TSTP Solution File: SET729+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET729+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 00:21:41 EDT 2022
% Result : Theorem 54.84s 25.41s
% Output : Proof 295.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET729+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 11:46:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.66/0.64 ____ _
% 0.66/0.64 ___ / __ \_____(_)___ ________ __________
% 0.66/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.66/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.66/0.64
% 0.66/0.64 A Theorem Prover for First-Order Logic
% 0.66/0.64 (ePrincess v.1.0)
% 0.66/0.64
% 0.66/0.64 (c) Philipp Rümmer, 2009-2015
% 0.66/0.64 (c) Peter Backeman, 2014-2015
% 0.66/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.64 Bug reports to peter@backeman.se
% 0.66/0.64
% 0.66/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.64
% 0.66/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.83/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.16/1.09 Prover 0: Preprocessing ...
% 3.36/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.78/1.49 Prover 0: Constructing countermodel ...
% 4.70/1.72 Prover 0: gave up
% 4.70/1.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.70/1.78 Prover 1: Preprocessing ...
% 6.09/2.02 Prover 1: Constructing countermodel ...
% 6.09/2.07 Prover 1: gave up
% 6.09/2.07 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.57/2.11 Prover 2: Preprocessing ...
% 7.49/2.39 Prover 2: Warning: ignoring some quantifiers
% 7.89/2.41 Prover 2: Constructing countermodel ...
% 15.32/4.26 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.76/4.32 Prover 3: Preprocessing ...
% 15.85/4.40 Prover 3: Warning: ignoring some quantifiers
% 15.85/4.41 Prover 3: Constructing countermodel ...
% 16.29/4.48 Prover 3: gave up
% 16.29/4.48 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 16.61/4.51 Prover 4: Preprocessing ...
% 17.59/4.75 Prover 4: Warning: ignoring some quantifiers
% 17.59/4.77 Prover 4: Constructing countermodel ...
% 20.62/5.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.94/5.55 Prover 5: Preprocessing ...
% 21.88/5.73 Prover 5: Constructing countermodel ...
% 47.24/20.92 Prover 5: stopped
% 47.76/21.12 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 47.76/21.17 Prover 6: Preprocessing ...
% 48.50/21.33 Prover 6: Warning: ignoring some quantifiers
% 48.50/21.34 Prover 6: Constructing countermodel ...
% 54.84/25.41 Prover 6: proved (4282ms)
% 54.84/25.41 Prover 4: stopped
% 54.84/25.41 Prover 2: stopped
% 54.84/25.41
% 54.84/25.41 No countermodel exists, formula is valid
% 54.84/25.41 % SZS status Theorem for theBenchmark
% 54.84/25.41
% 54.84/25.41 Generating proof ... Warning: ignoring some quantifiers
% 293.49/235.40 found it (size 1049)
% 293.49/235.40
% 293.49/235.40 % SZS output start Proof for theBenchmark
% 293.49/235.40 Assumed formulas after preprocessing and simplification:
% 293.49/235.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (identity(v4, v1) = v5 & compose_function(v0, v0, v1, v1, v1) = v4 & maps(v0, v1, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = 0) | ~ (apply(v8, v11, v13) = v15) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v14, v12) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v8, v11, v13) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v11, v13) = v16) | ( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (apply(v7, v11, v15) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v15, v12) = v16) | ( ~ (v16 = 0) & member(v15, v9) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (apply(v6, v15, v12) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v11, v15) = v16) | ( ~ (v16 = 0) & member(v15, v9) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = v14) | ~ (member(v15, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v11, v15) = v16) | ( ~ (v16 = 0) & apply(v6, v15, v12) = v16) | ( ~ (v16 = 0) & member(v12, v10) = v16) | ( ~ (v16 = 0) & member(v11, v8) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v8, v12, v15) = 0) | ~ (apply(v6, v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v7, v15, v13) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v7, v15, v13) = 0) | ~ (apply(v6, v12, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v12, v15) = v16) | ( ~ (v16 = 0) & member(v15, v10) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v6, v12, v13) = v14) | ~ (member(v15, v10) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v8, v12, v15) = v16) | ( ~ (v16 = 0) & apply(v7, v15, v13) = v16) | ( ~ (v16 = 0) & member(v13, v11) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v13, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v10, v12, v14) = v15) | ~ (member(v13, v7) = 0) | ~ (member(v11, v7) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v8, v11, v13) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v8, v11, v13) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v14, v9) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v12, v9) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = v15) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v16] : (( ~ (v16 = 0) & apply(v6, v13, v14) = v16) | ( ~ (v16 = 0) & apply(v6, v11, v12) = v16) | ( ~ (v16 = 0) & member(v13, v7) = v16) | ( ~ (v16 = 0) & member(v11, v7) = v16) | (( ~ (v15 = 0) | (v16 = 0 & apply(v10, v12, v14) = 0)) & (v15 = 0 | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | (((v16 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15)) & ((v15 = 0 & apply(v8, v11, v13) = 0) | ( ~ (v16 = 0) & apply(v10, v12, v14) = v16))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (decreasing(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v14, v12) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v8, v11, v13) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v12, v9) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (apply(v6, v11, v12) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v13, v14) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15) | ( ~ (v15 = 0) & member(v14, v9) = v15) | ( ~ (v15 = 0) & member(v13, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (apply(v6, v11, v12) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & member(v12, v9) = v15) | ( ~ (v15 = 0) & member(v11, v7) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (increasing(v6, v7, v8, v9, v10) = 0) | ~ (member(v14, v9) = 0) | ~ (member(v13, v7) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v7) = 0) | ? [v15] : ((v15 = 0 & apply(v10, v12, v14) = 0) | ( ~ (v15 = 0) & apply(v8, v11, v13) = v15) | ( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ~ (v15 = 0) & apply(v6, v11, v12) = v15))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v7 = v6 | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v7) | ~ (compose_predicate(v13, v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_function(v6, v7, v8, v9, v10) = v13) | ~ (apply(v13, v11, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v7, v11, v14) = 0 & apply(v6, v14, v12) = 0 & member(v14, v9) = 0) | ( ~ (v14 = 0) & member(v12, v10) = v14) | ( ~ (v14 = 0) & member(v11, v8) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = 0) | ~ (apply(v6, v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & apply(v8, v12, v14) = 0 & apply(v7, v14, v13) = 0 & member(v14, v10) = 0) | ( ~ (v14 = 0) & member(v13, v11) = v14) | ( ~ (v14 = 0) & member(v12, v9) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (apply(v6, v10, v11) = 0) | ? [v13] : (( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v12) = 0) | ~ (member(v11, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v10, v11) = v13) | ( ~ (v13 = 0) & member(v12, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (member(v12, v9) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (equal_maps(v6, v7, v8, v9) = 0) | ~ (member(v12, v9) = 0) | ~ (member(v11, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : (( ~ (v13 = 0) & apply(v7, v10, v12) = v13) | ( ~ (v13 = 0) & apply(v6, v10, v11) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (compose_predicate(v6, v7, v8, v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (member(v14, v11) = 0 & member(v13, v9) = 0 & ((v19 = 0 & v18 = 0 & v17 = 0 & apply(v8, v13, v16) = 0 & apply(v7, v16, v14) = 0 & member(v16, v10) = 0) | (v15 = 0 & apply(v6, v13, v14) = 0)) & (( ~ (v15 = 0) & apply(v6, v13, v14) = v15) | ( ! [v20] : ( ~ (apply(v8, v13, v20) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v7, v20, v14) = v21) | ( ~ (v21 = 0) & member(v20, v10) = v21))) & ! [v20] : ( ~ (apply(v7, v20, v14) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v8, v13, v20) = v21) | ( ~ (v21 = 0) & member(v20, v10) = v21))) & ! [v20] : ( ~ (member(v20, v10) = 0) | ? [v21] : (( ~ (v21 = 0) & apply(v8, v13, v20) = v21) | ( ~ (v21 = 0) & apply(v7, v20, v14) = v21))))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image3(v6, v7, v8) = v10) | ~ (apply(v6, v9, v12) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v12, v7) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v9, v12) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image3(v6, v7, v8) = v10) | ~ (apply(v6, v12, v9) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & member(v12, v7) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (image3(v6, v7, v8) = v10) | ~ (member(v12, v7) = 0) | ~ (member(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & apply(v6, v12, v9) = v13) | ( ~ (v13 = 0) & member(v9, v8) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (isomorphism(v12, v11, v10, v9, v8) = v7) | ~ (isomorphism(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (decreasing(v12, v11, v10, v9, v8) = v7) | ~ (decreasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (increasing(v12, v11, v10, v9, v8) = v7) | ~ (increasing(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v7 = v6 | ~ (compose_function(v12, v11, v10, v9, v8) = v7) | ~ (compose_function(v12, v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_function(v6, v7, v8) = v11) | ~ (apply(v11, v10, v9) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v10, v8) = v13) | ( ~ (v13 = 0) & member(v9, v7) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v6, v9, v10) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v6, v9, v10) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_predicate(v6, v7, v8, v9) = 0) | ~ (apply(v7, v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v6, v11, v10) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v6, v11, v10) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (inverse_predicate(v6, v7, v8, v9) = 0) | ~ (apply(v6, v11, v10) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v11, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13) | (( ~ (v12 = 0) | (v13 = 0 & apply(v7, v10, v11) = 0)) & (v12 = 0 | ( ~ (v13 = 0) & apply(v7, v10, v11) = v13))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (apply(v6, v9, v10) = 0) | ? [v12] : (( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (member(v10, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v10) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (apply(v6, v9, v10) = 0) | ~ (member(v11, v8) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & member(v10, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (maps(v6, v7, v8) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & apply(v6, v9, v10) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (isomorphism(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v21 = 0 & v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0 & ((v23 = 0 & apply(v10, v13, v15) = 0) | (v22 = 0 & apply(v8, v12, v14) = 0)) & (( ~ (v23 = 0) & apply(v10, v13, v15) = v23) | ( ~ (v22 = 0) & apply(v8, v12, v14) = v22))) | ( ~ (v12 = 0) & one_to_one(v6, v7, v9) = v12) | ( ~ (v12 = 0) & maps(v6, v7, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (decreasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v15, v13) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (increasing(v6, v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & apply(v10, v13, v15) = v16 & apply(v8, v12, v14) = 0 & apply(v6, v14, v15) = 0 & apply(v6, v12, v13) = 0 & member(v15, v9) = 0 & member(v14, v7) = 0 & member(v13, v9) = 0 & member(v12, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (apply(v6, v9, v11) = 0) | ? [v12] : (( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v7) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v10, v11) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v9, v11) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v10, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (apply(v6, v9, v11) = 0) | ~ (member(v10, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v10, v11) = v12) | ( ~ (v12 = 0) & member(v11, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (injective(v6, v7, v8) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v7) = 0) | ~ (member(v9, v7) = 0) | ? [v12] : (( ~ (v12 = 0) & apply(v6, v10, v11) = v12) | ( ~ (v12 = 0) & apply(v6, v9, v11) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image2(v6, v7) = v9) | ~ (apply(v6, v8, v11) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (inverse_image2(v6, v7) = v9) | ~ (member(v11, v7) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v8, v11) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image2(v6, v7) = v9) | ~ (apply(v6, v11, v8) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (image2(v6, v7) = v9) | ~ (member(v11, v7) = 0) | ~ (member(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v11, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (inverse_predicate(v11, v10, v9, v8) = v7) | ~ (inverse_predicate(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (equal_maps(v11, v10, v9, v8) = v7) | ~ (equal_maps(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (inverse_predicate(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (member(v12, v9) = 0 & member(v11, v8) = 0 & ((v14 = 0 & apply(v6, v12, v11) = 0) | (v13 = 0 & apply(v7, v11, v12) = 0)) & (( ~ (v14 = 0) & apply(v6, v12, v11) = v14) | ( ~ (v13 = 0) & apply(v7, v11, v12) = v13)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_maps(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v12) & apply(v7, v11, v13) = 0 & apply(v6, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v9) = v10) | ~ (member(v6, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ((v11 = 0 & member(v6, v7) = 0) | ( ~ (v11 = 0) & member(v6, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ~ (v11 = 0) & member(v6, v8) = v12 & member(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & member(v6, v8) = v11) | ( ~ (v11 = 0) & member(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sum(v7) = v8) | ~ (member(v10, v7) = 0) | ~ (member(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (sum(v7) = v8) | ~ (member(v6, v10) = 0) | ~ (member(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_image3(v10, v9, v8) = v7) | ~ (inverse_image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (image3(v10, v9, v8) = v7) | ~ (image3(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (inverse_function(v10, v9, v8) = v7) | ~ (inverse_function(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (one_to_one(v10, v9, v8) = v7) | ~ (one_to_one(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (surjective(v10, v9, v8) = v7) | ~ (surjective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (injective(v10, v9, v8) = v7) | ~ (injective(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (maps(v10, v9, v8) = v7) | ~ (maps(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (apply(v10, v9, v8) = v7) | ~ (apply(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (isomorphism(v6, v7, v8, v9, v10) = 0) | (one_to_one(v6, v7, v9) = 0 & maps(v6, v7, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inverse_image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v9, v11) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | member(v9, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image3(v6, v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : (apply(v6, v11, v9) = 0 & member(v11, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (one_to_one(v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & surjective(v6, v7, v8) = v10) | ( ~ (v10 = 0) & injective(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (surjective(v6, v7, v8) = v9) | ? [v10] : (member(v10, v8) = 0 & ! [v11] : ( ~ (apply(v6, v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v11, v7) = v12)) & ! [v11] : ( ~ (member(v11, v7) = 0) | ? [v12] : ( ~ (v12 = 0) & apply(v6, v11, v10) = v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (injective(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v11 = v10) & apply(v6, v11, v12) = 0 & apply(v6, v10, v12) = 0 & member(v12, v8) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (identity(v6, v7) = 0) | ~ (apply(v6, v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (maps(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v12 = v11) & apply(v6, v10, v12) = 0 & apply(v6, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v7) = 0) | (v11 = 0 & member(v10, v7) = 0 & ! [v18] : ( ~ (apply(v6, v10, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & member(v18, v8) = v19)) & ! [v18] : ( ~ (member(v18, v8) = 0) | ? [v19] : ( ~ (v19 = 0) & apply(v6, v10, v18) = v19))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v7) = 0 & member(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v7, v6) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (power_set(v7) = v8) | ~ (member(v6, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v6, v7) = 0) | ~ (member(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = v6 | v7 = v6 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (inverse_image2(v9, v8) = v7) | ~ (inverse_image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (image2(v9, v8) = v7) | ~ (image2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (identity(v9, v8) = v7) | ~ (identity(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unordered_pair(v9, v8) = v7) | ~ (unordered_pair(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_set(v9, v8) = v7) | ~ (equal_set(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inverse_image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v8, v10) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (image2(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : (apply(v6, v10, v8) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v6, v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & injective(v6, v7, v8) = 0) | ( ~ (v10 = 0) & one_to_one(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (surjective(v6, v7, v8) = 0) | ~ (member(v9, v8) = 0) | ? [v10] : (apply(v6, v10, v9) = 0 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (injective(v6, v7, v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & surjective(v6, v7, v8) = 0) | ( ~ (v10 = 0) & one_to_one(v6, v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (maps(v6, v7, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v10] : (apply(v6, v9, v10) = 0 & member(v10, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v7) = v8) | ~ (member(v9, v7) = 0) | ~ (member(v6, v8) = 0) | member(v6, v9) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v8, v7) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v6, v8) = 0 & member(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7, v8) = v9) | ~ (member(v6, v9) = 0) | ? [v10] : ((v10 = 0 & member(v6, v8) = 0) | (v10 = 0 & member(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v7, v8) = v9) | ~ (member(v6, v9) = 0) | (member(v6, v8) = 0 & member(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (identity(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & apply(v6, v9, v9) = v10 & member(v9, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v6) = v7) | ~ (member(v6, v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_set(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & subset(v7, v6) = v9) | ( ~ (v9 = 0) & subset(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & power_set(v7) = v9 & member(v6, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (product(v8) = v7) | ~ (product(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (sum(v8) = v7) | ~ (sum(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v7) = v8) | ~ (member(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (power_set(v8) = v7) | ~ (power_set(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (one_to_one(v6, v7, v8) = 0) | (surjective(v6, v7, v8) = 0 & injective(v6, v7, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (surjective(v6, v7, v8) = 0) | ? [v9] : ((v9 = 0 & one_to_one(v6, v7, v8) = 0) | ( ~ (v9 = 0) & injective(v6, v7, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (injective(v6, v7, v8) = 0) | ? [v9] : ((v9 = 0 & one_to_one(v6, v7, v8) = 0) | ( ~ (v9 = 0) & surjective(v6, v7, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (identity(v6, v7) = 0) | ~ (member(v8, v7) = 0) | apply(v6, v8, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (sum(v7) = v8) | ~ (member(v6, v8) = 0) | ? [v9] : (member(v9, v7) = 0 & member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (power_set(v7) = v8) | ~ (member(v6, v8) = 0) | subset(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v7, v6) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & subset(v6, v7) = 0) | ( ~ (v9 = 0) & equal_set(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & subset(v7, v6) = 0) | ( ~ (v9 = 0) & equal_set(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ( ~ (equal_set(v6, v7) = 0) | (subset(v7, v6) = 0 & subset(v6, v7) = 0)) & ! [v6] : ! [v7] : ( ~ (subset(v7, v6) = 0) | ? [v8] : ((v8 = 0 & equal_set(v6, v7) = 0) | ( ~ (v8 = 0) & subset(v6, v7) = v8))) & ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ? [v8] : (power_set(v7) = v8 & member(v6, v8) = 0)) & ! [v6] : ! [v7] : ( ~ (subset(v6, v7) = 0) | ? [v8] : ((v8 = 0 & equal_set(v6, v7) = 0) | ( ~ (v8 = 0) & subset(v7, v6) = v8))) & ! [v6] : ~ (member(v6, empty_set) = 0) & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : compose_predicate(v11, v10, v9, v8, v7, v6) = v12 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : isomorphism(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : decreasing(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : increasing(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : compose_function(v10, v9, v8, v7, v6) = v11 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : inverse_predicate(v9, v8, v7, v6) = v10 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : equal_maps(v9, v8, v7, v6) = v10 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : inverse_image3(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : image3(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : inverse_function(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : one_to_one(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : surjective(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : injective(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : maps(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : apply(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : inverse_image2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : image2(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : identity(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unordered_pair(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : difference(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : union(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_set(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : subset(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : member(v7, v6) = v8 & ? [v6] : ? [v7] : product(v6) = v7 & ? [v6] : ? [v7] : sum(v6) = v7 & ? [v6] : ? [v7] : singleton(v6) = v7 & ? [v6] : ? [v7] : power_set(v6) = v7 & ((v5 = 0 & (( ~ (v3 = 0) & inverse_predicate(v0, v0, v1, v1) = v3) | ( ~ (v2 = 0) & one_to_one(v0, v1, v1) = v2))) | (v3 = 0 & v2 = 0 & ~ (v5 = 0) & inverse_predicate(v0, v0, v1, v1) = 0 & one_to_one(v0, v1, v1) = 0)))
% 293.92/235.54 | 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 yields:
% 293.92/235.54 | (1) identity(all_0_1_1, all_0_4_4) = all_0_0_0 & compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1 & maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0 & ! [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] : ( ~ (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_2_2 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = 0 & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = 0))
% 294.21/235.60 |
% 294.21/235.60 | Applying alpha-rule on (1) yields:
% 294.21/235.60 | (2) ! [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))
% 294.21/235.60 | (3) ! [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)))
% 294.21/235.60 | (4) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 294.21/235.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ? [v5] : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0))
% 294.21/235.60 | (6) ! [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)))
% 294.21/235.60 | (7) ! [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)))
% 294.21/235.60 | (8) ! [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))
% 294.21/235.60 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ (inverse_predicate(v5, v4, v3, v2) = v0))
% 294.21/235.61 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 294.21/235.61 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0))
% 294.21/235.61 | (12) ! [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))))
% 294.21/235.61 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (one_to_one(v0, v1, v2) = 0) | (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0))
% 294.21/235.61 | (14) ! [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))
% 294.21/235.61 | (15) ! [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)))
% 294.21/235.61 | (16) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : increasing(v4, v3, v2, v1, v0) = v5
% 294.21/235.61 | (17) ! [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))
% 294.21/235.61 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 294.21/235.61 | (19) ? [v0] : ? [v1] : ? [v2] : identity(v1, v0) = v2
% 294.21/235.61 | (20) maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0
% 294.21/235.61 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 294.21/235.61 | (22) ! [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)))
% 294.21/235.61 | (23) ! [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)))
% 294.21/235.61 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 294.21/235.61 | (25) ! [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)))
% 294.21/235.61 | (26) ! [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)))
% 294.21/235.61 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 294.21/235.61 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0))
% 294.21/235.61 | (29) ! [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)))
% 294.21/235.61 | (30) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : compose_function(v4, v3, v2, v1, v0) = v5
% 294.21/235.61 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 294.21/235.61 | (32) ! [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)))
% 294.21/235.61 | (33) ! [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)))
% 294.21/235.61 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 294.21/235.61 | (35) ! [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)))
% 294.21/235.61 | (36) ! [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)))
% 294.21/235.61 | (37) ? [v0] : ? [v1] : ? [v2] : ? [v3] : maps(v2, v1, v0) = v3
% 294.21/235.61 | (38) ! [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))
% 294.21/235.61 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0))
% 294.21/235.61 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 294.21/235.61 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 294.21/235.61 | (42) ! [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)))
% 294.21/235.61 | (43) ! [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)))
% 294.21/235.61 | (44) ! [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)))))))
% 294.21/235.62 | (45) (all_0_0_0 = 0 & (( ~ (all_0_2_2 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = 0 & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = 0)
% 294.21/235.62 | (46) ! [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)))
% 294.21/235.62 | (47) ? [v0] : ? [v1] : ? [v2] : ? [v3] : injective(v2, v1, v0) = v3
% 294.21/235.62 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 294.21/235.62 | (49) ! [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)))
% 294.21/235.62 | (50) ! [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)))
% 294.21/235.62 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 294.21/235.62 | (52) ? [v0] : ? [v1] : singleton(v0) = v1
% 294.21/235.62 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = v0))
% 294.21/235.62 | (54) ! [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)))))
% 294.21/235.62 | (55) ! [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)))
% 294.21/235.62 | (56) ! [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)))))
% 294.21/235.62 | (57) ! [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)))
% 294.21/235.62 | (58) ! [v0] : ~ (member(v0, empty_set) = 0)
% 294.21/235.62 | (59) ! [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)))
% 294.21/235.62 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0))
% 294.21/235.62 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | ~ (inverse_function(v4, v3, v2) = v0))
% 294.21/235.62 | (62) ! [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)))
% 294.21/235.62 | (63) ! [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)))
% 294.21/235.62 | (64) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_image3(v2, v1, v0) = v3
% 294.21/235.62 | (65) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 294.21/235.62 | (66) ! [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)))
% 294.21/235.62 | (67) ! [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))
% 294.21/235.62 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ (inverse_image3(v4, v3, v2) = v0))
% 294.21/235.62 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 294.21/235.62 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 294.21/235.62 | (71) ! [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)))
% 294.21/235.62 | (72) ! [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)))
% 294.21/235.62 | (73) ! [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)))
% 294.21/235.62 | (74) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 294.21/235.62 | (75) ? [v0] : ? [v1] : power_set(v0) = v1
% 294.21/235.62 | (76) ? [v0] : ? [v1] : ? [v2] : ? [v3] : inverse_function(v2, v1, v0) = v3
% 294.21/235.63 | (77) ! [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))
% 294.21/235.63 | (78) ! [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)))
% 294.21/235.63 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) | ? [v4] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0))
% 294.21/235.63 | (80) ? [v0] : ? [v1] : ? [v2] : ? [v3] : surjective(v2, v1, v0) = v3
% 294.21/235.63 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : decreasing(v4, v3, v2, v1, v0) = v5
% 294.21/235.63 | (82) ? [v0] : ? [v1] : ? [v2] : image2(v1, v0) = v2
% 294.21/235.63 | (83) ? [v0] : ? [v1] : sum(v0) = v1
% 294.21/235.63 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 294.21/235.63 | (85) ! [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)))))
% 294.21/235.63 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : equal_maps(v3, v2, v1, v0) = v4
% 294.21/235.63 | (87) ! [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)))
% 294.21/235.63 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (isomorphism(v6, v5, v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0))
% 294.21/235.63 | (89) compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1
% 294.21/235.63 | (90) ! [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))
% 294.21/235.63 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (apply(v0, v6, v3) = 0) | ~ (member(v3, v4) = v5) | ? [v7] : (( ~ (v7 = 0) & member(v6, v1) = v7) | ( ~ (v7 = 0) & member(v3, v2) = v7)))
% 294.21/235.63 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v4, v2) = 0 & member(v4, v1) = 0))
% 294.21/235.63 | (93) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : isomorphism(v4, v3, v2, v1, v0) = v5
% 294.21/235.63 | (94) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 294.21/235.63 | (95) ! [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)))
% 294.21/235.63 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : inverse_predicate(v3, v2, v1, v0) = v4
% 294.21/235.63 | (97) ! [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)))
% 294.21/235.63 | (98) ! [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)))
% 294.21/235.63 | (99) ! [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))))
% 294.21/235.63 | (100) ! [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)))
% 294.21/235.63 | (101) ! [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)))
% 294.21/235.63 | (102) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 294.21/235.63 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : (apply(v0, v4, v3) = 0 & member(v4, v1) = 0))
% 294.21/235.63 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 294.21/235.63 | (105) ! [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)))
% 294.21/235.63 | (106) ! [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)))
% 294.21/235.63 | (107) ! [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)))))
% 294.21/235.63 | (108) ! [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)))))
% 294.21/235.63 | (109) ! [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)))
% 294.21/235.64 | (110) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 294.21/235.64 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 294.21/235.64 | (112) ! [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)))))
% 294.21/235.64 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 294.21/235.64 | (114) ! [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)))
% 294.21/235.64 | (115) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : compose_predicate(v5, v4, v3, v2, v1, v0) = v6
% 294.21/235.64 | (116) ! [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)))
% 294.21/235.64 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 294.21/235.64 | (118) ! [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)))
% 294.21/235.64 | (119) ! [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)))
% 294.21/235.64 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | member(v3, v2) = 0)
% 294.21/235.64 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 294.21/235.64 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (increasing(v6, v5, v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0))
% 294.21/235.64 | (123) ! [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)))
% 294.21/235.64 | (124) ! [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)))
% 294.21/235.64 | (125) identity(all_0_1_1, all_0_4_4) = all_0_0_0
% 294.21/235.64 | (126) ! [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)))))
% 294.21/235.64 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (isomorphism(v0, v1, v2, v3, v4) = 0) | (one_to_one(v0, v1, v3) = 0 & maps(v0, v1, v3) = 0))
% 294.21/235.64 | (128) ! [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))
% 294.21/235.64 | (129) ! [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)))
% 294.21/235.64 | (130) ! [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))
% 294.21/235.64 | (131) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 294.21/235.64 | (132) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 294.21/235.64 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0))
% 294.21/235.64 | (134) ! [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))
% 294.21/235.64 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 294.21/235.64 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = v0 | ~ (decreasing(v6, v5, v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0))
% 294.21/235.64 | (137) ? [v0] : ? [v1] : ? [v2] : ? [v3] : one_to_one(v2, v1, v0) = v3
% 294.21/235.64 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 294.21/235.64 | (139) ! [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)))
% 294.21/235.64 | (140) ? [v0] : ? [v1] : product(v0) = v1
% 294.21/235.64 | (141) ! [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)))))
% 294.21/235.64 | (142) ! [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)))))
% 294.21/235.64 | (143) ! [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)))
% 294.21/235.65 | (144) ! [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)))))
% 294.21/235.65 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 294.21/235.65 | (146) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 294.21/235.65 | (147) ! [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)))
% 294.21/235.65 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 294.21/235.65 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ (inverse_image2(v3, v2) = v0))
% 294.21/235.65 | (150) ! [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)))
% 294.21/235.65 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ (image3(v4, v3, v2) = v0))
% 294.21/235.65 | (152) ! [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)))))
% 294.21/235.65 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (inverse_image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : (apply(v0, v2, v4) = 0 & member(v4, v1) = 0))
% 294.21/235.65 | (154) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 294.21/235.65 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 294.21/235.65 | (156) ! [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)))
% 294.21/235.65 | (157) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 294.21/235.65 | (158) ! [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)))
% 294.21/235.65 | (159) ! [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)))))
% 294.21/235.65 | (160) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 294.21/235.65 | (161) ! [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))
% 294.21/235.65 | (162) ? [v0] : ? [v1] : ? [v2] : inverse_image2(v1, v0) = v2
% 294.21/235.65 | (163) ! [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)))
% 294.21/235.65 | (164) ! [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)))
% 294.21/235.65 | (165) ? [v0] : ? [v1] : ? [v2] : ? [v3] : image3(v2, v1, v0) = v3
% 294.21/235.65 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 294.21/235.65 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | apply(v0, v2, v2) = 0)
% 294.21/235.65 | (168) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 294.21/235.65 | (169) ! [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)))
% 294.21/235.65 | (170) ! [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))
% 294.21/235.65 | (171) ! [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))
% 294.21/235.65 | (172) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 294.21/235.65 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, v4, v3, v2) = v0))
% 294.21/235.65 | (174) ! [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)))
% 294.21/235.65 | (175) ! [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))
% 294.21/235.65 | (176) ! [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)))))
% 294.21/235.65 | (177) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 294.21/235.65 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 294.21/235.65 | (179) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 294.21/235.65 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 294.55/235.65 | (181) ! [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)))))
% 294.55/235.66 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ (surjective(v4, v3, v2) = v0))
% 294.55/235.66 | (183) ! [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)))
% 294.55/235.66 | (184) ! [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)))
% 294.55/235.66 | (185) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 294.55/235.66 | (186) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (39) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 294.55/235.66 | (187) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, v0, v0) = v1 & member(v0, all_0_4_4) = 0)
% 294.55/235.66 |
% 294.55/235.66 +-Applying beta-rule and splitting (45), into two cases.
