~ (v20 = 0) & member(v17, v3) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (member(v19, v5) = 0) | ~ (member(v18, v5) = 0) | ~ (member(v17, v3) = 0) | ? [v20] : (( ~ (v20 = 0) & apply(v1, v17, v19) = v20) | ( ~ (v20 = 0) & apply(v0, v17, v18) = v20) | ( ~ (v20 = 0) & member(v17, v4) = v20))))))
% 21.72/5.60 | 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, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields:
% 21.72/5.60 | (1) maps(all_0_14_14, all_0_10_10, all_0_11_11) = all_0_9_9 & maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0 & maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0 & union(all_0_13_13, all_0_12_12) = all_0_10_10 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [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(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [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] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [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) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [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] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [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] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [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] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [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] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9))) & ! [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) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8))) & ! [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) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8))) & ! [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] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7))) & ! [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] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15))))))) & ! [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 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = 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] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = 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] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6))) & ! [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(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 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6))) & ! [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] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6))) & ! [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 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = 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] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = 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] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7)))) & ! [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] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [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] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4))) & ! [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)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = 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)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = 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] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = 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] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [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] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4))) & ! [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] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 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] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 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] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_14_14, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & apply(all_0_15_15, v0, v1) = 0 & member(v0, all_0_12_12) = 0) | (v4 = 0 & v3 = 0 & apply(all_0_16_16, v0, v1) = 0 & member(v0, all_0_13_13) = 0)) & (v2 = 0 | ((( ~ (v6 = 0) & apply(all_0_15_15, v0, v1) = v6) | ( ~ (v5 = 0) & member(v0, all_0_12_12) = v5)) & (( ~ (v4 = 0) & apply(all_0_16_16, v0, v1) = v4) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_15_15, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (((v6 = 0 & v2 = 0 & member(v0, all_0_12_12) = 0) | (v5 = 0 & v4 = 0 & apply(all_0_16_16, v0, v1) = 0 & member(v0, all_0_13_13) = 0) | ( ~ (v3 = 0) & apply(all_0_14_14, v0, v1) = v3)) & ((v3 = 0 & apply(all_0_14_14, v0, v1) = 0) | (( ~ (v2 = 0) | ( ~ (v6 = 0) & member(v0, all_0_12_12) = v6)) & (( ~ (v5 = 0) & apply(all_0_16_16, v0, v1) = v5) | ( ~ (v4 = 0) & member(v0, all_0_13_13) = v4))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_16_16, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (((v6 = 0 & v5 = 0 & apply(all_0_15_15, v0, v1) = 0 & member(v0, all_0_12_12) = 0) | (v4 = 0 & v2 = 0 & member(v0, all_0_13_13) = 0) | ( ~ (v3 = 0) & apply(all_0_14_14, v0, v1) = v3)) & ((v3 = 0 & apply(all_0_14_14, v0, v1) = 0) | (( ~ (v2 = 0) | ( ~ (v4 = 0) & member(v0, all_0_13_13) = v4)) & (( ~ (v6 = 0) & apply(all_0_15_15, v0, v1) = v6) | ( ~ (v5 = 0) & member(v0, all_0_12_12) = v5))))))) & ! [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(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [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] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1 & ((all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_9_9 = 0 & ~ (all_0_6_6 = all_0_7_7) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_6_6, all_0_11_11) = 0 & member(all_0_7_7, all_0_11_11) = 0 & member(all_0_8_8, all_0_12_12) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_0_9_9 = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (apply(all_0_16_16, v0, v1) = 0) | ? [v3] : (( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (member(v1, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_16_16, v0, v1) = 0) | ~ (member(v2, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_12_12) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_13_13) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3)))))
% 21.72/5.65 |
% 21.72/5.65 | Applying alpha-rule on (1) yields:
% 21.72/5.66 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v3, v6) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 21.72/5.66 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 21.72/5.66 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 21.72/5.66 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 21.72/5.66 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 21.72/5.66 | (7) ! [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))
% 21.72/5.66 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 21.72/5.66 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (inverse_image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v2, v5) = v6))
% 21.72/5.66 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 21.72/5.66 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9)))
% 21.72/5.66 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 21.72/5.66 | (13) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 21.72/5.66 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 21.72/5.66 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 21.72/5.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 21.72/5.66 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 21.72/5.66 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 21.72/5.66 | (19) ! [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)))
% 21.72/5.66 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 21.72/5.66 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 21.72/5.66 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9)))
% 21.72/5.66 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v0, v6, v7) = v8) | ~ (member(v9, v4) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 21.72/5.66 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 21.72/5.66 | (25) ! [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))
% 21.72/5.66 | (26) ! [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)))
% 21.72/5.66 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 21.72/5.67 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 21.72/5.67 | (29) ! [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))
% 21.72/5.67 | (30) ! [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(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 & apply(v4, v7, v9) = 0) | (v16 = 0 & apply(v2, v6, v8) = 0)) & (( ~ (v17 = 0) & apply(v4, v7, v9) = v17) | ( ~ (v16 = 0) & apply(v2, v6, v8) = v16))) | ( ~ (v6 = 0) & one_to_one(v0, v1, v3) = v6) | ( ~ (v6 = 0) & maps(v0, v1, v3) = v6)))
% 21.72/5.67 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 21.72/5.67 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 21.72/5.67 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (injective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & surjective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4)))
% 21.72/5.67 | (34) ! [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))
% 21.72/5.67 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v6, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 21.72/5.67 | (36) ! [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))
% 21.72/5.67 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 21.72/5.67 | (38) ! [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))
% 21.72/5.67 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 21.72/5.67 | (40) ? [v0] : ? [v1] : power_set(v0) = v1
% 21.72/5.67 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5)))
% 21.72/5.67 | (42) maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0
% 21.72/5.67 | (43) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 21.72/5.67 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 21.72/5.67 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (one_to_one(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & surjective(v0, v1, v2) = v4) | ( ~ (v4 = 0) & injective(v0, v1, v2) = v4)))
% 21.72/5.67 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 21.72/5.67 | (47) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 21.72/5.67 | (48) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 21.72/5.67 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 21.72/5.67 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 21.72/5.67 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 21.72/5.67 | (52) maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0
% 21.72/5.67 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 21.72/5.67 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_14_14, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & apply(all_0_15_15, v0, v1) = 0 & member(v0, all_0_12_12) = 0) | (v4 = 0 & v3 = 0 & apply(all_0_16_16, v0, v1) = 0 & member(v0, all_0_13_13) = 0)) & (v2 = 0 | ((( ~ (v6 = 0) & apply(all_0_15_15, v0, v1) = v6) | ( ~ (v5 = 0) & member(v0, all_0_12_12) = v5)) & (( ~ (v4 = 0) & apply(all_0_16_16, v0, v1) = v4) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3)))))))
% 21.72/5.67 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9)))
% 21.72/5.67 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 21.72/5.67 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 21.72/5.67 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 21.72/5.68 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 21.72/5.68 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 21.72/5.68 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 21.72/5.68 | (62) ! [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))
% 21.72/5.68 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 21.72/5.68 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v7, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 21.72/5.68 | (65) ! [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) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v3) = v8)))
% 21.72/5.68 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 21.72/5.68 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 21.72/5.68 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 21.72/5.68 | (69) ! [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))
% 21.72/5.68 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 21.72/5.68 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 21.72/5.68 | (72) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 21.72/5.68 | (73) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 21.72/5.68 | (74) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 21.72/5.68 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 21.72/5.68 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 21.72/5.68 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 21.72/5.68 | (78) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 21.72/5.68 | (79) (all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_9_9 = 0 & ~ (all_0_6_6 = all_0_7_7) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_6_6, all_0_11_11) = 0 & member(all_0_7_7, all_0_11_11) = 0 & member(all_0_8_8, all_0_12_12) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_0_9_9 = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (apply(all_0_16_16, v0, v1) = 0) | ? [v3] : (( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (member(v1, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_16_16, v0, v1) = 0) | ~ (member(v2, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_12_12) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_13_13) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3))))
% 22.07/5.68 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 22.07/5.68 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (apply(v0, v5, v6) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 22.07/5.68 | (82) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 22.07/5.68 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v1, v4, v6) = v7) | ( ~ (v7 = 0) & apply(v0, v4, v5) = v7)))
% 22.07/5.68 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v1) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9)))
% 22.07/5.69 | (85) maps(all_0_14_14, all_0_10_10, all_0_11_11) = all_0_9_9
% 22.07/5.69 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 22.07/5.69 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 22.07/5.69 | (88) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 22.07/5.69 | (89) ! [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))
% 22.07/5.69 | (90) ! [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) | ~ (member(v9, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 22.07/5.69 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = 0) | ~ (apply(v2, v5, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 22.07/5.69 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = v9) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v4, v6, v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 22.07/5.69 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 22.07/5.69 | (94) ! [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)) & ! [v5] : ( ~ (member(v5, v1) = 0) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v4) = v6))))
% 22.07/5.69 | (95) ! [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) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v2) = v8)))
% 22.07/5.69 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 22.07/5.69 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 22.07/5.69 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v4) = v6)))
% 22.07/5.69 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 22.07/5.69 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 22.07/5.69 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 22.07/5.69 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_16_16, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (((v6 = 0 & v5 = 0 & apply(all_0_15_15, v0, v1) = 0 & member(v0, all_0_12_12) = 0) | (v4 = 0 & v2 = 0 & member(v0, all_0_13_13) = 0) | ( ~ (v3 = 0) & apply(all_0_14_14, v0, v1) = v3)) & ((v3 = 0 & apply(all_0_14_14, v0, v1) = 0) | (( ~ (v2 = 0) | ( ~ (v4 = 0) & member(v0, all_0_13_13) = v4)) & (( ~ (v6 = 0) & apply(all_0_15_15, v0, v1) = v6) | ( ~ (v5 = 0) & member(v0, all_0_12_12) = v5)))))))
% 22.07/5.69 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 22.07/5.69 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v6, v1) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v6, v3) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 22.07/5.69 | (105) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 22.07/5.69 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 22.07/5.69 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 22.07/5.69 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.69 | (109) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 22.07/5.69 | (110) ! [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(v1, v5, v9) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v9, v6) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 22.07/5.70 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 22.07/5.70 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 22.07/5.70 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 22.07/5.70 | (114) ! [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] : (( ~ (v10 = 0) & apply(v2, v6, v9) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 22.07/5.70 | (115) ? [v0] : ? [v1] : singleton(v0) = v1
% 22.07/5.70 | (116) ! [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] : (( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 22.07/5.70 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (compose_predicate(v0, v1, v2, v3, v4, v5) = 0) | ~ (apply(v2, v6, v9) = 0) | ~ (apply(v0, v6, v7) = v8) | ? [v10] : (( ~ (v10 = 0) & apply(v1, v9, v7) = v10) | ( ~ (v10 = 0) & member(v9, v4) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 22.07/5.70 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 22.07/5.70 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 22.07/5.70 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.70 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 22.07/5.70 | (122) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 22.07/5.70 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (member(v7, v1) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 22.07/5.70 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 22.07/5.70 | (125) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 22.07/5.70 | (126) ? [v0] : ? [v1] : sum(v0) = v1
% 22.07/5.70 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | (( ~ (v9 = 0) | (v10 = 0 & apply(v2, v5, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & apply(v2, v5, v7) = v10)))))
% 22.07/5.70 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 22.07/5.70 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 22.07/5.70 | (130) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 22.07/5.70 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 22.07/5.70 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 22.07/5.70 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 22.07/5.70 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 22.07/5.70 | (135) ! [v0] : ~ (member(v0, empty_set) = 0)
% 22.07/5.70 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (increasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.70 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 22.07/5.70 | (138) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 22.07/5.70 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 22.07/5.70 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | ? [v6] : ( ~ (v6 = 0) & apply(v0, v5, v2) = v6))
% 22.07/5.70 | (141) ! [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)) & ! [v12] : ( ~ (member(v12, v2) = 0) | ? [v13] : ( ~ (v13 = 0) & apply(v0, v4, v12) = v13)))))
% 22.07/5.70 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v0, v5, v6) = 0) | ~ (member(v8, v3) = 0) | ~ (member(v7, v1) = 0) | ? [v9] : ? [v10] : (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9) | (((v10 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9)) & ((v9 = 0 & apply(v2, v5, v7) = 0) | ( ~ (v10 = 0) & apply(v4, v6, v8) = v10)))))
% 22.07/5.71 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 22.07/5.71 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (inverse_predicate(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (member(v6, v3) = 0 & member(v5, v2) = 0 & ((v8 = 0 & apply(v0, v6, v5) = 0) | (v7 = 0 & apply(v1, v5, v6) = 0)) & (( ~ (v8 = 0) & apply(v0, v6, v5) = v8) | ( ~ (v7 = 0) & apply(v1, v5, v6) = v7))))
% 22.07/5.71 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ (member(v5, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 22.07/5.71 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ? [v6] : (( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v2) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6)))
% 22.07/5.71 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & injective(v0, v1, v2) = 0) | ( ~ (v4 = 0) & one_to_one(v0, v1, v2) = v4)))
% 22.07/5.71 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v6) = 0) | ~ (member(v5, v3) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v0, v4, v5) = v7) | ( ~ (v7 = 0) & member(v6, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7)))
% 22.07/5.71 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v4, v5) = v6) | ( ~ (v6 = 0) & apply(v0, v3, v5) = v6)))
% 22.07/5.71 | (150) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 22.07/5.71 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, v4, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v4, v2) = v7) | ( ~ (v7 = 0) & member(v3, v1) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v3, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v3, v4) = v7)))))
% 22.07/5.71 | (152) ! [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] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.71 | (153) ! [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] : (( ~ (v10 = 0) & apply(v1, v5, v9) = v10) | ( ~ (v10 = 0) & member(v9, v3) = v10) | ( ~ (v10 = 0) & member(v6, v4) = v10) | ( ~ (v10 = 0) & member(v5, v2) = v10)))
% 22.07/5.71 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v8, v6) = v9) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v5, v1) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v2, v5, v7) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10)))
% 22.07/5.71 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 22.07/5.71 | (156) ! [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))
% 22.07/5.71 | (157) ! [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] : (member(v8, v5) = 0 & member(v7, v3) = 0 & ((v13 = 0 & v12 = 0 & v11 = 0 & apply(v2, v7, v10) = 0 & apply(v1, v10, v8) = 0 & member(v10, v4) = 0) | (v9 = 0 & apply(v0, v7, v8) = 0)) & (( ~ (v9 = 0) & apply(v0, v7, v8) = v9) | ( ! [v14] : ( ~ (apply(v2, v7, v14) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v1, v14, v8) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (apply(v1, v14, v8) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & member(v14, v4) = v15))) & ! [v14] : ( ~ (member(v14, v4) = 0) | ? [v15] : (( ~ (v15 = 0) & apply(v2, v7, v14) = v15) | ( ~ (v15 = 0) & apply(v1, v14, v8) = v15)))))))
% 22.07/5.71 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5)))
% 22.07/5.71 | (159) ! [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))
% 22.07/5.71 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 22.07/5.71 | (161) union(all_0_13_13, all_0_12_12) = all_0_10_10
% 22.07/5.71 | (162) ! [v0] : ! [v1] : ! [v2] : ( ~ (injective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & surjective(v0, v1, v2) = v3)))
% 22.07/5.71 | (163) ! [v0] : ! [v1] : ! [v2] : ( ~ (surjective(v0, v1, v2) = 0) | ? [v3] : ((v3 = 0 & one_to_one(v0, v1, v2) = 0) | ( ~ (v3 = 0) & injective(v0, v1, v2) = v3)))
% 22.07/5.71 | (164) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 22.07/5.71 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 22.07/5.71 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 22.07/5.71 | (167) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 22.07/5.71 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(all_0_15_15, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_10_10) = v3) | (((v6 = 0 & v2 = 0 & member(v0, all_0_12_12) = 0) | (v5 = 0 & v4 = 0 & apply(all_0_16_16, v0, v1) = 0 & member(v0, all_0_13_13) = 0) | ( ~ (v3 = 0) & apply(all_0_14_14, v0, v1) = v3)) & ((v3 = 0 & apply(all_0_14_14, v0, v1) = 0) | (( ~ (v2 = 0) | ( ~ (v6 = 0) & member(v0, all_0_12_12) = v6)) & (( ~ (v5 = 0) & apply(all_0_16_16, v0, v1) = v5) | ( ~ (v4 = 0) & member(v0, all_0_13_13) = v4)))))))
% 22.07/5.72 | (169) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 22.07/5.72 | (170) ! [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))
% 22.07/5.72 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v5) = v6) | ( ~ (v6 = 0) & member(v5, v2) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6)))
% 22.07/5.72 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 22.07/5.72 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 22.07/5.72 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 22.07/5.72 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v1, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v0, v5, v4) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v0, v5, v4) = v7)))))
% 22.07/5.72 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (decreasing(v0, v1, v2, v3, v4) = 0) | ~ (apply(v2, v5, v7) = 0) | ~ (apply(v0, v7, v8) = 0) | ~ (member(v6, v3) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v8, v6) = 0) | ( ~ (v9 = 0) & apply(v0, v5, v6) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.72 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (inverse_predicate(v0, v1, v2, v3) = 0) | ~ (apply(v0, v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v5, v3) = v7) | ( ~ (v7 = 0) & member(v4, v2) = v7) | (( ~ (v6 = 0) | (v7 = 0 & apply(v1, v4, v5) = 0)) & (v6 = 0 | ( ~ (v7 = 0) & apply(v1, v4, v5) = v7)))))
% 22.07/5.72 | (178) ! [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))
% 22.07/5.72 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 22.07/5.72 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 22.07/5.72 | (181) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 22.07/5.72 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 22.07/5.72 | (183) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 22.07/5.72 | (184) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 22.07/5.72 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 22.07/5.72 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 22.07/5.72 | (187) ! [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] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v2, v5, v7) = v9) | ( ~ (v9 = 0) & member(v8, v3) = v9) | ( ~ (v9 = 0) & member(v7, v1) = v9) | ( ~ (v9 = 0) & member(v6, v3) = v9) | ( ~ (v9 = 0) & member(v5, v1) = v9)))
% 22.07/5.72 | (188) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 22.07/5.72 | (189) ? [v0] : ? [v1] : product(v0) = v1
% 22.07/5.72 | (190) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v2, v5, v7) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v0, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v0, v5, v6) = v10) | ( ~ (v10 = 0) & member(v8, v3) = v10) | ( ~ (v10 = 0) & member(v7, v1) = v10) | ( ~ (v10 = 0) & member(v6, v3) = v10) | ( ~ (v10 = 0) & member(v5, v1) = v10)))
% 22.07/5.72 |
% 22.07/5.72 | Instantiating formula (141) with all_0_9_9, all_0_11_11, all_0_10_10, all_0_14_14 and discharging atoms maps(all_0_14_14, all_0_10_10, all_0_11_11) = all_0_9_9, yields:
% 22.07/5.72 | (191) all_0_9_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_14_14, v0, v2) = 0 & apply(all_0_14_14, v0, v1) = 0 & member(v2, all_0_11_11) = 0 & member(v1, all_0_11_11) = 0 & member(v0, all_0_10_10) = 0) | (v1 = 0 & member(v0, all_0_10_10) = 0 & ! [v8] : ( ~ (apply(all_0_14_14, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_11_11) = v9)) & ! [v8] : ( ~ (member(v8, all_0_11_11) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_14_14, v0, v8) = v9))))
% 22.07/5.72 |
% 22.07/5.72 +-Applying beta-rule and splitting (79), into two cases.
