TSTP Solution File: SET802+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET802+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 00:22:10 EDT 2022
% Result : Theorem 13.43s 3.80s
% Output : Proof 15.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET802+4 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 09:18:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ____ _
% 0.18/0.59 ___ / __ \_____(_)___ ________ __________
% 0.18/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic
% 0.18/0.59 (ePrincess v.1.0)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2015
% 0.18/0.59 (c) Peter Backeman, 2014-2015
% 0.18/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.59 Bug reports to peter@backeman.se
% 0.18/0.59
% 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.01/1.07 Prover 0: Preprocessing ...
% 2.89/1.34 Prover 0: Warning: ignoring some quantifiers
% 3.13/1.37 Prover 0: Constructing countermodel ...
% 12.21/3.52 Prover 0: gave up
% 12.21/3.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.21/3.55 Prover 1: Preprocessing ...
% 13.05/3.72 Prover 1: Constructing countermodel ...
% 13.43/3.80 Prover 1: proved (276ms)
% 13.43/3.80
% 13.43/3.80 No countermodel exists, formula is valid
% 13.43/3.80 % SZS status Theorem for theBenchmark
% 13.43/3.80
% 13.43/3.80 Generating proof ... found it (size 84)
% 14.84/4.10
% 14.84/4.10 % SZS output start Proof for theBenchmark
% 14.84/4.10 Assumed formulas after preprocessing and simplification:
% 14.84/4.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (greatest_lower_bound(v3, v2, v0, v1) = v6 & least(v3, v0, v2) = v4 & order(v0, v1) = 0 & subset(v2, v1) = 0 & member(v3, v2) = v5 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (order(v7, v8) = 0) | ~ (apply(v7, v9, v11) = v12) | ~ (apply(v7, v9, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (apply(v7, v10, v11) = v16 & member(v11, v8) = v15 & member(v10, v8) = v14 & member(v9, v8) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (greatest_lower_bound(v12, v11, v10, v9) = v8) | ~ (greatest_lower_bound(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (least_upper_bound(v12, v11, v10, v9) = v8) | ~ (least_upper_bound(v12, v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (greatest_lower_bound(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & ~ (v15 = 0) & lower_bound(v12, v9, v8) = 0 & apply(v9, v12, v7) = v15 & member(v12, v10) = 0) | (lower_bound(v7, v9, v8) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (least_upper_bound(v7, v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & ~ (v15 = 0) & upper_bound(v12, v9, v8) = 0 & apply(v9, v7, v12) = v15 & member(v12, v10) = 0) | (upper_bound(v7, v9, v8) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (least(v9, v7, v8) = 0) | ~ (apply(v7, v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (greatest(v9, v7, v8) = 0) | ~ (apply(v7, v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lower_bound(v9, v7, v8) = 0) | ~ (apply(v7, v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (upper_bound(v9, v7, v8) = 0) | ~ (apply(v7, v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (total_order(v7, v8) = 0) | ~ (apply(v7, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (apply(v7, v10, v9) = v14 & member(v10, v8) = v13 & member(v9, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (min(v11, v10, v9) = v8) | ~ (min(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (max(v11, v10, v9) = v8) | ~ (max(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (least(v11, v10, v9) = v8) | ~ (least(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (greatest(v11, v10, v9) = v8) | ~ (greatest(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (lower_bound(v11, v10, v9) = v8) | ~ (lower_bound(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (upper_bound(v11, v10, v9) = v8) | ~ (upper_bound(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (apply(v11, v10, v9) = v8) | ~ (apply(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (greatest_lower_bound(v7, v8, v9, v10) = 0) | ~ (lower_bound(v11, v9, v8) = 0) | ? [v12] : ? [v13] : (apply(v9, v11, v7) = v13 & member(v11, v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (least_upper_bound(v7, v8, v9, v10) = 0) | ~ (upper_bound(v11, v9, v8) = 0) | ? [v12] : ? [v13] : (apply(v9, v7, v11) = v13 & member(v11, v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (min(v9, v7, v8) = 0) | ~ (apply(v7, v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (max(v9, v7, v8) = 0) | ~ (apply(v7, v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (order(v7, v8) = 0) | ~ (apply(v7, v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (apply(v7, v10, v9) = v13 & member(v10, v8) = v12 & member(v9, v8) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (min(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & ~ (v11 = v9) & apply(v7, v11, v9) = 0 & member(v11, v8) = 0) | ( ~ (v11 = 0) & member(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (max(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & ~ (v11 = v9) & apply(v7, v9, v11) = 0 & member(v11, v8) = 0) | ( ~ (v11 = 0) & member(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (least(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v12 = 0 & ~ (v13 = 0) & apply(v7, v9, v11) = v13 & member(v11, v8) = 0) | ( ~ (v11 = 0) & member(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (greatest(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v12 = 0 & ~ (v13 = 0) & apply(v7, v11, v9) = v13 & member(v11, v8) = 0) | ( ~ (v11 = 0) & member(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lower_bound(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & apply(v7, v9, v11) = v12 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (upper_bound(v9, v7, v8) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & apply(v7, v11, v9) = v12 & member(v11, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (order(v7, v8) = 0) | ~ (apply(v7, v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (total_order(v10, v9) = v8) | ~ (total_order(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (order(v10, v9) = v8) | ~ (order(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (greatest_lower_bound(v7, v8, v9, v10) = 0) | (lower_bound(v7, v9, v8) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (least_upper_bound(v7, v8, v9, v10) = 0) | (upper_bound(v7, v9, v8) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (total_order(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & v12 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & apply(v7, v11, v10) = v15 & apply(v7, v10, v11) = v14 & member(v11, v8) = 0 & member(v10, v8) = 0) | ( ~ (v10 = 0) & order(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (order(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v18 = 0) & apply(v7, v11, v12) = 0 & apply(v7, v10, v12) = v18 & apply(v7, v10, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0 & member(v10, v8) = 0) | (v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v11 = v10) & apply(v7, v11, v10) = 0 & apply(v7, v10, v11) = 0 & member(v11, v8) = 0 & member(v10, v8) = 0) | (v11 = 0 & ~ (v12 = 0) & apply(v7, v10, v10) = v12 & member(v10, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (min(v9, v7, v8) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (max(v9, v7, v8) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (least(v9, v7, v8) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (greatest(v9, v7, v8) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (total_order(v7, v8) = 0) | order(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ~ (member(v7, empty_set) = 0) & ((v6 = 0 & v5 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 15.13/4.16 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 15.13/4.16 | (1) greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = all_0_0_0 & least(all_0_3_3, all_0_6_6, all_0_4_4) = all_0_2_2 & order(all_0_6_6, all_0_5_5) = 0 & subset(all_0_4_4, all_0_5_5) = 0 & member(all_0_3_3, all_0_4_4) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(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] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(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] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) & ((all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0)) | (all_0_2_2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))
% 15.13/4.18 |
% 15.13/4.18 | Applying alpha-rule on (1) yields:
% 15.13/4.18 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 15.13/4.18 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 15.13/4.18 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 15.13/4.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0))
% 15.13/4.18 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 15.13/4.18 | (7) (all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0)) | (all_0_2_2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))
% 15.13/4.19 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 15.13/4.19 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 15.13/4.19 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 15.13/4.19 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0))
% 15.13/4.19 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0))
% 15.13/4.19 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 15.13/4.19 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 15.13/4.19 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0))
% 15.13/4.19 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 15.13/4.19 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 15.13/4.19 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 15.13/4.19 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 15.13/4.19 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 15.13/4.19 | (21) ! [v0] : ~ (member(v0, empty_set) = 0)
% 15.13/4.19 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 15.13/4.19 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 15.13/4.19 | (24) order(all_0_6_6, all_0_5_5) = 0
% 15.13/4.19 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 15.13/4.19 | (26) least(all_0_3_3, all_0_6_6, all_0_4_4) = all_0_2_2
% 15.13/4.19 | (27) ! [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))
% 15.13/4.19 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 15.13/4.19 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 15.13/4.19 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 15.13/4.19 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 15.13/4.19 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 15.13/4.19 | (33) ! [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))
% 15.13/4.19 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 15.13/4.20 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 15.13/4.20 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 15.13/4.20 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 15.13/4.20 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0))