% 294.55/235.66 |-Branch one:
% 294.55/235.66 | (188) all_0_0_0 = 0 & (( ~ (all_0_2_2 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3))
% 294.55/235.66 |
% 294.55/235.66 | Applying alpha-rule on (188) yields:
% 294.55/235.66 | (189) all_0_0_0 = 0
% 294.55/235.66 | (190) ( ~ (all_0_2_2 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3)
% 294.55/235.66 |
% 294.55/235.66 | From (189) and (125) follows:
% 294.55/235.66 | (191) identity(all_0_1_1, all_0_4_4) = 0
% 294.55/235.66 |
% 294.55/235.66 +-Applying beta-rule and splitting (190), into two cases.
% 294.55/235.66 |-Branch one:
% 294.55/235.66 | (192) ~ (all_0_2_2 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2
% 294.55/235.66 |
% 294.55/235.66 | Applying alpha-rule on (192) yields:
% 294.55/235.66 | (193) ~ (all_0_2_2 = 0)
% 294.55/235.66 | (194) inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (99) with all_0_2_2, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = all_0_2_2, yields:
% 294.55/235.66 | (195) all_0_2_2 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0 & ((v3 = 0 & apply(all_0_5_5, v1, v0) = 0) | (v2 = 0 & apply(all_0_5_5, v0, v1) = 0)) & (( ~ (v3 = 0) & apply(all_0_5_5, v1, v0) = v3) | ( ~ (v2 = 0) & apply(all_0_5_5, v0, v1) = v2)))
% 294.55/235.66 |
% 294.55/235.66 +-Applying beta-rule and splitting (195), into two cases.
% 294.55/235.66 |-Branch one:
% 294.55/235.66 | (196) all_0_2_2 = 0
% 294.55/235.66 |
% 294.55/235.66 | Equations (196) can reduce 193 to:
% 294.55/235.66 | (197) $false
% 294.55/235.66 |
% 294.55/235.66 |-The branch is then unsatisfiable
% 294.55/235.66 |-Branch two:
% 294.55/235.66 | (193) ~ (all_0_2_2 = 0)
% 294.55/235.66 | (199) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0 & ((v3 = 0 & apply(all_0_5_5, v1, v0) = 0) | (v2 = 0 & apply(all_0_5_5, v0, v1) = 0)) & (( ~ (v3 = 0) & apply(all_0_5_5, v1, v0) = v3) | ( ~ (v2 = 0) & apply(all_0_5_5, v0, v1) = v2)))
% 294.55/235.66 |
% 294.55/235.66 | Instantiating (199) with all_82_0_117, all_82_1_118, all_82_2_119, all_82_3_120 yields:
% 294.55/235.66 | (200) member(all_82_2_119, all_0_4_4) = 0 & member(all_82_3_120, all_0_4_4) = 0 & ((all_82_0_117 = 0 & apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0) | (all_82_1_118 = 0 & apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0)) & (( ~ (all_82_0_117 = 0) & apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_82_0_117) | ( ~ (all_82_1_118 = 0) & apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_82_1_118))
% 294.55/235.66 |
% 294.55/235.66 | Applying alpha-rule on (200) yields:
% 294.55/235.66 | (201) member(all_82_2_119, all_0_4_4) = 0
% 294.55/235.66 | (202) member(all_82_3_120, all_0_4_4) = 0
% 294.55/235.66 | (203) (all_82_0_117 = 0 & apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0) | (all_82_1_118 = 0 & apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0)
% 294.55/235.66 | (204) ( ~ (all_82_0_117 = 0) & apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_82_0_117) | ( ~ (all_82_1_118 = 0) & apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_82_1_118)
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (79) with all_82_2_119, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.55/235.66 | (205) ? [v0] : (apply(all_0_5_5, all_82_2_119, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (167) with all_82_2_119, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.55/235.66 | (206) apply(all_0_1_1, all_82_2_119, all_82_2_119) = 0
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (79) with all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.55/235.66 | (207) ? [v0] : (apply(all_0_5_5, all_82_3_120, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (167) with all_82_3_120, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.55/235.66 | (208) apply(all_0_1_1, all_82_3_120, all_82_3_120) = 0
% 294.55/235.66 |
% 294.55/235.66 | Instantiating (207) with all_90_0_121 yields:
% 294.55/235.66 | (209) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0 & member(all_90_0_121, all_0_4_4) = 0
% 294.55/235.66 |
% 294.55/235.66 | Applying alpha-rule on (209) yields:
% 294.55/235.66 | (210) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0
% 294.55/235.66 | (211) member(all_90_0_121, all_0_4_4) = 0
% 294.55/235.66 |
% 294.55/235.66 | Instantiating (205) with all_92_0_122 yields:
% 294.55/235.66 | (212) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0 & member(all_92_0_122, all_0_4_4) = 0
% 294.55/235.66 |
% 294.55/235.66 | Applying alpha-rule on (212) yields:
% 294.55/235.66 | (213) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0
% 294.55/235.66 | (214) member(all_92_0_122, all_0_4_4) = 0
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (183) with all_0_1_1, all_82_2_119, all_82_2_119, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_82_2_119, all_82_2_119) = 0, yields:
% 294.55/235.66 | (215) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_82_2_119) = 0 & apply(all_0_5_5, all_82_2_119, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (183) with all_0_1_1, all_82_3_120, all_82_3_120, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_82_3_120, all_82_3_120) = 0, yields:
% 294.55/235.66 | (216) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_82_3_120) = 0 & apply(all_0_5_5, all_82_3_120, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.55/235.66 |
% 294.55/235.66 | Instantiating formula (79) with all_92_0_122, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.55/235.67 | (217) ? [v0] : (apply(all_0_5_5, all_92_0_122, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (167) with all_92_0_122, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.55/235.67 | (218) apply(all_0_1_1, all_92_0_122, all_92_0_122) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (79) with all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.55/235.67 | (219) ? [v0] : (apply(all_0_5_5, all_90_0_121, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (167) with all_90_0_121, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.55/235.67 | (220) apply(all_0_1_1, all_90_0_121, all_90_0_121) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (219) with all_100_0_123 yields:
% 294.55/235.67 | (221) apply(all_0_5_5, all_90_0_121, all_100_0_123) = 0 & member(all_100_0_123, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (221) yields:
% 294.55/235.67 | (222) apply(all_0_5_5, all_90_0_121, all_100_0_123) = 0
% 294.55/235.67 | (223) member(all_100_0_123, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (217) with all_102_0_124 yields:
% 294.55/235.67 | (224) apply(all_0_5_5, all_92_0_122, all_102_0_124) = 0 & member(all_102_0_124, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (224) yields:
% 294.55/235.67 | (225) apply(all_0_5_5, all_92_0_122, all_102_0_124) = 0
% 294.55/235.67 | (226) member(all_102_0_124, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (216) with all_104_0_125, all_104_1_126, all_104_2_127, all_104_3_128 yields:
% 294.55/235.67 | (227) (all_104_0_125 = 0 & all_104_1_126 = 0 & all_104_2_127 = 0 & apply(all_0_5_5, all_104_3_128, all_82_3_120) = 0 & apply(all_0_5_5, all_82_3_120, all_104_3_128) = 0 & member(all_104_3_128, all_0_4_4) = 0) | ( ~ (all_104_3_128 = 0) & member(all_82_3_120, all_0_4_4) = all_104_3_128)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (215) with all_105_0_129, all_105_1_130, all_105_2_131, all_105_3_132 yields:
% 294.55/235.67 | (228) (all_105_0_129 = 0 & all_105_1_130 = 0 & all_105_2_131 = 0 & apply(all_0_5_5, all_105_3_132, all_82_2_119) = 0 & apply(all_0_5_5, all_82_2_119, all_105_3_132) = 0 & member(all_105_3_132, all_0_4_4) = 0) | ( ~ (all_105_3_132 = 0) & member(all_82_2_119, all_0_4_4) = all_105_3_132)
% 294.55/235.67 |
% 294.55/235.67 +-Applying beta-rule and splitting (227), into two cases.
% 294.55/235.67 |-Branch one:
% 294.55/235.67 | (229) all_104_0_125 = 0 & all_104_1_126 = 0 & all_104_2_127 = 0 & apply(all_0_5_5, all_104_3_128, all_82_3_120) = 0 & apply(all_0_5_5, all_82_3_120, all_104_3_128) = 0 & member(all_104_3_128, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (229) yields:
% 294.55/235.67 | (230) all_104_1_126 = 0
% 294.55/235.67 | (231) all_104_0_125 = 0
% 294.55/235.67 | (232) all_104_2_127 = 0
% 294.55/235.67 | (233) member(all_104_3_128, all_0_4_4) = 0
% 294.55/235.67 | (234) apply(all_0_5_5, all_104_3_128, all_82_3_120) = 0
% 294.55/235.67 | (235) apply(all_0_5_5, all_82_3_120, all_104_3_128) = 0
% 294.55/235.67 |
% 294.55/235.67 +-Applying beta-rule and splitting (228), into two cases.
% 294.55/235.67 |-Branch one:
% 294.55/235.67 | (236) all_105_0_129 = 0 & all_105_1_130 = 0 & all_105_2_131 = 0 & apply(all_0_5_5, all_105_3_132, all_82_2_119) = 0 & apply(all_0_5_5, all_82_2_119, all_105_3_132) = 0 & member(all_105_3_132, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (236) yields:
% 294.55/235.67 | (237) member(all_105_3_132, all_0_4_4) = 0
% 294.55/235.67 | (238) all_105_0_129 = 0
% 294.55/235.67 | (239) all_105_1_130 = 0
% 294.55/235.67 | (240) all_105_2_131 = 0
% 294.55/235.67 | (241) apply(all_0_5_5, all_105_3_132, all_82_2_119) = 0
% 294.55/235.67 | (242) apply(all_0_5_5, all_82_2_119, all_105_3_132) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (183) with all_0_1_1, all_92_0_122, all_92_0_122, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_92_0_122, all_92_0_122) = 0, yields:
% 294.55/235.67 | (243) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_92_0_122) = 0 & apply(all_0_5_5, all_92_0_122, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (183) with all_0_1_1, all_90_0_121, all_90_0_121, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_90_0_121, all_90_0_121) = 0, yields:
% 294.55/235.67 | (244) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_90_0_121) = 0 & apply(all_0_5_5, all_90_0_121, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (50) with all_100_0_123, all_82_3_120, all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_90_0_121, all_100_0_123) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.55/235.67 | (245) all_100_0_123 = all_82_3_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = v0) | ( ~ (v0 = 0) & member(all_100_0_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (50) with all_105_3_132, all_92_0_122, all_82_2_119, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_82_2_119, all_105_3_132) = 0, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.55/235.67 | (246) all_105_3_132 = all_92_0_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0) | ( ~ (v0 = 0) & member(all_105_3_132, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (79) with all_105_3_132, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_105_3_132, all_0_4_4) = 0, yields:
% 294.55/235.67 | (247) ? [v0] : (apply(all_0_5_5, all_105_3_132, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (174) with all_104_3_128, all_90_0_121, all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_104_3_128, all_0_4_4) = 0, member(all_90_0_121, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.55/235.67 | (248) all_104_3_128 = all_90_0_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_104_3_128) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (79) with all_104_3_128, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_104_3_128, all_0_4_4) = 0, yields:
% 294.55/235.67 | (249) ? [v0] : (apply(all_0_5_5, all_104_3_128, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (174) with all_102_0_124, all_82_2_119, all_92_0_122, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_102_0_124, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.55/235.67 | (250) all_102_0_124 = all_82_2_119 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_102_0_124) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (174) with all_102_0_124, all_82_2_119, all_105_3_132, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_105_3_132, all_0_4_4) = 0, member(all_102_0_124, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.55/235.67 | (251) all_102_0_124 = all_82_2_119 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_105_3_132, all_102_0_124) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_105_3_132, all_82_2_119) = v0))
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (79) with all_102_0_124, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_102_0_124, all_0_4_4) = 0, yields:
% 294.55/235.67 | (252) ? [v0] : (apply(all_0_5_5, all_102_0_124, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating formula (79) with all_100_0_123, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_100_0_123, all_0_4_4) = 0, yields:
% 294.55/235.67 | (253) ? [v0] : (apply(all_0_5_5, all_100_0_123, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (253) with all_120_0_133 yields:
% 294.55/235.67 | (254) apply(all_0_5_5, all_100_0_123, all_120_0_133) = 0 & member(all_120_0_133, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (254) yields:
% 294.55/235.67 | (255) apply(all_0_5_5, all_100_0_123, all_120_0_133) = 0
% 294.55/235.67 | (256) member(all_120_0_133, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (247) with all_122_0_134 yields:
% 294.55/235.67 | (257) apply(all_0_5_5, all_105_3_132, all_122_0_134) = 0 & member(all_122_0_134, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (257) yields:
% 294.55/235.67 | (258) apply(all_0_5_5, all_105_3_132, all_122_0_134) = 0
% 294.55/235.67 | (259) member(all_122_0_134, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (244) with all_124_0_135, all_124_1_136, all_124_2_137, all_124_3_138 yields:
% 294.55/235.67 | (260) (all_124_0_135 = 0 & all_124_1_136 = 0 & all_124_2_137 = 0 & apply(all_0_5_5, all_124_3_138, all_90_0_121) = 0 & apply(all_0_5_5, all_90_0_121, all_124_3_138) = 0 & member(all_124_3_138, all_0_4_4) = 0) | ( ~ (all_124_3_138 = 0) & member(all_90_0_121, all_0_4_4) = all_124_3_138)
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (249) with all_125_0_139 yields:
% 294.55/235.67 | (261) apply(all_0_5_5, all_104_3_128, all_125_0_139) = 0 & member(all_125_0_139, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (261) yields:
% 294.55/235.67 | (262) apply(all_0_5_5, all_104_3_128, all_125_0_139) = 0
% 294.55/235.67 | (263) member(all_125_0_139, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (252) with all_127_0_140 yields:
% 294.55/235.67 | (264) apply(all_0_5_5, all_102_0_124, all_127_0_140) = 0 & member(all_127_0_140, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Applying alpha-rule on (264) yields:
% 294.55/235.67 | (265) apply(all_0_5_5, all_102_0_124, all_127_0_140) = 0
% 294.55/235.67 | (266) member(all_127_0_140, all_0_4_4) = 0
% 294.55/235.67 |
% 294.55/235.67 | Instantiating (243) with all_129_0_141, all_129_1_142, all_129_2_143, all_129_3_144 yields:
% 294.55/235.67 | (267) (all_129_0_141 = 0 & all_129_1_142 = 0 & all_129_2_143 = 0 & apply(all_0_5_5, all_129_3_144, all_92_0_122) = 0 & apply(all_0_5_5, all_92_0_122, all_129_3_144) = 0 & member(all_129_3_144, all_0_4_4) = 0) | ( ~ (all_129_3_144 = 0) & member(all_92_0_122, all_0_4_4) = all_129_3_144)
% 294.55/235.67 |
% 294.55/235.67 +-Applying beta-rule and splitting (248), into two cases.
% 294.55/235.67 |-Branch one:
% 294.55/235.67 | (268) all_104_3_128 = all_90_0_121
% 294.55/235.67 |
% 294.55/235.67 | From (268) and (262) follows:
% 294.55/235.67 | (269) apply(all_0_5_5, all_90_0_121, all_125_0_139) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (268) and (234) follows:
% 294.55/235.68 | (270) apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (268) and (235) follows:
% 294.55/235.68 | (210) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (268) and (233) follows:
% 294.55/235.68 | (211) member(all_90_0_121, all_0_4_4) = 0
% 294.55/235.68 |
% 294.55/235.68 +-Applying beta-rule and splitting (245), into two cases.
% 294.55/235.68 |-Branch one:
% 294.55/235.68 | (273) all_100_0_123 = all_82_3_120
% 294.55/235.68 |
% 294.55/235.68 | From (273) and (255) follows:
% 294.55/235.68 | (274) apply(all_0_5_5, all_82_3_120, all_120_0_133) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (273) and (222) follows:
% 294.55/235.68 | (270) apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (273) and (223) follows:
% 294.55/235.68 | (202) member(all_82_3_120, all_0_4_4) = 0
% 294.55/235.68 |
% 294.55/235.68 +-Applying beta-rule and splitting (246), into two cases.
% 294.55/235.68 |-Branch one:
% 294.55/235.68 | (277) all_105_3_132 = all_92_0_122
% 294.55/235.68 |
% 294.55/235.68 | From (277) and (258) follows:
% 294.55/235.68 | (278) apply(all_0_5_5, all_92_0_122, all_122_0_134) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (277) and (241) follows:
% 294.55/235.68 | (279) apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (277) and (242) follows:
% 294.55/235.68 | (213) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (277) and (237) follows:
% 294.55/235.68 | (214) member(all_92_0_122, all_0_4_4) = 0
% 294.55/235.68 |
% 294.55/235.68 +-Applying beta-rule and splitting (251), into two cases.
% 294.55/235.68 |-Branch one:
% 294.55/235.68 | (282) all_102_0_124 = all_82_2_119
% 294.55/235.68 |
% 294.55/235.68 | From (282) and (265) follows:
% 294.55/235.68 | (283) apply(all_0_5_5, all_82_2_119, all_127_0_140) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (282) and (225) follows:
% 294.55/235.68 | (279) apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0
% 294.55/235.68 |
% 294.55/235.68 | From (282) and (226) follows:
% 294.55/235.68 | (201) member(all_82_2_119, all_0_4_4) = 0
% 294.55/235.68 |
% 294.55/235.68 +-Applying beta-rule and splitting (260), into two cases.
% 294.55/235.68 |-Branch one:
% 294.55/235.68 | (286) all_124_0_135 = 0 & all_124_1_136 = 0 & all_124_2_137 = 0 & apply(all_0_5_5, all_124_3_138, all_90_0_121) = 0 & apply(all_0_5_5, all_90_0_121, all_124_3_138) = 0 & member(all_124_3_138, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Applying alpha-rule on (286) yields:
% 294.66/235.68 | (287) all_124_0_135 = 0
% 294.66/235.68 | (288) apply(all_0_5_5, all_124_3_138, all_90_0_121) = 0
% 294.66/235.68 | (289) all_124_2_137 = 0
% 294.66/235.68 | (290) member(all_124_3_138, all_0_4_4) = 0
% 294.66/235.68 | (291) apply(all_0_5_5, all_90_0_121, all_124_3_138) = 0
% 294.66/235.68 | (292) all_124_1_136 = 0
% 294.66/235.68 |
% 294.66/235.68 +-Applying beta-rule and splitting (267), into two cases.