% 22.07/5.72 |-Branch one:
% 22.07/5.72 | (192) all_0_0_0 = 0 & all_0_1_1 = 0 & all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & all_0_9_9 = 0 & ~ (all_0_6_6 = all_0_7_7) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_6_6, all_0_11_11) = 0 & member(all_0_7_7, all_0_11_11) = 0 & member(all_0_8_8, all_0_12_12) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.72 |
% 22.07/5.72 | Applying alpha-rule on (192) yields:
% 22.07/5.72 | (193) all_0_0_0 = 0
% 22.07/5.72 | (194) apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0
% 22.07/5.72 | (195) all_0_9_9 = 0
% 22.07/5.72 | (196) all_0_2_2 = 0
% 22.07/5.72 | (197) member(all_0_6_6, all_0_11_11) = 0
% 22.07/5.72 | (198) all_0_4_4 = 0
% 22.07/5.72 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.72 | (200) all_0_3_3 = 0
% 22.07/5.72 | (201) member(all_0_7_7, all_0_11_11) = 0
% 22.07/5.72 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.07/5.72 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.72 | (204) all_0_5_5 = 0
% 22.07/5.72 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.72 | (206) all_0_1_1 = 0
% 22.07/5.72 |
% 22.07/5.72 | From (195) and (85) follows:
% 22.07/5.72 | (207) maps(all_0_14_14, all_0_10_10, all_0_11_11) = 0
% 22.07/5.72 |
% 22.07/5.72 | Instantiating formula (168) with 0, all_0_6_6, all_0_8_8 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0, yields:
% 22.07/5.73 | (208) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_0_6_6, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v2 = 0 & v1 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | ( ~ (v3 = 0) & member(all_0_8_8, all_0_12_12) = v3 & (( ~ (v2 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = v2) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1))))))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (102) with 0, all_0_7_7, all_0_8_8 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0, yields:
% 22.07/5.73 | (209) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v1 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1 & (( ~ (v3 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = v3) | ( ~ (v2 = 0) & member(all_0_8_8, all_0_12_12) = v2))))))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (60) with all_0_7_7, all_0_6_6, all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.07/5.73 | (210) all_0_6_6 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (60) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.07/5.73 | (211) all_0_6_6 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_0_6_6, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (98) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, member(all_0_6_6, all_0_11_11) = 0, member(all_0_7_7, all_0_11_11) = 0, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.07/5.73 | (212) all_0_6_6 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (182) with all_0_8_8, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.07/5.73 | (213) ? [v0] : (apply(all_0_15_15, all_0_8_8, v0) = 0 & member(v0, all_0_11_11) = 0)
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (98) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, member(all_0_6_6, all_0_11_11) = 0, member(all_0_7_7, all_0_11_11) = 0, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.73 | (214) all_0_6_6 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating formula (182) with all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.73 | (215) ? [v0] : (apply(all_0_16_16, all_0_8_8, v0) = 0 & member(v0, all_0_11_11) = 0)
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (215) with all_73_0_128 yields:
% 22.07/5.73 | (216) apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0 & member(all_73_0_128, all_0_11_11) = 0
% 22.07/5.73 |
% 22.07/5.73 | Applying alpha-rule on (216) yields:
% 22.07/5.73 | (217) apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0
% 22.07/5.73 | (218) member(all_73_0_128, all_0_11_11) = 0
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (209) with all_75_0_129, all_75_1_130, all_75_2_131, all_75_3_132 yields:
% 22.07/5.73 | (219) ( ~ (all_75_3_132 = 0) & member(all_0_7_7, all_0_11_11) = all_75_3_132) | ( ~ (all_75_3_132 = 0) & member(all_0_8_8, all_0_10_10) = all_75_3_132) | (((all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132)) & ((all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | ( ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130)))))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (208) with all_76_0_133, all_76_1_134, all_76_2_135, all_76_3_136 yields:
% 22.07/5.73 | (220) ( ~ (all_76_3_136 = 0) & member(all_0_6_6, all_0_11_11) = all_76_3_136) | ( ~ (all_76_3_136 = 0) & member(all_0_8_8, all_0_10_10) = all_76_3_136) | (((all_76_0_133 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_76_1_134 = 0 & all_76_2_135 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_76_3_136 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_76_3_136)) & ((all_76_3_136 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | ( ~ (all_76_0_133 = 0) & member(all_0_8_8, all_0_12_12) = all_76_0_133 & (( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135)))))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (213) with all_77_0_137 yields:
% 22.07/5.73 | (221) apply(all_0_15_15, all_0_8_8, all_77_0_137) = 0 & member(all_77_0_137, all_0_11_11) = 0
% 22.07/5.73 |
% 22.07/5.73 | Applying alpha-rule on (221) yields:
% 22.07/5.73 | (222) apply(all_0_15_15, all_0_8_8, all_77_0_137) = 0
% 22.07/5.73 | (223) member(all_77_0_137, all_0_11_11) = 0
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (210), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (224) all_0_6_6 = all_0_7_7
% 22.07/5.73 |
% 22.07/5.73 | Equations (224) can reduce 203 to:
% 22.07/5.73 | (225) $false
% 22.07/5.73 |
% 22.07/5.73 |-The branch is then unsatisfiable
% 22.07/5.73 |-Branch two:
% 22.07/5.73 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.73 | (227) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (227) with all_83_0_138 yields:
% 22.07/5.73 | (228) ( ~ (all_83_0_138 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138) | ( ~ (all_83_0_138 = 0) & member(all_0_7_7, all_0_11_11) = all_83_0_138) | ( ~ (all_83_0_138 = 0) & member(all_0_8_8, all_0_13_13) = all_83_0_138)
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (211), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (224) all_0_6_6 = all_0_7_7
% 22.07/5.73 |
% 22.07/5.73 | Equations (224) can reduce 203 to:
% 22.07/5.73 | (225) $false
% 22.07/5.73 |
% 22.07/5.73 |-The branch is then unsatisfiable
% 22.07/5.73 |-Branch two:
% 22.07/5.73 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.73 | (232) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & member(all_0_6_6, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (232) with all_87_0_139 yields:
% 22.07/5.73 | (233) ( ~ (all_87_0_139 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139) | ( ~ (all_87_0_139 = 0) & member(all_0_6_6, all_0_11_11) = all_87_0_139) | ( ~ (all_87_0_139 = 0) & member(all_0_8_8, all_0_12_12) = all_87_0_139)
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (212), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (224) all_0_6_6 = all_0_7_7
% 22.07/5.73 |
% 22.07/5.73 | Equations (224) can reduce 203 to:
% 22.07/5.73 | (225) $false
% 22.07/5.73 |
% 22.07/5.73 |-The branch is then unsatisfiable
% 22.07/5.73 |-Branch two:
% 22.07/5.73 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.73 | (237) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (237) with all_91_0_140 yields:
% 22.07/5.73 | (238) ( ~ (all_91_0_140 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_91_0_140) | ( ~ (all_91_0_140 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_91_0_140)
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (214), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (224) all_0_6_6 = all_0_7_7
% 22.07/5.73 |
% 22.07/5.73 | Equations (224) can reduce 203 to:
% 22.07/5.73 | (225) $false
% 22.07/5.73 |
% 22.07/5.73 |-The branch is then unsatisfiable
% 22.07/5.73 |-Branch two:
% 22.07/5.73 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.73 | (242) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = v0))
% 22.07/5.73 |
% 22.07/5.73 | Instantiating (242) with all_95_0_141 yields:
% 22.07/5.73 | (243) ( ~ (all_95_0_141 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_95_0_141) | ( ~ (all_95_0_141 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_95_0_141)
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (233), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (244) ( ~ (all_87_0_139 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139) | ( ~ (all_87_0_139 = 0) & member(all_0_6_6, all_0_11_11) = all_87_0_139)
% 22.07/5.73 |
% 22.07/5.73 +-Applying beta-rule and splitting (244), into two cases.
% 22.07/5.73 |-Branch one:
% 22.07/5.73 | (245) ~ (all_87_0_139 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139
% 22.07/5.73 |
% 22.07/5.73 | Applying alpha-rule on (245) yields:
% 22.07/5.73 | (246) ~ (all_87_0_139 = 0)
% 22.07/5.74 | (247) apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139
% 22.07/5.74 |
% 22.07/5.74 +-Applying beta-rule and splitting (238), into two cases.
% 22.07/5.74 |-Branch one:
% 22.07/5.74 | (248) ~ (all_91_0_140 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_91_0_140
% 22.07/5.74 |
% 22.07/5.74 | Applying alpha-rule on (248) yields:
% 22.07/5.74 | (249) ~ (all_91_0_140 = 0)
% 22.07/5.74 | (250) apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_91_0_140
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_6_6, all_91_0_140, 0 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_91_0_140, apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0, yields:
% 22.07/5.74 | (251) all_91_0_140 = 0
% 22.07/5.74 |
% 22.07/5.74 | Equations (251) can reduce 249 to:
% 22.07/5.74 | (225) $false
% 22.07/5.74 |
% 22.07/5.74 |-The branch is then unsatisfiable
% 22.07/5.74 |-Branch two:
% 22.07/5.74 | (253) ~ (all_91_0_140 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_91_0_140
% 22.07/5.74 |
% 22.07/5.74 | Applying alpha-rule on (253) yields:
% 22.07/5.74 | (249) ~ (all_91_0_140 = 0)
% 22.07/5.74 | (255) apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_91_0_140
% 22.07/5.74 |
% 22.07/5.74 +-Applying beta-rule and splitting (228), into two cases.
% 22.07/5.74 |-Branch one:
% 22.07/5.74 | (256) ( ~ (all_83_0_138 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138) | ( ~ (all_83_0_138 = 0) & member(all_0_7_7, all_0_11_11) = all_83_0_138)
% 22.07/5.74 |
% 22.07/5.74 +-Applying beta-rule and splitting (256), into two cases.
% 22.07/5.74 |-Branch one:
% 22.07/5.74 | (257) ~ (all_83_0_138 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138
% 22.07/5.74 |
% 22.07/5.74 | Applying alpha-rule on (257) yields:
% 22.07/5.74 | (258) ~ (all_83_0_138 = 0)
% 22.07/5.74 | (259) apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138
% 22.07/5.74 |
% 22.07/5.74 +-Applying beta-rule and splitting (243), into two cases.
% 22.07/5.74 |-Branch one:
% 22.07/5.74 | (260) ~ (all_95_0_141 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_95_0_141
% 22.07/5.74 |
% 22.07/5.74 | Applying alpha-rule on (260) yields:
% 22.07/5.74 | (261) ~ (all_95_0_141 = 0)
% 22.07/5.74 | (262) apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_95_0_141
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, all_87_0_139, all_91_0_140 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_91_0_140, apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, yields:
% 22.07/5.74 | (263) all_91_0_140 = all_87_0_139
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_0_6_6, all_83_0_138, all_95_0_141 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_95_0_141, apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138, yields:
% 22.07/5.74 | (264) all_95_0_141 = all_83_0_138
% 22.07/5.74 |
% 22.07/5.74 | Equations (264) can reduce 261 to:
% 22.07/5.74 | (258) ~ (all_83_0_138 = 0)
% 22.07/5.74 |
% 22.07/5.74 | Equations (263) can reduce 249 to:
% 22.07/5.74 | (246) ~ (all_87_0_139 = 0)
% 22.07/5.74 |
% 22.07/5.74 | From (263) and (255) follows:
% 22.07/5.74 | (247) apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139
% 22.07/5.74 |
% 22.07/5.74 | From (264) and (262) follows:
% 22.07/5.74 | (259) apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (60) with all_77_0_137, all_0_6_6, all_0_8_8, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, apply(all_0_15_15, all_0_8_8, all_77_0_137) = 0, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.07/5.74 | (269) all_77_0_137 = all_0_6_6 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_77_0_137, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v0))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (168) with 0, all_77_0_137, all_0_8_8 and discharging atoms apply(all_0_15_15, all_0_8_8, all_77_0_137) = 0, yields:
% 22.07/5.74 | (270) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_77_0_137, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v2 = 0 & v1 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0) | ( ~ (v3 = 0) & member(all_0_8_8, all_0_12_12) = v3 & (( ~ (v2 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = v2) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1))))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (168) with all_87_0_139, all_0_7_7, all_0_8_8 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, yields:
% 22.07/5.74 | (271) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v2 = 0 & v1 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | (( ~ (all_87_0_139 = 0) | ( ~ (v3 = 0) & member(all_0_8_8, all_0_12_12) = v3)) & (( ~ (v2 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = v2) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1))))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (102) with 0, all_73_0_128, all_0_8_8 and discharging atoms apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0, yields:
% 22.07/5.74 | (272) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_73_0_128, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v1 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1 & (( ~ (v3 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = v3) | ( ~ (v2 = 0) & member(all_0_8_8, all_0_12_12) = v2))))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (102) with all_83_0_138, all_0_6_6, all_0_8_8 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138, yields:
% 22.07/5.74 | (273) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_0_6_6, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0) | (((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (v1 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | (( ~ (all_83_0_138 = 0) | ( ~ (v1 = 0) & member(all_0_8_8, all_0_13_13) = v1)) & (( ~ (v3 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = v3) | ( ~ (v2 = 0) & member(all_0_8_8, all_0_12_12) = v2))))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (60) with all_0_7_7, all_77_0_137, all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0, member(all_77_0_137, all_0_11_11) = 0, yields:
% 22.07/5.74 | (274) all_77_0_137 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (60) with all_73_0_128, all_77_0_137, all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0, member(all_77_0_137, all_0_11_11) = 0, yields:
% 22.07/5.74 | (275) all_77_0_137 = all_73_0_128 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = v0) | ( ~ (v0 = 0) & member(all_73_0_128, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating formula (60) with all_0_7_7, all_73_0_128, all_0_8_8, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0, member(all_73_0_128, all_0_11_11) = 0, yields:
% 22.07/5.74 | (276) all_73_0_128 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_73_0_128) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating (273) with all_121_0_142, all_121_1_143, all_121_2_144, all_121_3_145 yields:
% 22.07/5.74 | (277) ( ~ (all_121_3_145 = 0) & member(all_0_6_6, all_0_11_11) = all_121_3_145) | ( ~ (all_121_3_145 = 0) & member(all_0_8_8, all_0_10_10) = all_121_3_145) | (((all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_121_3_145 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145)) & ((all_121_3_145 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | (( ~ (all_83_0_138 = 0) | ( ~ (all_121_2_144 = 0) & member(all_0_8_8, all_0_13_13) = all_121_2_144)) & (( ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142) | ( ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143)))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating (272) with all_122_0_146, all_122_1_147, all_122_2_148, all_122_3_149 yields:
% 22.07/5.74 | (278) ( ~ (all_122_3_149 = 0) & member(all_73_0_128, all_0_11_11) = all_122_3_149) | ( ~ (all_122_3_149 = 0) & member(all_0_8_8, all_0_10_10) = all_122_3_149) | (((all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149)) & ((all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0) | ( ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating (271) with all_123_0_150, all_123_1_151, all_123_2_152, all_123_3_153 yields:
% 22.07/5.74 | (279) ( ~ (all_123_3_153 = 0) & member(all_0_7_7, all_0_11_11) = all_123_3_153) | ( ~ (all_123_3_153 = 0) & member(all_0_8_8, all_0_10_10) = all_123_3_153) | (((all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153)) & ((all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | (( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152)))))
% 22.07/5.74 |
% 22.07/5.74 | Instantiating (270) with all_124_0_154, all_124_1_155, all_124_2_156, all_124_3_157 yields:
% 22.07/5.74 | (280) ( ~ (all_124_3_157 = 0) & member(all_77_0_137, all_0_11_11) = all_124_3_157) | ( ~ (all_124_3_157 = 0) & member(all_0_8_8, all_0_10_10) = all_124_3_157) | (((all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_124_3_157 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157)) & ((all_124_3_157 = 0 & apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0) | ( ~ (all_124_0_154 = 0) & member(all_0_8_8, all_0_12_12) = all_124_0_154 & (( ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155) | ( ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156)))))
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (219), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (281) ( ~ (all_75_3_132 = 0) & member(all_0_7_7, all_0_11_11) = all_75_3_132) | ( ~ (all_75_3_132 = 0) & member(all_0_8_8, all_0_10_10) = all_75_3_132)
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (281), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (282) ~ (all_75_3_132 = 0) & member(all_0_7_7, all_0_11_11) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (282) yields:
% 22.07/5.75 | (283) ~ (all_75_3_132 = 0)
% 22.07/5.75 | (284) member(all_0_7_7, all_0_11_11) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_75_3_132, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_75_3_132, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.07/5.75 | (285) all_75_3_132 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (285) can reduce 283 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (287) ~ (all_75_3_132 = 0) & member(all_0_8_8, all_0_10_10) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (287) yields:
% 22.07/5.75 | (283) ~ (all_75_3_132 = 0)
% 22.07/5.75 | (289) member(all_0_8_8, all_0_10_10) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (159) with all_75_3_132, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_75_3_132, yields:
% 22.07/5.75 | (290) all_75_3_132 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (290), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (285) all_75_3_132 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (285) can reduce 283 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (283) ~ (all_75_3_132 = 0)
% 22.07/5.75 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.75 |
% 22.07/5.75 | Instantiating (294) with all_146_0_167, all_146_1_168 yields:
% 22.07/5.75 | (295) ~ (all_146_0_167 = 0) & ~ (all_146_1_168 = 0) & member(all_0_8_8, all_0_12_12) = all_146_0_167 & member(all_0_8_8, all_0_13_13) = all_146_1_168
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (295) yields:
% 22.07/5.75 | (296) ~ (all_146_0_167 = 0)
% 22.07/5.75 | (297) ~ (all_146_1_168 = 0)
% 22.07/5.75 | (298) member(all_0_8_8, all_0_12_12) = all_146_0_167
% 22.07/5.75 | (299) member(all_0_8_8, all_0_13_13) = all_146_1_168
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_146_1_168, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_146_1_168, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.75 | (300) all_146_1_168 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (300) can reduce 297 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (302) ((all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132)) & ((all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | ( ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130))))
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (302) yields:
% 22.07/5.75 | (303) (all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132)
% 22.07/5.75 | (304) (all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | ( ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130)))
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (220), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (305) ( ~ (all_76_3_136 = 0) & member(all_0_6_6, all_0_11_11) = all_76_3_136) | ( ~ (all_76_3_136 = 0) & member(all_0_8_8, all_0_10_10) = all_76_3_136)
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (305), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (306) ~ (all_76_3_136 = 0) & member(all_0_6_6, all_0_11_11) = all_76_3_136
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (306) yields:
% 22.07/5.75 | (307) ~ (all_76_3_136 = 0)
% 22.07/5.75 | (308) member(all_0_6_6, all_0_11_11) = all_76_3_136
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (132) with all_0_6_6, all_0_11_11, all_76_3_136, 0 and discharging atoms member(all_0_6_6, all_0_11_11) = all_76_3_136, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.07/5.75 | (309) all_76_3_136 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (309) can reduce 307 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (311) ~ (all_76_3_136 = 0) & member(all_0_8_8, all_0_10_10) = all_76_3_136
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (311) yields:
% 22.07/5.75 | (307) ~ (all_76_3_136 = 0)
% 22.07/5.75 | (313) member(all_0_8_8, all_0_10_10) = all_76_3_136
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (304), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (314) all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (314) yields:
% 22.07/5.75 | (285) all_75_3_132 = 0
% 22.07/5.75 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (303), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (317) (all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (317), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (318) all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (318) yields:
% 22.07/5.75 | (319) all_75_0_129 = 0
% 22.07/5.75 | (320) all_75_1_130 = 0
% 22.07/5.75 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.07/5.75 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.07/5.75 | (323) all_87_0_139 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (323) can reduce 246 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (325) all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (325) yields:
% 22.07/5.75 | (326) all_75_2_131 = 0
% 22.07/5.75 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (159) with all_76_3_136, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_76_3_136, yields:
% 22.07/5.75 | (328) all_76_3_136 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.75 |
% 22.07/5.75 +-Applying beta-rule and splitting (328), into two cases.
% 22.07/5.75 |-Branch one:
% 22.07/5.75 | (309) all_76_3_136 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (309) can reduce 307 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (307) ~ (all_76_3_136 = 0)
% 22.07/5.75 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.75 |
% 22.07/5.75 | Instantiating (294) with all_156_0_182, all_156_1_183 yields:
% 22.07/5.75 | (333) ~ (all_156_0_182 = 0) & ~ (all_156_1_183 = 0) & member(all_0_8_8, all_0_12_12) = all_156_0_182 & member(all_0_8_8, all_0_13_13) = all_156_1_183
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (333) yields:
% 22.07/5.75 | (334) ~ (all_156_0_182 = 0)
% 22.07/5.75 | (335) ~ (all_156_1_183 = 0)
% 22.07/5.75 | (336) member(all_0_8_8, all_0_12_12) = all_156_0_182
% 22.07/5.75 | (337) member(all_0_8_8, all_0_13_13) = all_156_1_183
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_156_1_183, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_156_1_183, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.75 | (338) all_156_1_183 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (338) can reduce 335 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (340) ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (340) yields:
% 22.07/5.75 | (283) ~ (all_75_3_132 = 0)
% 22.07/5.75 | (342) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.07/5.75 |
% 22.07/5.75 | Equations (285) can reduce 283 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (344) ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130))
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (344) yields:
% 22.07/5.75 | (345) ~ (all_75_2_131 = 0)
% 22.07/5.75 | (346) member(all_0_8_8, all_0_13_13) = all_75_2_131
% 22.07/5.75 | (347) ( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130)
% 22.07/5.75 |
% 22.07/5.75 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_75_2_131, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_75_2_131, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.75 | (326) all_75_2_131 = 0
% 22.07/5.75 |
% 22.07/5.75 | Equations (326) can reduce 345 to:
% 22.07/5.75 | (225) $false
% 22.07/5.75 |
% 22.07/5.75 |-The branch is then unsatisfiable
% 22.07/5.75 |-Branch two:
% 22.07/5.75 | (350) ((all_76_0_133 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_76_1_134 = 0 & all_76_2_135 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_76_3_136 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_76_3_136)) & ((all_76_3_136 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | ( ~ (all_76_0_133 = 0) & member(all_0_8_8, all_0_12_12) = all_76_0_133 & (( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135))))
% 22.07/5.75 |
% 22.07/5.75 | Applying alpha-rule on (350) yields:
% 22.07/5.75 | (351) (all_76_0_133 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_76_1_134 = 0 & all_76_2_135 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_76_3_136 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_76_3_136)
% 22.07/5.75 | (352) (all_76_3_136 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | ( ~ (all_76_0_133 = 0) & member(all_0_8_8, all_0_12_12) = all_76_0_133 & (( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135)))
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (275), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (353) all_77_0_137 = all_73_0_128
% 22.07/5.76 |
% 22.07/5.76 | From (353) and (222) follows:
% 22.07/5.76 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (274), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (355) all_77_0_137 = all_0_7_7
% 22.07/5.76 |
% 22.07/5.76 | Combining equations (355,353) yields a new equation:
% 22.07/5.76 | (356) all_73_0_128 = all_0_7_7
% 22.07/5.76 |
% 22.07/5.76 | From (356) and (354) follows:
% 22.07/5.76 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.07/5.76 | (323) all_87_0_139 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (323) can reduce 246 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (360) ~ (all_77_0_137 = all_0_7_7)
% 22.07/5.76 | (361) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.76 |
% 22.07/5.76 | Instantiating (361) with all_133_0_189 yields:
% 22.07/5.76 | (362) ( ~ (all_133_0_189 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_133_0_189) | ( ~ (all_133_0_189 = 0) & member(all_0_7_7, all_0_11_11) = all_133_0_189) | ( ~ (all_133_0_189 = 0) & member(all_0_8_8, all_0_13_13) = all_133_0_189)
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (304), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (314) all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (314) yields:
% 22.07/5.76 | (285) all_75_3_132 = 0
% 22.07/5.76 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (303), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (317) (all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (317), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (318) all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (318) yields:
% 22.07/5.76 | (319) all_75_0_129 = 0
% 22.07/5.76 | (320) all_75_1_130 = 0
% 22.07/5.76 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.07/5.76 | (323) all_87_0_139 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (323) can reduce 246 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (325) all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (325) yields:
% 22.07/5.76 | (326) all_75_2_131 = 0
% 22.07/5.76 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (362), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (377) ( ~ (all_133_0_189 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_133_0_189) | ( ~ (all_133_0_189 = 0) & member(all_0_7_7, all_0_11_11) = all_133_0_189)
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (377), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (378) ~ (all_133_0_189 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (378) yields:
% 22.07/5.76 | (379) ~ (all_133_0_189 = 0)
% 22.07/5.76 | (380) apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | From (353) and (380) follows:
% 22.07/5.76 | (381) apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_73_0_128, all_133_0_189, 0 and discharging atoms apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_133_0_189, apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0, yields:
% 22.07/5.76 | (382) all_133_0_189 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (382) can reduce 379 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (384) ~ (all_133_0_189 = 0) & member(all_0_7_7, all_0_11_11) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (384) yields:
% 22.07/5.76 | (379) ~ (all_133_0_189 = 0)
% 22.07/5.76 | (386) member(all_0_7_7, all_0_11_11) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_133_0_189, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_133_0_189, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.07/5.76 | (382) all_133_0_189 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (382) can reduce 379 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (389) ~ (all_133_0_189 = 0) & member(all_0_8_8, all_0_13_13) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (389) yields:
% 22.07/5.76 | (379) ~ (all_133_0_189 = 0)
% 22.07/5.76 | (391) member(all_0_8_8, all_0_13_13) = all_133_0_189
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_133_0_189, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_133_0_189, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.76 | (382) all_133_0_189 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (382) can reduce 379 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (340) ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (340) yields:
% 22.07/5.76 | (283) ~ (all_75_3_132 = 0)
% 22.07/5.76 | (342) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.07/5.76 |
% 22.07/5.76 | Equations (285) can reduce 283 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (344) ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130))
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (344) yields:
% 22.07/5.76 | (345) ~ (all_75_2_131 = 0)
% 22.07/5.76 | (346) member(all_0_8_8, all_0_13_13) = all_75_2_131
% 22.07/5.76 | (347) ( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130)
% 22.07/5.76 |
% 22.07/5.76 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_75_2_131, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_75_2_131, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.76 | (326) all_75_2_131 = 0
% 22.07/5.76 |
% 22.07/5.76 | Equations (326) can reduce 345 to:
% 22.07/5.76 | (225) $false
% 22.07/5.76 |
% 22.07/5.76 |-The branch is then unsatisfiable
% 22.07/5.76 |-Branch two:
% 22.07/5.76 | (404) ~ (all_77_0_137 = all_73_0_128)
% 22.07/5.76 | (405) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = v0) | ( ~ (v0 = 0) & member(all_73_0_128, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.07/5.76 |
% 22.07/5.76 | Instantiating (405) with all_129_0_206 yields:
% 22.07/5.76 | (406) ( ~ (all_129_0_206 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_129_0_206) | ( ~ (all_129_0_206 = 0) & member(all_73_0_128, all_0_11_11) = all_129_0_206) | ( ~ (all_129_0_206 = 0) & member(all_0_8_8, all_0_13_13) = all_129_0_206)
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (406), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (407) ( ~ (all_129_0_206 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_129_0_206) | ( ~ (all_129_0_206 = 0) & member(all_73_0_128, all_0_11_11) = all_129_0_206)
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (407), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (408) ~ (all_129_0_206 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_129_0_206
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (408) yields:
% 22.07/5.76 | (409) ~ (all_129_0_206 = 0)
% 22.07/5.76 | (410) apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_129_0_206
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (269), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (411) all_77_0_137 = all_0_6_6
% 22.07/5.76 |
% 22.07/5.76 | Equations (411) can reduce 404 to:
% 22.07/5.76 | (412) ~ (all_73_0_128 = all_0_6_6)
% 22.07/5.76 |
% 22.07/5.76 | Simplifying 412 yields:
% 22.07/5.76 | (413) ~ (all_73_0_128 = all_0_6_6)
% 22.07/5.76 |
% 22.07/5.76 | From (411) and (410) follows:
% 22.07/5.76 | (414) apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_129_0_206
% 22.07/5.76 |
% 22.07/5.76 | From (411) and (223) follows:
% 22.07/5.76 | (197) member(all_0_6_6, all_0_11_11) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (304), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (314) all_75_3_132 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (314) yields:
% 22.07/5.76 | (285) all_75_3_132 = 0
% 22.07/5.76 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (352), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (419) all_76_3_136 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.07/5.76 |
% 22.07/5.76 | Applying alpha-rule on (419) yields:
% 22.07/5.76 | (309) all_76_3_136 = 0
% 22.07/5.76 | (421) apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.07/5.76 |
% 22.07/5.76 +-Applying beta-rule and splitting (276), into two cases.