% 15.13/4.20 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 15.13/4.20 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3)))
% 15.13/4.20 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 15.13/4.20 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 15.13/4.20 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0))
% 15.13/4.20 | (44) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0)
% 15.13/4.20 | (45) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 15.13/4.20 | (46) ! [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))
% 15.13/4.20 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 15.13/4.20 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 15.13/4.20 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 15.13/4.20 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 15.13/4.20 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 15.13/4.20 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 15.13/4.20 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 15.13/4.20 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 15.13/4.20 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0))
% 15.13/4.20 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0))
% 15.13/4.20 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 15.13/4.20 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0))
% 15.13/4.21 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 15.13/4.21 | (60) ! [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))
% 15.13/4.21 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 15.13/4.21 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0))
% 15.13/4.21 | (63) greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = all_0_0_0
% 15.13/4.21 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 15.13/4.21 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 15.13/4.21 | (66) member(all_0_3_3, all_0_4_4) = all_0_1_1
% 15.13/4.21 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 15.13/4.21 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0)))
% 15.13/4.21 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 15.13/4.21 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 15.13/4.21 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 15.13/4.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0))
% 15.13/4.21 | (73) subset(all_0_4_4, all_0_5_5) = 0
% 15.13/4.21 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 15.13/4.21 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 15.13/4.21 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 15.13/4.21 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 15.13/4.21 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 15.13/4.21 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 15.13/4.21 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 15.13/4.21 |
% 15.13/4.21 | Instantiating formula (17) with all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3 yields:
% 15.13/4.21 | (81) ~ (greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = 0) | (lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = 0 & member(all_0_3_3, all_0_4_4) = 0)
% 15.13/4.21 |
% 15.13/4.21 | Instantiating formula (74) with all_0_0_0, all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3 and discharging atoms greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = all_0_0_0, yields:
% 15.13/4.21 | (82) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & lower_bound(v0, all_0_6_6, all_0_4_4) = 0 & apply(all_0_6_6, v0, all_0_3_3) = v3 & member(v0, all_0_5_5) = 0) | (lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = v1 & member(all_0_3_3, all_0_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 15.13/4.21 |
% 15.13/4.21 | Instantiating formula (34) with all_0_3_3, all_0_4_4, all_0_6_6 yields:
% 15.13/4.21 | (83) ~ (least(all_0_3_3, all_0_6_6, all_0_4_4) = 0) | member(all_0_3_3, all_0_4_4) = 0
% 15.13/4.21 |
% 15.13/4.21 | Instantiating formula (54) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms least(all_0_3_3, all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 15.13/4.21 | (84) all_0_2_2 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & apply(all_0_6_6, all_0_3_3, v0) = v2 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_0_3_3, all_0_4_4) = v0))
% 15.13/4.22 |
% 15.13/4.22 +-Applying beta-rule and splitting (83), into two cases.
% 15.13/4.22 |-Branch one:
% 15.13/4.22 | (85) member(all_0_3_3, all_0_4_4) = 0
% 15.13/4.22 |
% 15.13/4.22 | Instantiating formula (53) with all_0_3_3, all_0_4_4, 0, all_0_1_1 and discharging atoms member(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_0_3_3, all_0_4_4) = 0, yields:
% 15.13/4.22 | (86) all_0_1_1 = 0
% 15.13/4.22 |
% 15.13/4.22 | From (86) and (66) follows:
% 15.13/4.22 | (85) member(all_0_3_3, all_0_4_4) = 0
% 15.13/4.22 |
% 15.13/4.22 +-Applying beta-rule and splitting (7), into two cases.
% 15.13/4.22 |-Branch one:
% 15.13/4.22 | (88) all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0)
% 15.13/4.22 |
% 15.13/4.22 | Applying alpha-rule on (88) yields:
% 15.13/4.22 | (89) all_0_0_0 = 0
% 15.13/4.22 | (86) all_0_1_1 = 0
% 15.13/4.22 | (91) ~ (all_0_2_2 = 0)
% 15.13/4.22 |
% 15.13/4.22 | From (89) and (63) follows:
% 15.13/4.22 | (92) greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = 0
% 15.13/4.22 |
% 15.13/4.22 +-Applying beta-rule and splitting (81), into two cases.