% 294.66/235.68 |-Branch one:
% 294.66/235.68 | (293) all_129_0_141 = 0 & all_129_1_142 = 0 & all_129_2_143 = 0 & apply(all_0_5_5, all_129_3_144, all_92_0_122) = 0 & apply(all_0_5_5, all_92_0_122, all_129_3_144) = 0 & member(all_129_3_144, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Applying alpha-rule on (293) yields:
% 294.66/235.68 | (294) apply(all_0_5_5, all_92_0_122, all_129_3_144) = 0
% 294.66/235.68 | (295) all_129_0_141 = 0
% 294.66/235.68 | (296) apply(all_0_5_5, all_129_3_144, all_92_0_122) = 0
% 294.66/235.68 | (297) all_129_1_142 = 0
% 294.66/235.68 | (298) all_129_2_143 = 0
% 294.66/235.68 | (299) member(all_129_3_144, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (95) with all_124_3_138, all_125_0_139, all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_90_0_121, all_125_0_139) = 0, apply(all_0_5_5, all_90_0_121, all_124_3_138) = 0, yields:
% 294.66/235.68 | (300) all_125_0_139 = all_124_3_138 | ? [v0] : (( ~ (v0 = 0) & member(all_125_0_139, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_124_3_138, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (95) with all_82_3_120, all_125_0_139, all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_90_0_121, all_125_0_139) = 0, apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0, yields:
% 294.66/235.68 | (301) all_125_0_139 = all_82_3_120 | ? [v0] : (( ~ (v0 = 0) & member(all_125_0_139, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (50) with all_120_0_133, all_90_0_121, all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_82_3_120, all_120_0_133) = 0, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.66/235.68 | (302) all_120_0_133 = all_90_0_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0) | ( ~ (v0 = 0) & member(all_120_0_133, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_129_3_144, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_129_3_144, all_0_4_4) = 0, yields:
% 294.66/235.68 | (303) ? [v0] : (apply(all_0_5_5, all_129_3_144, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (174) with all_127_0_140, all_92_0_122, all_82_2_119, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_127_0_140, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.66/235.68 | (304) all_127_0_140 = all_92_0_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_127_0_140) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_127_0_140, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_127_0_140, all_0_4_4) = 0, yields:
% 294.66/235.68 | (305) ? [v0] : (apply(all_0_5_5, all_127_0_140, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_125_0_139, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_125_0_139, all_0_4_4) = 0, yields:
% 294.66/235.68 | (306) ? [v0] : (apply(all_0_5_5, all_125_0_139, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (50) with all_82_3_120, all_124_3_138, all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0, member(all_124_3_138, all_0_4_4) = 0, yields:
% 294.66/235.68 | (307) all_124_3_138 = all_82_3_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_124_3_138) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (174) with all_124_3_138, all_92_0_122, all_129_3_144, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_129_3_144, all_0_4_4) = 0, member(all_124_3_138, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.66/235.68 | (308) all_124_3_138 = all_92_0_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_129_3_144, all_124_3_138) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_129_3_144, all_92_0_122) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_124_3_138, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_124_3_138, all_0_4_4) = 0, yields:
% 294.66/235.68 | (309) ? [v0] : (apply(all_0_5_5, all_124_3_138, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (50) with all_129_3_144, all_122_0_134, all_92_0_122, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_92_0_122, all_129_3_144) = 0, member(all_122_0_134, all_0_4_4) = 0, yields:
% 294.66/235.68 | (310) all_129_3_144 = all_122_0_134 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = v0) | ( ~ (v0 = 0) & member(all_129_3_144, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (50) with all_82_2_119, all_122_0_134, all_92_0_122, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0, member(all_122_0_134, all_0_4_4) = 0, yields:
% 294.66/235.68 | (311) all_122_0_134 = all_82_2_119 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_122_0_134, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_122_0_134, all_0_4_4) = 0, yields:
% 294.66/235.68 | (312) ? [v0] : (apply(all_0_5_5, all_122_0_134, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (174) with all_120_0_133, all_122_0_134, all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_122_0_134, all_0_4_4) = 0, member(all_120_0_133, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.66/235.68 | (313) all_122_0_134 = all_120_0_133 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_122_0_134) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_120_0_133) = v0))
% 294.66/235.68 |
% 294.66/235.68 | Instantiating formula (79) with all_120_0_133, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_120_0_133, all_0_4_4) = 0, yields:
% 294.66/235.68 | (314) ? [v0] : (apply(all_0_5_5, all_120_0_133, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.66/235.68 |
% 294.66/235.68 | Instantiating (312) with all_160_0_145 yields:
% 294.66/235.68 | (315) apply(all_0_5_5, all_122_0_134, all_160_0_145) = 0 & member(all_160_0_145, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Applying alpha-rule on (315) yields:
% 294.66/235.68 | (316) apply(all_0_5_5, all_122_0_134, all_160_0_145) = 0
% 294.66/235.68 | (317) member(all_160_0_145, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Instantiating (309) with all_162_0_146 yields:
% 294.66/235.68 | (318) apply(all_0_5_5, all_124_3_138, all_162_0_146) = 0 & member(all_162_0_146, all_0_4_4) = 0
% 294.66/235.68 |
% 294.66/235.68 | Applying alpha-rule on (318) yields:
% 294.66/235.68 | (319) apply(all_0_5_5, all_124_3_138, all_162_0_146) = 0
% 294.66/235.68 | (320) member(all_162_0_146, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Instantiating (306) with all_164_0_147 yields:
% 294.66/235.69 | (321) apply(all_0_5_5, all_125_0_139, all_164_0_147) = 0 & member(all_164_0_147, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (321) yields:
% 294.66/235.69 | (322) apply(all_0_5_5, all_125_0_139, all_164_0_147) = 0
% 294.66/235.69 | (323) member(all_164_0_147, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Instantiating (305) with all_166_0_148 yields:
% 294.66/235.69 | (324) apply(all_0_5_5, all_127_0_140, all_166_0_148) = 0 & member(all_166_0_148, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (324) yields:
% 294.66/235.69 | (325) apply(all_0_5_5, all_127_0_140, all_166_0_148) = 0
% 294.66/235.69 | (326) member(all_166_0_148, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Instantiating (314) with all_168_0_149 yields:
% 294.66/235.69 | (327) apply(all_0_5_5, all_120_0_133, all_168_0_149) = 0 & member(all_168_0_149, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (327) yields:
% 294.66/235.69 | (328) apply(all_0_5_5, all_120_0_133, all_168_0_149) = 0
% 294.66/235.69 | (329) member(all_168_0_149, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Instantiating (303) with all_170_0_150 yields:
% 294.66/235.69 | (330) apply(all_0_5_5, all_129_3_144, all_170_0_150) = 0 & member(all_170_0_150, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (330) yields:
% 294.66/235.69 | (331) apply(all_0_5_5, all_129_3_144, all_170_0_150) = 0
% 294.66/235.69 | (332) member(all_170_0_150, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (307), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (333) all_124_3_138 = all_82_3_120
% 294.66/235.69 |
% 294.66/235.69 | From (333) and (319) follows:
% 294.66/235.69 | (334) apply(all_0_5_5, all_82_3_120, all_162_0_146) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (333) and (288) follows:
% 294.66/235.69 | (210) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (333) and (290) follows:
% 294.66/235.69 | (202) member(all_82_3_120, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (304), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (337) all_127_0_140 = all_92_0_122
% 294.66/235.69 |
% 294.66/235.69 | From (337) and (325) follows:
% 294.66/235.69 | (338) apply(all_0_5_5, all_92_0_122, all_166_0_148) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (337) and (266) follows:
% 294.66/235.69 | (214) member(all_92_0_122, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (311), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (340) all_122_0_134 = all_82_2_119
% 294.66/235.69 |
% 294.66/235.69 | From (340) and (316) follows:
% 294.66/235.69 | (341) apply(all_0_5_5, all_82_2_119, all_160_0_145) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (340) and (278) follows:
% 294.66/235.69 | (279) apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (302), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (343) all_120_0_133 = all_90_0_121
% 294.66/235.69 |
% 294.66/235.69 | From (343) and (328) follows:
% 294.66/235.69 | (344) apply(all_0_5_5, all_90_0_121, all_168_0_149) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (343) and (274) follows:
% 294.66/235.69 | (210) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (343) and (256) follows:
% 294.66/235.69 | (211) member(all_90_0_121, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (300), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (347) all_125_0_139 = all_124_3_138
% 294.66/235.69 |
% 294.66/235.69 | Combining equations (333,347) yields a new equation:
% 294.66/235.69 | (348) all_125_0_139 = all_82_3_120
% 294.66/235.69 |
% 294.66/235.69 | From (348) and (322) follows:
% 294.66/235.69 | (349) apply(all_0_5_5, all_82_3_120, all_164_0_147) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (348) and (269) follows:
% 294.66/235.69 | (270) apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (348) and (263) follows:
% 294.66/235.69 | (202) member(all_82_3_120, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (310), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (352) all_129_3_144 = all_122_0_134
% 294.66/235.69 |
% 294.66/235.69 | Combining equations (340,352) yields a new equation:
% 294.66/235.69 | (353) all_129_3_144 = all_82_2_119
% 294.66/235.69 |
% 294.66/235.69 | From (353) and (331) follows:
% 294.66/235.69 | (354) apply(all_0_5_5, all_82_2_119, all_170_0_150) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (353) and (296) follows:
% 294.66/235.69 | (213) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (353) and (294) follows:
% 294.66/235.69 | (279) apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (353) and (299) follows:
% 294.66/235.69 | (201) member(all_82_2_119, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (50) with all_166_0_148, all_82_2_119, all_92_0_122, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_92_0_122, all_166_0_148) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.66/235.69 | (358) all_166_0_148 = all_82_2_119 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = v0) | ( ~ (v0 = 0) & member(all_166_0_148, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0))
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (174) with all_168_0_149, all_82_3_120, all_90_0_121, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_168_0_149, all_0_4_4) = 0, member(all_90_0_121, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.66/235.69 | (359) all_168_0_149 = all_82_3_120 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_168_0_149) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = v0))
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (50) with all_162_0_146, all_164_0_147, all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_82_3_120, all_162_0_146) = 0, member(all_164_0_147, all_0_4_4) = 0, yields:
% 294.66/235.69 | (360) all_164_0_147 = all_162_0_146 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = v0) | ( ~ (v0 = 0) & member(all_162_0_146, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (174) with all_164_0_147, all_90_0_121, all_82_3_120, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_164_0_147, all_0_4_4) = 0, member(all_90_0_121, all_0_4_4) = 0, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.66/235.69 | (361) all_164_0_147 = all_90_0_121 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0))
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (50) with all_170_0_150, all_160_0_145, all_82_2_119, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_82_2_119, all_170_0_150) = 0, member(all_160_0_145, all_0_4_4) = 0, yields:
% 294.66/235.69 | (362) all_170_0_150 = all_160_0_145 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = v0) | ( ~ (v0 = 0) & member(all_170_0_150, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.66/235.69 |
% 294.66/235.69 | Instantiating formula (174) with all_160_0_145, all_92_0_122, all_82_2_119, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_160_0_145, all_0_4_4) = 0, member(all_92_0_122, all_0_4_4) = 0, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.66/235.69 | (363) all_160_0_145 = all_92_0_122 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0))
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (360), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (364) all_164_0_147 = all_162_0_146
% 294.66/235.69 |
% 294.66/235.69 | From (364) and (349) follows:
% 294.66/235.69 | (334) apply(all_0_5_5, all_82_3_120, all_162_0_146) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (361), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (366) all_164_0_147 = all_90_0_121
% 294.66/235.69 |
% 294.66/235.69 | Combining equations (366,364) yields a new equation:
% 294.66/235.69 | (367) all_162_0_146 = all_90_0_121
% 294.66/235.69 |
% 294.66/235.69 | From (367) and (334) follows:
% 294.66/235.69 | (210) apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (363), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (369) all_160_0_145 = all_92_0_122
% 294.66/235.69 |
% 294.66/235.69 | From (369) and (341) follows:
% 294.66/235.69 | (213) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (362), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (371) all_170_0_150 = all_160_0_145
% 294.66/235.69 |
% 294.66/235.69 | Combining equations (369,371) yields a new equation:
% 294.66/235.69 | (372) all_170_0_150 = all_92_0_122
% 294.66/235.69 |
% 294.66/235.69 | From (372) and (354) follows:
% 294.66/235.69 | (213) apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0
% 294.66/235.69 |
% 294.66/235.69 | From (372) and (332) follows:
% 294.66/235.69 | (214) member(all_92_0_122, all_0_4_4) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (359), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (375) all_168_0_149 = all_82_3_120
% 294.66/235.69 |
% 294.66/235.69 | From (375) and (344) follows:
% 294.66/235.69 | (270) apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (358), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (377) all_166_0_148 = all_82_2_119
% 294.66/235.69 |
% 294.66/235.69 | From (377) and (338) follows:
% 294.66/235.69 | (279) apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (204), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (379) ~ (all_82_0_117 = 0) & apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_82_0_117
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (379) yields:
% 294.66/235.69 | (380) ~ (all_82_0_117 = 0)
% 294.66/235.69 | (381) apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_82_0_117
% 294.66/235.69 |
% 294.66/235.69 +-Applying beta-rule and splitting (203), into two cases.
% 294.66/235.69 |-Branch one:
% 294.66/235.69 | (382) all_82_0_117 = 0 & apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0
% 294.66/235.69 |
% 294.66/235.69 | Applying alpha-rule on (382) yields:
% 294.66/235.69 | (383) all_82_0_117 = 0
% 294.66/235.69 | (384) apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (383) can reduce 380 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (386) all_82_1_118 = 0 & apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (386) yields:
% 294.66/235.70 | (387) all_82_1_118 = 0
% 294.66/235.70 | (388) apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (313), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (389) all_122_0_134 = all_120_0_133
% 294.66/235.70 |
% 294.66/235.70 | Combining equations (340,389) yields a new equation:
% 294.66/235.70 | (390) all_120_0_133 = all_82_2_119
% 294.66/235.70 |
% 294.66/235.70 | Combining equations (390,343) yields a new equation:
% 294.66/235.70 | (391) all_90_0_121 = all_82_2_119
% 294.66/235.70 |
% 294.66/235.70 | From (391) and (270) follows:
% 294.66/235.70 | (384) apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_82_3_120, 0, all_82_0_117 and discharging atoms apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_82_0_117, apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0, yields:
% 294.66/235.70 | (383) all_82_0_117 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (383) can reduce 380 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (395) ~ (all_122_0_134 = all_120_0_133)
% 294.66/235.70 | (396) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_122_0_134) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_120_0_133) = v0))
% 294.66/235.70 |
% 294.66/235.70 | Instantiating (396) with all_252_0_300 yields:
% 294.66/235.70 | (397) ( ~ (all_252_0_300 = 0) & apply(all_0_5_5, all_82_3_120, all_122_0_134) = all_252_0_300) | ( ~ (all_252_0_300 = 0) & apply(all_0_5_5, all_82_3_120, all_120_0_133) = all_252_0_300)
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (397), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (398) ~ (all_252_0_300 = 0) & apply(all_0_5_5, all_82_3_120, all_122_0_134) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (398) yields:
% 294.66/235.70 | (399) ~ (all_252_0_300 = 0)
% 294.66/235.70 | (400) apply(all_0_5_5, all_82_3_120, all_122_0_134) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | From (340) and (400) follows:
% 294.66/235.70 | (401) apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_82_2_119, 0, all_252_0_300 and discharging atoms apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_252_0_300, apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0, yields:
% 294.66/235.70 | (402) all_252_0_300 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (402) can reduce 399 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (404) ~ (all_252_0_300 = 0) & apply(all_0_5_5, all_82_3_120, all_120_0_133) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (404) yields:
% 294.66/235.70 | (399) ~ (all_252_0_300 = 0)
% 294.66/235.70 | (406) apply(all_0_5_5, all_82_3_120, all_120_0_133) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | From (343) and (406) follows:
% 294.66/235.70 | (407) apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_252_0_300
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_90_0_121, all_252_0_300, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_252_0_300, apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0, yields:
% 294.66/235.70 | (402) all_252_0_300 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (402) can reduce 399 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (410) ~ (all_82_1_118 = 0) & apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_82_1_118
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (410) yields:
% 294.66/235.70 | (411) ~ (all_82_1_118 = 0)
% 294.66/235.70 | (412) apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_82_1_118
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (203), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (382) all_82_0_117 = 0 & apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (382) yields:
% 294.66/235.70 | (383) all_82_0_117 = 0
% 294.66/235.70 | (384) apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (308), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (416) all_124_3_138 = all_92_0_122
% 294.66/235.70 |
% 294.66/235.70 | Combining equations (333,416) yields a new equation:
% 294.66/235.70 | (417) all_92_0_122 = all_82_3_120
% 294.66/235.70 |
% 294.66/235.70 | From (417) and (279) follows:
% 294.66/235.70 | (388) apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_82_2_119, 0, all_82_1_118 and discharging atoms apply(all_0_5_5, all_82_3_120, all_82_2_119) = all_82_1_118, apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0, yields:
% 294.66/235.70 | (387) all_82_1_118 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (387) can reduce 411 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (421) ~ (all_124_3_138 = all_92_0_122)
% 294.66/235.70 | (422) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_129_3_144, all_124_3_138) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_129_3_144, all_92_0_122) = v0))
% 294.66/235.70 |
% 294.66/235.70 | Instantiating (422) with all_252_0_721 yields:
% 294.66/235.70 | (423) ( ~ (all_252_0_721 = 0) & apply(all_0_5_5, all_129_3_144, all_124_3_138) = all_252_0_721) | ( ~ (all_252_0_721 = 0) & apply(all_0_5_5, all_129_3_144, all_92_0_122) = all_252_0_721)
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (423), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (424) ~ (all_252_0_721 = 0) & apply(all_0_5_5, all_129_3_144, all_124_3_138) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (424) yields:
% 294.66/235.70 | (425) ~ (all_252_0_721 = 0)
% 294.66/235.70 | (426) apply(all_0_5_5, all_129_3_144, all_124_3_138) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | From (353)(333) and (426) follows:
% 294.66/235.70 | (427) apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_82_3_120, 0, all_252_0_721 and discharging atoms apply(all_0_5_5, all_82_2_119, all_82_3_120) = all_252_0_721, apply(all_0_5_5, all_82_2_119, all_82_3_120) = 0, yields:
% 294.66/235.70 | (428) all_252_0_721 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (428) can reduce 425 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (430) ~ (all_252_0_721 = 0) & apply(all_0_5_5, all_129_3_144, all_92_0_122) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (430) yields:
% 294.66/235.70 | (425) ~ (all_252_0_721 = 0)
% 294.66/235.70 | (432) apply(all_0_5_5, all_129_3_144, all_92_0_122) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | From (353) and (432) follows:
% 294.66/235.70 | (433) apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_252_0_721
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_92_0_122, all_252_0_721, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_252_0_721, apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0, yields:
% 294.66/235.70 | (428) all_252_0_721 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (428) can reduce 425 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (386) all_82_1_118 = 0 & apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (386) yields:
% 294.66/235.70 | (387) all_82_1_118 = 0
% 294.66/235.70 | (388) apply(all_0_5_5, all_82_3_120, all_82_2_119) = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (387) can reduce 411 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (440) ~ (all_166_0_148 = all_82_2_119)
% 294.66/235.70 | (441) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = v0) | ( ~ (v0 = 0) & member(all_166_0_148, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0))
% 294.66/235.70 |
% 294.66/235.70 | Instantiating (441) with all_238_0_1002 yields:
% 294.66/235.70 | (442) ( ~ (all_238_0_1002 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_238_0_1002) | ( ~ (all_238_0_1002 = 0) & member(all_166_0_148, all_0_4_4) = all_238_0_1002) | ( ~ (all_238_0_1002 = 0) & member(all_92_0_122, all_0_4_4) = all_238_0_1002)
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (442), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (443) ( ~ (all_238_0_1002 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_238_0_1002) | ( ~ (all_238_0_1002 = 0) & member(all_166_0_148, all_0_4_4) = all_238_0_1002)
% 294.66/235.70 |
% 294.66/235.70 +-Applying beta-rule and splitting (443), into two cases.
% 294.66/235.70 |-Branch one:
% 294.66/235.70 | (444) ~ (all_238_0_1002 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (444) yields:
% 294.66/235.70 | (445) ~ (all_238_0_1002 = 0)
% 294.66/235.70 | (446) apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_82_2_119, all_238_0_1002, 0 and discharging atoms apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_238_0_1002, apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0, yields:
% 294.66/235.70 | (447) all_238_0_1002 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (447) can reduce 445 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (449) ~ (all_238_0_1002 = 0) & member(all_166_0_148, all_0_4_4) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (449) yields:
% 294.66/235.70 | (445) ~ (all_238_0_1002 = 0)
% 294.66/235.70 | (451) member(all_166_0_148, all_0_4_4) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (84) with all_166_0_148, all_0_4_4, all_238_0_1002, 0 and discharging atoms member(all_166_0_148, all_0_4_4) = all_238_0_1002, member(all_166_0_148, all_0_4_4) = 0, yields:
% 294.66/235.70 | (447) all_238_0_1002 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (447) can reduce 445 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (454) ~ (all_238_0_1002 = 0) & member(all_92_0_122, all_0_4_4) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Applying alpha-rule on (454) yields:
% 294.66/235.70 | (445) ~ (all_238_0_1002 = 0)
% 294.66/235.70 | (456) member(all_92_0_122, all_0_4_4) = all_238_0_1002
% 294.66/235.70 |
% 294.66/235.70 | Instantiating formula (84) with all_92_0_122, all_0_4_4, all_238_0_1002, 0 and discharging atoms member(all_92_0_122, all_0_4_4) = all_238_0_1002, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.66/235.70 | (447) all_238_0_1002 = 0
% 294.66/235.70 |
% 294.66/235.70 | Equations (447) can reduce 445 to:
% 294.66/235.70 | (197) $false
% 294.66/235.70 |
% 294.66/235.70 |-The branch is then unsatisfiable
% 294.66/235.70 |-Branch two:
% 294.66/235.70 | (459) ~ (all_168_0_149 = all_82_3_120)
% 294.66/235.70 | (460) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_168_0_149) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = v0))
% 294.66/235.70 |
% 294.66/235.70 | Instantiating (460) with all_234_0_1039 yields:
% 294.66/235.70 | (461) ( ~ (all_234_0_1039 = 0) & apply(all_0_5_5, all_90_0_121, all_168_0_149) = all_234_0_1039) | ( ~ (all_234_0_1039 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_234_0_1039)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (461), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (462) ~ (all_234_0_1039 = 0) & apply(all_0_5_5, all_90_0_121, all_168_0_149) = all_234_0_1039
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (462) yields:
% 294.66/235.71 | (463) ~ (all_234_0_1039 = 0)
% 294.66/235.71 | (464) apply(all_0_5_5, all_90_0_121, all_168_0_149) = all_234_0_1039
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_90_0_121, all_168_0_149, all_234_0_1039, 0 and discharging atoms apply(all_0_5_5, all_90_0_121, all_168_0_149) = all_234_0_1039, apply(all_0_5_5, all_90_0_121, all_168_0_149) = 0, yields:
% 294.66/235.71 | (465) all_234_0_1039 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (465) can reduce 463 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (467) ~ (all_234_0_1039 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_234_0_1039
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (467) yields:
% 294.66/235.71 | (463) ~ (all_234_0_1039 = 0)
% 294.66/235.71 | (469) apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_234_0_1039
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_90_0_121, all_82_3_120, all_234_0_1039, 0 and discharging atoms apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_234_0_1039, apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0, yields:
% 294.66/235.71 | (465) all_234_0_1039 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (465) can reduce 463 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (472) ~ (all_170_0_150 = all_160_0_145)
% 294.66/235.71 | (473) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = v0) | ( ~ (v0 = 0) & member(all_170_0_150, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.66/235.71 |
% 294.66/235.71 | Instantiating (473) with all_230_0_1066 yields:
% 294.66/235.71 | (474) ( ~ (all_230_0_1066 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_230_0_1066) | ( ~ (all_230_0_1066 = 0) & member(all_170_0_150, all_0_4_4) = all_230_0_1066) | ( ~ (all_230_0_1066 = 0) & member(all_82_2_119, all_0_4_4) = all_230_0_1066)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (474), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (475) ( ~ (all_230_0_1066 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_230_0_1066) | ( ~ (all_230_0_1066 = 0) & member(all_170_0_150, all_0_4_4) = all_230_0_1066)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (475), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (476) ~ (all_230_0_1066 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (476) yields:
% 294.66/235.71 | (477) ~ (all_230_0_1066 = 0)
% 294.66/235.71 | (478) apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | From (369) and (478) follows:
% 294.66/235.71 | (479) apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_92_0_122, all_230_0_1066, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_230_0_1066, apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0, yields:
% 294.66/235.71 | (480) all_230_0_1066 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (480) can reduce 477 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (482) ~ (all_230_0_1066 = 0) & member(all_170_0_150, all_0_4_4) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (482) yields:
% 294.66/235.71 | (477) ~ (all_230_0_1066 = 0)
% 294.66/235.71 | (484) member(all_170_0_150, all_0_4_4) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (84) with all_170_0_150, all_0_4_4, all_230_0_1066, 0 and discharging atoms member(all_170_0_150, all_0_4_4) = all_230_0_1066, member(all_170_0_150, all_0_4_4) = 0, yields:
% 294.66/235.71 | (480) all_230_0_1066 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (480) can reduce 477 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (487) ~ (all_230_0_1066 = 0) & member(all_82_2_119, all_0_4_4) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (487) yields:
% 294.66/235.71 | (477) ~ (all_230_0_1066 = 0)
% 294.66/235.71 | (489) member(all_82_2_119, all_0_4_4) = all_230_0_1066
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (84) with all_82_2_119, all_0_4_4, all_230_0_1066, 0 and discharging atoms member(all_82_2_119, all_0_4_4) = all_230_0_1066, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.66/235.71 | (480) all_230_0_1066 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (480) can reduce 477 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (492) ~ (all_160_0_145 = all_92_0_122)
% 294.66/235.71 | (493) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0))
% 294.66/235.71 |
% 294.66/235.71 | Instantiating (493) with all_226_0_1175 yields:
% 294.66/235.71 | (494) ( ~ (all_226_0_1175 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_226_0_1175) | ( ~ (all_226_0_1175 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_226_0_1175)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (494), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (495) ~ (all_226_0_1175 = 0) & apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_226_0_1175
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (495) yields:
% 294.66/235.71 | (496) ~ (all_226_0_1175 = 0)
% 294.66/235.71 | (497) apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_226_0_1175
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_160_0_145, all_226_0_1175, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_160_0_145) = all_226_0_1175, apply(all_0_5_5, all_82_2_119, all_160_0_145) = 0, yields:
% 294.66/235.71 | (498) all_226_0_1175 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (498) can reduce 496 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (500) ~ (all_226_0_1175 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_226_0_1175
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (500) yields:
% 294.66/235.71 | (496) ~ (all_226_0_1175 = 0)
% 294.66/235.71 | (502) apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_226_0_1175
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_92_0_122, all_226_0_1175, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_226_0_1175, apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0, yields:
% 294.66/235.71 | (498) all_226_0_1175 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (498) can reduce 496 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (505) ~ (all_164_0_147 = all_90_0_121)
% 294.66/235.71 | (506) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0))
% 294.66/235.71 |
% 294.66/235.71 | Instantiating (506) with all_222_0_1218 yields:
% 294.66/235.71 | (507) ( ~ (all_222_0_1218 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_222_0_1218) | ( ~ (all_222_0_1218 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_222_0_1218)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (507), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (508) ~ (all_222_0_1218 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_222_0_1218
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (508) yields:
% 294.66/235.71 | (509) ~ (all_222_0_1218 = 0)
% 294.66/235.71 | (510) apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_222_0_1218
% 294.66/235.71 |
% 294.66/235.71 | From (364) and (510) follows:
% 294.66/235.71 | (511) apply(all_0_5_5, all_82_3_120, all_162_0_146) = all_222_0_1218
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_162_0_146, all_222_0_1218, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_162_0_146) = all_222_0_1218, apply(all_0_5_5, all_82_3_120, all_162_0_146) = 0, yields:
% 294.66/235.71 | (512) all_222_0_1218 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (512) can reduce 509 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (514) ~ (all_222_0_1218 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_222_0_1218
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (514) yields:
% 294.66/235.71 | (509) ~ (all_222_0_1218 = 0)
% 294.66/235.71 | (516) apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_222_0_1218
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_90_0_121, all_222_0_1218, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_222_0_1218, apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0, yields:
% 294.66/235.71 | (512) all_222_0_1218 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (512) can reduce 509 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (519) ~ (all_164_0_147 = all_162_0_146)
% 294.66/235.71 | (520) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = v0) | ( ~ (v0 = 0) & member(all_162_0_146, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.71 |
% 294.66/235.71 | Instantiating (520) with all_218_0_1312 yields:
% 294.66/235.71 | (521) ( ~ (all_218_0_1312 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_218_0_1312) | ( ~ (all_218_0_1312 = 0) & member(all_162_0_146, all_0_4_4) = all_218_0_1312) | ( ~ (all_218_0_1312 = 0) & member(all_82_3_120, all_0_4_4) = all_218_0_1312)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (521), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (522) ( ~ (all_218_0_1312 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_218_0_1312) | ( ~ (all_218_0_1312 = 0) & member(all_162_0_146, all_0_4_4) = all_218_0_1312)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (522), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (523) ~ (all_218_0_1312 = 0) & apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (523) yields:
% 294.66/235.71 | (524) ~ (all_218_0_1312 = 0)
% 294.66/235.71 | (525) apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_164_0_147, all_218_0_1312, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_164_0_147) = all_218_0_1312, apply(all_0_5_5, all_82_3_120, all_164_0_147) = 0, yields:
% 294.66/235.71 | (526) all_218_0_1312 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (526) can reduce 524 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (528) ~ (all_218_0_1312 = 0) & member(all_162_0_146, all_0_4_4) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (528) yields:
% 294.66/235.71 | (524) ~ (all_218_0_1312 = 0)
% 294.66/235.71 | (530) member(all_162_0_146, all_0_4_4) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (84) with all_162_0_146, all_0_4_4, all_218_0_1312, 0 and discharging atoms member(all_162_0_146, all_0_4_4) = all_218_0_1312, member(all_162_0_146, all_0_4_4) = 0, yields:
% 294.66/235.71 | (526) all_218_0_1312 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (526) can reduce 524 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (533) ~ (all_218_0_1312 = 0) & member(all_82_3_120, all_0_4_4) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (533) yields:
% 294.66/235.71 | (524) ~ (all_218_0_1312 = 0)
% 294.66/235.71 | (535) member(all_82_3_120, all_0_4_4) = all_218_0_1312
% 294.66/235.71 |
% 294.66/235.71 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_218_0_1312, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_218_0_1312, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.66/235.71 | (526) all_218_0_1312 = 0
% 294.66/235.71 |
% 294.66/235.71 | Equations (526) can reduce 524 to:
% 294.66/235.71 | (197) $false
% 294.66/235.71 |
% 294.66/235.71 |-The branch is then unsatisfiable
% 294.66/235.71 |-Branch two:
% 294.66/235.71 | (538) ~ (all_129_3_144 = all_122_0_134)
% 294.66/235.71 | (539) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = v0) | ( ~ (v0 = 0) & member(all_129_3_144, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0))
% 294.66/235.71 |
% 294.66/235.71 | Instantiating (539) with all_196_0_1585 yields:
% 294.66/235.71 | (540) ( ~ (all_196_0_1585 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_196_0_1585) | ( ~ (all_196_0_1585 = 0) & member(all_129_3_144, all_0_4_4) = all_196_0_1585) | ( ~ (all_196_0_1585 = 0) & member(all_92_0_122, all_0_4_4) = all_196_0_1585)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (540), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (541) ( ~ (all_196_0_1585 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_196_0_1585) | ( ~ (all_196_0_1585 = 0) & member(all_129_3_144, all_0_4_4) = all_196_0_1585)
% 294.66/235.71 |
% 294.66/235.71 +-Applying beta-rule and splitting (541), into two cases.