% 22.07/5.76 |-Branch one:
% 22.07/5.76 | (356) all_73_0_128 = all_0_7_7
% 22.07/5.76 |
% 22.07/5.76 | Equations (356) can reduce 413 to:
% 22.07/5.76 | (423) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.76 |
% 22.07/5.76 | Simplifying 423 yields:
% 22.07/5.76 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.07/5.76 |
% 22.07/5.76 | From (356) and (218) follows:
% 22.07/5.76 | (201) member(all_0_7_7, all_0_11_11) = 0
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (303), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (317) (all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (317), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (318) all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (318) yields:
% 22.07/5.77 | (319) all_75_0_129 = 0
% 22.07/5.77 | (320) all_75_1_130 = 0
% 22.07/5.77 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.07/5.77 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.07/5.77 | (323) all_87_0_139 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (323) can reduce 246 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (325) all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (325) yields:
% 22.07/5.77 | (326) all_75_2_131 = 0
% 22.07/5.77 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_0_6_6, all_129_0_206, all_83_0_138 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_129_0_206, apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138, yields:
% 22.07/5.77 | (437) all_129_0_206 = all_83_0_138
% 22.07/5.77 |
% 22.07/5.77 | Equations (437) can reduce 409 to:
% 22.07/5.77 | (258) ~ (all_83_0_138 = 0)
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (60) with all_0_7_7, all_0_6_6, all_0_8_8, all_0_11_11, all_0_10_10, all_0_14_14 and discharging atoms maps(all_0_14_14, all_0_10_10, all_0_11_11) = 0, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.07/5.77 | (439) all_0_6_6 = all_0_7_7 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0))
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (277), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (440) ( ~ (all_121_3_145 = 0) & member(all_0_6_6, all_0_11_11) = all_121_3_145) | ( ~ (all_121_3_145 = 0) & member(all_0_8_8, all_0_10_10) = all_121_3_145)
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (440), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (441) ~ (all_121_3_145 = 0) & member(all_0_6_6, all_0_11_11) = all_121_3_145
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (441) yields:
% 22.07/5.77 | (442) ~ (all_121_3_145 = 0)
% 22.07/5.77 | (443) member(all_0_6_6, all_0_11_11) = all_121_3_145
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (132) with all_0_6_6, all_0_11_11, all_121_3_145, 0 and discharging atoms member(all_0_6_6, all_0_11_11) = all_121_3_145, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.07/5.77 | (444) all_121_3_145 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (444) can reduce 442 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (446) ~ (all_121_3_145 = 0) & member(all_0_8_8, all_0_10_10) = all_121_3_145
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (446) yields:
% 22.07/5.77 | (442) ~ (all_121_3_145 = 0)
% 22.07/5.77 | (448) member(all_0_8_8, all_0_10_10) = all_121_3_145
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (159) with all_121_3_145, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_121_3_145, yields:
% 22.07/5.77 | (449) all_121_3_145 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (449), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (444) all_121_3_145 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (444) can reduce 442 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (442) ~ (all_121_3_145 = 0)
% 22.07/5.77 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.77 |
% 22.07/5.77 | Instantiating (294) with all_182_0_220, all_182_1_221 yields:
% 22.07/5.77 | (454) ~ (all_182_0_220 = 0) & ~ (all_182_1_221 = 0) & member(all_0_8_8, all_0_12_12) = all_182_0_220 & member(all_0_8_8, all_0_13_13) = all_182_1_221
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (454) yields:
% 22.07/5.77 | (455) ~ (all_182_0_220 = 0)
% 22.07/5.77 | (456) ~ (all_182_1_221 = 0)
% 22.07/5.77 | (457) member(all_0_8_8, all_0_12_12) = all_182_0_220
% 22.07/5.77 | (458) member(all_0_8_8, all_0_13_13) = all_182_1_221
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_182_1_221, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_182_1_221, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.77 | (459) all_182_1_221 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (459) can reduce 456 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (461) ((all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_121_3_145 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145)) & ((all_121_3_145 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | (( ~ (all_83_0_138 = 0) | ( ~ (all_121_2_144 = 0) & member(all_0_8_8, all_0_13_13) = all_121_2_144)) & (( ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142) | ( ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143))))
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (461) yields:
% 22.07/5.77 | (462) (all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_121_3_145 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145)
% 22.07/5.77 | (463) (all_121_3_145 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0) | (( ~ (all_83_0_138 = 0) | ( ~ (all_121_2_144 = 0) & member(all_0_8_8, all_0_13_13) = all_121_2_144)) & (( ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142) | ( ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143)))
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (278), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (464) ( ~ (all_122_3_149 = 0) & member(all_73_0_128, all_0_11_11) = all_122_3_149) | ( ~ (all_122_3_149 = 0) & member(all_0_8_8, all_0_10_10) = all_122_3_149)
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (464), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (465) ~ (all_122_3_149 = 0) & member(all_73_0_128, all_0_11_11) = all_122_3_149
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (465) yields:
% 22.07/5.77 | (466) ~ (all_122_3_149 = 0)
% 22.07/5.77 | (467) member(all_73_0_128, all_0_11_11) = all_122_3_149
% 22.07/5.77 |
% 22.07/5.77 | From (356) and (467) follows:
% 22.07/5.77 | (468) member(all_0_7_7, all_0_11_11) = all_122_3_149
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_122_3_149, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_122_3_149, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.07/5.77 | (469) all_122_3_149 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (469) can reduce 466 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (471) ~ (all_122_3_149 = 0) & member(all_0_8_8, all_0_10_10) = all_122_3_149
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (471) yields:
% 22.07/5.77 | (466) ~ (all_122_3_149 = 0)
% 22.07/5.77 | (473) member(all_0_8_8, all_0_10_10) = all_122_3_149
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (159) with all_122_3_149, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_122_3_149, yields:
% 22.07/5.77 | (474) all_122_3_149 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.77 |
% 22.07/5.77 +-Applying beta-rule and splitting (474), into two cases.
% 22.07/5.77 |-Branch one:
% 22.07/5.77 | (469) all_122_3_149 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (469) can reduce 466 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (466) ~ (all_122_3_149 = 0)
% 22.07/5.77 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.07/5.77 |
% 22.07/5.77 | Instantiating (294) with all_191_0_227, all_191_1_228 yields:
% 22.07/5.77 | (479) ~ (all_191_0_227 = 0) & ~ (all_191_1_228 = 0) & member(all_0_8_8, all_0_12_12) = all_191_0_227 & member(all_0_8_8, all_0_13_13) = all_191_1_228
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (479) yields:
% 22.07/5.77 | (480) ~ (all_191_0_227 = 0)
% 22.07/5.77 | (481) ~ (all_191_1_228 = 0)
% 22.07/5.77 | (482) member(all_0_8_8, all_0_12_12) = all_191_0_227
% 22.07/5.77 | (483) member(all_0_8_8, all_0_13_13) = all_191_1_228
% 22.07/5.77 |
% 22.07/5.77 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_191_1_228, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_191_1_228, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.07/5.77 | (484) all_191_1_228 = 0
% 22.07/5.77 |
% 22.07/5.77 | Equations (484) can reduce 481 to:
% 22.07/5.77 | (225) $false
% 22.07/5.77 |
% 22.07/5.77 |-The branch is then unsatisfiable
% 22.07/5.77 |-Branch two:
% 22.07/5.77 | (486) ((all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149)) & ((all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0) | ( ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))))
% 22.07/5.77 |
% 22.07/5.77 | Applying alpha-rule on (486) yields:
% 22.07/5.77 | (487) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149)
% 22.07/5.77 | (488) (all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0) | ( ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)))
% 22.07/5.78 |
% 22.07/5.78 +-Applying beta-rule and splitting (279), into two cases.
% 22.07/5.78 |-Branch one:
% 22.07/5.78 | (489) ( ~ (all_123_3_153 = 0) & member(all_0_7_7, all_0_11_11) = all_123_3_153) | ( ~ (all_123_3_153 = 0) & member(all_0_8_8, all_0_10_10) = all_123_3_153)
% 22.07/5.78 |
% 22.07/5.78 +-Applying beta-rule and splitting (489), into two cases.
% 22.07/5.78 |-Branch one:
% 22.07/5.78 | (490) ~ (all_123_3_153 = 0) & member(all_0_7_7, all_0_11_11) = all_123_3_153
% 22.07/5.78 |
% 22.07/5.78 | Applying alpha-rule on (490) yields:
% 22.07/5.78 | (491) ~ (all_123_3_153 = 0)
% 22.07/5.78 | (492) member(all_0_7_7, all_0_11_11) = all_123_3_153
% 22.07/5.78 |
% 22.07/5.78 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_123_3_153, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_123_3_153, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.48/5.78 | (493) all_123_3_153 = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (493) can reduce 491 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (495) ~ (all_123_3_153 = 0) & member(all_0_8_8, all_0_10_10) = all_123_3_153
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (495) yields:
% 22.48/5.78 | (491) ~ (all_123_3_153 = 0)
% 22.48/5.78 | (497) member(all_0_8_8, all_0_10_10) = all_123_3_153
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (488), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (498) all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (498) yields:
% 22.48/5.78 | (469) all_122_3_149 = 0
% 22.48/5.78 | (500) apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (487), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (501), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (502) yields:
% 22.48/5.78 | (503) all_122_0_146 = 0
% 22.48/5.78 | (504) all_122_1_147 = 0
% 22.48/5.78 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.48/5.78 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.78 |
% 22.48/5.78 | From (356) and (354) follows:
% 22.48/5.78 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.48/5.78 |
% 22.48/5.78 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.48/5.78 | (323) all_87_0_139 = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (323) can reduce 246 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (510) yields:
% 22.48/5.78 | (511) all_122_2_148 = 0
% 22.48/5.78 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.78 |
% 22.48/5.78 | Instantiating formula (159) with all_123_3_153, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_123_3_153, yields:
% 22.48/5.78 | (513) all_123_3_153 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (513), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (493) all_123_3_153 = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (493) can reduce 491 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (491) ~ (all_123_3_153 = 0)
% 22.48/5.78 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.48/5.78 |
% 22.48/5.78 | Instantiating (294) with all_200_0_234, all_200_1_235 yields:
% 22.48/5.78 | (518) ~ (all_200_0_234 = 0) & ~ (all_200_1_235 = 0) & member(all_0_8_8, all_0_12_12) = all_200_0_234 & member(all_0_8_8, all_0_13_13) = all_200_1_235
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (518) yields:
% 22.48/5.78 | (519) ~ (all_200_0_234 = 0)
% 22.48/5.78 | (520) ~ (all_200_1_235 = 0)
% 22.48/5.78 | (521) member(all_0_8_8, all_0_12_12) = all_200_0_234
% 22.48/5.78 | (522) member(all_0_8_8, all_0_13_13) = all_200_1_235
% 22.48/5.78 |
% 22.48/5.78 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_200_1_235, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_200_1_235, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.48/5.78 | (523) all_200_1_235 = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (523) can reduce 520 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (525) yields:
% 22.48/5.78 | (466) ~ (all_122_3_149 = 0)
% 22.48/5.78 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.48/5.78 |
% 22.48/5.78 | Equations (469) can reduce 466 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (529) ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (529) yields:
% 22.48/5.78 | (530) ~ (all_122_2_148 = 0)
% 22.48/5.78 | (531) member(all_0_8_8, all_0_13_13) = all_122_2_148
% 22.48/5.78 | (532) ( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (487), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (501), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (502) yields:
% 22.48/5.78 | (503) all_122_0_146 = 0
% 22.48/5.78 | (504) all_122_1_147 = 0
% 22.48/5.78 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.48/5.78 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (532), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.78 | (539) ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (539) yields:
% 22.48/5.78 | (540) ~ (all_122_0_146 = 0)
% 22.48/5.78 | (541) apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.48/5.78 |
% 22.48/5.78 | Equations (503) can reduce 540 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (543) ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (543) yields:
% 22.48/5.78 | (544) ~ (all_122_1_147 = 0)
% 22.48/5.78 | (545) member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.48/5.78 |
% 22.48/5.78 | Equations (504) can reduce 544 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (510) yields:
% 22.48/5.78 | (511) all_122_2_148 = 0
% 22.48/5.78 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (511) can reduce 530 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (525) yields:
% 22.48/5.78 | (466) ~ (all_122_3_149 = 0)
% 22.48/5.78 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.48/5.78 |
% 22.48/5.78 | From (356) and (527) follows:
% 22.48/5.78 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.48/5.78 |
% 22.48/5.78 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.48/5.78 | (469) all_122_3_149 = 0
% 22.48/5.78 |
% 22.48/5.78 | Equations (469) can reduce 466 to:
% 22.48/5.78 | (225) $false
% 22.48/5.78 |
% 22.48/5.78 |-The branch is then unsatisfiable
% 22.48/5.78 |-Branch two:
% 22.48/5.78 | (557) ((all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153)) & ((all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | (( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152))))
% 22.48/5.78 |
% 22.48/5.78 | Applying alpha-rule on (557) yields:
% 22.48/5.78 | (558) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153)
% 22.48/5.78 | (559) (all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0) | (( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152)))
% 22.48/5.78 |
% 22.48/5.78 +-Applying beta-rule and splitting (280), into two cases.
% 22.48/5.78 |-Branch one:
% 22.48/5.79 | (560) ( ~ (all_124_3_157 = 0) & member(all_77_0_137, all_0_11_11) = all_124_3_157) | ( ~ (all_124_3_157 = 0) & member(all_0_8_8, all_0_10_10) = all_124_3_157)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (560), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (561) ~ (all_124_3_157 = 0) & member(all_77_0_137, all_0_11_11) = all_124_3_157
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (561) yields:
% 22.48/5.79 | (562) ~ (all_124_3_157 = 0)
% 22.48/5.79 | (563) member(all_77_0_137, all_0_11_11) = all_124_3_157
% 22.48/5.79 |
% 22.48/5.79 | From (411) and (563) follows:
% 22.48/5.79 | (564) member(all_0_6_6, all_0_11_11) = all_124_3_157
% 22.48/5.79 |
% 22.48/5.79 | Instantiating formula (132) with all_0_6_6, all_0_11_11, all_124_3_157, 0 and discharging atoms member(all_0_6_6, all_0_11_11) = all_124_3_157, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.48/5.79 | (565) all_124_3_157 = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (565) can reduce 562 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (567) ~ (all_124_3_157 = 0) & member(all_0_8_8, all_0_10_10) = all_124_3_157
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (567) yields:
% 22.48/5.79 | (562) ~ (all_124_3_157 = 0)
% 22.48/5.79 | (569) member(all_0_8_8, all_0_10_10) = all_124_3_157
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (488), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (498) all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (498) yields:
% 22.48/5.79 | (469) all_122_3_149 = 0
% 22.48/5.79 | (500) apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.48/5.79 |
% 22.48/5.79 | From (356) and (500) follows:
% 22.48/5.79 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (559), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (574) all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (574) yields:
% 22.48/5.79 | (493) all_123_3_153 = 0
% 22.48/5.79 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (558), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (577), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (578) yields:
% 22.48/5.79 | (579) all_123_0_150 = 0
% 22.48/5.79 | (323) all_87_0_139 = 0
% 22.48/5.79 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (323) can reduce 246 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (583) yields:
% 22.48/5.79 | (584) all_123_1_151 = 0
% 22.48/5.79 | (585) all_123_2_152 = 0
% 22.48/5.79 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.48/5.79 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.79 |
% 22.48/5.79 | Instantiating formula (159) with all_124_3_157, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_124_3_157, yields:
% 22.48/5.79 | (588) all_124_3_157 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (588), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (565) all_124_3_157 = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (565) can reduce 562 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (562) ~ (all_124_3_157 = 0)
% 22.48/5.79 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.48/5.79 |
% 22.48/5.79 | Instantiating (294) with all_209_0_245, all_209_1_246 yields:
% 22.48/5.79 | (593) ~ (all_209_0_245 = 0) & ~ (all_209_1_246 = 0) & member(all_0_8_8, all_0_12_12) = all_209_0_245 & member(all_0_8_8, all_0_13_13) = all_209_1_246
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (593) yields:
% 22.48/5.79 | (594) ~ (all_209_0_245 = 0)
% 22.48/5.79 | (595) ~ (all_209_1_246 = 0)
% 22.48/5.79 | (596) member(all_0_8_8, all_0_12_12) = all_209_0_245
% 22.48/5.79 | (597) member(all_0_8_8, all_0_13_13) = all_209_1_246
% 22.48/5.79 |
% 22.48/5.79 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_209_1_246, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_209_1_246, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.48/5.79 | (598) all_209_1_246 = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (598) can reduce 595 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (600) yields:
% 22.48/5.79 | (491) ~ (all_123_3_153 = 0)
% 22.48/5.79 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.48/5.79 |
% 22.48/5.79 | Equations (493) can reduce 491 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (604) ( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152))
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (604) yields:
% 22.48/5.79 | (605) ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)
% 22.48/5.79 | (606) ( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (606), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (607) ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (607) yields:
% 22.48/5.79 | (608) ~ (all_123_1_151 = 0)
% 22.48/5.79 | (609) apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (558), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (577), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (578) yields:
% 22.48/5.79 | (579) all_123_0_150 = 0
% 22.48/5.79 | (323) all_87_0_139 = 0
% 22.48/5.79 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (323) can reduce 246 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (583) yields:
% 22.48/5.79 | (584) all_123_1_151 = 0
% 22.48/5.79 | (585) all_123_2_152 = 0
% 22.48/5.79 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.48/5.79 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (584) can reduce 608 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (600) yields:
% 22.48/5.79 | (491) ~ (all_123_3_153 = 0)
% 22.48/5.79 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.48/5.79 |
% 22.48/5.79 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.48/5.79 | (493) all_123_3_153 = 0
% 22.48/5.79 |
% 22.48/5.79 | Equations (493) can reduce 491 to:
% 22.48/5.79 | (225) $false
% 22.48/5.79 |
% 22.48/5.79 |-The branch is then unsatisfiable
% 22.48/5.79 |-Branch two:
% 22.48/5.79 | (627) ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.48/5.79 |
% 22.48/5.79 | Applying alpha-rule on (627) yields:
% 22.48/5.79 | (628) ~ (all_123_2_152 = 0)
% 22.48/5.79 | (629) member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (558), into two cases.