% 15.13/4.22 |-Branch one:
% 15.13/4.22 | (93) ~ (greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = 0)
% 15.13/4.22 |
% 15.13/4.22 | Using (92) and (93) yields:
% 15.13/4.22 | (94) $false
% 15.13/4.22 |
% 15.13/4.22 |-The branch is then unsatisfiable
% 15.13/4.22 |-Branch two:
% 15.13/4.22 | (92) greatest_lower_bound(all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5) = 0
% 15.13/4.22 | (96) lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = 0 & member(all_0_3_3, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (96) yields:
% 15.49/4.22 | (97) lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = 0
% 15.49/4.22 | (85) member(all_0_3_3, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (84), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (99) all_0_2_2 = 0
% 15.49/4.22 |
% 15.49/4.22 | Equations (99) can reduce 91 to:
% 15.49/4.22 | (100) $false
% 15.49/4.22 |
% 15.49/4.22 |-The branch is then unsatisfiable
% 15.49/4.22 |-Branch two:
% 15.49/4.22 | (91) ~ (all_0_2_2 = 0)
% 15.49/4.22 | (102) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & apply(all_0_6_6, all_0_3_3, v0) = v2 & member(v0, all_0_4_4) = 0) | ( ~ (v0 = 0) & member(all_0_3_3, all_0_4_4) = v0))
% 15.49/4.22 |
% 15.49/4.22 | Instantiating (102) with all_43_0_7, all_43_1_8, all_43_2_9 yields:
% 15.49/4.22 | (103) (all_43_1_8 = 0 & ~ (all_43_0_7 = 0) & apply(all_0_6_6, all_0_3_3, all_43_2_9) = all_43_0_7 & member(all_43_2_9, all_0_4_4) = 0) | ( ~ (all_43_2_9 = 0) & member(all_0_3_3, all_0_4_4) = all_43_2_9)
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (103), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (104) all_43_1_8 = 0 & ~ (all_43_0_7 = 0) & apply(all_0_6_6, all_0_3_3, all_43_2_9) = all_43_0_7 & member(all_43_2_9, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (104) yields:
% 15.49/4.22 | (105) all_43_1_8 = 0
% 15.49/4.22 | (106) ~ (all_43_0_7 = 0)
% 15.49/4.22 | (107) apply(all_0_6_6, all_0_3_3, all_43_2_9) = all_43_0_7
% 15.49/4.22 | (108) member(all_43_2_9, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 | Instantiating formula (4) with all_43_0_7, all_43_2_9, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = 0, apply(all_0_6_6, all_0_3_3, all_43_2_9) = all_43_0_7, yields:
% 15.49/4.22 | (109) all_43_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_43_2_9, all_0_4_4) = v0)
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (109), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (110) all_43_0_7 = 0
% 15.49/4.22 |
% 15.49/4.22 | Equations (110) can reduce 106 to:
% 15.49/4.22 | (100) $false
% 15.49/4.22 |
% 15.49/4.22 |-The branch is then unsatisfiable
% 15.49/4.22 |-Branch two:
% 15.49/4.22 | (106) ~ (all_43_0_7 = 0)
% 15.49/4.22 | (113) ? [v0] : ( ~ (v0 = 0) & member(all_43_2_9, all_0_4_4) = v0)
% 15.49/4.22 |
% 15.49/4.22 | Instantiating (113) with all_60_0_12 yields:
% 15.49/4.22 | (114) ~ (all_60_0_12 = 0) & member(all_43_2_9, all_0_4_4) = all_60_0_12