% 294.66/235.71 |-Branch one:
% 294.66/235.71 | (542) ~ (all_196_0_1585 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_196_0_1585
% 294.66/235.71 |
% 294.66/235.71 | Applying alpha-rule on (542) yields:
% 294.66/235.71 | (543) ~ (all_196_0_1585 = 0)
% 294.66/235.72 | (544) apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | From (340) and (544) follows:
% 294.66/235.72 | (545) apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_82_2_119, all_196_0_1585, 0 and discharging atoms apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_196_0_1585, apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0, yields:
% 294.66/235.72 | (546) all_196_0_1585 = 0
% 294.66/235.72 |
% 294.66/235.72 | Equations (546) can reduce 543 to:
% 294.66/235.72 | (197) $false
% 294.66/235.72 |
% 294.66/235.72 |-The branch is then unsatisfiable
% 294.66/235.72 |-Branch two:
% 294.66/235.72 | (548) ~ (all_196_0_1585 = 0) & member(all_129_3_144, all_0_4_4) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | Applying alpha-rule on (548) yields:
% 294.66/235.72 | (543) ~ (all_196_0_1585 = 0)
% 294.66/235.72 | (550) member(all_129_3_144, all_0_4_4) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (84) with all_129_3_144, all_0_4_4, all_196_0_1585, 0 and discharging atoms member(all_129_3_144, all_0_4_4) = all_196_0_1585, member(all_129_3_144, all_0_4_4) = 0, yields:
% 294.66/235.72 | (546) all_196_0_1585 = 0
% 294.66/235.72 |
% 294.66/235.72 | Equations (546) can reduce 543 to:
% 294.66/235.72 | (197) $false
% 294.66/235.72 |
% 294.66/235.72 |-The branch is then unsatisfiable
% 294.66/235.72 |-Branch two:
% 294.66/235.72 | (553) ~ (all_196_0_1585 = 0) & member(all_92_0_122, all_0_4_4) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | Applying alpha-rule on (553) yields:
% 294.66/235.72 | (543) ~ (all_196_0_1585 = 0)
% 294.66/235.72 | (555) member(all_92_0_122, all_0_4_4) = all_196_0_1585
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (84) with all_92_0_122, all_0_4_4, all_196_0_1585, 0 and discharging atoms member(all_92_0_122, all_0_4_4) = all_196_0_1585, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.66/235.72 | (546) all_196_0_1585 = 0
% 294.66/235.72 |
% 294.66/235.72 | Equations (546) can reduce 543 to:
% 294.66/235.72 | (197) $false
% 294.66/235.72 |
% 294.66/235.72 |-The branch is then unsatisfiable
% 294.66/235.72 |-Branch two:
% 294.66/235.72 | (558) ~ (all_125_0_139 = all_124_3_138)
% 294.66/235.72 | (559) ? [v0] : (( ~ (v0 = 0) & member(all_125_0_139, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_124_3_138, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0))
% 294.66/235.72 |
% 294.66/235.72 | Instantiating (559) with all_192_0_1642 yields:
% 294.66/235.72 | (560) ( ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642) | ( ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642) | ( ~ (all_192_0_1642 = 0) & member(all_90_0_121, all_0_4_4) = all_192_0_1642)
% 294.66/235.72 |
% 294.66/235.72 | Equations (333) can reduce 558 to:
% 294.66/235.72 | (561) ~ (all_125_0_139 = all_82_3_120)
% 294.66/235.72 |
% 294.66/235.72 +-Applying beta-rule and splitting (301), into two cases.
% 294.66/235.72 |-Branch one:
% 294.66/235.72 | (348) all_125_0_139 = all_82_3_120
% 294.66/235.72 |
% 294.66/235.72 | Equations (348) can reduce 561 to:
% 294.66/235.72 | (197) $false
% 294.66/235.72 |
% 294.66/235.72 |-The branch is then unsatisfiable
% 294.66/235.72 |-Branch two:
% 294.66/235.72 | (561) ~ (all_125_0_139 = all_82_3_120)
% 294.66/235.72 | (565) ? [v0] : (( ~ (v0 = 0) & member(all_125_0_139, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.66/235.72 |
% 294.66/235.72 | Instantiating (565) with all_197_0_1643 yields:
% 294.66/235.72 | (566) ( ~ (all_197_0_1643 = 0) & member(all_125_0_139, all_0_4_4) = all_197_0_1643) | ( ~ (all_197_0_1643 = 0) & member(all_90_0_121, all_0_4_4) = all_197_0_1643) | ( ~ (all_197_0_1643 = 0) & member(all_82_3_120, all_0_4_4) = all_197_0_1643)
% 294.66/235.72 |
% 294.66/235.72 +-Applying beta-rule and splitting (566), into two cases.
% 294.66/235.72 |-Branch one:
% 294.66/235.72 | (567) ( ~ (all_197_0_1643 = 0) & member(all_125_0_139, all_0_4_4) = all_197_0_1643) | ( ~ (all_197_0_1643 = 0) & member(all_90_0_121, all_0_4_4) = all_197_0_1643)
% 294.66/235.72 |
% 294.66/235.72 +-Applying beta-rule and splitting (567), into two cases.
% 294.66/235.72 |-Branch one:
% 294.66/235.72 | (568) ~ (all_197_0_1643 = 0) & member(all_125_0_139, all_0_4_4) = all_197_0_1643
% 294.66/235.72 |
% 294.66/235.72 | Applying alpha-rule on (568) yields:
% 294.66/235.72 | (569) ~ (all_197_0_1643 = 0)
% 294.66/235.72 | (570) member(all_125_0_139, all_0_4_4) = all_197_0_1643
% 294.66/235.72 |
% 294.66/235.72 +-Applying beta-rule and splitting (560), into two cases.
% 294.66/235.72 |-Branch one:
% 294.66/235.72 | (571) ( ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642) | ( ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642)
% 294.66/235.72 |
% 294.66/235.72 +-Applying beta-rule and splitting (571), into two cases.
% 294.66/235.72 |-Branch one:
% 294.66/235.72 | (572) ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | Applying alpha-rule on (572) yields:
% 294.66/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.66/235.72 | (574) member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (84) with all_125_0_139, all_0_4_4, all_197_0_1643, 0 and discharging atoms member(all_125_0_139, all_0_4_4) = all_197_0_1643, member(all_125_0_139, all_0_4_4) = 0, yields:
% 294.66/235.72 | (575) all_197_0_1643 = 0
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (84) with all_125_0_139, all_0_4_4, all_192_0_1642, all_197_0_1643 and discharging atoms member(all_125_0_139, all_0_4_4) = all_197_0_1643, member(all_125_0_139, all_0_4_4) = all_192_0_1642, yields:
% 294.66/235.72 | (576) all_197_0_1643 = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | Combining equations (576,575) yields a new equation:
% 294.66/235.72 | (577) all_192_0_1642 = 0
% 294.66/235.72 |
% 294.66/235.72 | Simplifying 577 yields:
% 294.66/235.72 | (578) all_192_0_1642 = 0
% 294.66/235.72 |
% 294.66/235.72 | Equations (578) can reduce 573 to:
% 294.66/235.72 | (197) $false
% 294.66/235.72 |
% 294.66/235.72 |-The branch is then unsatisfiable
% 294.66/235.72 |-Branch two:
% 294.66/235.72 | (580) ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | Applying alpha-rule on (580) yields:
% 294.66/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.66/235.72 | (582) member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | From (333) and (582) follows:
% 294.66/235.72 | (583) member(all_82_3_120, all_0_4_4) = all_192_0_1642
% 294.66/235.72 |
% 294.66/235.72 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_192_0_1642, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (586) ~ (all_192_0_1642 = 0) & member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (586) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (588) member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_192_0_1642, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (591) ~ (all_197_0_1643 = 0) & member(all_90_0_121, all_0_4_4) = all_197_0_1643
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (591) yields:
% 294.84/235.72 | (569) ~ (all_197_0_1643 = 0)
% 294.84/235.72 | (593) member(all_90_0_121, all_0_4_4) = all_197_0_1643
% 294.84/235.72 |
% 294.84/235.72 +-Applying beta-rule and splitting (560), into two cases.
% 294.84/235.72 |-Branch one:
% 294.84/235.72 | (571) ( ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642) | ( ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642)
% 294.84/235.72 |
% 294.84/235.72 +-Applying beta-rule and splitting (571), into two cases.
% 294.84/235.72 |-Branch one:
% 294.84/235.72 | (572) ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (572) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (574) member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_125_0_139, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_125_0_139, all_0_4_4) = all_192_0_1642, member(all_125_0_139, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (580) ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (580) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (582) member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | From (333) and (582) follows:
% 294.84/235.72 | (583) member(all_82_3_120, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_192_0_1642, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (586) ~ (all_192_0_1642 = 0) & member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (586) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (588) member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_197_0_1643, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_197_0_1643, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.84/235.72 | (575) all_197_0_1643 = 0
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_192_0_1642, all_197_0_1643 and discharging atoms member(all_90_0_121, all_0_4_4) = all_197_0_1643, member(all_90_0_121, all_0_4_4) = all_192_0_1642, yields:
% 294.84/235.72 | (576) all_197_0_1643 = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Combining equations (576,575) yields a new equation:
% 294.84/235.72 | (577) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Simplifying 577 yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (614) ~ (all_197_0_1643 = 0) & member(all_82_3_120, all_0_4_4) = all_197_0_1643
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (614) yields:
% 294.84/235.72 | (569) ~ (all_197_0_1643 = 0)
% 294.84/235.72 | (616) member(all_82_3_120, all_0_4_4) = all_197_0_1643
% 294.84/235.72 |
% 294.84/235.72 +-Applying beta-rule and splitting (560), into two cases.
% 294.84/235.72 |-Branch one:
% 294.84/235.72 | (571) ( ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642) | ( ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642)
% 294.84/235.72 |
% 294.84/235.72 +-Applying beta-rule and splitting (571), into two cases.
% 294.84/235.72 |-Branch one:
% 294.84/235.72 | (572) ~ (all_192_0_1642 = 0) & member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (572) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (574) member(all_125_0_139, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_125_0_139, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_125_0_139, all_0_4_4) = all_192_0_1642, member(all_125_0_139, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (580) ~ (all_192_0_1642 = 0) & member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (580) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (582) member(all_124_3_138, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | From (333) and (582) follows:
% 294.84/235.72 | (583) member(all_82_3_120, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_197_0_1643, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_197_0_1643, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.72 | (575) all_197_0_1643 = 0
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_192_0_1642, all_197_0_1643 and discharging atoms member(all_82_3_120, all_0_4_4) = all_197_0_1643, member(all_82_3_120, all_0_4_4) = all_192_0_1642, yields:
% 294.84/235.72 | (576) all_197_0_1643 = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Combining equations (575,576) yields a new equation:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (586) ~ (all_192_0_1642 = 0) & member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Applying alpha-rule on (586) yields:
% 294.84/235.72 | (573) ~ (all_192_0_1642 = 0)
% 294.84/235.72 | (588) member(all_90_0_121, all_0_4_4) = all_192_0_1642
% 294.84/235.72 |
% 294.84/235.72 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_192_0_1642, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_192_0_1642, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.84/235.72 | (578) all_192_0_1642 = 0
% 294.84/235.72 |
% 294.84/235.72 | Equations (578) can reduce 573 to:
% 294.84/235.72 | (197) $false
% 294.84/235.72 |
% 294.84/235.72 |-The branch is then unsatisfiable
% 294.84/235.72 |-Branch two:
% 294.84/235.72 | (636) ~ (all_120_0_133 = all_90_0_121)
% 294.84/235.73 | (637) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0) | ( ~ (v0 = 0) & member(all_120_0_133, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.84/235.73 |
% 294.84/235.73 | Instantiating (637) with all_188_0_1766 yields:
% 294.84/235.73 | (638) ( ~ (all_188_0_1766 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_188_0_1766) | ( ~ (all_188_0_1766 = 0) & member(all_120_0_133, all_0_4_4) = all_188_0_1766) | ( ~ (all_188_0_1766 = 0) & member(all_82_3_120, all_0_4_4) = all_188_0_1766)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (638), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (639) ( ~ (all_188_0_1766 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_188_0_1766) | ( ~ (all_188_0_1766 = 0) & member(all_120_0_133, all_0_4_4) = all_188_0_1766)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (639), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (640) ~ (all_188_0_1766 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (640) yields:
% 294.84/235.73 | (641) ~ (all_188_0_1766 = 0)
% 294.84/235.73 | (642) apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_90_0_121, all_188_0_1766, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_188_0_1766, apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0, yields:
% 294.84/235.73 | (643) all_188_0_1766 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (643) can reduce 641 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (645) ~ (all_188_0_1766 = 0) & member(all_120_0_133, all_0_4_4) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (645) yields:
% 294.84/235.73 | (641) ~ (all_188_0_1766 = 0)
% 294.84/235.73 | (647) member(all_120_0_133, all_0_4_4) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_120_0_133, all_0_4_4, all_188_0_1766, 0 and discharging atoms member(all_120_0_133, all_0_4_4) = all_188_0_1766, member(all_120_0_133, all_0_4_4) = 0, yields:
% 294.84/235.73 | (643) all_188_0_1766 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (643) can reduce 641 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (650) ~ (all_188_0_1766 = 0) & member(all_82_3_120, all_0_4_4) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (650) yields:
% 294.84/235.73 | (641) ~ (all_188_0_1766 = 0)
% 294.84/235.73 | (652) member(all_82_3_120, all_0_4_4) = all_188_0_1766
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_188_0_1766, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_188_0_1766, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.73 | (643) all_188_0_1766 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (643) can reduce 641 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (655) ~ (all_122_0_134 = all_82_2_119)
% 294.84/235.73 | (656) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = v0) | ( ~ (v0 = 0) & member(all_92_0_122, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.84/235.73 |
% 294.84/235.73 | Instantiating (656) with all_184_0_1896 yields:
% 294.84/235.73 | (657) ( ~ (all_184_0_1896 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_184_0_1896) | ( ~ (all_184_0_1896 = 0) & member(all_92_0_122, all_0_4_4) = all_184_0_1896) | ( ~ (all_184_0_1896 = 0) & member(all_82_2_119, all_0_4_4) = all_184_0_1896)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (657), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (658) ( ~ (all_184_0_1896 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_184_0_1896) | ( ~ (all_184_0_1896 = 0) & member(all_92_0_122, all_0_4_4) = all_184_0_1896)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (658), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (659) ~ (all_184_0_1896 = 0) & apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (659) yields:
% 294.84/235.73 | (660) ~ (all_184_0_1896 = 0)
% 294.84/235.73 | (661) apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_122_0_134, all_184_0_1896, 0 and discharging atoms apply(all_0_5_5, all_92_0_122, all_122_0_134) = all_184_0_1896, apply(all_0_5_5, all_92_0_122, all_122_0_134) = 0, yields:
% 294.84/235.73 | (662) all_184_0_1896 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (662) can reduce 660 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (664) ~ (all_184_0_1896 = 0) & member(all_92_0_122, all_0_4_4) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (664) yields:
% 294.84/235.73 | (660) ~ (all_184_0_1896 = 0)
% 294.84/235.73 | (666) member(all_92_0_122, all_0_4_4) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_92_0_122, all_0_4_4, all_184_0_1896, 0 and discharging atoms member(all_92_0_122, all_0_4_4) = all_184_0_1896, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.84/235.73 | (662) all_184_0_1896 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (662) can reduce 660 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (669) ~ (all_184_0_1896 = 0) & member(all_82_2_119, all_0_4_4) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (669) yields:
% 294.84/235.73 | (660) ~ (all_184_0_1896 = 0)
% 294.84/235.73 | (671) member(all_82_2_119, all_0_4_4) = all_184_0_1896
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_82_2_119, all_0_4_4, all_184_0_1896, 0 and discharging atoms member(all_82_2_119, all_0_4_4) = all_184_0_1896, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.84/235.73 | (662) all_184_0_1896 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (662) can reduce 660 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (674) ~ (all_127_0_140 = all_92_0_122)
% 294.84/235.73 | (675) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_127_0_140) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0))
% 294.84/235.73 |
% 294.84/235.73 | Instantiating (675) with all_180_0_2320 yields:
% 294.84/235.73 | (676) ( ~ (all_180_0_2320 = 0) & apply(all_0_5_5, all_82_2_119, all_127_0_140) = all_180_0_2320) | ( ~ (all_180_0_2320 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_180_0_2320)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (676), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (677) ~ (all_180_0_2320 = 0) & apply(all_0_5_5, all_82_2_119, all_127_0_140) = all_180_0_2320
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (677) yields:
% 294.84/235.73 | (678) ~ (all_180_0_2320 = 0)
% 294.84/235.73 | (679) apply(all_0_5_5, all_82_2_119, all_127_0_140) = all_180_0_2320
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_127_0_140, all_180_0_2320, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_127_0_140) = all_180_0_2320, apply(all_0_5_5, all_82_2_119, all_127_0_140) = 0, yields:
% 294.84/235.73 | (680) all_180_0_2320 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (680) can reduce 678 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (682) ~ (all_180_0_2320 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_180_0_2320
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (682) yields:
% 294.84/235.73 | (678) ~ (all_180_0_2320 = 0)
% 294.84/235.73 | (684) apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_180_0_2320
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_92_0_122, all_180_0_2320, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_180_0_2320, apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0, yields:
% 294.84/235.73 | (680) all_180_0_2320 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (680) can reduce 678 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (687) ~ (all_124_3_138 = all_82_3_120)
% 294.84/235.73 | (688) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_124_3_138) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.84/235.73 |
% 294.84/235.73 | Instantiating (688) with all_176_0_2403 yields:
% 294.84/235.73 | (689) ( ~ (all_176_0_2403 = 0) & apply(all_0_5_5, all_90_0_121, all_124_3_138) = all_176_0_2403) | ( ~ (all_176_0_2403 = 0) & member(all_90_0_121, all_0_4_4) = all_176_0_2403) | ( ~ (all_176_0_2403 = 0) & member(all_82_3_120, all_0_4_4) = all_176_0_2403)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (302), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (343) all_120_0_133 = all_90_0_121
% 294.84/235.73 |
% 294.84/235.73 | From (343) and (256) follows:
% 294.84/235.73 | (211) member(all_90_0_121, all_0_4_4) = 0
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (689), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (692) ( ~ (all_176_0_2403 = 0) & apply(all_0_5_5, all_90_0_121, all_124_3_138) = all_176_0_2403) | ( ~ (all_176_0_2403 = 0) & member(all_90_0_121, all_0_4_4) = all_176_0_2403)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (692), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (693) ~ (all_176_0_2403 = 0) & apply(all_0_5_5, all_90_0_121, all_124_3_138) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (693) yields:
% 294.84/235.73 | (694) ~ (all_176_0_2403 = 0)
% 294.84/235.73 | (695) apply(all_0_5_5, all_90_0_121, all_124_3_138) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_90_0_121, all_124_3_138, all_176_0_2403, 0 and discharging atoms apply(all_0_5_5, all_90_0_121, all_124_3_138) = all_176_0_2403, apply(all_0_5_5, all_90_0_121, all_124_3_138) = 0, yields:
% 294.84/235.73 | (696) all_176_0_2403 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (696) can reduce 694 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (698) ~ (all_176_0_2403 = 0) & member(all_90_0_121, all_0_4_4) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (698) yields:
% 294.84/235.73 | (694) ~ (all_176_0_2403 = 0)
% 294.84/235.73 | (700) member(all_90_0_121, all_0_4_4) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_176_0_2403, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_176_0_2403, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.84/235.73 | (696) all_176_0_2403 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (696) can reduce 694 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (703) ~ (all_176_0_2403 = 0) & member(all_82_3_120, all_0_4_4) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (703) yields:
% 294.84/235.73 | (694) ~ (all_176_0_2403 = 0)
% 294.84/235.73 | (705) member(all_82_3_120, all_0_4_4) = all_176_0_2403
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_176_0_2403, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_176_0_2403, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.73 | (696) all_176_0_2403 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (696) can reduce 694 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (636) ~ (all_120_0_133 = all_90_0_121)
% 294.84/235.73 | (637) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0) | ( ~ (v0 = 0) & member(all_120_0_133, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_3_120, all_0_4_4) = v0))
% 294.84/235.73 |
% 294.84/235.73 | Instantiating (637) with all_193_0_2559 yields:
% 294.84/235.73 | (710) ( ~ (all_193_0_2559 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_193_0_2559) | ( ~ (all_193_0_2559 = 0) & member(all_120_0_133, all_0_4_4) = all_193_0_2559) | ( ~ (all_193_0_2559 = 0) & member(all_82_3_120, all_0_4_4) = all_193_0_2559)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (710), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (711) ( ~ (all_193_0_2559 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_193_0_2559) | ( ~ (all_193_0_2559 = 0) & member(all_120_0_133, all_0_4_4) = all_193_0_2559)
% 294.84/235.73 |
% 294.84/235.73 +-Applying beta-rule and splitting (711), into two cases.