% 22.48/5.79 |-Branch one:
% 22.48/5.79 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.48/5.79 |
% 22.48/5.79 +-Applying beta-rule and splitting (577), into two cases.
% 22.48/5.79 |-Branch one:
% 22.54/5.79 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (578) yields:
% 22.54/5.79 | (579) all_123_0_150 = 0
% 22.54/5.79 | (323) all_87_0_139 = 0
% 22.54/5.79 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.79 |
% 22.54/5.79 | Equations (323) can reduce 246 to:
% 22.54/5.79 | (225) $false
% 22.54/5.79 |
% 22.54/5.79 |-The branch is then unsatisfiable
% 22.54/5.79 |-Branch two:
% 22.54/5.79 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (583) yields:
% 22.54/5.79 | (584) all_123_1_151 = 0
% 22.54/5.79 | (585) all_123_2_152 = 0
% 22.54/5.79 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.54/5.79 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.79 |
% 22.54/5.79 | Equations (585) can reduce 628 to:
% 22.54/5.79 | (225) $false
% 22.54/5.79 |
% 22.54/5.79 |-The branch is then unsatisfiable
% 22.54/5.79 |-Branch two:
% 22.54/5.79 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (600) yields:
% 22.54/5.79 | (491) ~ (all_123_3_153 = 0)
% 22.54/5.79 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.54/5.79 |
% 22.54/5.79 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.54/5.79 | (493) all_123_3_153 = 0
% 22.54/5.79 |
% 22.54/5.79 | Equations (493) can reduce 491 to:
% 22.54/5.79 | (225) $false
% 22.54/5.79 |
% 22.54/5.79 |-The branch is then unsatisfiable
% 22.54/5.79 |-Branch two:
% 22.54/5.79 | (529) ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (529) yields:
% 22.54/5.79 | (530) ~ (all_122_2_148 = 0)
% 22.54/5.79 | (531) member(all_0_8_8, all_0_13_13) = all_122_2_148
% 22.54/5.79 | (532) ( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)
% 22.54/5.79 |
% 22.54/5.79 +-Applying beta-rule and splitting (558), into two cases.
% 22.54/5.79 |-Branch one:
% 22.54/5.79 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.79 |
% 22.54/5.79 +-Applying beta-rule and splitting (577), into two cases.
% 22.54/5.79 |-Branch one:
% 22.54/5.79 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (578) yields:
% 22.54/5.79 | (579) all_123_0_150 = 0
% 22.54/5.79 | (323) all_87_0_139 = 0
% 22.54/5.79 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.79 |
% 22.54/5.79 | Equations (323) can reduce 246 to:
% 22.54/5.79 | (225) $false
% 22.54/5.79 |
% 22.54/5.79 |-The branch is then unsatisfiable
% 22.54/5.79 |-Branch two:
% 22.54/5.79 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (583) yields:
% 22.54/5.79 | (584) all_123_1_151 = 0
% 22.54/5.79 | (585) all_123_2_152 = 0
% 22.54/5.79 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.54/5.79 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.79 |
% 22.54/5.79 +-Applying beta-rule and splitting (559), into two cases.
% 22.54/5.79 |-Branch one:
% 22.54/5.79 | (574) all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.54/5.79 |
% 22.54/5.79 | Applying alpha-rule on (574) yields:
% 22.54/5.79 | (493) all_123_3_153 = 0
% 22.54/5.79 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (532), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (539) ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (539) yields:
% 22.54/5.80 | (540) ~ (all_122_0_146 = 0)
% 22.54/5.80 | (541) apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (487), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (501), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (502) yields:
% 22.54/5.80 | (503) all_122_0_146 = 0
% 22.54/5.80 | (504) all_122_1_147 = 0
% 22.54/5.80 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.54/5.80 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (503) can reduce 540 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (510) yields:
% 22.54/5.80 | (511) all_122_2_148 = 0
% 22.54/5.80 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (511) can reduce 530 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (525) yields:
% 22.54/5.80 | (466) ~ (all_122_3_149 = 0)
% 22.54/5.80 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | From (356) and (527) follows:
% 22.54/5.80 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.54/5.80 | (469) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (469) can reduce 466 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (543) ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (543) yields:
% 22.54/5.80 | (544) ~ (all_122_1_147 = 0)
% 22.54/5.80 | (545) member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (487), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (501), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (502) yields:
% 22.54/5.80 | (503) all_122_0_146 = 0
% 22.54/5.80 | (504) all_122_1_147 = 0
% 22.54/5.80 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.54/5.80 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (504) can reduce 544 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (510) yields:
% 22.54/5.80 | (511) all_122_2_148 = 0
% 22.54/5.80 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (511) can reduce 530 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (525) yields:
% 22.54/5.80 | (466) ~ (all_122_3_149 = 0)
% 22.54/5.80 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | From (356) and (527) follows:
% 22.54/5.80 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.54/5.80 | (469) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (469) can reduce 466 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (604) ( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152))
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (604) yields:
% 22.54/5.80 | (605) ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)
% 22.54/5.80 | (606) ( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152)
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (606), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (607) ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (607) yields:
% 22.54/5.80 | (608) ~ (all_123_1_151 = 0)
% 22.54/5.80 | (609) apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.54/5.80 |
% 22.54/5.80 | Equations (584) can reduce 608 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (627) ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (627) yields:
% 22.54/5.80 | (628) ~ (all_123_2_152 = 0)
% 22.54/5.80 | (629) member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.54/5.80 |
% 22.54/5.80 | Equations (585) can reduce 628 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (600) yields:
% 22.54/5.80 | (491) ~ (all_123_3_153 = 0)
% 22.54/5.80 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (532), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (539) ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (539) yields:
% 22.54/5.80 | (540) ~ (all_122_0_146 = 0)
% 22.54/5.80 | (541) apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (487), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (501), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (502) yields:
% 22.54/5.80 | (503) all_122_0_146 = 0
% 22.54/5.80 | (504) all_122_1_147 = 0
% 22.54/5.80 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.54/5.80 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (503) can reduce 540 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (510) yields:
% 22.54/5.80 | (511) all_122_2_148 = 0
% 22.54/5.80 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (511) can reduce 530 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (525) yields:
% 22.54/5.80 | (466) ~ (all_122_3_149 = 0)
% 22.54/5.80 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | From (356) and (527) follows:
% 22.54/5.80 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.54/5.80 | (493) all_123_3_153 = 0
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, all_123_3_153 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, yields:
% 22.54/5.80 | (738) all_123_3_153 = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Combining equations (738,493) yields a new equation:
% 22.54/5.80 | (739) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Simplifying 739 yields:
% 22.54/5.80 | (469) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (469) can reduce 466 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (543) ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (543) yields:
% 22.54/5.80 | (544) ~ (all_122_1_147 = 0)
% 22.54/5.80 | (545) member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (487), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.80 |
% 22.54/5.80 +-Applying beta-rule and splitting (501), into two cases.
% 22.54/5.80 |-Branch one:
% 22.54/5.80 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (502) yields:
% 22.54/5.80 | (503) all_122_0_146 = 0
% 22.54/5.80 | (504) all_122_1_147 = 0
% 22.54/5.80 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.54/5.80 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (504) can reduce 544 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (510) yields:
% 22.54/5.80 | (511) all_122_2_148 = 0
% 22.54/5.80 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (511) can reduce 530 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Applying alpha-rule on (525) yields:
% 22.54/5.80 | (466) ~ (all_122_3_149 = 0)
% 22.54/5.80 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | From (356) and (527) follows:
% 22.54/5.80 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.54/5.80 | (493) all_123_3_153 = 0
% 22.54/5.80 |
% 22.54/5.80 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, all_123_3_153 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, yields:
% 22.54/5.80 | (738) all_123_3_153 = all_122_3_149
% 22.54/5.80 |
% 22.54/5.80 | Combining equations (738,493) yields a new equation:
% 22.54/5.80 | (739) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Simplifying 739 yields:
% 22.54/5.80 | (469) all_122_3_149 = 0
% 22.54/5.80 |
% 22.54/5.80 | Equations (469) can reduce 466 to:
% 22.54/5.80 | (225) $false
% 22.54/5.80 |
% 22.54/5.80 |-The branch is then unsatisfiable
% 22.54/5.80 |-Branch two:
% 22.54/5.80 | (765) ((all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_124_3_157 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157)) & ((all_124_3_157 = 0 & apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0) | ( ~ (all_124_0_154 = 0) & member(all_0_8_8, all_0_12_12) = all_124_0_154 & (( ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155) | ( ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156))))
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (765) yields:
% 22.54/5.81 | (766) (all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0) | ( ~ (all_124_3_157 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157)
% 22.54/5.81 | (767) (all_124_3_157 = 0 & apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0) | ( ~ (all_124_0_154 = 0) & member(all_0_8_8, all_0_12_12) = all_124_0_154 & (( ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155) | ( ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156)))
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (439), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (224) all_0_6_6 = all_0_7_7
% 22.54/5.81 |
% 22.54/5.81 | Equations (224) can reduce 203 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (203) ~ (all_0_6_6 = all_0_7_7)
% 22.54/5.81 | (771) ? [v0] : (( ~ (v0 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_10_10) = v0))
% 22.54/5.81 |
% 22.54/5.81 | Instantiating (771) with all_175_0_247 yields:
% 22.54/5.81 | (772) ( ~ (all_175_0_247 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247) | ( ~ (all_175_0_247 = 0) & member(all_0_7_7, all_0_11_11) = all_175_0_247) | ( ~ (all_175_0_247 = 0) & member(all_0_8_8, all_0_10_10) = all_175_0_247)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (772), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (773) ( ~ (all_175_0_247 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247) | ( ~ (all_175_0_247 = 0) & member(all_0_7_7, all_0_11_11) = all_175_0_247)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (773), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (774) ~ (all_175_0_247 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (774) yields:
% 22.54/5.81 | (775) ~ (all_175_0_247 = 0)
% 22.54/5.81 | (776) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (767), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (777) all_124_3_157 = 0 & apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (777) yields:
% 22.54/5.81 | (565) all_124_3_157 = 0
% 22.54/5.81 | (779) apply(all_0_14_14, all_0_8_8, all_77_0_137) = 0
% 22.54/5.81 |
% 22.54/5.81 | From (411) and (779) follows:
% 22.54/5.81 | (421) apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (463), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (781) all_121_3_145 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (781) yields:
% 22.54/5.81 | (444) all_121_3_145 = 0
% 22.54/5.81 | (421) apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.54/5.81 |
% 22.54/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_175_0_247, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0, yields:
% 22.54/5.81 | (784) all_175_0_247 = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (784) can reduce 775 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (786) ( ~ (all_83_0_138 = 0) | ( ~ (all_121_2_144 = 0) & member(all_0_8_8, all_0_13_13) = all_121_2_144)) & (( ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142) | ( ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143))
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (786) yields:
% 22.54/5.81 | (787) ~ (all_83_0_138 = 0) | ( ~ (all_121_2_144 = 0) & member(all_0_8_8, all_0_13_13) = all_121_2_144)
% 22.54/5.81 | (788) ( ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142) | ( ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (788), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (789) ~ (all_121_0_142 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (789) yields:
% 22.54/5.81 | (790) ~ (all_121_0_142 = 0)
% 22.54/5.81 | (791) apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_121_0_142
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (462), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (792) (all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (792), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (793) all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (793) yields:
% 22.54/5.81 | (794) all_121_0_142 = 0
% 22.54/5.81 | (795) all_121_1_143 = 0
% 22.54/5.81 | (194) apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0
% 22.54/5.81 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (794) can reduce 790 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (799) all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (799) yields:
% 22.54/5.81 | (800) all_121_2_144 = 0
% 22.54/5.81 | (801) all_83_0_138 = 0
% 22.54/5.81 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (801) can reduce 258 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (804) ~ (all_121_3_145 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (804) yields:
% 22.54/5.81 | (442) ~ (all_121_3_145 = 0)
% 22.54/5.81 | (806) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_175_0_247, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0, yields:
% 22.54/5.81 | (784) all_175_0_247 = 0
% 22.54/5.81 |
% 22.54/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_121_3_145, all_175_0_247 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145, yields:
% 22.54/5.81 | (808) all_175_0_247 = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Combining equations (808,784) yields a new equation:
% 22.54/5.81 | (809) all_121_3_145 = 0
% 22.54/5.81 |
% 22.54/5.81 | Simplifying 809 yields:
% 22.54/5.81 | (444) all_121_3_145 = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (444) can reduce 442 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (812) ~ (all_121_1_143 = 0) & member(all_0_8_8, all_0_12_12) = all_121_1_143
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (812) yields:
% 22.54/5.81 | (813) ~ (all_121_1_143 = 0)
% 22.54/5.81 | (814) member(all_0_8_8, all_0_12_12) = all_121_1_143
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (462), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (792) (all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (792), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (793) all_121_0_142 = 0 & all_121_1_143 = 0 & apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (793) yields:
% 22.54/5.81 | (794) all_121_0_142 = 0
% 22.54/5.81 | (795) all_121_1_143 = 0
% 22.54/5.81 | (194) apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0
% 22.54/5.81 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (795) can reduce 813 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (799) all_121_2_144 = 0 & all_83_0_138 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (799) yields:
% 22.54/5.81 | (800) all_121_2_144 = 0
% 22.54/5.81 | (801) all_83_0_138 = 0
% 22.54/5.81 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (801) can reduce 258 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (804) ~ (all_121_3_145 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (804) yields:
% 22.54/5.81 | (442) ~ (all_121_3_145 = 0)
% 22.54/5.81 | (806) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_175_0_247, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0, yields:
% 22.54/5.81 | (784) all_175_0_247 = 0
% 22.54/5.81 |
% 22.54/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_121_3_145, all_175_0_247 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_121_3_145, yields:
% 22.54/5.81 | (808) all_175_0_247 = all_121_3_145
% 22.54/5.81 |
% 22.54/5.81 | Combining equations (784,808) yields a new equation:
% 22.54/5.81 | (444) all_121_3_145 = 0
% 22.54/5.81 |
% 22.54/5.81 | Equations (444) can reduce 442 to:
% 22.54/5.81 | (225) $false
% 22.54/5.81 |
% 22.54/5.81 |-The branch is then unsatisfiable
% 22.54/5.81 |-Branch two:
% 22.54/5.81 | (834) ~ (all_124_0_154 = 0) & member(all_0_8_8, all_0_12_12) = all_124_0_154 & (( ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155) | ( ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156))
% 22.54/5.81 |
% 22.54/5.81 | Applying alpha-rule on (834) yields:
% 22.54/5.81 | (835) ~ (all_124_0_154 = 0)
% 22.54/5.81 | (836) member(all_0_8_8, all_0_12_12) = all_124_0_154
% 22.54/5.81 | (837) ( ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155) | ( ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156)
% 22.54/5.81 |
% 22.54/5.81 +-Applying beta-rule and splitting (837), into two cases.
% 22.54/5.81 |-Branch one:
% 22.54/5.81 | (838) ~ (all_124_1_155 = 0) & apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155
% 22.54/5.81 |
% 22.64/5.81 | Applying alpha-rule on (838) yields:
% 22.64/5.81 | (839) ~ (all_124_1_155 = 0)
% 22.64/5.81 | (840) apply(all_0_16_16, all_0_8_8, all_77_0_137) = all_124_1_155
% 22.64/5.81 |
% 22.64/5.81 +-Applying beta-rule and splitting (766), into two cases.
% 22.64/5.81 |-Branch one:
% 22.64/5.81 | (841) (all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.64/5.81 |
% 22.64/5.81 +-Applying beta-rule and splitting (841), into two cases.
% 22.64/5.81 |-Branch one:
% 22.64/5.81 | (842) all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.64/5.81 |
% 22.64/5.81 | Applying alpha-rule on (842) yields:
% 22.64/5.81 | (843) all_124_0_154 = 0
% 22.64/5.81 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.64/5.81 |
% 22.64/5.81 | Equations (843) can reduce 835 to:
% 22.64/5.81 | (225) $false
% 22.64/5.81 |
% 22.64/5.81 |-The branch is then unsatisfiable
% 22.64/5.81 |-Branch two:
% 22.64/5.81 | (846) all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.64/5.81 |
% 22.64/5.81 | Applying alpha-rule on (846) yields:
% 22.64/5.81 | (847) all_124_1_155 = 0
% 22.64/5.81 | (848) all_124_2_156 = 0
% 22.64/5.81 | (849) apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0
% 22.64/5.81 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.64/5.81 |
% 22.64/5.81 | Equations (847) can reduce 839 to:
% 22.64/5.81 | (225) $false
% 22.64/5.81 |
% 22.64/5.81 |-The branch is then unsatisfiable
% 22.64/5.81 |-Branch two:
% 22.64/5.81 | (852) ~ (all_124_3_157 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157
% 22.64/5.81 |
% 22.64/5.81 | Applying alpha-rule on (852) yields:
% 22.64/5.81 | (562) ~ (all_124_3_157 = 0)
% 22.64/5.81 | (854) apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157
% 22.64/5.81 |
% 22.64/5.81 | From (411) and (854) follows:
% 22.64/5.81 | (855) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_124_3_157
% 22.64/5.81 |
% 22.64/5.81 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_175_0_247, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0, yields:
% 22.64/5.82 | (784) all_175_0_247 = 0
% 22.64/5.82 |
% 22.64/5.82 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_124_3_157, all_175_0_247 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_124_3_157, yields:
% 22.64/5.82 | (857) all_175_0_247 = all_124_3_157
% 22.64/5.82 |
% 22.64/5.82 | Combining equations (784,857) yields a new equation:
% 22.64/5.82 | (565) all_124_3_157 = 0
% 22.64/5.82 |
% 22.64/5.82 | Equations (565) can reduce 562 to:
% 22.64/5.82 | (225) $false
% 22.64/5.82 |
% 22.64/5.82 |-The branch is then unsatisfiable
% 22.64/5.82 |-Branch two:
% 22.64/5.82 | (860) ~ (all_124_2_156 = 0) & member(all_0_8_8, all_0_13_13) = all_124_2_156
% 22.64/5.82 |
% 22.64/5.82 | Applying alpha-rule on (860) yields:
% 22.64/5.82 | (861) ~ (all_124_2_156 = 0)
% 22.64/5.82 | (862) member(all_0_8_8, all_0_13_13) = all_124_2_156
% 22.64/5.82 |
% 22.64/5.82 +-Applying beta-rule and splitting (766), into two cases.
% 22.64/5.82 |-Branch one:
% 22.64/5.82 | (841) (all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.64/5.82 |
% 22.64/5.82 +-Applying beta-rule and splitting (841), into two cases.