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (114) yields:
% 15.49/4.22 | (115) ~ (all_60_0_12 = 0)
% 15.49/4.22 | (116) member(all_43_2_9, all_0_4_4) = all_60_0_12
% 15.49/4.22 |
% 15.49/4.22 | Instantiating formula (53) with all_43_2_9, all_0_4_4, all_60_0_12, 0 and discharging atoms member(all_43_2_9, all_0_4_4) = all_60_0_12, member(all_43_2_9, all_0_4_4) = 0, yields:
% 15.49/4.22 | (117) all_60_0_12 = 0
% 15.49/4.22 |
% 15.49/4.22 | Equations (117) can reduce 115 to:
% 15.49/4.22 | (100) $false
% 15.49/4.22 |
% 15.49/4.22 |-The branch is then unsatisfiable
% 15.49/4.22 |-Branch two:
% 15.49/4.22 | (119) ~ (all_43_2_9 = 0) & member(all_0_3_3, all_0_4_4) = all_43_2_9
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (119) yields:
% 15.49/4.22 | (120) ~ (all_43_2_9 = 0)
% 15.49/4.22 | (121) member(all_0_3_3, all_0_4_4) = all_43_2_9
% 15.49/4.22 |
% 15.49/4.22 | Instantiating formula (53) with all_0_3_3, all_0_4_4, all_43_2_9, 0 and discharging atoms member(all_0_3_3, all_0_4_4) = all_43_2_9, member(all_0_3_3, all_0_4_4) = 0, yields:
% 15.49/4.22 | (122) all_43_2_9 = 0
% 15.49/4.22 |
% 15.49/4.22 | Equations (122) can reduce 120 to:
% 15.49/4.22 | (100) $false
% 15.49/4.22 |
% 15.49/4.22 |-The branch is then unsatisfiable
% 15.49/4.22 |-Branch two:
% 15.49/4.22 | (124) all_0_2_2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (124) yields:
% 15.49/4.22 | (99) all_0_2_2 = 0
% 15.49/4.22 | (126) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 15.49/4.22 |
% 15.49/4.22 | From (99) and (26) follows:
% 15.49/4.22 | (127) least(all_0_3_3, all_0_6_6, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (126), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (128) ~ (all_0_0_0 = 0)
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (82), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (89) all_0_0_0 = 0
% 15.49/4.22 |
% 15.49/4.22 | Equations (89) can reduce 128 to:
% 15.49/4.22 | (100) $false
% 15.49/4.22 |
% 15.49/4.22 |-The branch is then unsatisfiable
% 15.49/4.22 |-Branch two:
% 15.49/4.22 | (128) ~ (all_0_0_0 = 0)
% 15.49/4.22 | (132) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & lower_bound(v0, all_0_6_6, all_0_4_4) = 0 & apply(all_0_6_6, v0, all_0_3_3) = v3 & member(v0, all_0_5_5) = 0) | (lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = v1 & member(all_0_3_3, all_0_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 15.49/4.22 |
% 15.49/4.22 | Instantiating (132) with all_43_0_13, all_43_1_14, all_43_2_15, all_43_3_16 yields:
% 15.49/4.22 | (133) (all_43_1_14 = 0 & all_43_2_15 = 0 & ~ (all_43_0_13 = 0) & lower_bound(all_43_3_16, all_0_6_6, all_0_4_4) = 0 & apply(all_0_6_6, all_43_3_16, all_0_3_3) = all_43_0_13 & member(all_43_3_16, all_0_5_5) = 0) | (lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = all_43_2_15 & member(all_0_3_3, all_0_4_4) = all_43_3_16 & ( ~ (all_43_2_15 = 0) | ~ (all_43_3_16 = 0)))
% 15.49/4.22 |
% 15.49/4.22 +-Applying beta-rule and splitting (133), into two cases.