% 294.84/235.73 |-Branch one:
% 294.84/235.73 | (712) ~ (all_193_0_2559 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_193_0_2559
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (712) yields:
% 294.84/235.73 | (713) ~ (all_193_0_2559 = 0)
% 294.84/235.73 | (714) apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_193_0_2559
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_90_0_121, all_193_0_2559, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_193_0_2559, apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0, yields:
% 294.84/235.73 | (715) all_193_0_2559 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (715) can reduce 713 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.73 | (717) ~ (all_193_0_2559 = 0) & member(all_120_0_133, all_0_4_4) = all_193_0_2559
% 294.84/235.73 |
% 294.84/235.73 | Applying alpha-rule on (717) yields:
% 294.84/235.73 | (713) ~ (all_193_0_2559 = 0)
% 294.84/235.73 | (719) member(all_120_0_133, all_0_4_4) = all_193_0_2559
% 294.84/235.73 |
% 294.84/235.73 | Instantiating formula (84) with all_120_0_133, all_0_4_4, all_193_0_2559, 0 and discharging atoms member(all_120_0_133, all_0_4_4) = all_193_0_2559, member(all_120_0_133, all_0_4_4) = 0, yields:
% 294.84/235.73 | (715) all_193_0_2559 = 0
% 294.84/235.73 |
% 294.84/235.73 | Equations (715) can reduce 713 to:
% 294.84/235.73 | (197) $false
% 294.84/235.73 |
% 294.84/235.73 |-The branch is then unsatisfiable
% 294.84/235.73 |-Branch two:
% 294.84/235.74 | (722) ~ (all_193_0_2559 = 0) & member(all_82_3_120, all_0_4_4) = all_193_0_2559
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (722) yields:
% 294.84/235.74 | (713) ~ (all_193_0_2559 = 0)
% 294.84/235.74 | (724) member(all_82_3_120, all_0_4_4) = all_193_0_2559
% 294.84/235.74 |
% 294.84/235.74 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_193_0_2559, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_193_0_2559, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.84/235.74 | (715) all_193_0_2559 = 0
% 294.84/235.74 |
% 294.84/235.74 | Equations (715) can reduce 713 to:
% 294.84/235.74 | (197) $false
% 294.84/235.74 |
% 294.84/235.74 |-The branch is then unsatisfiable
% 294.84/235.74 |-Branch two:
% 294.84/235.74 | (727) ~ (all_129_3_144 = 0) & member(all_92_0_122, all_0_4_4) = all_129_3_144
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (727) yields:
% 294.84/235.74 | (728) ~ (all_129_3_144 = 0)
% 294.84/235.74 | (729) member(all_92_0_122, all_0_4_4) = all_129_3_144
% 294.84/235.74 |
% 294.84/235.74 | Instantiating formula (84) with all_92_0_122, all_0_4_4, all_129_3_144, 0 and discharging atoms member(all_92_0_122, all_0_4_4) = all_129_3_144, member(all_92_0_122, all_0_4_4) = 0, yields:
% 294.84/235.74 | (730) all_129_3_144 = 0
% 294.84/235.74 |
% 294.84/235.74 | Equations (730) can reduce 728 to:
% 294.84/235.74 | (197) $false
% 294.84/235.74 |
% 294.84/235.74 |-The branch is then unsatisfiable
% 294.84/235.74 |-Branch two:
% 294.84/235.74 | (732) ~ (all_124_3_138 = 0) & member(all_90_0_121, all_0_4_4) = all_124_3_138
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (732) yields:
% 294.84/235.74 | (733) ~ (all_124_3_138 = 0)
% 294.84/235.74 | (734) member(all_90_0_121, all_0_4_4) = all_124_3_138
% 294.84/235.74 |
% 294.84/235.74 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_124_3_138, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_124_3_138, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.84/235.74 | (735) all_124_3_138 = 0
% 294.84/235.74 |
% 294.84/235.74 | Equations (735) can reduce 733 to:
% 294.84/235.74 | (197) $false
% 294.84/235.74 |
% 294.84/235.74 |-The branch is then unsatisfiable
% 294.84/235.74 |-Branch two:
% 294.84/235.74 | (737) ~ (all_102_0_124 = all_82_2_119)
% 294.84/235.74 | (738) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_105_3_132, all_102_0_124) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_105_3_132, all_82_2_119) = v0))
% 294.84/235.74 |
% 294.84/235.74 | Instantiating (738) with all_146_0_2896 yields:
% 294.84/235.74 | (739) ( ~ (all_146_0_2896 = 0) & apply(all_0_5_5, all_105_3_132, all_102_0_124) = all_146_0_2896) | ( ~ (all_146_0_2896 = 0) & apply(all_0_5_5, all_105_3_132, all_82_2_119) = all_146_0_2896)
% 294.84/235.74 |
% 294.84/235.74 +-Applying beta-rule and splitting (250), into two cases.
% 294.84/235.74 |-Branch one:
% 294.84/235.74 | (282) all_102_0_124 = all_82_2_119
% 294.84/235.74 |
% 294.84/235.74 | Equations (282) can reduce 737 to:
% 294.84/235.74 | (197) $false
% 294.84/235.74 |
% 294.84/235.74 |-The branch is then unsatisfiable
% 294.84/235.74 |-Branch two:
% 294.84/235.74 | (737) ~ (all_102_0_124 = all_82_2_119)
% 294.84/235.74 | (743) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_102_0_124) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = v0))
% 294.84/235.74 |
% 294.84/235.74 | Instantiating (743) with all_151_0_2897 yields:
% 294.84/235.74 | (744) ( ~ (all_151_0_2897 = 0) & apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_151_0_2897) | ( ~ (all_151_0_2897 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_151_0_2897)
% 294.84/235.74 |
% 294.84/235.74 +-Applying beta-rule and splitting (744), into two cases.
% 294.84/235.74 |-Branch one:
% 294.84/235.74 | (745) ~ (all_151_0_2897 = 0) & apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_151_0_2897
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (745) yields:
% 294.84/235.74 | (746) ~ (all_151_0_2897 = 0)
% 294.84/235.74 | (747) apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_151_0_2897
% 294.84/235.74 |
% 294.84/235.74 +-Applying beta-rule and splitting (739), into two cases.
% 294.84/235.74 |-Branch one:
% 294.84/235.74 | (748) ~ (all_146_0_2896 = 0) & apply(all_0_5_5, all_105_3_132, all_102_0_124) = all_146_0_2896
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (748) yields:
% 294.84/235.74 | (749) ~ (all_146_0_2896 = 0)
% 294.84/235.74 | (750) apply(all_0_5_5, all_105_3_132, all_102_0_124) = all_146_0_2896
% 294.84/235.74 |
% 294.84/235.74 | From (277) and (750) follows:
% 294.84/235.74 | (751) apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_146_0_2896
% 294.84/235.74 |
% 294.84/235.74 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_102_0_124, all_151_0_2897, 0 and discharging atoms apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_151_0_2897, apply(all_0_5_5, all_92_0_122, all_102_0_124) = 0, yields:
% 294.84/235.74 | (752) all_151_0_2897 = 0
% 294.84/235.74 |
% 294.84/235.74 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_102_0_124, all_146_0_2896, all_151_0_2897 and discharging atoms apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_151_0_2897, apply(all_0_5_5, all_92_0_122, all_102_0_124) = all_146_0_2896, yields:
% 294.84/235.74 | (753) all_151_0_2897 = all_146_0_2896
% 294.84/235.74 |
% 294.84/235.74 | Combining equations (752,753) yields a new equation:
% 294.84/235.74 | (754) all_146_0_2896 = 0
% 294.84/235.74 |
% 294.84/235.74 | Equations (754) can reduce 749 to:
% 294.84/235.74 | (197) $false
% 294.84/235.74 |
% 294.84/235.74 |-The branch is then unsatisfiable
% 294.84/235.74 |-Branch two:
% 294.84/235.74 | (756) ~ (all_146_0_2896 = 0) & apply(all_0_5_5, all_105_3_132, all_82_2_119) = all_146_0_2896
% 294.84/235.74 |
% 294.84/235.74 | Applying alpha-rule on (756) yields:
% 294.84/235.74 | (749) ~ (all_146_0_2896 = 0)
% 294.92/235.74 | (758) apply(all_0_5_5, all_105_3_132, all_82_2_119) = all_146_0_2896
% 294.92/235.74 |
% 294.92/235.74 | From (277) and (758) follows:
% 294.92/235.74 | (759) apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_146_0_2896
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_82_2_119, 0, all_146_0_2896 and discharging atoms apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_146_0_2896, apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0, yields:
% 294.92/235.74 | (754) all_146_0_2896 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (754) can reduce 749 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (762) ~ (all_151_0_2897 = 0) & apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_151_0_2897
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (762) yields:
% 294.92/235.74 | (746) ~ (all_151_0_2897 = 0)
% 294.92/235.74 | (764) apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_151_0_2897
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (113) with all_0_5_5, all_92_0_122, all_82_2_119, 0, all_151_0_2897 and discharging atoms apply(all_0_5_5, all_92_0_122, all_82_2_119) = all_151_0_2897, apply(all_0_5_5, all_92_0_122, all_82_2_119) = 0, yields:
% 294.92/235.74 | (752) all_151_0_2897 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (752) can reduce 746 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (767) ~ (all_105_3_132 = all_92_0_122)
% 294.92/235.74 | (768) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = v0) | ( ~ (v0 = 0) & member(all_105_3_132, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_82_2_119, all_0_4_4) = v0))
% 294.92/235.74 |
% 294.92/235.74 | Instantiating (768) with all_142_0_2911 yields:
% 294.92/235.74 | (769) ( ~ (all_142_0_2911 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_142_0_2911) | ( ~ (all_142_0_2911 = 0) & member(all_105_3_132, all_0_4_4) = all_142_0_2911) | ( ~ (all_142_0_2911 = 0) & member(all_82_2_119, all_0_4_4) = all_142_0_2911)
% 294.92/235.74 |
% 294.92/235.74 +-Applying beta-rule and splitting (769), into two cases.
% 294.92/235.74 |-Branch one:
% 294.92/235.74 | (770) ( ~ (all_142_0_2911 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_142_0_2911) | ( ~ (all_142_0_2911 = 0) & member(all_105_3_132, all_0_4_4) = all_142_0_2911)
% 294.92/235.74 |
% 294.92/235.74 +-Applying beta-rule and splitting (770), into two cases.
% 294.92/235.74 |-Branch one:
% 294.92/235.74 | (771) ~ (all_142_0_2911 = 0) & apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (771) yields:
% 294.92/235.74 | (772) ~ (all_142_0_2911 = 0)
% 294.92/235.74 | (773) apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (113) with all_0_5_5, all_82_2_119, all_92_0_122, all_142_0_2911, 0 and discharging atoms apply(all_0_5_5, all_82_2_119, all_92_0_122) = all_142_0_2911, apply(all_0_5_5, all_82_2_119, all_92_0_122) = 0, yields:
% 294.92/235.74 | (774) all_142_0_2911 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (774) can reduce 772 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (776) ~ (all_142_0_2911 = 0) & member(all_105_3_132, all_0_4_4) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (776) yields:
% 294.92/235.74 | (772) ~ (all_142_0_2911 = 0)
% 294.92/235.74 | (778) member(all_105_3_132, all_0_4_4) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (84) with all_105_3_132, all_0_4_4, all_142_0_2911, 0 and discharging atoms member(all_105_3_132, all_0_4_4) = all_142_0_2911, member(all_105_3_132, all_0_4_4) = 0, yields:
% 294.92/235.74 | (774) all_142_0_2911 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (774) can reduce 772 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (781) ~ (all_142_0_2911 = 0) & member(all_82_2_119, all_0_4_4) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (781) yields:
% 294.92/235.74 | (772) ~ (all_142_0_2911 = 0)
% 294.92/235.74 | (783) member(all_82_2_119, all_0_4_4) = all_142_0_2911
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (84) with all_82_2_119, all_0_4_4, all_142_0_2911, 0 and discharging atoms member(all_82_2_119, all_0_4_4) = all_142_0_2911, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.92/235.74 | (774) all_142_0_2911 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (774) can reduce 772 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (786) ~ (all_100_0_123 = all_82_3_120)
% 294.92/235.74 | (787) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = v0) | ( ~ (v0 = 0) & member(all_100_0_123, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_90_0_121, all_0_4_4) = v0))
% 294.92/235.74 |
% 294.92/235.74 | Instantiating (787) with all_138_0_2962 yields:
% 294.92/235.74 | (788) ( ~ (all_138_0_2962 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_138_0_2962) | ( ~ (all_138_0_2962 = 0) & member(all_100_0_123, all_0_4_4) = all_138_0_2962) | ( ~ (all_138_0_2962 = 0) & member(all_90_0_121, all_0_4_4) = all_138_0_2962)
% 294.92/235.74 |
% 294.92/235.74 +-Applying beta-rule and splitting (788), into two cases.
% 294.92/235.74 |-Branch one:
% 294.92/235.74 | (789) ( ~ (all_138_0_2962 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_138_0_2962) | ( ~ (all_138_0_2962 = 0) & member(all_100_0_123, all_0_4_4) = all_138_0_2962)
% 294.92/235.74 |
% 294.92/235.74 +-Applying beta-rule and splitting (789), into two cases.
% 294.92/235.74 |-Branch one:
% 294.92/235.74 | (790) ~ (all_138_0_2962 = 0) & apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (790) yields:
% 294.92/235.74 | (791) ~ (all_138_0_2962 = 0)
% 294.92/235.74 | (792) apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (113) with all_0_5_5, all_90_0_121, all_82_3_120, 0, all_138_0_2962 and discharging atoms apply(all_0_5_5, all_90_0_121, all_82_3_120) = all_138_0_2962, apply(all_0_5_5, all_90_0_121, all_82_3_120) = 0, yields:
% 294.92/235.74 | (793) all_138_0_2962 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (793) can reduce 791 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (795) ~ (all_138_0_2962 = 0) & member(all_100_0_123, all_0_4_4) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (795) yields:
% 294.92/235.74 | (791) ~ (all_138_0_2962 = 0)
% 294.92/235.74 | (797) member(all_100_0_123, all_0_4_4) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (84) with all_100_0_123, all_0_4_4, all_138_0_2962, 0 and discharging atoms member(all_100_0_123, all_0_4_4) = all_138_0_2962, member(all_100_0_123, all_0_4_4) = 0, yields:
% 294.92/235.74 | (793) all_138_0_2962 = 0
% 294.92/235.74 |
% 294.92/235.74 | Equations (793) can reduce 791 to:
% 294.92/235.74 | (197) $false
% 294.92/235.74 |
% 294.92/235.74 |-The branch is then unsatisfiable
% 294.92/235.74 |-Branch two:
% 294.92/235.74 | (800) ~ (all_138_0_2962 = 0) & member(all_90_0_121, all_0_4_4) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Applying alpha-rule on (800) yields:
% 294.92/235.74 | (791) ~ (all_138_0_2962 = 0)
% 294.92/235.74 | (802) member(all_90_0_121, all_0_4_4) = all_138_0_2962
% 294.92/235.74 |
% 294.92/235.74 | Instantiating formula (84) with all_90_0_121, all_0_4_4, all_138_0_2962, 0 and discharging atoms member(all_90_0_121, all_0_4_4) = all_138_0_2962, member(all_90_0_121, all_0_4_4) = 0, yields:
% 294.92/235.74 | (793) all_138_0_2962 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (793) can reduce 791 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (805) ~ (all_104_3_128 = all_90_0_121)
% 294.92/235.75 | (806) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_104_3_128) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = v0))
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (806) with all_134_0_2987 yields:
% 294.92/235.75 | (807) ( ~ (all_134_0_2987 = 0) & apply(all_0_5_5, all_82_3_120, all_104_3_128) = all_134_0_2987) | ( ~ (all_134_0_2987 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_134_0_2987)
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (807), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (808) ~ (all_134_0_2987 = 0) & apply(all_0_5_5, all_82_3_120, all_104_3_128) = all_134_0_2987
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (808) yields:
% 294.92/235.75 | (809) ~ (all_134_0_2987 = 0)
% 294.92/235.75 | (810) apply(all_0_5_5, all_82_3_120, all_104_3_128) = all_134_0_2987
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_104_3_128, all_134_0_2987, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_104_3_128) = all_134_0_2987, apply(all_0_5_5, all_82_3_120, all_104_3_128) = 0, yields:
% 294.92/235.75 | (811) all_134_0_2987 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (811) can reduce 809 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (813) ~ (all_134_0_2987 = 0) & apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_134_0_2987
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (813) yields:
% 294.92/235.75 | (809) ~ (all_134_0_2987 = 0)
% 294.92/235.75 | (815) apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_134_0_2987
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (113) with all_0_5_5, all_82_3_120, all_90_0_121, all_134_0_2987, 0 and discharging atoms apply(all_0_5_5, all_82_3_120, all_90_0_121) = all_134_0_2987, apply(all_0_5_5, all_82_3_120, all_90_0_121) = 0, yields:
% 294.92/235.75 | (811) all_134_0_2987 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (811) can reduce 809 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (818) ~ (all_105_3_132 = 0) & member(all_82_2_119, all_0_4_4) = all_105_3_132
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (818) yields:
% 294.92/235.75 | (819) ~ (all_105_3_132 = 0)
% 294.92/235.75 | (820) member(all_82_2_119, all_0_4_4) = all_105_3_132
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (84) with all_82_2_119, all_0_4_4, all_105_3_132, 0 and discharging atoms member(all_82_2_119, all_0_4_4) = all_105_3_132, member(all_82_2_119, all_0_4_4) = 0, yields:
% 294.92/235.75 | (821) all_105_3_132 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (821) can reduce 819 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (823) ~ (all_104_3_128 = 0) & member(all_82_3_120, all_0_4_4) = all_104_3_128
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (823) yields:
% 294.92/235.75 | (824) ~ (all_104_3_128 = 0)
% 294.92/235.75 | (825) member(all_82_3_120, all_0_4_4) = all_104_3_128
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (84) with all_82_3_120, all_0_4_4, all_104_3_128, 0 and discharging atoms member(all_82_3_120, all_0_4_4) = all_104_3_128, member(all_82_3_120, all_0_4_4) = 0, yields:
% 294.92/235.75 | (826) all_104_3_128 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (826) can reduce 824 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (828) ~ (all_0_3_3 = 0) & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (828) yields:
% 294.92/235.75 | (829) ~ (all_0_3_3 = 0)
% 294.92/235.75 | (830) one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (72) with all_0_3_3, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = all_0_3_3, yields:
% 294.92/235.75 | (831) all_0_3_3 = 0 | ? [v0] : (( ~ (v0 = 0) & surjective(all_0_5_5, all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & injective(all_0_5_5, all_0_4_4, all_0_4_4) = v0))
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (831), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (832) all_0_3_3 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (832) can reduce 829 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (829) ~ (all_0_3_3 = 0)
% 294.92/235.75 | (835) ? [v0] : (( ~ (v0 = 0) & surjective(all_0_5_5, all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & injective(all_0_5_5, all_0_4_4, all_0_4_4) = v0))
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (835) with all_82_0_3029 yields:
% 294.92/235.75 | (836) ( ~ (all_82_0_3029 = 0) & surjective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029) | ( ~ (all_82_0_3029 = 0) & injective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029)
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (836), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (837) ~ (all_82_0_3029 = 0) & surjective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (837) yields:
% 294.92/235.75 | (838) ~ (all_82_0_3029 = 0)
% 294.92/235.75 | (839) surjective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (12) with all_82_0_3029, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms surjective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029, yields:
% 294.92/235.75 | (840) all_82_0_3029 = 0 | ? [v0] : (member(v0, all_0_4_4) = 0 & ! [v1] : ( ~ (apply(all_0_5_5, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_4_4) = v2)) & ! [v1] : ( ~ (member(v1, all_0_4_4) = 0) | ? [v2] : ( ~ (v2 = 0) & apply(all_0_5_5, v1, v0) = v2)))
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (840), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (841) all_82_0_3029 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (841) can reduce 838 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (838) ~ (all_82_0_3029 = 0)
% 294.92/235.75 | (844) ? [v0] : (member(v0, all_0_4_4) = 0 & ! [v1] : ( ~ (apply(all_0_5_5, v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & member(v1, all_0_4_4) = v2)) & ! [v1] : ( ~ (member(v1, all_0_4_4) = 0) | ? [v2] : ( ~ (v2 = 0) & apply(all_0_5_5, v1, v0) = v2)))
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (844) with all_97_0_3030 yields:
% 294.92/235.75 | (845) member(all_97_0_3030, all_0_4_4) = 0 & ! [v0] : ( ~ (apply(all_0_5_5, v0, all_97_0_3030) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1)) & ! [v0] : ( ~ (member(v0, all_0_4_4) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_97_0_3030) = v1))
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (845) yields:
% 294.92/235.75 | (846) member(all_97_0_3030, all_0_4_4) = 0
% 294.92/235.75 | (847) ! [v0] : ( ~ (apply(all_0_5_5, v0, all_97_0_3030) = 0) | ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1))
% 294.92/235.75 | (848) ! [v0] : ( ~ (member(v0, all_0_4_4) = 0) | ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_97_0_3030) = v1))
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (167) with all_97_0_3030, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_97_0_3030, all_0_4_4) = 0, yields:
% 294.92/235.75 | (849) apply(all_0_1_1, all_97_0_3030, all_97_0_3030) = 0
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (183) with all_0_1_1, all_97_0_3030, all_97_0_3030, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_97_0_3030, all_97_0_3030) = 0, yields:
% 294.92/235.75 | (850) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_97_0_3030) = 0 & apply(all_0_5_5, all_97_0_3030, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_97_0_3030, all_0_4_4) = v0))
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (850) with all_120_0_3035, all_120_1_3036, all_120_2_3037, all_120_3_3038 yields:
% 294.92/235.75 | (851) (all_120_0_3035 = 0 & all_120_1_3036 = 0 & all_120_2_3037 = 0 & apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = 0 & apply(all_0_5_5, all_97_0_3030, all_120_3_3038) = 0 & member(all_120_3_3038, all_0_4_4) = 0) | ( ~ (all_120_3_3038 = 0) & member(all_97_0_3030, all_0_4_4) = all_120_3_3038)
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (851), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (852) all_120_0_3035 = 0 & all_120_1_3036 = 0 & all_120_2_3037 = 0 & apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = 0 & apply(all_0_5_5, all_97_0_3030, all_120_3_3038) = 0 & member(all_120_3_3038, all_0_4_4) = 0
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (852) yields:
% 294.92/235.75 | (853) apply(all_0_5_5, all_97_0_3030, all_120_3_3038) = 0
% 294.92/235.75 | (854) all_120_2_3037 = 0
% 294.92/235.75 | (855) all_120_1_3036 = 0
% 294.92/235.75 | (856) all_120_0_3035 = 0
% 294.92/235.75 | (857) apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = 0
% 294.92/235.75 | (858) member(all_120_3_3038, all_0_4_4) = 0
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (848) with all_120_3_3038 and discharging atoms member(all_120_3_3038, all_0_4_4) = 0, yields:
% 294.92/235.75 | (859) ? [v0] : ( ~ (v0 = 0) & apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = v0)
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (859) with all_135_0_3041 yields:
% 294.92/235.75 | (860) ~ (all_135_0_3041 = 0) & apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = all_135_0_3041
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (860) yields:
% 294.92/235.75 | (861) ~ (all_135_0_3041 = 0)
% 294.92/235.75 | (862) apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = all_135_0_3041
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (113) with all_0_5_5, all_120_3_3038, all_97_0_3030, all_135_0_3041, 0 and discharging atoms apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = all_135_0_3041, apply(all_0_5_5, all_120_3_3038, all_97_0_3030) = 0, yields:
% 294.92/235.75 | (863) all_135_0_3041 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (863) can reduce 861 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (865) ~ (all_120_3_3038 = 0) & member(all_97_0_3030, all_0_4_4) = all_120_3_3038
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (865) yields:
% 294.92/235.75 | (866) ~ (all_120_3_3038 = 0)
% 294.92/235.75 | (867) member(all_97_0_3030, all_0_4_4) = all_120_3_3038
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (84) with all_97_0_3030, all_0_4_4, all_120_3_3038, 0 and discharging atoms member(all_97_0_3030, all_0_4_4) = all_120_3_3038, member(all_97_0_3030, all_0_4_4) = 0, yields:
% 294.92/235.75 | (868) all_120_3_3038 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (868) can reduce 866 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (870) ~ (all_82_0_3029 = 0) & injective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (870) yields:
% 294.92/235.75 | (838) ~ (all_82_0_3029 = 0)
% 294.92/235.75 | (872) injective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029
% 294.92/235.75 |
% 294.92/235.75 | Instantiating formula (134) with all_82_0_3029, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms injective(all_0_5_5, all_0_4_4, all_0_4_4) = all_82_0_3029, yields:
% 294.92/235.75 | (873) all_82_0_3029 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_5_5, v1, v2) = 0 & apply(all_0_5_5, v0, v2) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.75 |
% 294.92/235.75 +-Applying beta-rule and splitting (873), into two cases.