% 22.64/5.82 |-Branch one:
% 22.64/5.82 | (842) all_124_0_154 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.64/5.82 |
% 22.64/5.82 | Applying alpha-rule on (842) yields:
% 22.64/5.82 | (843) all_124_0_154 = 0
% 22.64/5.82 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.64/5.82 |
% 22.64/5.82 | Equations (843) can reduce 835 to:
% 22.64/5.82 | (225) $false
% 22.64/5.82 |
% 22.64/5.82 |-The branch is then unsatisfiable
% 22.64/5.82 |-Branch two:
% 22.64/5.82 | (846) all_124_1_155 = 0 & all_124_2_156 = 0 & apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.64/5.82 |
% 22.64/5.82 | Applying alpha-rule on (846) yields:
% 22.64/5.82 | (847) all_124_1_155 = 0
% 22.64/5.82 | (848) all_124_2_156 = 0
% 22.64/5.82 | (849) apply(all_0_16_16, all_0_8_8, all_77_0_137) = 0
% 22.64/5.82 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.64/5.82 |
% 22.64/5.82 | Equations (848) can reduce 861 to:
% 22.64/5.82 | (225) $false
% 22.64/5.82 |
% 22.64/5.82 |-The branch is then unsatisfiable
% 22.64/5.82 |-Branch two:
% 22.64/5.82 | (852) ~ (all_124_3_157 = 0) & apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157
% 22.64/5.82 |
% 22.64/5.82 | Applying alpha-rule on (852) yields:
% 22.64/5.82 | (562) ~ (all_124_3_157 = 0)
% 22.64/5.82 | (854) apply(all_0_14_14, all_0_8_8, all_77_0_137) = all_124_3_157
% 22.64/5.82 |
% 22.64/5.82 | From (411) and (854) follows:
% 22.64/5.82 | (855) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_124_3_157
% 22.64/5.82 |
% 22.64/5.82 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_175_0_247, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0, yields:
% 22.64/5.82 | (784) all_175_0_247 = 0
% 22.64/5.82 |
% 22.64/5.82 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_6_6, all_124_3_157, all_175_0_247 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_175_0_247, apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_124_3_157, yields:
% 22.64/5.82 | (857) all_175_0_247 = all_124_3_157
% 22.64/5.82 |
% 22.64/5.82 | Combining equations (857,784) yields a new equation:
% 22.64/5.82 | (880) all_124_3_157 = 0
% 22.64/5.82 |
% 22.64/5.82 | Simplifying 880 yields:
% 22.64/5.82 | (565) all_124_3_157 = 0
% 22.64/5.82 |
% 22.64/5.82 | Equations (565) can reduce 562 to:
% 22.64/5.82 | (225) $false
% 22.64/5.82 |
% 22.64/5.82 |-The branch is then unsatisfiable
% 22.64/5.82 |-Branch two:
% 22.64/5.82 | (883) ~ (all_175_0_247 = 0) & member(all_0_7_7, all_0_11_11) = all_175_0_247
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (883) yields:
% 22.66/5.82 | (775) ~ (all_175_0_247 = 0)
% 22.66/5.82 | (885) member(all_0_7_7, all_0_11_11) = all_175_0_247
% 22.66/5.82 |
% 22.66/5.82 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_175_0_247, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_175_0_247, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.66/5.82 | (784) all_175_0_247 = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (784) can reduce 775 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (888) ~ (all_175_0_247 = 0) & member(all_0_8_8, all_0_10_10) = all_175_0_247
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (888) yields:
% 22.66/5.82 | (775) ~ (all_175_0_247 = 0)
% 22.66/5.82 | (890) member(all_0_8_8, all_0_10_10) = all_175_0_247
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (559), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (574) all_123_3_153 = 0 & apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (574) yields:
% 22.66/5.82 | (493) all_123_3_153 = 0
% 22.66/5.82 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (488), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (498) all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (498) yields:
% 22.66/5.82 | (469) all_122_3_149 = 0
% 22.66/5.82 | (500) apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (487), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (501), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (502) yields:
% 22.66/5.82 | (503) all_122_0_146 = 0
% 22.66/5.82 | (504) all_122_1_147 = 0
% 22.66/5.82 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.66/5.82 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.82 |
% 22.66/5.82 | From (356) and (354) follows:
% 22.66/5.82 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.66/5.82 |
% 22.66/5.82 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.82 | (323) all_87_0_139 = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (323) can reduce 246 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (510) yields:
% 22.66/5.82 | (511) all_122_2_148 = 0
% 22.66/5.82 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.82 |
% 22.66/5.82 | Instantiating formula (159) with all_175_0_247, all_0_10_10, all_0_12_12, all_0_13_13, all_0_8_8 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_0_8_8, all_0_10_10) = all_175_0_247, yields:
% 22.66/5.82 | (909) all_175_0_247 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (909), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (784) all_175_0_247 = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (784) can reduce 775 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (775) ~ (all_175_0_247 = 0)
% 22.66/5.82 | (294) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v1 & member(all_0_8_8, all_0_13_13) = v0)
% 22.66/5.82 |
% 22.66/5.82 | Instantiating (294) with all_223_0_262, all_223_1_263 yields:
% 22.66/5.82 | (914) ~ (all_223_0_262 = 0) & ~ (all_223_1_263 = 0) & member(all_0_8_8, all_0_12_12) = all_223_0_262 & member(all_0_8_8, all_0_13_13) = all_223_1_263
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (914) yields:
% 22.66/5.82 | (915) ~ (all_223_0_262 = 0)
% 22.66/5.82 | (916) ~ (all_223_1_263 = 0)
% 22.66/5.82 | (917) member(all_0_8_8, all_0_12_12) = all_223_0_262
% 22.66/5.82 | (918) member(all_0_8_8, all_0_13_13) = all_223_1_263
% 22.66/5.82 |
% 22.66/5.82 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_223_1_263, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_223_1_263, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.66/5.82 | (919) all_223_1_263 = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (919) can reduce 916 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (525) yields:
% 22.66/5.82 | (466) ~ (all_122_3_149 = 0)
% 22.66/5.82 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.82 |
% 22.66/5.82 | Equations (469) can reduce 466 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (529) ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (529) yields:
% 22.66/5.82 | (530) ~ (all_122_2_148 = 0)
% 22.66/5.82 | (531) member(all_0_8_8, all_0_13_13) = all_122_2_148
% 22.66/5.82 | (532) ( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (487), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (501), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (502) yields:
% 22.66/5.82 | (503) all_122_0_146 = 0
% 22.66/5.82 | (504) all_122_1_147 = 0
% 22.66/5.82 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.66/5.82 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.82 |
% 22.66/5.82 +-Applying beta-rule and splitting (532), into two cases.
% 22.66/5.82 |-Branch one:
% 22.66/5.82 | (539) ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (539) yields:
% 22.66/5.82 | (540) ~ (all_122_0_146 = 0)
% 22.66/5.82 | (541) apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.66/5.82 |
% 22.66/5.82 | Equations (503) can reduce 540 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (543) ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (543) yields:
% 22.66/5.82 | (544) ~ (all_122_1_147 = 0)
% 22.66/5.82 | (545) member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.66/5.82 |
% 22.66/5.82 | Equations (504) can reduce 544 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (510) yields:
% 22.66/5.82 | (511) all_122_2_148 = 0
% 22.66/5.82 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (511) can reduce 530 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (525) yields:
% 22.66/5.82 | (466) ~ (all_122_3_149 = 0)
% 22.66/5.82 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.82 |
% 22.66/5.82 | From (356) and (527) follows:
% 22.66/5.82 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.66/5.82 |
% 22.66/5.82 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.82 | (469) all_122_3_149 = 0
% 22.66/5.82 |
% 22.66/5.82 | Equations (469) can reduce 466 to:
% 22.66/5.82 | (225) $false
% 22.66/5.82 |
% 22.66/5.82 |-The branch is then unsatisfiable
% 22.66/5.82 |-Branch two:
% 22.66/5.82 | (604) ( ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)) & (( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152))
% 22.66/5.82 |
% 22.66/5.82 | Applying alpha-rule on (604) yields:
% 22.66/5.82 | (605) ~ (all_87_0_139 = 0) | ( ~ (all_123_0_150 = 0) & member(all_0_8_8, all_0_12_12) = all_123_0_150)
% 22.66/5.82 | (606) ( ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151) | ( ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152)
% 22.66/5.82 |
% 22.66/5.83 +-Applying beta-rule and splitting (606), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (607) ~ (all_123_1_151 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (607) yields:
% 22.66/5.83 | (608) ~ (all_123_1_151 = 0)
% 22.66/5.83 | (609) apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_123_1_151
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (488), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (498) all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (498) yields:
% 22.66/5.83 | (469) all_122_3_149 = 0
% 22.66/5.83 | (500) apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 |
% 22.66/5.83 | From (356) and (500) follows:
% 22.66/5.83 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (558), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (577), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (578) yields:
% 22.66/5.83 | (579) all_123_0_150 = 0
% 22.66/5.83 | (323) all_87_0_139 = 0
% 22.66/5.83 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (323) can reduce 246 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (583) yields:
% 22.66/5.83 | (584) all_123_1_151 = 0
% 22.66/5.83 | (585) all_123_2_152 = 0
% 22.66/5.83 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (584) can reduce 608 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (600) yields:
% 22.66/5.83 | (491) ~ (all_123_3_153 = 0)
% 22.66/5.83 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.83 | (493) all_123_3_153 = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (493) can reduce 491 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (529) ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (529) yields:
% 22.66/5.83 | (530) ~ (all_122_2_148 = 0)
% 22.66/5.83 | (531) member(all_0_8_8, all_0_13_13) = all_122_2_148
% 22.66/5.83 | (532) ( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (487), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (501), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (502) yields:
% 22.66/5.83 | (503) all_122_0_146 = 0
% 22.66/5.83 | (504) all_122_1_147 = 0
% 22.66/5.83 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (532), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (539) ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (539) yields:
% 22.66/5.83 | (540) ~ (all_122_0_146 = 0)
% 22.66/5.83 | (541) apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146
% 22.66/5.83 |
% 22.66/5.83 | Equations (503) can reduce 540 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (543) ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (543) yields:
% 22.66/5.83 | (544) ~ (all_122_1_147 = 0)
% 22.66/5.83 | (545) member(all_0_8_8, all_0_12_12) = all_122_1_147
% 22.66/5.83 |
% 22.66/5.83 | Equations (504) can reduce 544 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (510) yields:
% 22.66/5.83 | (511) all_122_2_148 = 0
% 22.66/5.83 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (511) can reduce 530 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (525) yields:
% 22.66/5.83 | (466) ~ (all_122_3_149 = 0)
% 22.66/5.83 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 | From (356) and (527) follows:
% 22.66/5.83 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (558), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (577), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (578) yields:
% 22.66/5.83 | (579) all_123_0_150 = 0
% 22.66/5.83 | (323) all_87_0_139 = 0
% 22.66/5.83 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (323) can reduce 246 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (583) yields:
% 22.66/5.83 | (584) all_123_1_151 = 0
% 22.66/5.83 | (585) all_123_2_152 = 0
% 22.66/5.83 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (584) can reduce 608 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (600) yields:
% 22.66/5.83 | (491) ~ (all_123_3_153 = 0)
% 22.66/5.83 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.83 | (493) all_123_3_153 = 0
% 22.66/5.83 |
% 22.66/5.83 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, all_123_3_153 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, yields:
% 22.66/5.83 | (738) all_123_3_153 = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 | Combining equations (738,493) yields a new equation:
% 22.66/5.83 | (739) all_122_3_149 = 0
% 22.66/5.83 |
% 22.66/5.83 | Simplifying 739 yields:
% 22.66/5.83 | (469) all_122_3_149 = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (469) can reduce 466 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (627) ~ (all_123_2_152 = 0) & member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (627) yields:
% 22.66/5.83 | (628) ~ (all_123_2_152 = 0)
% 22.66/5.83 | (629) member(all_0_8_8, all_0_13_13) = all_123_2_152
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (487), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (501) (all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (501), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (502) all_122_0_146 = 0 & all_122_1_147 = 0 & apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (502) yields:
% 22.66/5.83 | (503) all_122_0_146 = 0
% 22.66/5.83 | (504) all_122_1_147 = 0
% 22.66/5.83 | (354) apply(all_0_15_15, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | From (356) and (354) follows:
% 22.66/5.83 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 |
% 22.66/5.83 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.83 | (323) all_87_0_139 = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (323) can reduce 246 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (510) all_122_2_148 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (510) yields:
% 22.66/5.83 | (511) all_122_2_148 = 0
% 22.66/5.83 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (558), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (577), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (578) yields:
% 22.66/5.83 | (579) all_123_0_150 = 0
% 22.66/5.83 | (323) all_87_0_139 = 0
% 22.66/5.83 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (323) can reduce 246 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (583) yields:
% 22.66/5.83 | (584) all_123_1_151 = 0
% 22.66/5.83 | (585) all_123_2_152 = 0
% 22.66/5.83 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (585) can reduce 628 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (600) yields:
% 22.66/5.83 | (491) ~ (all_123_3_153 = 0)
% 22.66/5.83 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (488), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (498) all_122_3_149 = 0 & apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (498) yields:
% 22.66/5.83 | (469) all_122_3_149 = 0
% 22.66/5.83 | (500) apply(all_0_14_14, all_0_8_8, all_73_0_128) = 0
% 22.66/5.83 |
% 22.66/5.83 | From (356) and (500) follows:
% 22.66/5.83 | (316) apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0
% 22.66/5.83 |
% 22.66/5.83 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.83 | (493) all_123_3_153 = 0
% 22.66/5.83 |
% 22.66/5.83 | Equations (493) can reduce 491 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (529) ~ (all_122_2_148 = 0) & member(all_0_8_8, all_0_13_13) = all_122_2_148 & (( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147))
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (529) yields:
% 22.66/5.83 | (530) ~ (all_122_2_148 = 0)
% 22.66/5.83 | (531) member(all_0_8_8, all_0_13_13) = all_122_2_148
% 22.66/5.83 | (532) ( ~ (all_122_0_146 = 0) & apply(all_0_15_15, all_0_8_8, all_73_0_128) = all_122_0_146) | ( ~ (all_122_1_147 = 0) & member(all_0_8_8, all_0_12_12) = all_122_1_147)
% 22.66/5.83 |
% 22.66/5.83 | Equations (511) can reduce 530 to:
% 22.66/5.83 | (225) $false
% 22.66/5.83 |
% 22.66/5.83 |-The branch is then unsatisfiable
% 22.66/5.83 |-Branch two:
% 22.66/5.83 | (525) ~ (all_122_3_149 = 0) & apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 | Applying alpha-rule on (525) yields:
% 22.66/5.83 | (466) ~ (all_122_3_149 = 0)
% 22.66/5.83 | (527) apply(all_0_14_14, all_0_8_8, all_73_0_128) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 | From (356) and (527) follows:
% 22.66/5.83 | (554) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (558), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (577) (all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.83 |
% 22.66/5.83 +-Applying beta-rule and splitting (577), into two cases.
% 22.66/5.83 |-Branch one:
% 22.66/5.83 | (578) all_123_0_150 = 0 & all_87_0_139 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (578) yields:
% 22.66/5.84 | (579) all_123_0_150 = 0
% 22.66/5.84 | (323) all_87_0_139 = 0
% 22.66/5.84 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (323) can reduce 246 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (583) all_123_1_151 = 0 & all_123_2_152 = 0 & apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (583) yields:
% 22.66/5.84 | (584) all_123_1_151 = 0
% 22.66/5.84 | (585) all_123_2_152 = 0
% 22.66/5.84 | (202) apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0
% 22.66/5.84 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (585) can reduce 628 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (600) ~ (all_123_3_153 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (600) yields:
% 22.66/5.84 | (491) ~ (all_123_3_153 = 0)
% 22.66/5.84 | (602) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_123_3_153, 0 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.84 | (493) all_123_3_153 = 0
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (96) with all_0_14_14, all_0_8_8, all_0_7_7, all_122_3_149, all_123_3_153 and discharging atoms apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_123_3_153, apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_122_3_149, yields:
% 22.66/5.84 | (738) all_123_3_153 = all_122_3_149
% 22.66/5.84 |
% 22.66/5.84 | Combining equations (738,493) yields a new equation:
% 22.66/5.84 | (739) all_122_3_149 = 0
% 22.66/5.84 |
% 22.66/5.84 | Simplifying 739 yields:
% 22.66/5.84 | (469) all_122_3_149 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (469) can reduce 466 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (340) ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (340) yields:
% 22.66/5.84 | (283) ~ (all_75_3_132 = 0)
% 22.66/5.84 | (342) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.66/5.84 |
% 22.66/5.84 | Equations (285) can reduce 283 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1095) ~ (all_73_0_128 = all_0_7_7)
% 22.66/5.84 | (1096) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_0_8_8, all_73_0_128) = v0) | ( ~ (v0 = 0) & member(all_0_7_7, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_13_13) = v0))
% 22.66/5.84 |
% 22.66/5.84 | Instantiating (1096) with all_154_0_264 yields:
% 22.66/5.84 | (1097) ( ~ (all_154_0_264 = 0) & apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_154_0_264) | ( ~ (all_154_0_264 = 0) & member(all_0_7_7, all_0_11_11) = all_154_0_264) | ( ~ (all_154_0_264 = 0) & member(all_0_8_8, all_0_13_13) = all_154_0_264)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (1097), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1098) ( ~ (all_154_0_264 = 0) & apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_154_0_264) | ( ~ (all_154_0_264 = 0) & member(all_0_7_7, all_0_11_11) = all_154_0_264)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (1098), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1099) ~ (all_154_0_264 = 0) & apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1099) yields:
% 22.66/5.84 | (1100) ~ (all_154_0_264 = 0)
% 22.66/5.84 | (1101) apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_73_0_128, all_154_0_264, 0 and discharging atoms apply(all_0_16_16, all_0_8_8, all_73_0_128) = all_154_0_264, apply(all_0_16_16, all_0_8_8, all_73_0_128) = 0, yields:
% 22.66/5.84 | (1102) all_154_0_264 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1102) can reduce 1100 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1104) ~ (all_154_0_264 = 0) & member(all_0_7_7, all_0_11_11) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1104) yields:
% 22.66/5.84 | (1100) ~ (all_154_0_264 = 0)
% 22.66/5.84 | (1106) member(all_0_7_7, all_0_11_11) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_154_0_264, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_154_0_264, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.66/5.84 | (1102) all_154_0_264 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1102) can reduce 1100 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1109) ~ (all_154_0_264 = 0) & member(all_0_8_8, all_0_13_13) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1109) yields:
% 22.66/5.84 | (1100) ~ (all_154_0_264 = 0)
% 22.66/5.84 | (1111) member(all_0_8_8, all_0_13_13) = all_154_0_264
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (303), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (317) (all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (317), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (318) all_75_0_129 = 0 & all_75_1_130 = 0 & apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (318) yields:
% 22.66/5.84 | (319) all_75_0_129 = 0
% 22.66/5.84 | (320) all_75_1_130 = 0
% 22.66/5.84 | (321) apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0
% 22.66/5.84 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_7_7, 0, all_87_0_139 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_87_0_139, apply(all_0_15_15, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.84 | (323) all_87_0_139 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (323) can reduce 246 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (325) all_75_2_131 = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (325) yields:
% 22.66/5.84 | (326) all_75_2_131 = 0
% 22.66/5.84 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_154_0_264, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_154_0_264, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.66/5.84 | (1102) all_154_0_264 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1102) can reduce 1100 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (340) ~ (all_75_3_132 = 0) & apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (340) yields:
% 22.66/5.84 | (283) ~ (all_75_3_132 = 0)
% 22.66/5.84 | (342) apply(all_0_14_14, all_0_8_8, all_0_7_7) = all_75_3_132
% 22.66/5.84 |
% 22.66/5.84 | Equations (285) can reduce 283 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1129) ~ (all_76_0_133 = 0) & member(all_0_8_8, all_0_12_12) = all_76_0_133 & (( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135))
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1129) yields:
% 22.66/5.84 | (1130) ~ (all_76_0_133 = 0)
% 22.66/5.84 | (1131) member(all_0_8_8, all_0_12_12) = all_76_0_133
% 22.66/5.84 | (1132) ( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135)
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (132) with all_0_8_8, all_0_12_12, all_76_0_133, 0 and discharging atoms member(all_0_8_8, all_0_12_12) = all_76_0_133, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.66/5.84 | (1133) all_76_0_133 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1133) can reduce 1130 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (344) ~ (all_75_2_131 = 0) & member(all_0_8_8, all_0_13_13) = all_75_2_131 & (( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130))
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (344) yields:
% 22.66/5.84 | (345) ~ (all_75_2_131 = 0)
% 22.66/5.84 | (346) member(all_0_8_8, all_0_13_13) = all_75_2_131
% 22.66/5.84 | (347) ( ~ (all_75_0_129 = 0) & apply(all_0_15_15, all_0_8_8, all_0_7_7) = all_75_0_129) | ( ~ (all_75_1_130 = 0) & member(all_0_8_8, all_0_12_12) = all_75_1_130)
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_75_2_131, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_75_2_131, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.66/5.84 | (326) all_75_2_131 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (326) can reduce 345 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1141) ~ (all_77_0_137 = all_0_6_6)
% 22.66/5.84 | (1142) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & member(all_77_0_137, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_0_8_8, all_0_12_12) = v0))
% 22.66/5.84 |
% 22.66/5.84 | Instantiating (1142) with all_138_0_316 yields:
% 22.66/5.84 | (1143) ( ~ (all_138_0_316 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_138_0_316) | ( ~ (all_138_0_316 = 0) & member(all_77_0_137, all_0_11_11) = all_138_0_316) | ( ~ (all_138_0_316 = 0) & member(all_0_8_8, all_0_12_12) = all_138_0_316)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (352), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (419) all_76_3_136 = 0 & apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (419) yields:
% 22.66/5.84 | (309) all_76_3_136 = 0
% 22.66/5.84 | (421) apply(all_0_14_14, all_0_8_8, all_0_6_6) = 0
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (351), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1147) (all_76_0_133 = 0 & member(all_0_8_8, all_0_12_12) = 0) | (all_76_1_134 = 0 & all_76_2_135 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (1147), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1148) all_76_0_133 = 0 & member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1148) yields:
% 22.66/5.84 | (1133) all_76_0_133 = 0
% 22.66/5.84 | (199) member(all_0_8_8, all_0_12_12) = 0
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (1143), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1151) ( ~ (all_138_0_316 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_138_0_316) | ( ~ (all_138_0_316 = 0) & member(all_77_0_137, all_0_11_11) = all_138_0_316)
% 22.66/5.84 |
% 22.66/5.84 +-Applying beta-rule and splitting (1151), into two cases.