% 294.92/235.75 |-Branch one:
% 294.92/235.75 | (841) all_82_0_3029 = 0
% 294.92/235.75 |
% 294.92/235.75 | Equations (841) can reduce 838 to:
% 294.92/235.75 | (197) $false
% 294.92/235.75 |
% 294.92/235.75 |-The branch is then unsatisfiable
% 294.92/235.75 |-Branch two:
% 294.92/235.75 | (838) ~ (all_82_0_3029 = 0)
% 294.92/235.75 | (877) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & apply(all_0_5_5, v1, v2) = 0 & apply(all_0_5_5, v0, v2) = 0 & member(v2, all_0_4_4) = 0 & member(v1, all_0_4_4) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.75 |
% 294.92/235.75 | Instantiating (877) with all_97_0_3052, all_97_1_3053, all_97_2_3054 yields:
% 294.92/235.75 | (878) ~ (all_97_1_3053 = all_97_2_3054) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0 & apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = 0 & member(all_97_0_3052, all_0_4_4) = 0 & member(all_97_1_3053, all_0_4_4) = 0 & member(all_97_2_3054, all_0_4_4) = 0
% 294.92/235.75 |
% 294.92/235.75 | Applying alpha-rule on (878) yields:
% 294.92/235.75 | (879) member(all_97_1_3053, all_0_4_4) = 0
% 294.92/235.76 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.76 | (881) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0
% 294.92/235.76 | (882) member(all_97_0_3052, all_0_4_4) = 0
% 294.92/235.76 | (883) member(all_97_2_3054, all_0_4_4) = 0
% 294.92/235.76 | (884) apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.76 | (885) ? [v0] : (apply(all_0_5_5, all_97_0_3052, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (167) with all_97_0_3052, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.76 | (886) apply(all_0_1_1, all_97_0_3052, all_97_0_3052) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_97_1_3053, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.76 | (887) ? [v0] : (apply(all_0_5_5, all_97_1_3053, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (167) with all_97_1_3053, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.76 | (888) apply(all_0_1_1, all_97_1_3053, all_97_1_3053) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_2_3054, all_97_1_3053, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_0_3052, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (889) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_2_3054, all_97_1_3053, all_97_1_3053, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (890) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_2_3054, all_97_1_3053, all_97_2_3054, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (891) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_97_2_3054, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (892) ? [v0] : (apply(all_0_5_5, all_97_2_3054, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (167) with all_97_2_3054, all_0_4_4, all_0_1_1 and discharging atoms identity(all_0_1_1, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (893) apply(all_0_1_1, all_97_2_3054, all_97_2_3054) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (887) with all_105_0_3055 yields:
% 294.92/235.76 | (894) apply(all_0_5_5, all_97_1_3053, all_105_0_3055) = 0 & member(all_105_0_3055, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (894) yields:
% 294.92/235.76 | (895) apply(all_0_5_5, all_97_1_3053, all_105_0_3055) = 0
% 294.92/235.76 | (896) member(all_105_0_3055, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (885) with all_107_0_3056 yields:
% 294.92/235.76 | (897) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0 & member(all_107_0_3056, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (897) yields:
% 294.92/235.76 | (898) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0
% 294.92/235.76 | (899) member(all_107_0_3056, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (892) with all_109_0_3057 yields:
% 294.92/235.76 | (900) apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = 0 & member(all_109_0_3057, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (900) yields:
% 294.92/235.76 | (901) apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = 0
% 294.92/235.76 | (902) member(all_109_0_3057, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 +-Applying beta-rule and splitting (889), into two cases.
% 294.92/235.76 |-Branch one:
% 294.92/235.76 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.76 |
% 294.92/235.76 | Equations (903) can reduce 880 to:
% 294.92/235.76 | (197) $false
% 294.92/235.76 |
% 294.92/235.76 |-The branch is then unsatisfiable
% 294.92/235.76 |-Branch two:
% 294.92/235.76 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.76 | (906) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (906) with all_115_0_3058 yields:
% 294.92/235.76 | (907) ( ~ (all_115_0_3058 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_115_0_3058) | ( ~ (all_115_0_3058 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_115_0_3058)
% 294.92/235.76 |
% 294.92/235.76 +-Applying beta-rule and splitting (890), into two cases.
% 294.92/235.76 |-Branch one:
% 294.92/235.76 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.76 |
% 294.92/235.76 | Equations (903) can reduce 880 to:
% 294.92/235.76 | (197) $false
% 294.92/235.76 |
% 294.92/235.76 |-The branch is then unsatisfiable
% 294.92/235.76 |-Branch two:
% 294.92/235.76 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.76 | (911) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 +-Applying beta-rule and splitting (891), into two cases.
% 294.92/235.76 |-Branch one:
% 294.92/235.76 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.76 |
% 294.92/235.76 | Equations (903) can reduce 880 to:
% 294.92/235.76 | (197) $false
% 294.92/235.76 |
% 294.92/235.76 |-The branch is then unsatisfiable
% 294.92/235.76 |-Branch two:
% 294.92/235.76 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.76 | (915) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (183) with all_0_1_1, all_97_0_3052, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_97_0_3052, all_97_0_3052) = 0, yields:
% 294.92/235.76 | (916) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_97_0_3052) = 0 & apply(all_0_5_5, all_97_0_3052, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (183) with all_0_1_1, all_97_1_3053, all_97_1_3053, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_97_1_3053, all_97_1_3053) = 0, yields:
% 294.92/235.76 | (917) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_97_1_3053) = 0 & apply(all_0_5_5, all_97_1_3053, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (183) with all_0_1_1, all_97_2_3054, all_97_2_3054, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_97_2_3054, all_97_2_3054) = 0, yields:
% 294.92/235.76 | (918) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & apply(all_0_5_5, v0, all_97_2_3054) = 0 & apply(all_0_5_5, all_97_2_3054, v0) = 0 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_97_2_3054, all_0_4_4) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (50) with all_105_0_3055, all_97_0_3052, all_97_1_3053, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_1_3053, all_105_0_3055) = 0, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.76 | (919) all_105_0_3055 = all_97_0_3052 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = v0) | ( ~ (v0 = 0) & member(all_105_0_3055, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_109_0_3057, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_109_0_3057, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (920) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_109_0_3057, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_109_0_3057, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_109_0_3057, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_109_0_3057, all_0_4_4) = 0, yields:
% 294.92/235.76 | (921) ? [v0] : (apply(all_0_5_5, all_109_0_3057, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_107_0_3056, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_107_0_3056, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (922) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_107_0_3056, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 294.92/235.76 | (923) ? [v0] : (apply(all_0_5_5, all_107_0_3056, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_105_0_3055, all_109_0_3057, all_97_2_3054, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_109_0_3057, all_0_4_4) = 0, member(all_105_0_3055, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (924) all_109_0_3057 = all_105_0_3055 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_105_0_3055) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_105_0_3055, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_105_0_3055, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.76 | (925) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_105_0_3055, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_105_0_3055, all_97_2_3054) = v0))
% 294.92/235.76 |
% 294.92/235.76 | Instantiating formula (79) with all_105_0_3055, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_105_0_3055, all_0_4_4) = 0, yields:
% 294.92/235.76 | (926) ? [v0] : (apply(all_0_5_5, all_105_0_3055, v0) = 0 & member(v0, all_0_4_4) = 0)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (921) with all_130_0_3061 yields:
% 294.92/235.76 | (927) apply(all_0_5_5, all_109_0_3057, all_130_0_3061) = 0 & member(all_130_0_3061, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (927) yields:
% 294.92/235.76 | (928) apply(all_0_5_5, all_109_0_3057, all_130_0_3061) = 0
% 294.92/235.76 | (929) member(all_130_0_3061, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (918) with all_132_0_3062, all_132_1_3063, all_132_2_3064, all_132_3_3065 yields:
% 294.92/235.76 | (930) (all_132_0_3062 = 0 & all_132_1_3063 = 0 & all_132_2_3064 = 0 & apply(all_0_5_5, all_132_3_3065, all_97_2_3054) = 0 & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = 0 & member(all_132_3_3065, all_0_4_4) = 0) | ( ~ (all_132_3_3065 = 0) & member(all_97_2_3054, all_0_4_4) = all_132_3_3065)
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (926) with all_133_0_3066 yields:
% 294.92/235.76 | (931) apply(all_0_5_5, all_105_0_3055, all_133_0_3066) = 0 & member(all_133_0_3066, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (931) yields:
% 294.92/235.76 | (932) apply(all_0_5_5, all_105_0_3055, all_133_0_3066) = 0
% 294.92/235.76 | (933) member(all_133_0_3066, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Instantiating (923) with all_135_0_3067 yields:
% 294.92/235.76 | (934) apply(all_0_5_5, all_107_0_3056, all_135_0_3067) = 0 & member(all_135_0_3067, all_0_4_4) = 0
% 294.92/235.76 |
% 294.92/235.76 | Applying alpha-rule on (934) yields:
% 294.92/235.76 | (935) apply(all_0_5_5, all_107_0_3056, all_135_0_3067) = 0
% 294.92/235.76 | (936) member(all_135_0_3067, all_0_4_4) = 0
% 294.92/235.77 |
% 294.92/235.77 | Instantiating (917) with all_137_0_3068, all_137_1_3069, all_137_2_3070, all_137_3_3071 yields:
% 294.92/235.77 | (937) (all_137_0_3068 = 0 & all_137_1_3069 = 0 & all_137_2_3070 = 0 & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = 0 & apply(all_0_5_5, all_97_1_3053, all_137_3_3071) = 0 & member(all_137_3_3071, all_0_4_4) = 0) | ( ~ (all_137_3_3071 = 0) & member(all_97_1_3053, all_0_4_4) = all_137_3_3071)
% 294.92/235.77 |
% 294.92/235.77 | Instantiating (916) with all_138_0_3072, all_138_1_3073, all_138_2_3074, all_138_3_3075 yields:
% 294.92/235.77 | (938) (all_138_0_3072 = 0 & all_138_1_3073 = 0 & all_138_2_3074 = 0 & apply(all_0_5_5, all_138_3_3075, all_97_0_3052) = 0 & apply(all_0_5_5, all_97_0_3052, all_138_3_3075) = 0 & member(all_138_3_3075, all_0_4_4) = 0) | ( ~ (all_138_3_3075 = 0) & member(all_97_0_3052, all_0_4_4) = all_138_3_3075)
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (930), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (939) all_132_0_3062 = 0 & all_132_1_3063 = 0 & all_132_2_3064 = 0 & apply(all_0_5_5, all_132_3_3065, all_97_2_3054) = 0 & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = 0 & member(all_132_3_3065, all_0_4_4) = 0
% 294.92/235.77 |
% 294.92/235.77 | Applying alpha-rule on (939) yields:
% 294.92/235.77 | (940) all_132_1_3063 = 0
% 294.92/235.77 | (941) apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = 0
% 294.92/235.77 | (942) member(all_132_3_3065, all_0_4_4) = 0
% 294.92/235.77 | (943) apply(all_0_5_5, all_132_3_3065, all_97_2_3054) = 0
% 294.92/235.77 | (944) all_132_2_3064 = 0
% 294.92/235.77 | (945) all_132_0_3062 = 0
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (925), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.77 |
% 294.92/235.77 | Equations (903) can reduce 880 to:
% 294.92/235.77 | (197) $false
% 294.92/235.77 |
% 294.92/235.77 |-The branch is then unsatisfiable
% 294.92/235.77 |-Branch two:
% 294.92/235.77 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.77 | (949) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_105_0_3055, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_105_0_3055, all_97_2_3054) = v0))
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (920), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.77 |
% 294.92/235.77 | Equations (903) can reduce 880 to:
% 294.92/235.77 | (197) $false
% 294.92/235.77 |
% 294.92/235.77 |-The branch is then unsatisfiable
% 294.92/235.77 |-Branch two:
% 294.92/235.77 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.77 | (953) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_109_0_3057, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_109_0_3057, all_97_2_3054) = v0))
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (938), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (954) all_138_0_3072 = 0 & all_138_1_3073 = 0 & all_138_2_3074 = 0 & apply(all_0_5_5, all_138_3_3075, all_97_0_3052) = 0 & apply(all_0_5_5, all_97_0_3052, all_138_3_3075) = 0 & member(all_138_3_3075, all_0_4_4) = 0
% 294.92/235.77 |
% 294.92/235.77 | Applying alpha-rule on (954) yields:
% 294.92/235.77 | (955) member(all_138_3_3075, all_0_4_4) = 0
% 294.92/235.77 | (956) all_138_0_3072 = 0
% 294.92/235.77 | (957) apply(all_0_5_5, all_138_3_3075, all_97_0_3052) = 0
% 294.92/235.77 | (958) all_138_2_3074 = 0
% 294.92/235.77 | (959) apply(all_0_5_5, all_97_0_3052, all_138_3_3075) = 0
% 294.92/235.77 | (960) all_138_1_3073 = 0
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (919), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (961) all_105_0_3055 = all_97_0_3052
% 294.92/235.77 |
% 294.92/235.77 | From (961) and (932) follows:
% 294.92/235.77 | (962) apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = 0
% 294.92/235.77 |
% 294.92/235.77 | From (961) and (895) follows:
% 294.92/235.77 | (881) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (924), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (964) all_109_0_3057 = all_105_0_3055
% 294.92/235.77 |
% 294.92/235.77 | Combining equations (961,964) yields a new equation:
% 294.92/235.77 | (965) all_109_0_3057 = all_97_0_3052
% 294.92/235.77 |
% 294.92/235.77 | From (965) and (928) follows:
% 294.92/235.77 | (966) apply(all_0_5_5, all_97_0_3052, all_130_0_3061) = 0
% 294.92/235.77 |
% 294.92/235.77 | From (965) and (901) follows:
% 294.92/235.77 | (884) apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = 0
% 294.92/235.77 |
% 294.92/235.77 | From (965) and (902) follows:
% 294.92/235.77 | (882) member(all_97_0_3052, all_0_4_4) = 0
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (937), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (969) all_137_0_3068 = 0 & all_137_1_3069 = 0 & all_137_2_3070 = 0 & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = 0 & apply(all_0_5_5, all_97_1_3053, all_137_3_3071) = 0 & member(all_137_3_3071, all_0_4_4) = 0
% 294.92/235.77 |
% 294.92/235.77 | Applying alpha-rule on (969) yields:
% 294.92/235.77 | (970) all_137_2_3070 = 0
% 294.92/235.77 | (971) member(all_137_3_3071, all_0_4_4) = 0
% 294.92/235.77 | (972) apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = 0
% 294.92/235.77 | (973) all_137_1_3069 = 0
% 294.92/235.77 | (974) all_137_0_3068 = 0
% 294.92/235.77 | (975) apply(all_0_5_5, all_97_1_3053, all_137_3_3071) = 0
% 294.92/235.77 |
% 294.92/235.77 +-Applying beta-rule and splitting (922), into two cases.
% 294.92/235.77 |-Branch one:
% 294.92/235.77 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.77 |
% 294.92/235.77 | Equations (903) can reduce 880 to:
% 294.92/235.77 | (197) $false
% 294.92/235.77 |
% 294.92/235.77 |-The branch is then unsatisfiable
% 294.92/235.77 |-Branch two:
% 294.92/235.77 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.77 | (979) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_2_3054) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_97_2_3054, all_97_1_3053, all_132_3_3065, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_132_3_3065, all_97_2_3054) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.77 | (980) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = v0) | ( ~ (v0 = 0) & member(all_132_3_3065, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_2_3054, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_135_0_3067, all_97_0_3052, all_107_0_3056, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_107_0_3056, all_135_0_3067) = 0, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.77 | (981) all_135_0_3067 = all_97_0_3052 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = v0) | ( ~ (v0 = 0) & member(all_135_0_3067, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_107_0_3056, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_138_3_3075, all_107_0_3056, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_0_3052, all_138_3_3075) = 0, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 294.92/235.77 | (982) all_138_3_3075 = all_107_0_3056 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = v0) | ( ~ (v0 = 0) & member(all_138_3_3075, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_130_0_3061, all_107_0_3056, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_0_3052, all_130_0_3061) = 0, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 294.92/235.77 | (983) all_130_0_3061 = all_107_0_3056 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = v0) | ( ~ (v0 = 0) & member(all_130_0_3061, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_130_0_3061, all_97_2_3054, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_0_3052, all_130_0_3061) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.77 | (984) all_130_0_3061 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = v0) | ( ~ (v0 = 0) & member(all_130_0_3061, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_138_3_3075, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_138_3_3075, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.77 | (985) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_138_3_3075, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_138_3_3075, all_97_2_3054) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_137_3_3071, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_137_3_3071, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.77 | (986) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_2_3054) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (174) with all_97_1_3053, all_138_3_3075, all_137_3_3071, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_138_3_3075, all_0_4_4) = 0, member(all_137_3_3071, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.77 | (987) all_138_3_3075 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_138_3_3075) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_137_3_3071, all_135_0_3067, all_97_1_3053, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_1_3053, all_137_3_3071) = 0, member(all_135_0_3067, all_0_4_4) = 0, yields:
% 294.92/235.77 | (988) all_137_3_3071 = all_135_0_3067 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_97_1_3053, all_133_0_3066, all_137_3_3071, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = 0, member(all_133_0_3066, all_0_4_4) = 0, yields:
% 294.92/235.77 | (989) all_133_0_3066 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (50) with all_138_3_3075, all_133_0_3066, all_97_0_3052, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_0_3052, all_138_3_3075) = 0, member(all_133_0_3066, all_0_4_4) = 0, yields:
% 294.92/235.77 | (990) all_138_3_3075 = all_133_0_3066 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = v0) | ( ~ (v0 = 0) & member(all_138_3_3075, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (174) with all_133_0_3066, all_97_1_3053, all_107_0_3056, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_107_0_3056, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.77 | (991) all_133_0_3066 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_1_3053) = v0))
% 294.92/235.77 |
% 294.92/235.77 | Instantiating formula (174) with all_133_0_3066, all_97_1_3053, all_137_3_3071, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_137_3_3071, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.77 | (992) all_133_0_3066 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (174) with all_133_0_3066, all_97_1_3053, all_135_0_3067, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_135_0_3067, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.78 | (993) all_133_0_3066 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_135_0_3067, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_135_0_3067, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (174) with all_107_0_3056, all_97_1_3053, all_133_0_3066, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_107_0_3056, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.78 | (994) all_107_0_3056 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_107_0_3056) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (174) with all_97_1_3053, all_97_2_3054, all_133_0_3066, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.78 | (995) all_97_1_3053 = all_97_2_3054 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_2_3054) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (174) with all_97_1_3053, all_138_3_3075, all_133_0_3066, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_138_3_3075, all_0_4_4) = 0, member(all_133_0_3066, all_0_4_4) = 0, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.78 | (996) all_138_3_3075 = all_97_1_3053 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_138_3_3075) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (50) with all_137_3_3071, all_132_3_3065, all_97_1_3053, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_97_1_3053, all_137_3_3071) = 0, member(all_132_3_3065, all_0_4_4) = 0, yields:
% 294.92/235.78 | (997) all_137_3_3071 = all_132_3_3065 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating formula (174) with all_132_3_3065, all_97_0_3052, all_97_2_3054, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_132_3_3065, all_0_4_4) = 0, member(all_97_0_3052, all_0_4_4) = 0, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.78 | (998) all_132_3_3065 = all_97_0_3052 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = v0))
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (982), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (999) all_138_3_3075 = all_107_0_3056
% 294.92/235.78 |
% 294.92/235.78 | From (999) and (957) follows:
% 294.92/235.78 | (1000) apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (999) and (959) follows:
% 294.92/235.78 | (898) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (999) and (955) follows:
% 294.92/235.78 | (899) member(all_107_0_3056, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (981), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1003) all_135_0_3067 = all_97_0_3052
% 294.92/235.78 |
% 294.92/235.78 | From (1003) and (936) follows:
% 294.92/235.78 | (882) member(all_97_0_3052, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (983), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1005) all_130_0_3061 = all_107_0_3056
% 294.92/235.78 |
% 294.92/235.78 | From (1005) and (929) follows:
% 294.92/235.78 | (899) member(all_107_0_3056, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (980), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 | (1010) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = v0) | ( ~ (v0 = 0) & member(all_132_3_3065, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_2_3054, all_0_4_4) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating (1010) with all_205_0_3089 yields:
% 294.92/235.78 | (1011) ( ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089) | ( ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089) | ( ~ (all_205_0_3089 = 0) & member(all_97_2_3054, all_0_4_4) = all_205_0_3089)
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (985), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 | (1015) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_138_3_3075, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_138_3_3075, all_97_2_3054) = v0))
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (990), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1016) all_138_3_3075 = all_133_0_3066
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1016,999) yields a new equation:
% 294.92/235.78 | (1017) all_133_0_3066 = all_107_0_3056
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1017 yields:
% 294.92/235.78 | (1018) all_133_0_3066 = all_107_0_3056
% 294.92/235.78 |
% 294.92/235.78 | From (1018) and (962) follows:
% 294.92/235.78 | (898) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (1018) and (933) follows:
% 294.92/235.78 | (899) member(all_107_0_3056, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (998), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1021) all_132_3_3065 = all_97_0_3052
% 294.92/235.78 |
% 294.92/235.78 | From (1021) and (943) follows:
% 294.92/235.78 | (1022) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (1021) and (942) follows:
% 294.92/235.78 | (882) member(all_97_0_3052, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (984), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1024) all_130_0_3061 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1024,1005) yields a new equation:
% 294.92/235.78 | (1025) all_107_0_3056 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1025,1018) yields a new equation:
% 294.92/235.78 | (1026) all_133_0_3066 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1025,999) yields a new equation:
% 294.92/235.78 | (1027) all_138_3_3075 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | From (1025) and (898) follows:
% 294.92/235.78 | (1022) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (1025) and (899) follows:
% 294.92/235.78 | (883) member(all_97_2_3054, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (988), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1030) all_137_3_3071 = all_135_0_3067
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1003,1030) yields a new equation:
% 294.92/235.78 | (1031) all_137_3_3071 = all_97_0_3052
% 294.92/235.78 |
% 294.92/235.78 | From (1031) and (972) follows:
% 294.92/235.78 | (1032) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = 0
% 294.92/235.78 |
% 294.92/235.78 | From (1031) and (971) follows:
% 294.92/235.78 | (882) member(all_97_0_3052, all_0_4_4) = 0
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (989), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1034) all_133_0_3066 = all_97_1_3053
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1034,1026) yields a new equation:
% 294.92/235.78 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1035 yields:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (1038) ~ (all_133_0_3066 = all_97_1_3053)
% 294.92/235.78 | (1039) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Equations (1026) can reduce 1038 to:
% 294.92/235.78 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1040 yields:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (986), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 | (1045) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_2_3054) = v0))
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (987), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1046) all_138_3_3075 = all_97_1_3053
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1046,1027) yields a new equation:
% 294.92/235.78 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1035 yields:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (1050) ~ (all_138_3_3075 = all_97_1_3053)
% 294.92/235.78 | (1051) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_138_3_3075) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Instantiating (1051) with all_237_0_3093 yields:
% 294.92/235.78 | (1052) ( ~ (all_237_0_3093 = 0) & apply(all_0_5_5, all_137_3_3071, all_138_3_3075) = all_237_0_3093) | ( ~ (all_237_0_3093 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_237_0_3093)
% 294.92/235.78 |
% 294.92/235.78 | Equations (1027) can reduce 1050 to:
% 294.92/235.78 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1040 yields:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (995), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 | (1058) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_2_3054) = v0))
% 294.92/235.78 |
% 294.92/235.78 +-Applying beta-rule and splitting (996), into two cases.