% 22.66/5.84 |-Branch one:
% 22.66/5.84 | (1152) ~ (all_138_0_316 = 0) & apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_138_0_316
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1152) yields:
% 22.66/5.84 | (1153) ~ (all_138_0_316 = 0)
% 22.66/5.84 | (1154) apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_138_0_316
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (96) with all_0_15_15, all_0_8_8, all_0_6_6, all_138_0_316, 0 and discharging atoms apply(all_0_15_15, all_0_8_8, all_0_6_6) = all_138_0_316, apply(all_0_15_15, all_0_8_8, all_0_6_6) = 0, yields:
% 22.66/5.84 | (1155) all_138_0_316 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1155) can reduce 1153 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1157) ~ (all_138_0_316 = 0) & member(all_77_0_137, all_0_11_11) = all_138_0_316
% 22.66/5.84 |
% 22.66/5.84 | Applying alpha-rule on (1157) yields:
% 22.66/5.84 | (1153) ~ (all_138_0_316 = 0)
% 22.66/5.84 | (1159) member(all_77_0_137, all_0_11_11) = all_138_0_316
% 22.66/5.84 |
% 22.66/5.84 | Instantiating formula (132) with all_77_0_137, all_0_11_11, all_138_0_316, 0 and discharging atoms member(all_77_0_137, all_0_11_11) = all_138_0_316, member(all_77_0_137, all_0_11_11) = 0, yields:
% 22.66/5.84 | (1155) all_138_0_316 = 0
% 22.66/5.84 |
% 22.66/5.84 | Equations (1155) can reduce 1153 to:
% 22.66/5.84 | (225) $false
% 22.66/5.84 |
% 22.66/5.84 |-The branch is then unsatisfiable
% 22.66/5.84 |-Branch two:
% 22.66/5.84 | (1162) ~ (all_138_0_316 = 0) & member(all_0_8_8, all_0_12_12) = all_138_0_316
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1162) yields:
% 22.66/5.85 | (1153) ~ (all_138_0_316 = 0)
% 22.66/5.85 | (1164) member(all_0_8_8, all_0_12_12) = all_138_0_316
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_8_8, all_0_12_12, all_138_0_316, 0 and discharging atoms member(all_0_8_8, all_0_12_12) = all_138_0_316, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.66/5.85 | (1155) all_138_0_316 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (1155) can reduce 1153 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1167) all_76_1_134 = 0 & all_76_2_135 = 0 & apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0 & member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1167) yields:
% 22.66/5.85 | (1168) all_76_1_134 = 0
% 22.66/5.85 | (1169) all_76_2_135 = 0
% 22.66/5.85 | (1170) apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0
% 22.66/5.85 | (205) member(all_0_8_8, all_0_13_13) = 0
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_0_6_6, 0, all_83_0_138 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_83_0_138, apply(all_0_16_16, all_0_8_8, all_0_6_6) = 0, yields:
% 22.66/5.85 | (801) all_83_0_138 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (801) can reduce 258 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1174) ~ (all_76_3_136 = 0) & apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_76_3_136
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1174) yields:
% 22.66/5.85 | (307) ~ (all_76_3_136 = 0)
% 22.66/5.85 | (1176) apply(all_0_14_14, all_0_8_8, all_0_6_6) = all_76_3_136
% 22.66/5.85 |
% 22.66/5.85 | Equations (309) can reduce 307 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1129) ~ (all_76_0_133 = 0) & member(all_0_8_8, all_0_12_12) = all_76_0_133 & (( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135))
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1129) yields:
% 22.66/5.85 | (1130) ~ (all_76_0_133 = 0)
% 22.66/5.85 | (1131) member(all_0_8_8, all_0_12_12) = all_76_0_133
% 22.66/5.85 | (1132) ( ~ (all_76_1_134 = 0) & apply(all_0_16_16, all_0_8_8, all_0_6_6) = all_76_1_134) | ( ~ (all_76_2_135 = 0) & member(all_0_8_8, all_0_13_13) = all_76_2_135)
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_8_8, all_0_12_12, all_76_0_133, 0 and discharging atoms member(all_0_8_8, all_0_12_12) = all_76_0_133, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.66/5.85 | (1133) all_76_0_133 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (1133) can reduce 1130 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1184) ~ (all_129_0_206 = 0) & member(all_73_0_128, all_0_11_11) = all_129_0_206
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1184) yields:
% 22.66/5.85 | (409) ~ (all_129_0_206 = 0)
% 22.66/5.85 | (1186) member(all_73_0_128, all_0_11_11) = all_129_0_206
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_73_0_128, all_0_11_11, all_129_0_206, 0 and discharging atoms member(all_73_0_128, all_0_11_11) = all_129_0_206, member(all_73_0_128, all_0_11_11) = 0, yields:
% 22.66/5.85 | (1187) all_129_0_206 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (1187) can reduce 409 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1189) ~ (all_129_0_206 = 0) & member(all_0_8_8, all_0_13_13) = all_129_0_206
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1189) yields:
% 22.66/5.85 | (409) ~ (all_129_0_206 = 0)
% 22.66/5.85 | (1191) member(all_0_8_8, all_0_13_13) = all_129_0_206
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_129_0_206, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_129_0_206, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.66/5.85 | (1187) all_129_0_206 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (1187) can reduce 409 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1194) ~ (all_95_0_141 = 0) & apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_95_0_141
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1194) yields:
% 22.66/5.85 | (261) ~ (all_95_0_141 = 0)
% 22.66/5.85 | (1196) apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_95_0_141
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (96) with all_0_16_16, all_0_8_8, all_0_7_7, all_95_0_141, 0 and discharging atoms apply(all_0_16_16, all_0_8_8, all_0_7_7) = all_95_0_141, apply(all_0_16_16, all_0_8_8, all_0_7_7) = 0, yields:
% 22.66/5.85 | (1197) all_95_0_141 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (1197) can reduce 261 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1199) ~ (all_83_0_138 = 0) & member(all_0_7_7, all_0_11_11) = all_83_0_138
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1199) yields:
% 22.66/5.85 | (258) ~ (all_83_0_138 = 0)
% 22.66/5.85 | (1201) member(all_0_7_7, all_0_11_11) = all_83_0_138
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_7_7, all_0_11_11, all_83_0_138, 0 and discharging atoms member(all_0_7_7, all_0_11_11) = all_83_0_138, member(all_0_7_7, all_0_11_11) = 0, yields:
% 22.66/5.85 | (801) all_83_0_138 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (801) can reduce 258 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1204) ~ (all_83_0_138 = 0) & member(all_0_8_8, all_0_13_13) = all_83_0_138
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1204) yields:
% 22.66/5.85 | (258) ~ (all_83_0_138 = 0)
% 22.66/5.85 | (1206) member(all_0_8_8, all_0_13_13) = all_83_0_138
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_8_8, all_0_13_13, all_83_0_138, 0 and discharging atoms member(all_0_8_8, all_0_13_13) = all_83_0_138, member(all_0_8_8, all_0_13_13) = 0, yields:
% 22.66/5.85 | (801) all_83_0_138 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (801) can reduce 258 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1209) ~ (all_87_0_139 = 0) & member(all_0_6_6, all_0_11_11) = all_87_0_139
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1209) yields:
% 22.66/5.85 | (246) ~ (all_87_0_139 = 0)
% 22.66/5.85 | (1211) member(all_0_6_6, all_0_11_11) = all_87_0_139
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_6_6, all_0_11_11, all_87_0_139, 0 and discharging atoms member(all_0_6_6, all_0_11_11) = all_87_0_139, member(all_0_6_6, all_0_11_11) = 0, yields:
% 22.66/5.85 | (323) all_87_0_139 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (323) can reduce 246 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1214) ~ (all_87_0_139 = 0) & member(all_0_8_8, all_0_12_12) = all_87_0_139
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1214) yields:
% 22.66/5.85 | (246) ~ (all_87_0_139 = 0)
% 22.66/5.85 | (1216) member(all_0_8_8, all_0_12_12) = all_87_0_139
% 22.66/5.85 |
% 22.66/5.85 | Instantiating formula (132) with all_0_8_8, all_0_12_12, all_87_0_139, 0 and discharging atoms member(all_0_8_8, all_0_12_12) = all_87_0_139, member(all_0_8_8, all_0_12_12) = 0, yields:
% 22.66/5.85 | (323) all_87_0_139 = 0
% 22.66/5.85 |
% 22.66/5.85 | Equations (323) can reduce 246 to:
% 22.66/5.85 | (225) $false
% 22.66/5.85 |
% 22.66/5.85 |-The branch is then unsatisfiable
% 22.66/5.85 |-Branch two:
% 22.66/5.85 | (1219) ~ (all_0_9_9 = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (apply(all_0_16_16, v0, v1) = 0) | ? [v3] : (( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (member(v1, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_16_16, v0, v1) = 0) | ~ (member(v2, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_12_12) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_13_13) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3)))
% 22.66/5.85 |
% 22.66/5.85 | Applying alpha-rule on (1219) yields:
% 22.66/5.85 | (1220) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (apply(all_0_16_16, v0, v1) = 0) | ? [v3] : (( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3)))
% 22.66/5.85 | (1221) ~ (all_0_9_9 = 0)
% 22.66/5.85 | (1222) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_13_13) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3)))
% 22.66/5.85 | (1223) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (member(v2, all_0_11_11) = 0) | ~ (member(v1, all_0_11_11) = 0) | ~ (member(v0, all_0_12_12) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3)))
% 22.66/5.85 | (1224) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_15_15, v0, v2) = 0) | ~ (member(v1, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_16_16, v0, v1) = v3) | ( ~ (v3 = 0) & member(v2, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3)))
% 22.66/5.85 | (1225) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (apply(all_0_16_16, v0, v1) = 0) | ~ (member(v2, all_0_11_11) = 0) | ? [v3] : (( ~ (v3 = 0) & apply(all_0_15_15, v0, v2) = v3) | ( ~ (v3 = 0) & member(v1, all_0_11_11) = v3) | ( ~ (v3 = 0) & member(v0, all_0_12_12) = v3) | ( ~ (v3 = 0) & member(v0, all_0_13_13) = v3)))
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (191), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (195) all_0_9_9 = 0
% 22.66/5.86 |
% 22.66/5.86 | Equations (195) can reduce 1221 to:
% 22.66/5.86 | (225) $false
% 22.66/5.86 |
% 22.66/5.86 |-The branch is then unsatisfiable
% 22.66/5.86 |-Branch two:
% 22.66/5.86 | (1221) ~ (all_0_9_9 = 0)
% 22.66/5.86 | (1229) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_0_14_14, v0, v2) = 0 & apply(all_0_14_14, v0, v1) = 0 & member(v2, all_0_11_11) = 0 & member(v1, all_0_11_11) = 0 & member(v0, all_0_10_10) = 0) | (v1 = 0 & member(v0, all_0_10_10) = 0 & ! [v8] : ( ~ (apply(all_0_14_14, v0, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, all_0_11_11) = v9)) & ! [v8] : ( ~ (member(v8, all_0_11_11) = 0) | ? [v9] : ( ~ (v9 = 0) & apply(all_0_14_14, v0, v8) = v9))))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1229) with all_73_0_359, all_73_1_360, all_73_2_361, all_73_3_362, all_73_4_363, all_73_5_364, all_73_6_365, all_73_7_366 yields:
% 22.66/5.86 | (1230) (all_73_0_359 = 0 & all_73_1_360 = 0 & all_73_2_361 = 0 & all_73_3_362 = 0 & all_73_4_363 = 0 & ~ (all_73_5_364 = all_73_6_365) & apply(all_0_14_14, all_73_7_366, all_73_5_364) = 0 & apply(all_0_14_14, all_73_7_366, all_73_6_365) = 0 & member(all_73_5_364, all_0_11_11) = 0 & member(all_73_6_365, all_0_11_11) = 0 & member(all_73_7_366, all_0_10_10) = 0) | (all_73_6_365 = 0 & member(all_73_7_366, all_0_10_10) = 0 & ! [v0] : ( ~ (apply(all_0_14_14, all_73_7_366, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_11_11) = v1)) & ! [v0] : ( ~ (member(v0, all_0_11_11) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_14_14, all_73_7_366, v0) = v1)))
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (1230), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (1231) all_73_0_359 = 0 & all_73_1_360 = 0 & all_73_2_361 = 0 & all_73_3_362 = 0 & all_73_4_363 = 0 & ~ (all_73_5_364 = all_73_6_365) & apply(all_0_14_14, all_73_7_366, all_73_5_364) = 0 & apply(all_0_14_14, all_73_7_366, all_73_6_365) = 0 & member(all_73_5_364, all_0_11_11) = 0 & member(all_73_6_365, all_0_11_11) = 0 & member(all_73_7_366, all_0_10_10) = 0
% 22.66/5.86 |
% 22.66/5.86 | Applying alpha-rule on (1231) yields:
% 22.66/5.86 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.86 | (1233) all_73_1_360 = 0
% 22.66/5.86 | (1234) member(all_73_7_366, all_0_10_10) = 0
% 22.66/5.86 | (1235) all_73_4_363 = 0
% 22.66/5.86 | (1236) all_73_2_361 = 0
% 22.66/5.86 | (1237) member(all_73_5_364, all_0_11_11) = 0
% 22.66/5.86 | (1238) all_73_0_359 = 0
% 22.66/5.86 | (1239) apply(all_0_14_14, all_73_7_366, all_73_6_365) = 0
% 22.66/5.86 | (1240) apply(all_0_14_14, all_73_7_366, all_73_5_364) = 0
% 22.66/5.86 | (1241) all_73_3_362 = 0
% 22.66/5.86 | (1242) member(all_73_6_365, all_0_11_11) = 0
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (54) with 0, all_73_5_364, all_73_7_366 and discharging atoms apply(all_0_14_14, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.86 | (1243) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v1 = 0 & v0 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (v0 = 0) & member(all_73_5_364, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_10_10) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (54) with 0, all_73_6_365, all_73_7_366 and discharging atoms apply(all_0_14_14, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.86 | (1244) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v1 = 0 & v0 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (v0 = 0) & member(all_73_6_365, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_10_10) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (134) with all_0_10_10, all_0_12_12, all_0_13_13, all_73_7_366 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.86 | (1245) ? [v0] : ((v0 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v0 = 0 & member(all_73_7_366, all_0_13_13) = 0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1245) with all_86_0_367 yields:
% 22.66/5.86 | (1246) (all_86_0_367 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_86_0_367 = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1244) with all_87_0_368, all_87_1_369, all_87_2_370, all_87_3_371 yields:
% 22.66/5.86 | (1247) (all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_87_3_371 = 0) & member(all_73_6_365, all_0_11_11) = all_87_3_371) | ( ~ (all_87_3_371 = 0) & member(all_73_7_366, all_0_10_10) = all_87_3_371)
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1243) with all_88_0_372, all_88_1_373, all_88_2_374, all_88_3_375 yields:
% 22.66/5.86 | (1248) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375) | ( ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375)
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (1246), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (1249) all_86_0_367 = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.86 |
% 22.66/5.86 | Applying alpha-rule on (1249) yields:
% 22.66/5.86 | (1250) all_86_0_367 = 0
% 22.66/5.86 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (98) with all_73_5_364, all_73_6_365, all_73_7_366, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 22.66/5.86 | (1252) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (182) with all_73_7_366, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 22.66/5.86 | (1253) ? [v0] : (apply(all_0_15_15, all_73_7_366, v0) = 0 & member(v0, all_0_11_11) = 0)
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (1223) with all_73_5_364, all_73_6_365, all_73_7_366 and discharging atoms member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 22.66/5.86 | (1254) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating formula (1223) with all_73_6_365, all_73_5_364, all_73_7_366 and discharging atoms member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 22.66/5.86 | (1255) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1253) with all_96_0_376 yields:
% 22.66/5.86 | (1256) apply(all_0_15_15, all_73_7_366, all_96_0_376) = 0 & member(all_96_0_376, all_0_11_11) = 0
% 22.66/5.86 |
% 22.66/5.86 | Applying alpha-rule on (1256) yields:
% 22.66/5.86 | (1257) apply(all_0_15_15, all_73_7_366, all_96_0_376) = 0
% 22.66/5.86 | (1258) member(all_96_0_376, all_0_11_11) = 0
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (1254), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.86 |
% 22.66/5.86 | Equations (1259) can reduce 1232 to:
% 22.66/5.86 | (225) $false
% 22.66/5.86 |
% 22.66/5.86 |-The branch is then unsatisfiable
% 22.66/5.86 |-Branch two:
% 22.66/5.86 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.86 | (1262) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1262) with all_102_0_377 yields:
% 22.66/5.86 | (1263) ( ~ (all_102_0_377 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377) | ( ~ (all_102_0_377 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_377) | ( ~ (all_102_0_377 = 0) & member(all_73_7_366, all_0_13_13) = all_102_0_377)
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (1255), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.86 |
% 22.66/5.86 | Equations (1259) can reduce 1232 to:
% 22.66/5.86 | (225) $false
% 22.66/5.86 |
% 22.66/5.86 |-The branch is then unsatisfiable
% 22.66/5.86 |-Branch two:
% 22.66/5.86 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.86 | (1267) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.86 |
% 22.66/5.86 | Instantiating (1267) with all_106_0_378 yields:
% 22.66/5.86 | (1268) ( ~ (all_106_0_378 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378) | ( ~ (all_106_0_378 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378) | ( ~ (all_106_0_378 = 0) & member(all_73_7_366, all_0_13_13) = all_106_0_378)
% 22.66/5.86 |
% 22.66/5.86 +-Applying beta-rule and splitting (1252), into two cases.
% 22.66/5.86 |-Branch one:
% 22.66/5.86 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.86 |
% 22.66/5.86 | Equations (1259) can reduce 1232 to:
% 22.66/5.86 | (225) $false
% 22.66/5.86 |
% 22.66/5.86 |-The branch is then unsatisfiable
% 22.66/5.86 |-Branch two:
% 22.66/5.86 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.86 | (1272) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0))
% 22.66/5.86 |
% 22.66/5.87 | Instantiating (1272) with all_110_0_379 yields:
% 22.66/5.87 | (1273) ( ~ (all_110_0_379 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_110_0_379) | ( ~ (all_110_0_379 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_110_0_379)
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (1223) with all_96_0_376, all_73_6_365, all_73_7_366 and discharging atoms member(all_96_0_376, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 22.66/5.87 | (1274) all_96_0_376 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_96_0_376) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1247), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1275) (all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_87_3_371 = 0) & member(all_73_6_365, all_0_11_11) = all_87_3_371)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1275), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1276) (all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1276), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1277) all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1277) yields:
% 22.66/5.87 | (1278) all_87_0_368 = 0
% 22.66/5.87 | (1279) all_87_1_369 = 0
% 22.66/5.87 | (1280) apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0
% 22.66/5.87 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1273), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1282) ~ (all_110_0_379 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_110_0_379
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1282) yields:
% 22.66/5.87 | (1283) ~ (all_110_0_379 = 0)
% 22.66/5.87 | (1284) apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_110_0_379
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1248), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1285), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1286), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1287) yields:
% 22.66/5.87 | (1288) all_88_0_372 = 0
% 22.66/5.87 | (1289) all_88_1_373 = 0
% 22.66/5.87 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 22.66/5.87 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_110_0_379 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_110_0_379, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.87 | (1292) all_110_0_379 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1292) can reduce 1283 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1294) yields:
% 22.66/5.87 | (1295) all_88_2_374 = 0
% 22.66/5.87 | (1296) all_88_3_375 = 0
% 22.66/5.87 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 22.66/5.87 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1268), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1299) ( ~ (all_106_0_378 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378) | ( ~ (all_106_0_378 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1299), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1300) ~ (all_106_0_378 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1300) yields:
% 22.66/5.87 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.87 | (1302) apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_6_365, 0, all_106_0_378 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378, apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.87 | (1303) all_106_0_378 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1303) can reduce 1301 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1305) ~ (all_106_0_378 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1305) yields:
% 22.66/5.87 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.87 | (1307) apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_5_364, 0, all_106_0_378 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378, apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.87 | (1303) all_106_0_378 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1303) can reduce 1301 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1310) ~ (all_106_0_378 = 0) & member(all_73_7_366, all_0_13_13) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1310) yields:
% 22.66/5.87 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.87 | (1312) member(all_73_7_366, all_0_13_13) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (132) with all_73_7_366, all_0_13_13, 0, all_106_0_378 and discharging atoms member(all_73_7_366, all_0_13_13) = all_106_0_378, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.87 | (1303) all_106_0_378 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1303) can reduce 1301 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1315) yields:
% 22.66/5.87 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.87 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 22.66/5.87 | (1296) all_88_3_375 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1296) can reduce 1316 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1320) yields:
% 22.66/5.87 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.87 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.87 | (1296) all_88_3_375 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1296) can reduce 1316 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1325) ~ (all_110_0_379 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_110_0_379
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1325) yields:
% 22.66/5.87 | (1283) ~ (all_110_0_379 = 0)
% 22.66/5.87 | (1327) apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_110_0_379
% 22.66/5.87 |
% 22.66/5.87 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_6_365, 0, all_110_0_379 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_110_0_379, apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.87 | (1292) all_110_0_379 = 0
% 22.66/5.87 |
% 22.66/5.87 | Equations (1292) can reduce 1283 to:
% 22.66/5.87 | (225) $false
% 22.66/5.87 |
% 22.66/5.87 |-The branch is then unsatisfiable
% 22.66/5.87 |-Branch two:
% 22.66/5.87 | (1330) all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1330) yields:
% 22.66/5.87 | (1331) all_87_2_370 = 0
% 22.66/5.87 | (1332) all_87_3_371 = 0
% 22.66/5.87 | (1333) apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0
% 22.66/5.87 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1263), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1335) ( ~ (all_102_0_377 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377) | ( ~ (all_102_0_377 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_377)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1335), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1336) ~ (all_102_0_377 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1336) yields:
% 22.66/5.87 | (1337) ~ (all_102_0_377 = 0)
% 22.66/5.87 | (1338) apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1274), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1339) all_96_0_376 = all_73_6_365
% 22.66/5.87 |
% 22.66/5.87 | From (1339) and (1257) follows:
% 22.66/5.87 | (1280) apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1268), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1299) ( ~ (all_106_0_378 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378) | ( ~ (all_106_0_378 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378)
% 22.66/5.87 |
% 22.66/5.87 +-Applying beta-rule and splitting (1299), into two cases.
% 22.66/5.87 |-Branch one:
% 22.66/5.87 | (1300) ~ (all_106_0_378 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378
% 22.66/5.87 |
% 22.66/5.87 | Applying alpha-rule on (1300) yields:
% 22.66/5.88 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.88 | (1302) apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_6_365, 0, all_106_0_378 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_378, apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.88 | (1303) all_106_0_378 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1303) can reduce 1301 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1305) ~ (all_106_0_378 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1305) yields:
% 22.66/5.88 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.88 | (1307) apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1248), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1285), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1286), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1287) yields:
% 22.66/5.88 | (1288) all_88_0_372 = 0
% 22.66/5.88 | (1289) all_88_1_373 = 0
% 22.66/5.88 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 22.66/5.88 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_102_0_377 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.88 | (1357) all_102_0_377 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1357) can reduce 1337 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1294) yields:
% 22.66/5.88 | (1295) all_88_2_374 = 0
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 22.66/5.88 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_5_364, 0, all_106_0_378 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_378, apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.88 | (1303) all_106_0_378 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1303) can reduce 1301 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1315) yields:
% 22.66/5.88 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.88 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1296) can reduce 1316 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1320) yields:
% 22.66/5.88 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.88 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1296) can reduce 1316 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1310) ~ (all_106_0_378 = 0) & member(all_73_7_366, all_0_13_13) = all_106_0_378
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1310) yields:
% 22.66/5.88 | (1301) ~ (all_106_0_378 = 0)
% 22.66/5.88 | (1312) member(all_73_7_366, all_0_13_13) = all_106_0_378
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1248), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1285), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1286), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1287) yields:
% 22.66/5.88 | (1288) all_88_0_372 = 0
% 22.66/5.88 | (1289) all_88_1_373 = 0
% 22.66/5.88 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 22.66/5.88 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_102_0_377 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.88 | (1357) all_102_0_377 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1357) can reduce 1337 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1294) yields:
% 22.66/5.88 | (1295) all_88_2_374 = 0
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 22.66/5.88 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (132) with all_73_7_366, all_0_13_13, 0, all_106_0_378 and discharging atoms member(all_73_7_366, all_0_13_13) = all_106_0_378, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.88 | (1303) all_106_0_378 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1303) can reduce 1301 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1315) yields:
% 22.66/5.88 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.88 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1296) can reduce 1316 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1320) yields:
% 22.66/5.88 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.88 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.88 | (1296) all_88_3_375 = 0
% 22.66/5.88 |
% 22.66/5.88 | Equations (1296) can reduce 1316 to:
% 22.66/5.88 | (225) $false
% 22.66/5.88 |
% 22.66/5.88 |-The branch is then unsatisfiable
% 22.66/5.88 |-Branch two:
% 22.66/5.88 | (1405) ~ (all_96_0_376 = all_73_6_365)
% 22.66/5.88 | (1406) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_96_0_376) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_13_13) = v0))
% 22.66/5.88 |
% 22.66/5.88 | Instantiating (1406) with all_127_0_424 yields:
% 22.66/5.88 | (1407) ( ~ (all_127_0_424 = 0) & apply(all_0_15_15, all_73_7_366, all_96_0_376) = all_127_0_424) | ( ~ (all_127_0_424 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_127_0_424) | ( ~ (all_127_0_424 = 0) & member(all_73_7_366, all_0_13_13) = all_127_0_424)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1248), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1285), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.88 |
% 22.66/5.88 +-Applying beta-rule and splitting (1286), into two cases.