% 294.92/235.78 |-Branch one:
% 294.92/235.78 | (1046) all_138_3_3075 = all_97_1_3053
% 294.92/235.78 |
% 294.92/235.78 | Combining equations (1046,1027) yields a new equation:
% 294.92/235.78 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1035 yields:
% 294.92/235.78 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.78 |
% 294.92/235.78 | Equations (903) can reduce 880 to:
% 294.92/235.78 | (197) $false
% 294.92/235.78 |
% 294.92/235.78 |-The branch is then unsatisfiable
% 294.92/235.78 |-Branch two:
% 294.92/235.78 | (1050) ~ (all_138_3_3075 = all_97_1_3053)
% 294.92/235.78 | (1064) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_138_3_3075) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0))
% 294.92/235.78 |
% 294.92/235.78 | Equations (1027) can reduce 1050 to:
% 294.92/235.78 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.78 | Simplifying 1040 yields:
% 294.92/235.78 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.78 |
% 294.92/235.79 +-Applying beta-rule and splitting (994), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1067) all_107_0_3056 = all_97_1_3053
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1025,1067) yields a new equation:
% 294.92/235.79 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Equations (903) can reduce 880 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1070) ~ (all_107_0_3056 = all_97_1_3053)
% 294.92/235.79 | (1071) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_107_0_3056) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_133_0_3066, all_97_1_3053) = v0))
% 294.92/235.79 |
% 294.92/235.79 | Equations (1025) can reduce 1070 to:
% 294.92/235.79 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1040 yields:
% 294.92/235.79 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (991), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1034) all_133_0_3066 = all_97_1_3053
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1034,1026) yields a new equation:
% 294.92/235.79 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1035 yields:
% 294.92/235.79 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Equations (903) can reduce 880 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1038) ~ (all_133_0_3066 = all_97_1_3053)
% 294.92/235.79 | (1079) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_1_3053) = v0))
% 294.92/235.79 |
% 294.92/235.79 | Equations (1026) can reduce 1038 to:
% 294.92/235.79 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1040 yields:
% 294.92/235.79 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (992), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1034) all_133_0_3066 = all_97_1_3053
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1034,1026) yields a new equation:
% 294.92/235.79 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1035 yields:
% 294.92/235.79 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Equations (903) can reduce 880 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1038) ~ (all_133_0_3066 = all_97_1_3053)
% 294.92/235.79 | (1087) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = v0))
% 294.92/235.79 |
% 294.92/235.79 | Instantiating (1087) with all_257_0_3098 yields:
% 294.92/235.79 | (1088) ( ~ (all_257_0_3098 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = all_257_0_3098) | ( ~ (all_257_0_3098 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_257_0_3098)
% 294.92/235.79 |
% 294.92/235.79 | Equations (1026) can reduce 1038 to:
% 294.92/235.79 | (1040) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1040 yields:
% 294.92/235.79 | (880) ~ (all_97_1_3053 = all_97_2_3054)
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (993), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1034) all_133_0_3066 = all_97_1_3053
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1034,1026) yields a new equation:
% 294.92/235.79 | (1035) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1035 yields:
% 294.92/235.79 | (903) all_97_1_3053 = all_97_2_3054
% 294.92/235.79 |
% 294.92/235.79 | Equations (903) can reduce 880 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1038) ~ (all_133_0_3066 = all_97_1_3053)
% 294.92/235.79 | (1096) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_135_0_3067, all_133_0_3066) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_135_0_3067, all_97_1_3053) = v0))
% 294.92/235.79 |
% 294.92/235.79 | Instantiating (1096) with all_261_0_3099 yields:
% 294.92/235.79 | (1097) ( ~ (all_261_0_3099 = 0) & apply(all_0_5_5, all_135_0_3067, all_133_0_3066) = all_261_0_3099) | ( ~ (all_261_0_3099 = 0) & apply(all_0_5_5, all_135_0_3067, all_97_1_3053) = all_261_0_3099)
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (1097), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1098) ~ (all_261_0_3099 = 0) & apply(all_0_5_5, all_135_0_3067, all_133_0_3066) = all_261_0_3099
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1098) yields:
% 294.92/235.79 | (1099) ~ (all_261_0_3099 = 0)
% 294.92/235.79 | (1100) apply(all_0_5_5, all_135_0_3067, all_133_0_3066) = all_261_0_3099
% 294.92/235.79 |
% 294.92/235.79 | From (1003)(1026) and (1100) follows:
% 294.92/235.79 | (1101) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_261_0_3099
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (1052), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1102) ~ (all_237_0_3093 = 0) & apply(all_0_5_5, all_137_3_3071, all_138_3_3075) = all_237_0_3093
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1102) yields:
% 294.92/235.79 | (1103) ~ (all_237_0_3093 = 0)
% 294.92/235.79 | (1104) apply(all_0_5_5, all_137_3_3071, all_138_3_3075) = all_237_0_3093
% 294.92/235.79 |
% 294.92/235.79 | From (1031)(1027) and (1104) follows:
% 294.92/235.79 | (1105) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_237_0_3093
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (1088), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1106) ~ (all_257_0_3098 = 0) & apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1106) yields:
% 294.92/235.79 | (1107) ~ (all_257_0_3098 = 0)
% 294.92/235.79 | (1108) apply(all_0_5_5, all_137_3_3071, all_133_0_3066) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 | From (1031)(1026) and (1108) follows:
% 294.92/235.79 | (1109) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (907), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1110) ~ (all_115_0_3058 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_115_0_3058
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1110) yields:
% 294.92/235.79 | (1111) ~ (all_115_0_3058 = 0)
% 294.92/235.79 | (1112) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_115_0_3058
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, 0, all_115_0_3058 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_115_0_3058, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = 0, yields:
% 294.92/235.79 | (1113) all_115_0_3058 = 0
% 294.92/235.79 |
% 294.92/235.79 | Equations (1113) can reduce 1111 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1115) ~ (all_115_0_3058 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_115_0_3058
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1115) yields:
% 294.92/235.79 | (1111) ~ (all_115_0_3058 = 0)
% 294.92/235.79 | (1117) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_115_0_3058
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_2_3054, all_257_0_3098, all_261_0_3099 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_261_0_3099, apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_257_0_3098, yields:
% 294.92/235.79 | (1118) all_261_0_3099 = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_2_3054, all_237_0_3093, all_257_0_3098 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_257_0_3098, apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_237_0_3093, yields:
% 294.92/235.79 | (1119) all_257_0_3098 = all_237_0_3093
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_2_3054, all_115_0_3058, all_237_0_3093 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_237_0_3093, apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_115_0_3058, yields:
% 294.92/235.79 | (1120) all_237_0_3093 = all_115_0_3058
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_2_3054, 0, all_261_0_3099 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_261_0_3099, apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = 0, yields:
% 294.92/235.79 | (1121) all_261_0_3099 = 0
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1118,1121) yields a new equation:
% 294.92/235.79 | (1122) all_257_0_3098 = 0
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1122 yields:
% 294.92/235.79 | (1123) all_257_0_3098 = 0
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1119,1123) yields a new equation:
% 294.92/235.79 | (1124) all_237_0_3093 = 0
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1124 yields:
% 294.92/235.79 | (1125) all_237_0_3093 = 0
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1125,1120) yields a new equation:
% 294.92/235.79 | (1113) all_115_0_3058 = 0
% 294.92/235.79 |
% 294.92/235.79 | Equations (1113) can reduce 1111 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1128) ~ (all_257_0_3098 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1128) yields:
% 294.92/235.79 | (1107) ~ (all_257_0_3098 = 0)
% 294.92/235.79 | (1130) apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 | From (1031) and (1130) follows:
% 294.92/235.79 | (1131) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_257_0_3098
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (1011), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1132) ( ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089) | ( ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089)
% 294.92/235.79 |
% 294.92/235.79 +-Applying beta-rule and splitting (1132), into two cases.
% 294.92/235.79 |-Branch one:
% 294.92/235.79 | (1133) ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1133) yields:
% 294.92/235.79 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.79 | (1135) apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | From (1021) and (1135) follows:
% 294.92/235.79 | (1136) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, all_205_0_3089, all_257_0_3098 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_257_0_3098, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089, yields:
% 294.92/235.79 | (1137) all_257_0_3098 = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, 0, all_257_0_3098 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_257_0_3098, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = 0, yields:
% 294.92/235.79 | (1123) all_257_0_3098 = 0
% 294.92/235.79 |
% 294.92/235.79 | Combining equations (1137,1123) yields a new equation:
% 294.92/235.79 | (1139) all_205_0_3089 = 0
% 294.92/235.79 |
% 294.92/235.79 | Simplifying 1139 yields:
% 294.92/235.79 | (1140) all_205_0_3089 = 0
% 294.92/235.79 |
% 294.92/235.79 | Equations (1140) can reduce 1134 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1142) ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1142) yields:
% 294.92/235.79 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.79 | (1144) member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | From (1021) and (1144) follows:
% 294.92/235.79 | (1145) member(all_97_0_3052, all_0_4_4) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_205_0_3089, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.79 | (1140) all_205_0_3089 = 0
% 294.92/235.79 |
% 294.92/235.79 | Equations (1140) can reduce 1134 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.79 |-Branch two:
% 294.92/235.79 | (1148) ~ (all_205_0_3089 = 0) & member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Applying alpha-rule on (1148) yields:
% 294.92/235.79 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.79 | (1150) member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.79 |
% 294.92/235.79 | Instantiating formula (84) with all_97_2_3054, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_2_3054, all_0_4_4) = all_205_0_3089, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.79 | (1140) all_205_0_3089 = 0
% 294.92/235.79 |
% 294.92/235.79 | Equations (1140) can reduce 1134 to:
% 294.92/235.79 | (197) $false
% 294.92/235.79 |
% 294.92/235.79 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1153) ~ (all_237_0_3093 = 0) & apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_237_0_3093
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1153) yields:
% 294.92/235.80 | (1103) ~ (all_237_0_3093 = 0)
% 294.92/235.80 | (1155) apply(all_0_5_5, all_137_3_3071, all_97_1_3053) = all_237_0_3093
% 294.92/235.80 |
% 294.92/235.80 | From (1031) and (1155) follows:
% 294.92/235.80 | (1156) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_237_0_3093
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1011), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1132) ( ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089) | ( ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089)
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1132), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1133) ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1133) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1135) apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | From (1021) and (1135) follows:
% 294.92/235.80 | (1136) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, all_205_0_3089, all_237_0_3093 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_237_0_3093, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089, yields:
% 294.92/235.80 | (1162) all_237_0_3093 = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, 0, all_237_0_3093 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_237_0_3093, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = 0, yields:
% 294.92/235.80 | (1125) all_237_0_3093 = 0
% 294.92/235.80 |
% 294.92/235.80 | Combining equations (1162,1125) yields a new equation:
% 294.92/235.80 | (1139) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Simplifying 1139 yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1142) ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1142) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1144) member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | From (1021) and (1144) follows:
% 294.92/235.80 | (1145) member(all_97_0_3052, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_205_0_3089, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1148) ~ (all_205_0_3089 = 0) & member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1148) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1150) member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (84) with all_97_2_3054, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_2_3054, all_0_4_4) = all_205_0_3089, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1178) ~ (all_261_0_3099 = 0) & apply(all_0_5_5, all_135_0_3067, all_97_1_3053) = all_261_0_3099
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1178) yields:
% 294.92/235.80 | (1099) ~ (all_261_0_3099 = 0)
% 294.92/235.80 | (1180) apply(all_0_5_5, all_135_0_3067, all_97_1_3053) = all_261_0_3099
% 294.92/235.80 |
% 294.92/235.80 | From (1003) and (1180) follows:
% 294.92/235.80 | (1181) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_261_0_3099
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1011), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1132) ( ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089) | ( ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089)
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1132), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1133) ~ (all_205_0_3089 = 0) & apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1133) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1135) apply(all_0_5_5, all_132_3_3065, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | From (1021) and (1135) follows:
% 294.92/235.80 | (1136) apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, all_205_0_3089, all_261_0_3099 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_261_0_3099, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_205_0_3089, yields:
% 294.92/235.80 | (1187) all_261_0_3099 = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_1_3053, 0, all_261_0_3099 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = all_261_0_3099, apply(all_0_5_5, all_97_0_3052, all_97_1_3053) = 0, yields:
% 294.92/235.80 | (1121) all_261_0_3099 = 0
% 294.92/235.80 |
% 294.92/235.80 | Combining equations (1187,1121) yields a new equation:
% 294.92/235.80 | (1139) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Simplifying 1139 yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1142) ~ (all_205_0_3089 = 0) & member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1142) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1144) member(all_132_3_3065, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | From (1021) and (1144) follows:
% 294.92/235.80 | (1145) member(all_97_0_3052, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_205_0_3089, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1148) ~ (all_205_0_3089 = 0) & member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1148) yields:
% 294.92/235.80 | (1134) ~ (all_205_0_3089 = 0)
% 294.92/235.80 | (1150) member(all_97_2_3054, all_0_4_4) = all_205_0_3089
% 294.92/235.80 |
% 294.92/235.80 | Instantiating formula (84) with all_97_2_3054, all_0_4_4, all_205_0_3089, 0 and discharging atoms member(all_97_2_3054, all_0_4_4) = all_205_0_3089, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 294.92/235.80 | (1140) all_205_0_3089 = 0
% 294.92/235.80 |
% 294.92/235.80 | Equations (1140) can reduce 1134 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1203) ~ (all_137_3_3071 = all_135_0_3067)
% 294.92/235.80 | (1204) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.80 |
% 294.92/235.80 | Instantiating (1204) with all_226_0_3440 yields:
% 294.92/235.80 | (1205) ( ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440) | ( ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440) | ( ~ (all_226_0_3440 = 0) & member(all_97_1_3053, all_0_4_4) = all_226_0_3440)
% 294.92/235.80 |
% 294.92/235.80 | Equations (1003) can reduce 1203 to:
% 294.92/235.80 | (1206) ~ (all_137_3_3071 = all_97_0_3052)
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (997), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1207) all_137_3_3071 = all_132_3_3065
% 294.92/235.80 |
% 294.92/235.80 | Combining equations (1021,1207) yields a new equation:
% 294.92/235.80 | (1031) all_137_3_3071 = all_97_0_3052
% 294.92/235.80 |
% 294.92/235.80 | Equations (1031) can reduce 1206 to:
% 294.92/235.80 | (197) $false
% 294.92/235.80 |
% 294.92/235.80 |-The branch is then unsatisfiable
% 294.92/235.80 |-Branch two:
% 294.92/235.80 | (1210) ~ (all_137_3_3071 = all_132_3_3065)
% 294.92/235.80 | (1211) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = v0) | ( ~ (v0 = 0) & member(all_137_3_3071, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 294.92/235.80 |
% 294.92/235.80 | Instantiating (1211) with all_311_0_3458 yields:
% 294.92/235.80 | (1212) ( ~ (all_311_0_3458 = 0) & apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = all_311_0_3458) | ( ~ (all_311_0_3458 = 0) & member(all_137_3_3071, all_0_4_4) = all_311_0_3458) | ( ~ (all_311_0_3458 = 0) & member(all_97_1_3053, all_0_4_4) = all_311_0_3458)
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1212), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1213) ( ~ (all_311_0_3458 = 0) & apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = all_311_0_3458) | ( ~ (all_311_0_3458 = 0) & member(all_137_3_3071, all_0_4_4) = all_311_0_3458)
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1213), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1214) ~ (all_311_0_3458 = 0) & apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = all_311_0_3458
% 294.92/235.80 |
% 294.92/235.80 | Applying alpha-rule on (1214) yields:
% 294.92/235.80 | (1215) ~ (all_311_0_3458 = 0)
% 294.92/235.80 | (1216) apply(all_0_5_5, all_97_1_3053, all_132_3_3065) = all_311_0_3458
% 294.92/235.80 |
% 294.92/235.80 | From (1021) and (1216) follows:
% 294.92/235.80 | (1217) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_311_0_3458
% 294.92/235.80 |
% 294.92/235.80 +-Applying beta-rule and splitting (1205), into two cases.
% 294.92/235.80 |-Branch one:
% 294.92/235.80 | (1218) ( ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440) | ( ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440)
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1218), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1219) ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1219) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1221) apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | From (1003) and (1221) follows:
% 294.92/235.81 | (1222) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (113) with all_0_5_5, all_97_1_3053, all_97_0_3052, all_311_0_3458, 0 and discharging atoms apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_311_0_3458, apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0, yields:
% 294.92/235.81 | (1223) all_311_0_3458 = 0
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (113) with all_0_5_5, all_97_1_3053, all_97_0_3052, all_226_0_3440, all_311_0_3458 and discharging atoms apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_311_0_3458, apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440, yields:
% 294.92/235.81 | (1224) all_311_0_3458 = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Combining equations (1224,1223) yields a new equation:
% 294.92/235.81 | (1225) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Simplifying 1225 yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1228) ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1228) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1230) member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_137_3_3071, all_0_4_4, all_226_0_3440, 0 and discharging atoms member(all_137_3_3071, all_0_4_4) = all_226_0_3440, member(all_137_3_3071, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1233) ~ (all_226_0_3440 = 0) & member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1233) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1235) member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_226_0_3440, 0 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_226_0_3440, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1238) ~ (all_311_0_3458 = 0) & member(all_137_3_3071, all_0_4_4) = all_311_0_3458
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1238) yields:
% 294.92/235.81 | (1215) ~ (all_311_0_3458 = 0)
% 294.92/235.81 | (1240) member(all_137_3_3071, all_0_4_4) = all_311_0_3458
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1205), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1218) ( ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440) | ( ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440)
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1218), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1219) ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1219) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1221) apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | From (1003) and (1221) follows:
% 294.92/235.81 | (1222) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (113) with all_0_5_5, all_97_1_3053, all_97_0_3052, all_226_0_3440, 0 and discharging atoms apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440, apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1228) ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1228) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1230) member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_137_3_3071, all_0_4_4, all_311_0_3458, 0 and discharging atoms member(all_137_3_3071, all_0_4_4) = all_311_0_3458, member(all_137_3_3071, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1223) all_311_0_3458 = 0
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_137_3_3071, all_0_4_4, all_226_0_3440, all_311_0_3458 and discharging atoms member(all_137_3_3071, all_0_4_4) = all_311_0_3458, member(all_137_3_3071, all_0_4_4) = all_226_0_3440, yields:
% 294.92/235.81 | (1224) all_311_0_3458 = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Combining equations (1224,1223) yields a new equation:
% 294.92/235.81 | (1225) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Simplifying 1225 yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1233) ~ (all_226_0_3440 = 0) & member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1233) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1235) member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_226_0_3440, 0 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_226_0_3440, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1261) ~ (all_311_0_3458 = 0) & member(all_97_1_3053, all_0_4_4) = all_311_0_3458
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1261) yields:
% 294.92/235.81 | (1215) ~ (all_311_0_3458 = 0)
% 294.92/235.81 | (1263) member(all_97_1_3053, all_0_4_4) = all_311_0_3458
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1205), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1218) ( ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440) | ( ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440)
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1218), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1219) ~ (all_226_0_3440 = 0) & apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1219) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1221) apply(all_0_5_5, all_97_1_3053, all_135_0_3067) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | From (1003) and (1221) follows:
% 294.92/235.81 | (1222) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (113) with all_0_5_5, all_97_1_3053, all_97_0_3052, all_226_0_3440, 0 and discharging atoms apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_226_0_3440, apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1228) ~ (all_226_0_3440 = 0) & member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1228) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1230) member(all_137_3_3071, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_137_3_3071, all_0_4_4, all_226_0_3440, 0 and discharging atoms member(all_137_3_3071, all_0_4_4) = all_226_0_3440, member(all_137_3_3071, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1233) ~ (all_226_0_3440 = 0) & member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1233) yields:
% 294.92/235.81 | (1220) ~ (all_226_0_3440 = 0)
% 294.92/235.81 | (1235) member(all_97_1_3053, all_0_4_4) = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_311_0_3458, 0 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_311_0_3458, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 294.92/235.81 | (1223) all_311_0_3458 = 0
% 294.92/235.81 |
% 294.92/235.81 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_226_0_3440, all_311_0_3458 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_311_0_3458, member(all_97_1_3053, all_0_4_4) = all_226_0_3440, yields:
% 294.92/235.81 | (1224) all_311_0_3458 = all_226_0_3440
% 294.92/235.81 |
% 294.92/235.81 | Combining equations (1223,1224) yields a new equation:
% 294.92/235.81 | (1226) all_226_0_3440 = 0
% 294.92/235.81 |
% 294.92/235.81 | Equations (1226) can reduce 1220 to:
% 294.92/235.81 | (197) $false
% 294.92/235.81 |
% 294.92/235.81 |-The branch is then unsatisfiable
% 294.92/235.81 |-Branch two:
% 294.92/235.81 | (1283) ~ (all_130_0_3061 = all_97_2_3054)
% 294.92/235.81 | (1284) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = v0) | ( ~ (v0 = 0) & member(all_130_0_3061, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 294.92/235.81 |
% 294.92/235.81 | Instantiating (1284) with all_222_0_3933 yields:
% 294.92/235.81 | (1285) ( ~ (all_222_0_3933 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_222_0_3933) | ( ~ (all_222_0_3933 = 0) & member(all_130_0_3061, all_0_4_4) = all_222_0_3933) | ( ~ (all_222_0_3933 = 0) & member(all_97_0_3052, all_0_4_4) = all_222_0_3933)
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1285), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1286) ( ~ (all_222_0_3933 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_222_0_3933) | ( ~ (all_222_0_3933 = 0) & member(all_130_0_3061, all_0_4_4) = all_222_0_3933)
% 294.92/235.81 |
% 294.92/235.81 +-Applying beta-rule and splitting (1286), into two cases.
% 294.92/235.81 |-Branch one:
% 294.92/235.81 | (1287) ~ (all_222_0_3933 = 0) & apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_222_0_3933
% 294.92/235.81 |
% 294.92/235.81 | Applying alpha-rule on (1287) yields:
% 294.92/235.81 | (1288) ~ (all_222_0_3933 = 0)
% 294.92/235.81 | (1289) apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_222_0_3933
% 294.92/235.82 |
% 294.92/235.82 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_97_2_3054, 0, all_222_0_3933 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = all_222_0_3933, apply(all_0_5_5, all_97_0_3052, all_97_2_3054) = 0, yields:
% 294.92/235.82 | (1290) all_222_0_3933 = 0
% 294.92/235.82 |
% 294.92/235.82 | Equations (1290) can reduce 1288 to:
% 294.92/235.82 | (197) $false
% 294.92/235.82 |
% 294.92/235.82 |-The branch is then unsatisfiable
% 294.92/235.82 |-Branch two:
% 294.92/235.82 | (1292) ~ (all_222_0_3933 = 0) & member(all_130_0_3061, all_0_4_4) = all_222_0_3933
% 294.92/235.82 |
% 294.92/235.82 | Applying alpha-rule on (1292) yields:
% 294.92/235.82 | (1288) ~ (all_222_0_3933 = 0)
% 294.92/235.82 | (1294) member(all_130_0_3061, all_0_4_4) = all_222_0_3933
% 294.92/235.82 |
% 294.92/235.82 | From (1005) and (1294) follows:
% 294.92/235.82 | (1295) member(all_107_0_3056, all_0_4_4) = all_222_0_3933
% 294.92/235.82 |
% 294.92/235.82 | Instantiating formula (84) with all_107_0_3056, all_0_4_4, all_222_0_3933, 0 and discharging atoms member(all_107_0_3056, all_0_4_4) = all_222_0_3933, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 294.92/235.82 | (1290) all_222_0_3933 = 0
% 294.92/235.82 |
% 294.92/235.82 | Equations (1290) can reduce 1288 to:
% 294.92/235.82 | (197) $false
% 294.92/235.82 |
% 294.92/235.82 |-The branch is then unsatisfiable
% 294.92/235.82 |-Branch two:
% 294.92/235.82 | (1298) ~ (all_222_0_3933 = 0) & member(all_97_0_3052, all_0_4_4) = all_222_0_3933
% 294.92/235.82 |
% 294.92/235.82 | Applying alpha-rule on (1298) yields:
% 294.92/235.82 | (1288) ~ (all_222_0_3933 = 0)
% 294.92/235.82 | (1300) member(all_97_0_3052, all_0_4_4) = all_222_0_3933
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_222_0_3933, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_222_0_3933, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 295.25/235.82 | (1290) all_222_0_3933 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1290) can reduce 1288 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1303) ~ (all_132_3_3065 = all_97_0_3052)
% 295.25/235.82 | (1304) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = v0))
% 295.25/235.82 |
% 295.25/235.82 | Instantiating (1304) with all_218_0_5512 yields:
% 295.25/235.82 | (1305) ( ~ (all_218_0_5512 = 0) & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = all_218_0_5512) | ( ~ (all_218_0_5512 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_218_0_5512)
% 295.25/235.82 |
% 295.25/235.82 +-Applying beta-rule and splitting (1305), into two cases.
% 295.25/235.82 |-Branch one:
% 295.25/235.82 | (1306) ~ (all_218_0_5512 = 0) & apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = all_218_0_5512
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1306) yields:
% 295.25/235.82 | (1307) ~ (all_218_0_5512 = 0)
% 295.25/235.82 | (1308) apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = all_218_0_5512
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (113) with all_0_5_5, all_97_2_3054, all_132_3_3065, all_218_0_5512, 0 and discharging atoms apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = all_218_0_5512, apply(all_0_5_5, all_97_2_3054, all_132_3_3065) = 0, yields:
% 295.25/235.82 | (1309) all_218_0_5512 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1309) can reduce 1307 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1311) ~ (all_218_0_5512 = 0) & apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_218_0_5512
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1311) yields:
% 295.25/235.82 | (1307) ~ (all_218_0_5512 = 0)
% 295.25/235.82 | (1313) apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_218_0_5512
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (113) with all_0_5_5, all_97_2_3054, all_97_0_3052, all_218_0_5512, 0 and discharging atoms apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_218_0_5512, apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = 0, yields:
% 295.25/235.82 | (1309) all_218_0_5512 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1309) can reduce 1307 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1316) ~ (all_138_3_3075 = all_133_0_3066)
% 295.25/235.82 | (1317) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = v0) | ( ~ (v0 = 0) & member(all_138_3_3075, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 295.25/235.82 |
% 295.25/235.82 | Instantiating (1317) with all_214_0_5871 yields:
% 295.25/235.82 | (1318) ( ~ (all_214_0_5871 = 0) & apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = all_214_0_5871) | ( ~ (all_214_0_5871 = 0) & member(all_138_3_3075, all_0_4_4) = all_214_0_5871) | ( ~ (all_214_0_5871 = 0) & member(all_97_0_3052, all_0_4_4) = all_214_0_5871)
% 295.25/235.82 |
% 295.25/235.82 +-Applying beta-rule and splitting (1318), into two cases.
% 295.25/235.82 |-Branch one:
% 295.25/235.82 | (1319) ( ~ (all_214_0_5871 = 0) & apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = all_214_0_5871) | ( ~ (all_214_0_5871 = 0) & member(all_138_3_3075, all_0_4_4) = all_214_0_5871)
% 295.25/235.82 |
% 295.25/235.82 +-Applying beta-rule and splitting (1319), into two cases.
% 295.25/235.82 |-Branch one:
% 295.25/235.82 | (1320) ~ (all_214_0_5871 = 0) & apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1320) yields:
% 295.25/235.82 | (1321) ~ (all_214_0_5871 = 0)
% 295.25/235.82 | (1322) apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_133_0_3066, all_214_0_5871, 0 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = all_214_0_5871, apply(all_0_5_5, all_97_0_3052, all_133_0_3066) = 0, yields:
% 295.25/235.82 | (1323) all_214_0_5871 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1323) can reduce 1321 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1325) ~ (all_214_0_5871 = 0) & member(all_138_3_3075, all_0_4_4) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1325) yields:
% 295.25/235.82 | (1321) ~ (all_214_0_5871 = 0)
% 295.25/235.82 | (1327) member(all_138_3_3075, all_0_4_4) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | From (999) and (1327) follows:
% 295.25/235.82 | (1328) member(all_107_0_3056, all_0_4_4) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (84) with all_107_0_3056, all_0_4_4, all_214_0_5871, 0 and discharging atoms member(all_107_0_3056, all_0_4_4) = all_214_0_5871, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 295.25/235.82 | (1323) all_214_0_5871 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1323) can reduce 1321 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1331) ~ (all_214_0_5871 = 0) & member(all_97_0_3052, all_0_4_4) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1331) yields:
% 295.25/235.82 | (1321) ~ (all_214_0_5871 = 0)
% 295.25/235.82 | (1333) member(all_97_0_3052, all_0_4_4) = all_214_0_5871
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_214_0_5871, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_214_0_5871, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 295.25/235.82 | (1323) all_214_0_5871 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1323) can reduce 1321 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1336) ~ (all_130_0_3061 = all_107_0_3056)
% 295.25/235.82 | (1337) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = v0) | ( ~ (v0 = 0) & member(all_130_0_3061, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 295.25/235.82 |
% 295.25/235.82 | Instantiating (1337) with all_202_0_9810 yields:
% 295.25/235.82 | (1338) ( ~ (all_202_0_9810 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_202_0_9810) | ( ~ (all_202_0_9810 = 0) & member(all_130_0_3061, all_0_4_4) = all_202_0_9810) | ( ~ (all_202_0_9810 = 0) & member(all_97_0_3052, all_0_4_4) = all_202_0_9810)
% 295.25/235.82 |
% 295.25/235.82 +-Applying beta-rule and splitting (1338), into two cases.