% 22.66/5.88 |-Branch one:
% 22.66/5.88 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Applying alpha-rule on (1287) yields:
% 22.66/5.88 | (1288) all_88_0_372 = 0
% 22.66/5.88 | (1289) all_88_1_373 = 0
% 22.66/5.88 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 22.66/5.88 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.88 |
% 22.66/5.88 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_102_0_377 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_377, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.88 | (1357) all_102_0_377 = 0
% 22.66/5.88 |
% 22.66/5.89 | Equations (1357) can reduce 1337 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1294) yields:
% 22.66/5.89 | (1295) all_88_2_374 = 0
% 22.66/5.89 | (1296) all_88_3_375 = 0
% 22.66/5.89 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 22.66/5.89 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.89 |
% 22.66/5.89 +-Applying beta-rule and splitting (1407), into two cases.
% 22.66/5.89 |-Branch one:
% 22.66/5.89 | (1422) ( ~ (all_127_0_424 = 0) & apply(all_0_15_15, all_73_7_366, all_96_0_376) = all_127_0_424) | ( ~ (all_127_0_424 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_127_0_424)
% 22.66/5.89 |
% 22.66/5.89 +-Applying beta-rule and splitting (1422), into two cases.
% 22.66/5.89 |-Branch one:
% 22.66/5.89 | (1423) ~ (all_127_0_424 = 0) & apply(all_0_15_15, all_73_7_366, all_96_0_376) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1423) yields:
% 22.66/5.89 | (1424) ~ (all_127_0_424 = 0)
% 22.66/5.89 | (1425) apply(all_0_15_15, all_73_7_366, all_96_0_376) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_96_0_376, all_127_0_424, 0 and discharging atoms apply(all_0_15_15, all_73_7_366, all_96_0_376) = all_127_0_424, apply(all_0_15_15, all_73_7_366, all_96_0_376) = 0, yields:
% 22.66/5.89 | (1426) all_127_0_424 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1426) can reduce 1424 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1428) ~ (all_127_0_424 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1428) yields:
% 22.66/5.89 | (1424) ~ (all_127_0_424 = 0)
% 22.66/5.89 | (1430) apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_6_365, 0, all_127_0_424 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_127_0_424, apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.89 | (1426) all_127_0_424 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1426) can reduce 1424 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1433) ~ (all_127_0_424 = 0) & member(all_73_7_366, all_0_13_13) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1433) yields:
% 22.66/5.89 | (1424) ~ (all_127_0_424 = 0)
% 22.66/5.89 | (1435) member(all_73_7_366, all_0_13_13) = all_127_0_424
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_7_366, all_0_13_13, 0, all_127_0_424 and discharging atoms member(all_73_7_366, all_0_13_13) = all_127_0_424, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1426) all_127_0_424 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1426) can reduce 1424 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1315) yields:
% 22.66/5.89 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.89 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 22.66/5.89 | (1296) all_88_3_375 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1296) can reduce 1316 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1320) yields:
% 22.66/5.89 | (1316) ~ (all_88_3_375 = 0)
% 22.66/5.89 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.89 | (1296) all_88_3_375 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1296) can reduce 1316 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1448) ~ (all_102_0_377 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_377
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1448) yields:
% 22.66/5.89 | (1337) ~ (all_102_0_377 = 0)
% 22.66/5.89 | (1450) apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_377
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_6_365, 0, all_102_0_377 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_377, apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.89 | (1357) all_102_0_377 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1357) can reduce 1337 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1453) ~ (all_102_0_377 = 0) & member(all_73_7_366, all_0_13_13) = all_102_0_377
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1453) yields:
% 22.66/5.89 | (1337) ~ (all_102_0_377 = 0)
% 22.66/5.89 | (1455) member(all_73_7_366, all_0_13_13) = all_102_0_377
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_7_366, all_0_13_13, 0, all_102_0_377 and discharging atoms member(all_73_7_366, all_0_13_13) = all_102_0_377, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1357) all_102_0_377 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1357) can reduce 1337 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1458) ~ (all_87_3_371 = 0) & member(all_73_6_365, all_0_11_11) = all_87_3_371
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1458) yields:
% 22.66/5.89 | (1459) ~ (all_87_3_371 = 0)
% 22.66/5.89 | (1460) member(all_73_6_365, all_0_11_11) = all_87_3_371
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_6_365, all_0_11_11, all_87_3_371, 0 and discharging atoms member(all_73_6_365, all_0_11_11) = all_87_3_371, member(all_73_6_365, all_0_11_11) = 0, yields:
% 22.66/5.89 | (1332) all_87_3_371 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1332) can reduce 1459 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1463) ~ (all_87_3_371 = 0) & member(all_73_7_366, all_0_10_10) = all_87_3_371
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1463) yields:
% 22.66/5.89 | (1459) ~ (all_87_3_371 = 0)
% 22.66/5.89 | (1465) member(all_73_7_366, all_0_10_10) = all_87_3_371
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_87_3_371, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_87_3_371, member(all_73_7_366, all_0_10_10) = 0, yields:
% 22.66/5.89 | (1332) all_87_3_371 = 0
% 22.66/5.89 |
% 22.66/5.89 | Equations (1332) can reduce 1459 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1468) all_86_0_367 = 0 & member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1468) yields:
% 22.66/5.89 | (1250) all_86_0_367 = 0
% 22.66/5.89 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (98) with all_73_5_364, all_73_6_365, all_73_7_366, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1471) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0))
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (182) with all_73_7_366, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1472) ? [v0] : (apply(all_0_16_16, all_73_7_366, v0) = 0 & member(v0, all_0_11_11) = 0)
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (1222) with all_73_5_364, all_73_6_365, all_73_7_366 and discharging atoms member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1473) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 22.66/5.89 |
% 22.66/5.89 | Instantiating formula (1222) with all_73_6_365, all_73_5_364, all_73_7_366 and discharging atoms member(all_73_5_364, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.89 | (1474) all_73_5_364 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 22.66/5.89 |
% 22.66/5.89 | Instantiating (1472) with all_96_0_462 yields:
% 22.66/5.89 | (1475) apply(all_0_16_16, all_73_7_366, all_96_0_462) = 0 & member(all_96_0_462, all_0_11_11) = 0
% 22.66/5.89 |
% 22.66/5.89 | Applying alpha-rule on (1475) yields:
% 22.66/5.89 | (1476) apply(all_0_16_16, all_73_7_366, all_96_0_462) = 0
% 22.66/5.89 | (1477) member(all_96_0_462, all_0_11_11) = 0
% 22.66/5.89 |
% 22.66/5.89 +-Applying beta-rule and splitting (1473), into two cases.
% 22.66/5.89 |-Branch one:
% 22.66/5.89 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.89 |
% 22.66/5.89 | Equations (1259) can reduce 1232 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.89 | (1481) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 22.66/5.89 |
% 22.66/5.89 | Instantiating (1481) with all_102_0_463 yields:
% 22.66/5.89 | (1482) ( ~ (all_102_0_463 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463) | ( ~ (all_102_0_463 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463) | ( ~ (all_102_0_463 = 0) & member(all_73_7_366, all_0_12_12) = all_102_0_463)
% 22.66/5.89 |
% 22.66/5.89 +-Applying beta-rule and splitting (1474), into two cases.
% 22.66/5.89 |-Branch one:
% 22.66/5.89 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.89 |
% 22.66/5.89 | Equations (1259) can reduce 1232 to:
% 22.66/5.89 | (225) $false
% 22.66/5.89 |
% 22.66/5.89 |-The branch is then unsatisfiable
% 22.66/5.89 |-Branch two:
% 22.66/5.89 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.89 | (1486) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 22.66/5.90 |
% 22.66/5.90 | Instantiating (1486) with all_106_0_464 yields:
% 22.66/5.90 | (1487) ( ~ (all_106_0_464 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_464) | ( ~ (all_106_0_464 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_464) | ( ~ (all_106_0_464 = 0) & member(all_73_7_366, all_0_12_12) = all_106_0_464)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1471), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1259) all_73_5_364 = all_73_6_365
% 22.66/5.90 |
% 22.66/5.90 | Equations (1259) can reduce 1232 to:
% 22.66/5.90 | (225) $false
% 22.66/5.90 |
% 22.66/5.90 |-The branch is then unsatisfiable
% 22.66/5.90 |-Branch two:
% 22.66/5.90 | (1232) ~ (all_73_5_364 = all_73_6_365)
% 22.66/5.90 | (1491) ? [v0] : (( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = v0))
% 22.66/5.90 |
% 22.66/5.90 | Instantiating (1491) with all_110_0_465 yields:
% 22.66/5.90 | (1492) ( ~ (all_110_0_465 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_110_0_465) | ( ~ (all_110_0_465 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_110_0_465)
% 22.66/5.90 |
% 22.66/5.90 | Instantiating formula (1222) with all_73_6_365, all_96_0_462, all_73_7_366 and discharging atoms member(all_96_0_462, all_0_11_11) = 0, member(all_73_6_365, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 22.66/5.90 | (1493) all_96_0_462 = all_73_6_365 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_96_0_462) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1247), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1275) (all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_87_3_371 = 0) & member(all_73_6_365, all_0_11_11) = all_87_3_371)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1275), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1276) (all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1276), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1277) all_87_0_368 = 0 & all_87_1_369 = 0 & apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1277) yields:
% 22.66/5.90 | (1278) all_87_0_368 = 0
% 22.66/5.90 | (1279) all_87_1_369 = 0
% 22.66/5.90 | (1280) apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0
% 22.66/5.90 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1487), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1501) ( ~ (all_106_0_464 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_464) | ( ~ (all_106_0_464 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_464)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1501), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1502) ~ (all_106_0_464 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_464
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1502) yields:
% 22.66/5.90 | (1503) ~ (all_106_0_464 = 0)
% 22.66/5.90 | (1504) apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_464
% 22.66/5.90 |
% 22.66/5.90 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_6_365, 0, all_106_0_464 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_106_0_464, apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.90 | (1505) all_106_0_464 = 0
% 22.66/5.90 |
% 22.66/5.90 | Equations (1505) can reduce 1503 to:
% 22.66/5.90 | (225) $false
% 22.66/5.90 |
% 22.66/5.90 |-The branch is then unsatisfiable
% 22.66/5.90 |-Branch two:
% 22.66/5.90 | (1507) ~ (all_106_0_464 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_464
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1507) yields:
% 22.66/5.90 | (1503) ~ (all_106_0_464 = 0)
% 22.66/5.90 | (1509) apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_464
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1248), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1285), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1286), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1287) yields:
% 22.66/5.90 | (1288) all_88_0_372 = 0
% 22.66/5.90 | (1289) all_88_1_373 = 0
% 22.66/5.90 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 22.66/5.90 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1482), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1517) ( ~ (all_102_0_463 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463) | ( ~ (all_102_0_463 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463)
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1517), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1518) ~ (all_102_0_463 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1518) yields:
% 22.66/5.90 | (1519) ~ (all_102_0_463 = 0)
% 22.66/5.90 | (1520) apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463
% 22.66/5.90 |
% 22.66/5.90 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_102_0_463 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 22.66/5.90 | (1521) all_102_0_463 = 0
% 22.66/5.90 |
% 22.66/5.90 | Equations (1521) can reduce 1519 to:
% 22.66/5.90 | (225) $false
% 22.66/5.90 |
% 22.66/5.90 |-The branch is then unsatisfiable
% 22.66/5.90 |-Branch two:
% 22.66/5.90 | (1523) ~ (all_102_0_463 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463
% 22.66/5.90 |
% 22.66/5.90 | Applying alpha-rule on (1523) yields:
% 22.66/5.90 | (1519) ~ (all_102_0_463 = 0)
% 22.66/5.90 | (1525) apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463
% 22.66/5.90 |
% 22.66/5.90 +-Applying beta-rule and splitting (1493), into two cases.
% 22.66/5.90 |-Branch one:
% 22.66/5.90 | (1526) all_96_0_462 = all_73_6_365
% 22.66/5.90 |
% 22.66/5.90 | From (1526) and (1476) follows:
% 22.66/5.90 | (1333) apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0
% 22.66/5.90 |
% 22.66/5.90 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_6_365, 0, all_102_0_463 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463, apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0, yields:
% 22.66/5.90 | (1521) all_102_0_463 = 0
% 22.66/5.90 |
% 22.66/5.90 | Equations (1521) can reduce 1519 to:
% 22.66/5.90 | (225) $false
% 22.66/5.90 |
% 22.66/5.90 |-The branch is then unsatisfiable
% 22.66/5.90 |-Branch two:
% 22.66/5.90 | (1530) ~ (all_96_0_462 = all_73_6_365)
% 22.66/5.90 | (1531) ? [v0] : (( ~ (v0 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = v0) | ( ~ (v0 = 0) & apply(all_0_16_16, all_73_7_366, all_96_0_462) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_12_12) = v0))
% 23.04/5.90 |
% 23.04/5.90 | Instantiating (1531) with all_141_0_497 yields:
% 23.04/5.90 | (1532) ( ~ (all_141_0_497 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_141_0_497) | ( ~ (all_141_0_497 = 0) & apply(all_0_16_16, all_73_7_366, all_96_0_462) = all_141_0_497) | ( ~ (all_141_0_497 = 0) & member(all_73_7_366, all_0_12_12) = all_141_0_497)
% 23.04/5.90 |
% 23.04/5.90 +-Applying beta-rule and splitting (1532), into two cases.
% 23.04/5.90 |-Branch one:
% 23.04/5.90 | (1533) ( ~ (all_141_0_497 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_141_0_497) | ( ~ (all_141_0_497 = 0) & apply(all_0_16_16, all_73_7_366, all_96_0_462) = all_141_0_497)
% 23.04/5.90 |
% 23.04/5.90 +-Applying beta-rule and splitting (1533), into two cases.
% 23.04/5.90 |-Branch one:
% 23.04/5.90 | (1534) ~ (all_141_0_497 = 0) & apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Applying alpha-rule on (1534) yields:
% 23.04/5.90 | (1535) ~ (all_141_0_497 = 0)
% 23.04/5.90 | (1536) apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_6_365, 0, all_141_0_497 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_6_365) = all_141_0_497, apply(all_0_15_15, all_73_7_366, all_73_6_365) = 0, yields:
% 23.04/5.90 | (1537) all_141_0_497 = 0
% 23.04/5.90 |
% 23.04/5.90 | Equations (1537) can reduce 1535 to:
% 23.04/5.90 | (225) $false
% 23.04/5.90 |
% 23.04/5.90 |-The branch is then unsatisfiable
% 23.04/5.90 |-Branch two:
% 23.04/5.90 | (1539) ~ (all_141_0_497 = 0) & apply(all_0_16_16, all_73_7_366, all_96_0_462) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Applying alpha-rule on (1539) yields:
% 23.04/5.90 | (1535) ~ (all_141_0_497 = 0)
% 23.04/5.90 | (1541) apply(all_0_16_16, all_73_7_366, all_96_0_462) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_96_0_462, all_141_0_497, 0 and discharging atoms apply(all_0_16_16, all_73_7_366, all_96_0_462) = all_141_0_497, apply(all_0_16_16, all_73_7_366, all_96_0_462) = 0, yields:
% 23.04/5.90 | (1537) all_141_0_497 = 0
% 23.04/5.90 |
% 23.04/5.90 | Equations (1537) can reduce 1535 to:
% 23.04/5.90 | (225) $false
% 23.04/5.90 |
% 23.04/5.90 |-The branch is then unsatisfiable
% 23.04/5.90 |-Branch two:
% 23.04/5.90 | (1544) ~ (all_141_0_497 = 0) & member(all_73_7_366, all_0_12_12) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Applying alpha-rule on (1544) yields:
% 23.04/5.90 | (1535) ~ (all_141_0_497 = 0)
% 23.04/5.90 | (1546) member(all_73_7_366, all_0_12_12) = all_141_0_497
% 23.04/5.90 |
% 23.04/5.90 | Instantiating formula (132) with all_73_7_366, all_0_12_12, 0, all_141_0_497 and discharging atoms member(all_73_7_366, all_0_12_12) = all_141_0_497, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.90 | (1537) all_141_0_497 = 0
% 23.04/5.90 |
% 23.04/5.90 | Equations (1537) can reduce 1535 to:
% 23.04/5.90 | (225) $false
% 23.04/5.90 |
% 23.04/5.90 |-The branch is then unsatisfiable
% 23.04/5.90 |-Branch two:
% 23.04/5.90 | (1549) ~ (all_102_0_463 = 0) & member(all_73_7_366, all_0_12_12) = all_102_0_463
% 23.04/5.90 |
% 23.04/5.90 | Applying alpha-rule on (1549) yields:
% 23.04/5.90 | (1519) ~ (all_102_0_463 = 0)
% 23.04/5.90 | (1551) member(all_73_7_366, all_0_12_12) = all_102_0_463
% 23.04/5.90 |
% 23.04/5.90 | Instantiating formula (132) with all_73_7_366, all_0_12_12, 0, all_102_0_463 and discharging atoms member(all_73_7_366, all_0_12_12) = all_102_0_463, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.90 | (1521) all_102_0_463 = 0
% 23.04/5.90 |
% 23.04/5.91 | Equations (1521) can reduce 1519 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1294) yields:
% 23.04/5.91 | (1295) all_88_2_374 = 0
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 23.04/5.91 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_5_364, 0, all_106_0_464 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_106_0_464, apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0, yields:
% 23.04/5.91 | (1505) all_106_0_464 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1505) can reduce 1503 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1315) yields:
% 23.04/5.91 | (1316) ~ (all_88_3_375 = 0)
% 23.04/5.91 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1296) can reduce 1316 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1320) yields:
% 23.04/5.91 | (1316) ~ (all_88_3_375 = 0)
% 23.04/5.91 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1296) can reduce 1316 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1571) ~ (all_106_0_464 = 0) & member(all_73_7_366, all_0_12_12) = all_106_0_464
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1571) yields:
% 23.04/5.91 | (1503) ~ (all_106_0_464 = 0)
% 23.04/5.91 | (1573) member(all_73_7_366, all_0_12_12) = all_106_0_464
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_7_366, all_0_12_12, 0, all_106_0_464 and discharging atoms member(all_73_7_366, all_0_12_12) = all_106_0_464, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.91 | (1505) all_106_0_464 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1505) can reduce 1503 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1330) all_87_2_370 = 0 & all_87_3_371 = 0 & apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1330) yields:
% 23.04/5.91 | (1331) all_87_2_370 = 0
% 23.04/5.91 | (1332) all_87_3_371 = 0
% 23.04/5.91 | (1333) apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0
% 23.04/5.91 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1492), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1581) ~ (all_110_0_465 = 0) & apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_110_0_465
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1581) yields:
% 23.04/5.91 | (1582) ~ (all_110_0_465 = 0)
% 23.04/5.91 | (1583) apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_110_0_465
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1248), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1285) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375)
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1285), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1286) (all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1286), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1287) all_88_0_372 = 0 & all_88_1_373 = 0 & apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_12_12) = 0
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1287) yields:
% 23.04/5.91 | (1288) all_88_0_372 = 0
% 23.04/5.91 | (1289) all_88_1_373 = 0
% 23.04/5.91 | (1290) apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0
% 23.04/5.91 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1482), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1517) ( ~ (all_102_0_463 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463) | ( ~ (all_102_0_463 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463)
% 23.04/5.91 |
% 23.04/5.91 +-Applying beta-rule and splitting (1517), into two cases.