% 295.25/235.82 |-Branch one:
% 295.25/235.82 | (1339) ( ~ (all_202_0_9810 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_202_0_9810) | ( ~ (all_202_0_9810 = 0) & member(all_130_0_3061, all_0_4_4) = all_202_0_9810)
% 295.25/235.82 |
% 295.25/235.82 +-Applying beta-rule and splitting (1339), into two cases.
% 295.25/235.82 |-Branch one:
% 295.25/235.82 | (1340) ~ (all_202_0_9810 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1340) yields:
% 295.25/235.82 | (1341) ~ (all_202_0_9810 = 0)
% 295.25/235.82 | (1342) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_107_0_3056, all_202_0_9810, 0 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_202_0_9810, apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0, yields:
% 295.25/235.82 | (1343) all_202_0_9810 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1343) can reduce 1341 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1345) ~ (all_202_0_9810 = 0) & member(all_130_0_3061, all_0_4_4) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1345) yields:
% 295.25/235.82 | (1341) ~ (all_202_0_9810 = 0)
% 295.25/235.82 | (1347) member(all_130_0_3061, all_0_4_4) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (84) with all_130_0_3061, all_0_4_4, all_202_0_9810, 0 and discharging atoms member(all_130_0_3061, all_0_4_4) = all_202_0_9810, member(all_130_0_3061, all_0_4_4) = 0, yields:
% 295.25/235.82 | (1343) all_202_0_9810 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1343) can reduce 1341 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.82 |-Branch two:
% 295.25/235.82 | (1350) ~ (all_202_0_9810 = 0) & member(all_97_0_3052, all_0_4_4) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Applying alpha-rule on (1350) yields:
% 295.25/235.82 | (1341) ~ (all_202_0_9810 = 0)
% 295.25/235.82 | (1352) member(all_97_0_3052, all_0_4_4) = all_202_0_9810
% 295.25/235.82 |
% 295.25/235.82 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_202_0_9810, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_202_0_9810, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 295.25/235.82 | (1343) all_202_0_9810 = 0
% 295.25/235.82 |
% 295.25/235.82 | Equations (1343) can reduce 1341 to:
% 295.25/235.82 | (197) $false
% 295.25/235.82 |
% 295.25/235.82 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1355) ~ (all_135_0_3067 = all_97_0_3052)
% 295.25/235.83 | (1356) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = v0) | ( ~ (v0 = 0) & member(all_135_0_3067, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_107_0_3056, all_0_4_4) = v0))
% 295.25/235.83 |
% 295.25/235.83 | Instantiating (1356) with all_198_0_22156 yields:
% 295.25/235.83 | (1357) ( ~ (all_198_0_22156 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = all_198_0_22156) | ( ~ (all_198_0_22156 = 0) & member(all_135_0_3067, all_0_4_4) = all_198_0_22156) | ( ~ (all_198_0_22156 = 0) & member(all_107_0_3056, all_0_4_4) = all_198_0_22156)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1357), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1358) ( ~ (all_198_0_22156 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = all_198_0_22156) | ( ~ (all_198_0_22156 = 0) & member(all_135_0_3067, all_0_4_4) = all_198_0_22156)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1358), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1359) ~ (all_198_0_22156 = 0) & apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1359) yields:
% 295.25/235.83 | (1360) ~ (all_198_0_22156 = 0)
% 295.25/235.83 | (1361) apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (113) with all_0_5_5, all_107_0_3056, all_97_0_3052, 0, all_198_0_22156 and discharging atoms apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = all_198_0_22156, apply(all_0_5_5, all_107_0_3056, all_97_0_3052) = 0, yields:
% 295.25/235.83 | (1362) all_198_0_22156 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1362) can reduce 1360 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1364) ~ (all_198_0_22156 = 0) & member(all_135_0_3067, all_0_4_4) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1364) yields:
% 295.25/235.83 | (1360) ~ (all_198_0_22156 = 0)
% 295.25/235.83 | (1366) member(all_135_0_3067, all_0_4_4) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (84) with all_135_0_3067, all_0_4_4, all_198_0_22156, 0 and discharging atoms member(all_135_0_3067, all_0_4_4) = all_198_0_22156, member(all_135_0_3067, all_0_4_4) = 0, yields:
% 295.25/235.83 | (1362) all_198_0_22156 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1362) can reduce 1360 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1369) ~ (all_198_0_22156 = 0) & member(all_107_0_3056, all_0_4_4) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1369) yields:
% 295.25/235.83 | (1360) ~ (all_198_0_22156 = 0)
% 295.25/235.83 | (1371) member(all_107_0_3056, all_0_4_4) = all_198_0_22156
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (84) with all_107_0_3056, all_0_4_4, all_198_0_22156, 0 and discharging atoms member(all_107_0_3056, all_0_4_4) = all_198_0_22156, member(all_107_0_3056, all_0_4_4) = 0, yields:
% 295.25/235.83 | (1362) all_198_0_22156 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1362) can reduce 1360 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1374) ~ (all_138_3_3075 = all_107_0_3056)
% 295.25/235.83 | (1375) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = v0) | ( ~ (v0 = 0) & member(all_138_3_3075, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_0_3052, all_0_4_4) = v0))
% 295.25/235.83 |
% 295.25/235.83 | Instantiating (1375) with all_194_0_29144 yields:
% 295.25/235.83 | (1376) ( ~ (all_194_0_29144 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_194_0_29144) | ( ~ (all_194_0_29144 = 0) & member(all_138_3_3075, all_0_4_4) = all_194_0_29144) | ( ~ (all_194_0_29144 = 0) & member(all_97_0_3052, all_0_4_4) = all_194_0_29144)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1376), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1377) ( ~ (all_194_0_29144 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_194_0_29144) | ( ~ (all_194_0_29144 = 0) & member(all_138_3_3075, all_0_4_4) = all_194_0_29144)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1377), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1378) ~ (all_194_0_29144 = 0) & apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1378) yields:
% 295.25/235.83 | (1379) ~ (all_194_0_29144 = 0)
% 295.25/235.83 | (1380) apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (113) with all_0_5_5, all_97_0_3052, all_107_0_3056, all_194_0_29144, 0 and discharging atoms apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = all_194_0_29144, apply(all_0_5_5, all_97_0_3052, all_107_0_3056) = 0, yields:
% 295.25/235.83 | (1381) all_194_0_29144 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1381) can reduce 1379 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1383) ~ (all_194_0_29144 = 0) & member(all_138_3_3075, all_0_4_4) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1383) yields:
% 295.25/235.83 | (1379) ~ (all_194_0_29144 = 0)
% 295.25/235.83 | (1385) member(all_138_3_3075, all_0_4_4) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (84) with all_138_3_3075, all_0_4_4, all_194_0_29144, 0 and discharging atoms member(all_138_3_3075, all_0_4_4) = all_194_0_29144, member(all_138_3_3075, all_0_4_4) = 0, yields:
% 295.25/235.83 | (1381) all_194_0_29144 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1381) can reduce 1379 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1388) ~ (all_194_0_29144 = 0) & member(all_97_0_3052, all_0_4_4) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1388) yields:
% 295.25/235.83 | (1379) ~ (all_194_0_29144 = 0)
% 295.25/235.83 | (1390) member(all_97_0_3052, all_0_4_4) = all_194_0_29144
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_194_0_29144, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_194_0_29144, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 295.25/235.83 | (1381) all_194_0_29144 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1381) can reduce 1379 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1393) ~ (all_137_3_3071 = 0) & member(all_97_1_3053, all_0_4_4) = all_137_3_3071
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1393) yields:
% 295.25/235.83 | (1394) ~ (all_137_3_3071 = 0)
% 295.25/235.83 | (1395) member(all_97_1_3053, all_0_4_4) = all_137_3_3071
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_137_3_3071, 0 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_137_3_3071, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 295.25/235.83 | (1396) all_137_3_3071 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1396) can reduce 1394 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1398) ~ (all_109_0_3057 = all_105_0_3055)
% 295.25/235.83 | (1399) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_97_2_3054, all_105_0_3055) = v0))
% 295.25/235.83 |
% 295.25/235.83 | Instantiating (1399) with all_163_0_51938 yields:
% 295.25/235.83 | (1400) ( ~ (all_163_0_51938 = 0) & apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = all_163_0_51938) | ( ~ (all_163_0_51938 = 0) & apply(all_0_5_5, all_97_2_3054, all_105_0_3055) = all_163_0_51938)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1400), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1401) ~ (all_163_0_51938 = 0) & apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = all_163_0_51938
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1401) yields:
% 295.25/235.83 | (1402) ~ (all_163_0_51938 = 0)
% 295.25/235.83 | (1403) apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = all_163_0_51938
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (113) with all_0_5_5, all_97_2_3054, all_109_0_3057, all_163_0_51938, 0 and discharging atoms apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = all_163_0_51938, apply(all_0_5_5, all_97_2_3054, all_109_0_3057) = 0, yields:
% 295.25/235.83 | (1404) all_163_0_51938 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1404) can reduce 1402 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1406) ~ (all_163_0_51938 = 0) & apply(all_0_5_5, all_97_2_3054, all_105_0_3055) = all_163_0_51938
% 295.25/235.83 |
% 295.25/235.83 | Applying alpha-rule on (1406) yields:
% 295.25/235.83 | (1402) ~ (all_163_0_51938 = 0)
% 295.25/235.83 | (1408) apply(all_0_5_5, all_97_2_3054, all_105_0_3055) = all_163_0_51938
% 295.25/235.83 |
% 295.25/235.83 | From (961) and (1408) follows:
% 295.25/235.83 | (1409) apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_163_0_51938
% 295.25/235.83 |
% 295.25/235.83 | Instantiating formula (113) with all_0_5_5, all_97_2_3054, all_97_0_3052, all_163_0_51938, 0 and discharging atoms apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = all_163_0_51938, apply(all_0_5_5, all_97_2_3054, all_97_0_3052) = 0, yields:
% 295.25/235.83 | (1404) all_163_0_51938 = 0
% 295.25/235.83 |
% 295.25/235.83 | Equations (1404) can reduce 1402 to:
% 295.25/235.83 | (197) $false
% 295.25/235.83 |
% 295.25/235.83 |-The branch is then unsatisfiable
% 295.25/235.83 |-Branch two:
% 295.25/235.83 | (1412) ~ (all_105_0_3055 = all_97_0_3052)
% 295.25/235.83 | (1413) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = v0) | ( ~ (v0 = 0) & member(all_105_0_3055, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_97_1_3053, all_0_4_4) = v0))
% 295.25/235.83 |
% 295.25/235.83 | Instantiating (1413) with all_159_0_51968 yields:
% 295.25/235.83 | (1414) ( ~ (all_159_0_51968 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_159_0_51968) | ( ~ (all_159_0_51968 = 0) & member(all_105_0_3055, all_0_4_4) = all_159_0_51968) | ( ~ (all_159_0_51968 = 0) & member(all_97_1_3053, all_0_4_4) = all_159_0_51968)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1414), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1415) ( ~ (all_159_0_51968 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_159_0_51968) | ( ~ (all_159_0_51968 = 0) & member(all_105_0_3055, all_0_4_4) = all_159_0_51968)
% 295.25/235.83 |
% 295.25/235.83 +-Applying beta-rule and splitting (1415), into two cases.
% 295.25/235.83 |-Branch one:
% 295.25/235.83 | (1416) ~ (all_159_0_51968 = 0) & apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_159_0_51968
% 295.25/235.83 |
% 295.25/235.84 | Applying alpha-rule on (1416) yields:
% 295.25/235.84 | (1417) ~ (all_159_0_51968 = 0)
% 295.25/235.84 | (1418) apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_159_0_51968
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (113) with all_0_5_5, all_97_1_3053, all_97_0_3052, all_159_0_51968, 0 and discharging atoms apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = all_159_0_51968, apply(all_0_5_5, all_97_1_3053, all_97_0_3052) = 0, yields:
% 295.25/235.84 | (1419) all_159_0_51968 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1419) can reduce 1417 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1421) ~ (all_159_0_51968 = 0) & member(all_105_0_3055, all_0_4_4) = all_159_0_51968
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1421) yields:
% 295.25/235.84 | (1417) ~ (all_159_0_51968 = 0)
% 295.25/235.84 | (1423) member(all_105_0_3055, all_0_4_4) = all_159_0_51968
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (84) with all_105_0_3055, all_0_4_4, all_159_0_51968, 0 and discharging atoms member(all_105_0_3055, all_0_4_4) = all_159_0_51968, member(all_105_0_3055, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1419) all_159_0_51968 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1419) can reduce 1417 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1426) ~ (all_159_0_51968 = 0) & member(all_97_1_3053, all_0_4_4) = all_159_0_51968
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1426) yields:
% 295.25/235.84 | (1417) ~ (all_159_0_51968 = 0)
% 295.25/235.84 | (1428) member(all_97_1_3053, all_0_4_4) = all_159_0_51968
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (84) with all_97_1_3053, all_0_4_4, all_159_0_51968, 0 and discharging atoms member(all_97_1_3053, all_0_4_4) = all_159_0_51968, member(all_97_1_3053, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1419) all_159_0_51968 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1419) can reduce 1417 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1431) ~ (all_138_3_3075 = 0) & member(all_97_0_3052, all_0_4_4) = all_138_3_3075
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1431) yields:
% 295.25/235.84 | (1432) ~ (all_138_3_3075 = 0)
% 295.25/235.84 | (1433) member(all_97_0_3052, all_0_4_4) = all_138_3_3075
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (84) with all_97_0_3052, all_0_4_4, all_138_3_3075, 0 and discharging atoms member(all_97_0_3052, all_0_4_4) = all_138_3_3075, member(all_97_0_3052, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1434) all_138_3_3075 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1434) can reduce 1432 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1436) ~ (all_132_3_3065 = 0) & member(all_97_2_3054, all_0_4_4) = all_132_3_3065
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1436) yields:
% 295.25/235.84 | (1437) ~ (all_132_3_3065 = 0)
% 295.25/235.84 | (1438) member(all_97_2_3054, all_0_4_4) = all_132_3_3065
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (84) with all_97_2_3054, all_0_4_4, all_132_3_3065, 0 and discharging atoms member(all_97_2_3054, all_0_4_4) = all_132_3_3065, member(all_97_2_3054, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1439) all_132_3_3065 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1439) can reduce 1437 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1441) all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) & inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = 0 & one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1441) yields:
% 295.25/235.84 | (196) all_0_2_2 = 0
% 295.25/235.84 | (1443) ~ (all_0_0_0 = 0)
% 295.25/235.84 | (832) all_0_3_3 = 0
% 295.25/235.84 | (1445) inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = 0
% 295.25/235.84 | (1446) one_to_one(all_0_5_5, all_0_4_4, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (187), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (189) all_0_0_0 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (189) can reduce 1443 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1443) ~ (all_0_0_0 = 0)
% 295.25/235.84 | (1450) ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_1_1, v0, v0) = v1 & member(v0, all_0_4_4) = 0)
% 295.25/235.84 |
% 295.25/235.84 | Instantiating (1450) with all_72_0_52086, all_72_1_52087 yields:
% 295.25/235.84 | (1451) ~ (all_72_0_52086 = 0) & apply(all_0_1_1, all_72_1_52087, all_72_1_52087) = all_72_0_52086 & member(all_72_1_52087, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1451) yields:
% 295.25/235.84 | (1452) ~ (all_72_0_52086 = 0)
% 295.25/235.84 | (1453) apply(all_0_1_1, all_72_1_52087, all_72_1_52087) = all_72_0_52086
% 295.25/235.84 | (1454) member(all_72_1_52087, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (6) with all_72_1_52087, all_72_0_52086, all_0_1_1, all_72_1_52087, all_72_1_52087, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_72_1_52087, all_72_1_52087) = all_72_0_52086, member(all_72_1_52087, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1455) all_72_0_52086 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_72_1_52087, all_72_1_52087) = v0) | ( ~ (v0 = 0) & member(all_72_1_52087, all_0_4_4) = v0))
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (79) with all_72_1_52087, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms maps(all_0_5_5, all_0_4_4, all_0_4_4) = 0, member(all_72_1_52087, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1456) ? [v0] : (apply(all_0_5_5, all_72_1_52087, v0) = 0 & member(v0, all_0_4_4) = 0)
% 295.25/235.84 |
% 295.25/235.84 | Instantiating (1456) with all_80_0_52088 yields:
% 295.25/235.84 | (1457) apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = 0 & member(all_80_0_52088, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1457) yields:
% 295.25/235.84 | (1458) apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = 0
% 295.25/235.84 | (1459) member(all_80_0_52088, all_0_4_4) = 0
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1455), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1460) all_72_0_52086 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1460) can reduce 1452 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1452) ~ (all_72_0_52086 = 0)
% 295.25/235.84 | (1463) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_72_1_52087, all_72_1_52087) = v0) | ( ~ (v0 = 0) & member(all_72_1_52087, all_0_4_4) = v0))
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (85) with 0, all_80_0_52088, all_72_1_52087, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms inverse_predicate(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4) = 0, apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = 0, yields:
% 295.25/235.84 | (1464) ? [v0] : ((v0 = 0 & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0) | ( ~ (v0 = 0) & member(all_80_0_52088, all_0_4_4) = v0) | ( ~ (v0 = 0) & member(all_72_1_52087, all_0_4_4) = v0))
% 295.25/235.84 |
% 295.25/235.84 | Instantiating formula (6) with all_80_0_52088, all_72_0_52086, all_0_1_1, all_72_1_52087, all_72_1_52087, all_0_4_4, all_0_4_4, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms compose_function(all_0_5_5, all_0_5_5, all_0_4_4, all_0_4_4, all_0_4_4) = all_0_1_1, apply(all_0_1_1, all_72_1_52087, all_72_1_52087) = all_72_0_52086, member(all_80_0_52088, all_0_4_4) = 0, yields:
% 295.25/235.84 | (1465) all_72_0_52086 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = v0) | ( ~ (v0 = 0) & member(all_72_1_52087, all_0_4_4) = v0))
% 295.25/235.84 |
% 295.25/235.84 | Instantiating (1464) with all_100_0_52092 yields:
% 295.25/235.84 | (1466) (all_100_0_52092 = 0 & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0) | ( ~ (all_100_0_52092 = 0) & member(all_80_0_52088, all_0_4_4) = all_100_0_52092) | ( ~ (all_100_0_52092 = 0) & member(all_72_1_52087, all_0_4_4) = all_100_0_52092)
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1466), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1467) (all_100_0_52092 = 0 & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0) | ( ~ (all_100_0_52092 = 0) & member(all_80_0_52088, all_0_4_4) = all_100_0_52092)
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1467), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1468) all_100_0_52092 = 0 & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1468) yields:
% 295.25/235.84 | (1469) all_100_0_52092 = 0
% 295.25/235.84 | (1470) apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1465), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1460) all_72_0_52086 = 0
% 295.25/235.84 |
% 295.25/235.84 | Equations (1460) can reduce 1452 to:
% 295.25/235.84 | (197) $false
% 295.25/235.84 |
% 295.25/235.84 |-The branch is then unsatisfiable
% 295.25/235.84 |-Branch two:
% 295.25/235.84 | (1452) ~ (all_72_0_52086 = 0)
% 295.25/235.84 | (1474) ? [v0] : (( ~ (v0 = 0) & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = v0) | ( ~ (v0 = 0) & apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = v0) | ( ~ (v0 = 0) & member(all_72_1_52087, all_0_4_4) = v0))
% 295.25/235.84 |
% 295.25/235.84 | Instantiating (1474) with all_111_0_52094 yields:
% 295.25/235.84 | (1475) ( ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = all_111_0_52094) | ( ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = all_111_0_52094) | ( ~ (all_111_0_52094 = 0) & member(all_72_1_52087, all_0_4_4) = all_111_0_52094)
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1475), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1476) ( ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = all_111_0_52094) | ( ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = all_111_0_52094)
% 295.25/235.84 |
% 295.25/235.84 +-Applying beta-rule and splitting (1476), into two cases.
% 295.25/235.84 |-Branch one:
% 295.25/235.84 | (1477) ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = all_111_0_52094
% 295.25/235.84 |
% 295.25/235.84 | Applying alpha-rule on (1477) yields:
% 295.25/235.84 | (1478) ~ (all_111_0_52094 = 0)
% 295.25/235.84 | (1479) apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = all_111_0_52094
% 295.25/235.85 |
% 295.25/235.85 | Instantiating formula (113) with all_0_5_5, all_80_0_52088, all_72_1_52087, 0, all_111_0_52094 and discharging atoms apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = all_111_0_52094, apply(all_0_5_5, all_80_0_52088, all_72_1_52087) = 0, yields:
% 295.25/235.85 | (1480) all_111_0_52094 = 0
% 295.25/235.85 |
% 295.25/235.85 | Equations (1480) can reduce 1478 to:
% 295.25/235.85 | (197) $false
% 295.25/235.85 |
% 295.25/235.85 |-The branch is then unsatisfiable
% 295.25/235.85 |-Branch two:
% 295.25/235.85 | (1482) ~ (all_111_0_52094 = 0) & apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = all_111_0_52094
% 295.25/235.85 |
% 295.25/235.85 | Applying alpha-rule on (1482) yields:
% 295.25/235.85 | (1478) ~ (all_111_0_52094 = 0)
% 295.25/235.85 | (1484) apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = all_111_0_52094
% 295.25/235.85 |
% 295.25/235.85 | Instantiating formula (113) with all_0_5_5, all_72_1_52087, all_80_0_52088, all_111_0_52094, 0 and discharging atoms apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = all_111_0_52094, apply(all_0_5_5, all_72_1_52087, all_80_0_52088) = 0, yields:
% 295.25/235.85 | (1480) all_111_0_52094 = 0
% 295.25/235.85 |
% 295.25/235.85 | Equations (1480) can reduce 1478 to:
% 295.25/235.85 | (197) $false
% 295.25/235.85 |
% 295.25/235.85 |-The branch is then unsatisfiable
% 295.25/235.85 |-Branch two:
% 295.25/235.85 | (1487) ~ (all_111_0_52094 = 0) & member(all_72_1_52087, all_0_4_4) = all_111_0_52094
% 295.25/235.85 |
% 295.25/235.85 | Applying alpha-rule on (1487) yields:
% 295.25/235.85 | (1478) ~ (all_111_0_52094 = 0)
% 295.25/235.85 | (1489) member(all_72_1_52087, all_0_4_4) = all_111_0_52094
% 295.25/235.85 |
% 295.25/235.85 | Instantiating formula (84) with all_72_1_52087, all_0_4_4, all_111_0_52094, 0 and discharging atoms member(all_72_1_52087, all_0_4_4) = all_111_0_52094, member(all_72_1_52087, all_0_4_4) = 0, yields:
% 295.25/235.85 | (1480) all_111_0_52094 = 0
% 295.25/235.85 |
% 295.25/235.85 | Equations (1480) can reduce 1478 to:
% 295.25/235.85 | (197) $false
% 295.25/235.85 |
% 295.25/235.85 |-The branch is then unsatisfiable
% 295.25/235.85 |-Branch two:
% 295.25/235.85 | (1492) ~ (all_100_0_52092 = 0) & member(all_80_0_52088, all_0_4_4) = all_100_0_52092
% 295.25/235.85 |
% 295.25/235.85 | Applying alpha-rule on (1492) yields:
% 295.25/235.85 | (1493) ~ (all_100_0_52092 = 0)
% 295.25/235.85 | (1494) member(all_80_0_52088, all_0_4_4) = all_100_0_52092
% 295.25/235.85 |
% 295.25/235.85 | Instantiating formula (84) with all_80_0_52088, all_0_4_4, all_100_0_52092, 0 and discharging atoms member(all_80_0_52088, all_0_4_4) = all_100_0_52092, member(all_80_0_52088, all_0_4_4) = 0, yields:
% 295.25/235.85 | (1469) all_100_0_52092 = 0
% 295.25/235.85 |
% 295.25/235.85 | Equations (1469) can reduce 1493 to:
% 295.25/235.85 | (197) $false
% 295.25/235.85 |
% 295.25/235.85 |-The branch is then unsatisfiable
% 295.25/235.85 |-Branch two:
% 295.25/235.85 | (1497) ~ (all_100_0_52092 = 0) & member(all_72_1_52087, all_0_4_4) = all_100_0_52092
% 295.25/235.85 |
% 295.25/235.85 | Applying alpha-rule on (1497) yields:
% 295.25/235.85 | (1493) ~ (all_100_0_52092 = 0)
% 295.25/235.85 | (1499) member(all_72_1_52087, all_0_4_4) = all_100_0_52092
% 295.25/235.85 |
% 295.25/235.85 | Instantiating formula (84) with all_72_1_52087, all_0_4_4, all_100_0_52092, 0 and discharging atoms member(all_72_1_52087, all_0_4_4) = all_100_0_52092, member(all_72_1_52087, all_0_4_4) = 0, yields:
% 295.25/235.85 | (1469) all_100_0_52092 = 0
% 295.25/235.85 |
% 295.25/235.85 | Equations (1469) can reduce 1493 to:
% 295.25/235.85 | (197) $false
% 295.25/235.85 |
% 295.25/235.85 |-The branch is then unsatisfiable
% 295.25/235.85 % SZS output end Proof for theBenchmark
% 295.25/235.85
% 295.25/235.85 235190ms
%------------------------------------------------------------------------------