% 23.04/5.91 |-Branch one:
% 23.04/5.91 | (1518) ~ (all_102_0_463 = 0) & apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1518) yields:
% 23.04/5.91 | (1519) ~ (all_102_0_463 = 0)
% 23.04/5.91 | (1520) apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (96) with all_0_15_15, all_73_7_366, all_73_5_364, 0, all_102_0_463 and discharging atoms apply(all_0_15_15, all_73_7_366, all_73_5_364) = all_102_0_463, apply(all_0_15_15, all_73_7_366, all_73_5_364) = 0, yields:
% 23.04/5.91 | (1521) all_102_0_463 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1521) can reduce 1519 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1523) ~ (all_102_0_463 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1523) yields:
% 23.04/5.91 | (1519) ~ (all_102_0_463 = 0)
% 23.04/5.91 | (1525) apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_6_365, 0, all_102_0_463 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_102_0_463, apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0, yields:
% 23.04/5.91 | (1521) all_102_0_463 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1521) can reduce 1519 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1549) ~ (all_102_0_463 = 0) & member(all_73_7_366, all_0_12_12) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1549) yields:
% 23.04/5.91 | (1519) ~ (all_102_0_463 = 0)
% 23.04/5.91 | (1551) member(all_73_7_366, all_0_12_12) = all_102_0_463
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_7_366, all_0_12_12, 0, all_102_0_463 and discharging atoms member(all_73_7_366, all_0_12_12) = all_102_0_463, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.91 | (1521) all_102_0_463 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1521) can reduce 1519 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1294) all_88_2_374 = 0 & all_88_3_375 = 0 & apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0 & member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1294) yields:
% 23.04/5.91 | (1295) all_88_2_374 = 0
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 | (1297) apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0
% 23.04/5.91 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_5_364, 0, all_110_0_465 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_5_364) = all_110_0_465, apply(all_0_16_16, all_73_7_366, all_73_5_364) = 0, yields:
% 23.04/5.91 | (1612) all_110_0_465 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1612) can reduce 1582 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1315) ~ (all_88_3_375 = 0) & member(all_73_5_364, all_0_11_11) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1315) yields:
% 23.04/5.91 | (1316) ~ (all_88_3_375 = 0)
% 23.04/5.91 | (1317) member(all_73_5_364, all_0_11_11) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_5_364, all_0_11_11, all_88_3_375, 0 and discharging atoms member(all_73_5_364, all_0_11_11) = all_88_3_375, member(all_73_5_364, all_0_11_11) = 0, yields:
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1296) can reduce 1316 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1320) ~ (all_88_3_375 = 0) & member(all_73_7_366, all_0_10_10) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1320) yields:
% 23.04/5.91 | (1316) ~ (all_88_3_375 = 0)
% 23.04/5.91 | (1322) member(all_73_7_366, all_0_10_10) = all_88_3_375
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_88_3_375, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_88_3_375, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.91 | (1296) all_88_3_375 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1296) can reduce 1316 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.91 |-Branch two:
% 23.04/5.91 | (1624) ~ (all_110_0_465 = 0) & apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_110_0_465
% 23.04/5.91 |
% 23.04/5.91 | Applying alpha-rule on (1624) yields:
% 23.04/5.91 | (1582) ~ (all_110_0_465 = 0)
% 23.04/5.91 | (1626) apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_110_0_465
% 23.04/5.91 |
% 23.04/5.91 | Instantiating formula (96) with all_0_16_16, all_73_7_366, all_73_6_365, 0, all_110_0_465 and discharging atoms apply(all_0_16_16, all_73_7_366, all_73_6_365) = all_110_0_465, apply(all_0_16_16, all_73_7_366, all_73_6_365) = 0, yields:
% 23.04/5.91 | (1612) all_110_0_465 = 0
% 23.04/5.91 |
% 23.04/5.91 | Equations (1612) can reduce 1582 to:
% 23.04/5.91 | (225) $false
% 23.04/5.91 |
% 23.04/5.91 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1458) ~ (all_87_3_371 = 0) & member(all_73_6_365, all_0_11_11) = all_87_3_371
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1458) yields:
% 23.04/5.92 | (1459) ~ (all_87_3_371 = 0)
% 23.04/5.92 | (1460) member(all_73_6_365, all_0_11_11) = all_87_3_371
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (132) with all_73_6_365, all_0_11_11, all_87_3_371, 0 and discharging atoms member(all_73_6_365, all_0_11_11) = all_87_3_371, member(all_73_6_365, all_0_11_11) = 0, yields:
% 23.04/5.92 | (1332) all_87_3_371 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1332) can reduce 1459 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1463) ~ (all_87_3_371 = 0) & member(all_73_7_366, all_0_10_10) = all_87_3_371
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1463) yields:
% 23.04/5.92 | (1459) ~ (all_87_3_371 = 0)
% 23.04/5.92 | (1465) member(all_73_7_366, all_0_10_10) = all_87_3_371
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_87_3_371, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_87_3_371, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.92 | (1332) all_87_3_371 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1332) can reduce 1459 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1639) all_73_6_365 = 0 & member(all_73_7_366, all_0_10_10) = 0 & ! [v0] : ( ~ (apply(all_0_14_14, all_73_7_366, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_11_11) = v1)) & ! [v0] : ( ~ (member(v0, all_0_11_11) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_14_14, all_73_7_366, v0) = v1))
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1639) yields:
% 23.04/5.92 | (1640) all_73_6_365 = 0
% 23.04/5.92 | (1234) member(all_73_7_366, all_0_10_10) = 0
% 23.04/5.92 | (1642) ! [v0] : ( ~ (apply(all_0_14_14, all_73_7_366, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_11_11) = v1))
% 23.04/5.92 | (1643) ! [v0] : ( ~ (member(v0, all_0_11_11) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_14_14, all_73_7_366, v0) = v1))
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (134) with all_0_10_10, all_0_12_12, all_0_13_13, all_73_7_366 and discharging atoms union(all_0_13_13, all_0_12_12) = all_0_10_10, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.92 | (1245) ? [v0] : ((v0 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v0 = 0 & member(all_73_7_366, all_0_13_13) = 0))
% 23.04/5.92 |
% 23.04/5.92 | Instantiating (1245) with all_87_0_531 yields:
% 23.04/5.92 | (1645) (all_87_0_531 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_87_0_531 = 0 & member(all_73_7_366, all_0_13_13) = 0)
% 23.04/5.92 |
% 23.04/5.92 +-Applying beta-rule and splitting (1645), into two cases.
% 23.04/5.92 |-Branch one:
% 23.04/5.92 | (1646) all_87_0_531 = 0 & member(all_73_7_366, all_0_12_12) = 0
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1646) yields:
% 23.04/5.92 | (1647) all_87_0_531 = 0
% 23.04/5.92 | (1251) member(all_73_7_366, all_0_12_12) = 0
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (182) with all_73_7_366, all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms maps(all_0_15_15, all_0_12_12, all_0_11_11) = 0, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.92 | (1253) ? [v0] : (apply(all_0_15_15, all_73_7_366, v0) = 0 & member(v0, all_0_11_11) = 0)
% 23.04/5.92 |
% 23.04/5.92 | Instantiating (1253) with all_95_0_532 yields:
% 23.04/5.92 | (1650) apply(all_0_15_15, all_73_7_366, all_95_0_532) = 0 & member(all_95_0_532, all_0_11_11) = 0
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1650) yields:
% 23.04/5.92 | (1651) apply(all_0_15_15, all_73_7_366, all_95_0_532) = 0
% 23.04/5.92 | (1652) member(all_95_0_532, all_0_11_11) = 0
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (168) with 0, all_95_0_532, all_73_7_366 and discharging atoms apply(all_0_15_15, all_73_7_366, all_95_0_532) = 0, yields:
% 23.04/5.92 | (1653) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_95_0_532, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_10_10) = v0) | (((v3 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v2 = 0 & v1 = 0 & apply(all_0_16_16, all_73_7_366, all_95_0_532) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0) | ( ~ (v3 = 0) & member(all_73_7_366, all_0_12_12) = v3 & (( ~ (v2 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = v2) | ( ~ (v1 = 0) & member(all_73_7_366, all_0_13_13) = v1))))))
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (1643) with all_95_0_532 and discharging atoms member(all_95_0_532, all_0_11_11) = 0, yields:
% 23.04/5.92 | (1654) ? [v0] : ( ~ (v0 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = v0)
% 23.04/5.92 |
% 23.04/5.92 | Instantiating (1654) with all_102_0_533 yields:
% 23.04/5.92 | (1655) ~ (all_102_0_533 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_102_0_533
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1655) yields:
% 23.04/5.92 | (1656) ~ (all_102_0_533 = 0)
% 23.04/5.92 | (1657) apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_102_0_533
% 23.04/5.92 |
% 23.04/5.92 | Instantiating (1653) with all_104_0_534, all_104_1_535, all_104_2_536, all_104_3_537 yields:
% 23.04/5.92 | (1658) ( ~ (all_104_3_537 = 0) & member(all_95_0_532, all_0_11_11) = all_104_3_537) | ( ~ (all_104_3_537 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_537) | (((all_104_0_534 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_1_535 = 0 & all_104_2_536 = 0 & apply(all_0_16_16, all_73_7_366, all_95_0_532) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_537 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_104_3_537)) & ((all_104_3_537 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0) | ( ~ (all_104_0_534 = 0) & member(all_73_7_366, all_0_12_12) = all_104_0_534 & (( ~ (all_104_1_535 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = all_104_1_535) | ( ~ (all_104_2_536 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_536)))))
% 23.04/5.92 |
% 23.04/5.92 +-Applying beta-rule and splitting (1658), into two cases.
% 23.04/5.92 |-Branch one:
% 23.04/5.92 | (1659) ( ~ (all_104_3_537 = 0) & member(all_95_0_532, all_0_11_11) = all_104_3_537) | ( ~ (all_104_3_537 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_537)
% 23.04/5.92 |
% 23.04/5.92 +-Applying beta-rule and splitting (1659), into two cases.
% 23.04/5.92 |-Branch one:
% 23.04/5.92 | (1660) ~ (all_104_3_537 = 0) & member(all_95_0_532, all_0_11_11) = all_104_3_537
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1660) yields:
% 23.04/5.92 | (1661) ~ (all_104_3_537 = 0)
% 23.04/5.92 | (1662) member(all_95_0_532, all_0_11_11) = all_104_3_537
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (132) with all_95_0_532, all_0_11_11, all_104_3_537, 0 and discharging atoms member(all_95_0_532, all_0_11_11) = all_104_3_537, member(all_95_0_532, all_0_11_11) = 0, yields:
% 23.04/5.92 | (1663) all_104_3_537 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1663) can reduce 1661 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1665) ~ (all_104_3_537 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_537
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1665) yields:
% 23.04/5.92 | (1661) ~ (all_104_3_537 = 0)
% 23.04/5.92 | (1667) member(all_73_7_366, all_0_10_10) = all_104_3_537
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_104_3_537, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_104_3_537, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.92 | (1663) all_104_3_537 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1663) can reduce 1661 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1670) ((all_104_0_534 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_1_535 = 0 & all_104_2_536 = 0 & apply(all_0_16_16, all_73_7_366, all_95_0_532) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_537 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_104_3_537)) & ((all_104_3_537 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0) | ( ~ (all_104_0_534 = 0) & member(all_73_7_366, all_0_12_12) = all_104_0_534 & (( ~ (all_104_1_535 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = all_104_1_535) | ( ~ (all_104_2_536 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_536))))
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1670) yields:
% 23.04/5.92 | (1671) (all_104_0_534 = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_1_535 = 0 & all_104_2_536 = 0 & apply(all_0_16_16, all_73_7_366, all_95_0_532) = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_537 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_104_3_537)
% 23.04/5.92 | (1672) (all_104_3_537 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0) | ( ~ (all_104_0_534 = 0) & member(all_73_7_366, all_0_12_12) = all_104_0_534 & (( ~ (all_104_1_535 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = all_104_1_535) | ( ~ (all_104_2_536 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_536)))
% 23.04/5.92 |
% 23.04/5.92 +-Applying beta-rule and splitting (1672), into two cases.
% 23.04/5.92 |-Branch one:
% 23.04/5.92 | (1673) all_104_3_537 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1673) yields:
% 23.04/5.92 | (1663) all_104_3_537 = 0
% 23.04/5.92 | (1675) apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (96) with all_0_14_14, all_73_7_366, all_95_0_532, 0, all_102_0_533 and discharging atoms apply(all_0_14_14, all_73_7_366, all_95_0_532) = all_102_0_533, apply(all_0_14_14, all_73_7_366, all_95_0_532) = 0, yields:
% 23.04/5.92 | (1676) all_102_0_533 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1676) can reduce 1656 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1678) ~ (all_104_0_534 = 0) & member(all_73_7_366, all_0_12_12) = all_104_0_534 & (( ~ (all_104_1_535 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = all_104_1_535) | ( ~ (all_104_2_536 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_536))
% 23.04/5.92 |
% 23.04/5.92 | Applying alpha-rule on (1678) yields:
% 23.04/5.92 | (1679) ~ (all_104_0_534 = 0)
% 23.04/5.92 | (1680) member(all_73_7_366, all_0_12_12) = all_104_0_534
% 23.04/5.92 | (1681) ( ~ (all_104_1_535 = 0) & apply(all_0_16_16, all_73_7_366, all_95_0_532) = all_104_1_535) | ( ~ (all_104_2_536 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_536)
% 23.04/5.92 |
% 23.04/5.92 | Instantiating formula (132) with all_73_7_366, all_0_12_12, all_104_0_534, 0 and discharging atoms member(all_73_7_366, all_0_12_12) = all_104_0_534, member(all_73_7_366, all_0_12_12) = 0, yields:
% 23.04/5.92 | (1682) all_104_0_534 = 0
% 23.04/5.92 |
% 23.04/5.92 | Equations (1682) can reduce 1679 to:
% 23.04/5.92 | (225) $false
% 23.04/5.92 |
% 23.04/5.92 |-The branch is then unsatisfiable
% 23.04/5.92 |-Branch two:
% 23.04/5.92 | (1684) all_87_0_531 = 0 & member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.92 |
% 23.04/5.93 | Applying alpha-rule on (1684) yields:
% 23.04/5.93 | (1647) all_87_0_531 = 0
% 23.04/5.93 | (1298) member(all_73_7_366, all_0_13_13) = 0
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (182) with all_73_7_366, all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms maps(all_0_16_16, all_0_13_13, all_0_11_11) = 0, member(all_73_7_366, all_0_13_13) = 0, yields:
% 23.04/5.93 | (1472) ? [v0] : (apply(all_0_16_16, all_73_7_366, v0) = 0 & member(v0, all_0_11_11) = 0)
% 23.04/5.93 |
% 23.04/5.93 | Instantiating (1472) with all_95_0_538 yields:
% 23.04/5.93 | (1688) apply(all_0_16_16, all_73_7_366, all_95_0_538) = 0 & member(all_95_0_538, all_0_11_11) = 0
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1688) yields:
% 23.04/5.93 | (1689) apply(all_0_16_16, all_73_7_366, all_95_0_538) = 0
% 23.04/5.93 | (1690) member(all_95_0_538, all_0_11_11) = 0
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (102) with 0, all_95_0_538, all_73_7_366 and discharging atoms apply(all_0_16_16, all_73_7_366, all_95_0_538) = 0, yields:
% 23.04/5.93 | (1691) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & member(all_95_0_538, all_0_11_11) = v0) | ( ~ (v0 = 0) & member(all_73_7_366, all_0_10_10) = v0) | (((v3 = 0 & v2 = 0 & apply(all_0_15_15, all_73_7_366, all_95_0_538) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (v1 = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (v0 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = v0)) & ((v0 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0) | ( ~ (v1 = 0) & member(all_73_7_366, all_0_13_13) = v1 & (( ~ (v3 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = v3) | ( ~ (v2 = 0) & member(all_73_7_366, all_0_12_12) = v2))))))
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (1643) with all_95_0_538 and discharging atoms member(all_95_0_538, all_0_11_11) = 0, yields:
% 23.04/5.93 | (1692) ? [v0] : ( ~ (v0 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = v0)
% 23.04/5.93 |
% 23.04/5.93 | Instantiating (1692) with all_102_0_539 yields:
% 23.04/5.93 | (1693) ~ (all_102_0_539 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_102_0_539
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1693) yields:
% 23.04/5.93 | (1694) ~ (all_102_0_539 = 0)
% 23.04/5.93 | (1695) apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_102_0_539
% 23.04/5.93 |
% 23.04/5.93 | Instantiating (1691) with all_104_0_540, all_104_1_541, all_104_2_542, all_104_3_543 yields:
% 23.04/5.93 | (1696) ( ~ (all_104_3_543 = 0) & member(all_95_0_538, all_0_11_11) = all_104_3_543) | ( ~ (all_104_3_543 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_543) | (((all_104_0_540 = 0 & all_104_1_541 = 0 & apply(all_0_15_15, all_73_7_366, all_95_0_538) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_2_542 = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_543 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_104_3_543)) & ((all_104_3_543 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0) | ( ~ (all_104_2_542 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_542 & (( ~ (all_104_0_540 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = all_104_0_540) | ( ~ (all_104_1_541 = 0) & member(all_73_7_366, all_0_12_12) = all_104_1_541)))))
% 23.04/5.93 |
% 23.04/5.93 +-Applying beta-rule and splitting (1696), into two cases.
% 23.04/5.93 |-Branch one:
% 23.04/5.93 | (1697) ( ~ (all_104_3_543 = 0) & member(all_95_0_538, all_0_11_11) = all_104_3_543) | ( ~ (all_104_3_543 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_543)
% 23.04/5.93 |
% 23.04/5.93 +-Applying beta-rule and splitting (1697), into two cases.
% 23.04/5.93 |-Branch one:
% 23.04/5.93 | (1698) ~ (all_104_3_543 = 0) & member(all_95_0_538, all_0_11_11) = all_104_3_543
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1698) yields:
% 23.04/5.93 | (1699) ~ (all_104_3_543 = 0)
% 23.04/5.93 | (1700) member(all_95_0_538, all_0_11_11) = all_104_3_543
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (132) with all_95_0_538, all_0_11_11, all_104_3_543, 0 and discharging atoms member(all_95_0_538, all_0_11_11) = all_104_3_543, member(all_95_0_538, all_0_11_11) = 0, yields:
% 23.04/5.93 | (1701) all_104_3_543 = 0
% 23.04/5.93 |
% 23.04/5.93 | Equations (1701) can reduce 1699 to:
% 23.04/5.93 | (225) $false
% 23.04/5.93 |
% 23.04/5.93 |-The branch is then unsatisfiable
% 23.04/5.93 |-Branch two:
% 23.04/5.93 | (1703) ~ (all_104_3_543 = 0) & member(all_73_7_366, all_0_10_10) = all_104_3_543
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1703) yields:
% 23.04/5.93 | (1699) ~ (all_104_3_543 = 0)
% 23.04/5.93 | (1705) member(all_73_7_366, all_0_10_10) = all_104_3_543
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (132) with all_73_7_366, all_0_10_10, all_104_3_543, 0 and discharging atoms member(all_73_7_366, all_0_10_10) = all_104_3_543, member(all_73_7_366, all_0_10_10) = 0, yields:
% 23.04/5.93 | (1701) all_104_3_543 = 0
% 23.04/5.93 |
% 23.04/5.93 | Equations (1701) can reduce 1699 to:
% 23.04/5.93 | (225) $false
% 23.04/5.93 |
% 23.04/5.93 |-The branch is then unsatisfiable
% 23.04/5.93 |-Branch two:
% 23.04/5.93 | (1708) ((all_104_0_540 = 0 & all_104_1_541 = 0 & apply(all_0_15_15, all_73_7_366, all_95_0_538) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_2_542 = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_543 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_104_3_543)) & ((all_104_3_543 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0) | ( ~ (all_104_2_542 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_542 & (( ~ (all_104_0_540 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = all_104_0_540) | ( ~ (all_104_1_541 = 0) & member(all_73_7_366, all_0_12_12) = all_104_1_541))))
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1708) yields:
% 23.04/5.93 | (1709) (all_104_0_540 = 0 & all_104_1_541 = 0 & apply(all_0_15_15, all_73_7_366, all_95_0_538) = 0 & member(all_73_7_366, all_0_12_12) = 0) | (all_104_2_542 = 0 & member(all_73_7_366, all_0_13_13) = 0) | ( ~ (all_104_3_543 = 0) & apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_104_3_543)
% 23.04/5.93 | (1710) (all_104_3_543 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0) | ( ~ (all_104_2_542 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_542 & (( ~ (all_104_0_540 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = all_104_0_540) | ( ~ (all_104_1_541 = 0) & member(all_73_7_366, all_0_12_12) = all_104_1_541)))
% 23.04/5.93 |
% 23.04/5.93 +-Applying beta-rule and splitting (1710), into two cases.
% 23.04/5.93 |-Branch one:
% 23.04/5.93 | (1711) all_104_3_543 = 0 & apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1711) yields:
% 23.04/5.93 | (1701) all_104_3_543 = 0
% 23.04/5.93 | (1713) apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (96) with all_0_14_14, all_73_7_366, all_95_0_538, 0, all_102_0_539 and discharging atoms apply(all_0_14_14, all_73_7_366, all_95_0_538) = all_102_0_539, apply(all_0_14_14, all_73_7_366, all_95_0_538) = 0, yields:
% 23.04/5.93 | (1714) all_102_0_539 = 0
% 23.04/5.93 |
% 23.04/5.93 | Equations (1714) can reduce 1694 to:
% 23.04/5.93 | (225) $false
% 23.04/5.93 |
% 23.04/5.93 |-The branch is then unsatisfiable
% 23.04/5.93 |-Branch two:
% 23.04/5.93 | (1716) ~ (all_104_2_542 = 0) & member(all_73_7_366, all_0_13_13) = all_104_2_542 & (( ~ (all_104_0_540 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = all_104_0_540) | ( ~ (all_104_1_541 = 0) & member(all_73_7_366, all_0_12_12) = all_104_1_541))
% 23.04/5.93 |
% 23.04/5.93 | Applying alpha-rule on (1716) yields:
% 23.04/5.93 | (1717) ~ (all_104_2_542 = 0)
% 23.04/5.93 | (1718) member(all_73_7_366, all_0_13_13) = all_104_2_542
% 23.04/5.93 | (1719) ( ~ (all_104_0_540 = 0) & apply(all_0_15_15, all_73_7_366, all_95_0_538) = all_104_0_540) | ( ~ (all_104_1_541 = 0) & member(all_73_7_366, all_0_12_12) = all_104_1_541)
% 23.04/5.93 |
% 23.04/5.93 | Instantiating formula (132) with all_73_7_366, all_0_13_13, all_104_2_542, 0 and discharging atoms member(all_73_7_366, all_0_13_13) = all_104_2_542, member(all_73_7_366, all_0_13_13) = 0, yields:
% 23.04/5.93 | (1720) all_104_2_542 = 0
% 23.04/5.93 |
% 23.04/5.93 | Equations (1720) can reduce 1717 to:
% 23.04/5.93 | (225) $false
% 23.04/5.93 |
% 23.04/5.93 |-The branch is then unsatisfiable
% 23.04/5.93 % SZS output end Proof for theBenchmark
% 23.04/5.93
% 23.04/5.93 5336ms
%------------------------------------------------------------------------------