% 15.49/4.22 |-Branch one:
% 15.49/4.22 | (134) all_43_1_14 = 0 & all_43_2_15 = 0 & ~ (all_43_0_13 = 0) & lower_bound(all_43_3_16, all_0_6_6, all_0_4_4) = 0 & apply(all_0_6_6, all_43_3_16, all_0_3_3) = all_43_0_13 & member(all_43_3_16, all_0_5_5) = 0
% 15.49/4.22 |
% 15.49/4.22 | Applying alpha-rule on (134) yields:
% 15.49/4.22 | (135) apply(all_0_6_6, all_43_3_16, all_0_3_3) = all_43_0_13
% 15.49/4.22 | (136) ~ (all_43_0_13 = 0)
% 15.49/4.22 | (137) all_43_2_15 = 0
% 15.49/4.22 | (138) all_43_1_14 = 0
% 15.49/4.22 | (139) member(all_43_3_16, all_0_5_5) = 0
% 15.49/4.22 | (140) lower_bound(all_43_3_16, all_0_6_6, all_0_4_4) = 0
% 15.49/4.22 |
% 15.49/4.22 | Instantiating formula (4) with all_43_0_13, all_0_3_3, all_43_3_16, all_0_4_4, all_0_6_6 and discharging atoms lower_bound(all_43_3_16, all_0_6_6, all_0_4_4) = 0, apply(all_0_6_6, all_43_3_16, all_0_3_3) = all_43_0_13, yields:
% 15.49/4.23 | (141) all_43_0_13 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_4_4) = v0)
% 15.49/4.23 |
% 15.49/4.23 +-Applying beta-rule and splitting (141), into two cases.
% 15.49/4.23 |-Branch one:
% 15.49/4.23 | (142) all_43_0_13 = 0
% 15.49/4.23 |
% 15.49/4.23 | Equations (142) can reduce 136 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (136) ~ (all_43_0_13 = 0)
% 15.49/4.23 | (145) ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_4_4) = v0)
% 15.49/4.23 |
% 15.49/4.23 | Instantiating (145) with all_58_0_17 yields:
% 15.49/4.23 | (146) ~ (all_58_0_17 = 0) & member(all_0_3_3, all_0_4_4) = all_58_0_17
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (146) yields:
% 15.49/4.23 | (147) ~ (all_58_0_17 = 0)
% 15.49/4.23 | (148) member(all_0_3_3, all_0_4_4) = all_58_0_17
% 15.49/4.23 |
% 15.49/4.23 | Instantiating formula (53) with all_0_3_3, all_0_4_4, all_58_0_17, 0 and discharging atoms member(all_0_3_3, all_0_4_4) = all_58_0_17, member(all_0_3_3, all_0_4_4) = 0, yields:
% 15.49/4.23 | (149) all_58_0_17 = 0
% 15.49/4.23 |
% 15.49/4.23 | Equations (149) can reduce 147 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (151) lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = all_43_2_15 & member(all_0_3_3, all_0_4_4) = all_43_3_16 & ( ~ (all_43_2_15 = 0) | ~ (all_43_3_16 = 0))
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (151) yields:
% 15.49/4.23 | (152) lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = all_43_2_15
% 15.49/4.23 | (153) member(all_0_3_3, all_0_4_4) = all_43_3_16
% 15.49/4.23 | (154) ~ (all_43_2_15 = 0) | ~ (all_43_3_16 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Instantiating formula (53) with all_0_3_3, all_0_4_4, all_43_3_16, 0 and discharging atoms member(all_0_3_3, all_0_4_4) = all_43_3_16, member(all_0_3_3, all_0_4_4) = 0, yields:
% 15.49/4.23 | (155) all_43_3_16 = 0
% 15.49/4.23 |
% 15.49/4.23 +-Applying beta-rule and splitting (154), into two cases.
% 15.49/4.23 |-Branch one:
% 15.49/4.23 | (156) ~ (all_43_2_15 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Instantiating formula (56) with all_43_2_15, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms lower_bound(all_0_3_3, all_0_6_6, all_0_4_4) = all_43_2_15, yields:
% 15.49/4.23 | (157) all_43_2_15 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_6_6, all_0_3_3, v0) = v1 & member(v0, all_0_4_4) = 0)
% 15.49/4.23 |
% 15.49/4.23 +-Applying beta-rule and splitting (157), into two cases.
% 15.49/4.23 |-Branch one:
% 15.49/4.23 | (137) all_43_2_15 = 0
% 15.49/4.23 |
% 15.49/4.23 | Equations (137) can reduce 156 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (156) ~ (all_43_2_15 = 0)
% 15.49/4.23 | (161) ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_6_6, all_0_3_3, v0) = v1 & member(v0, all_0_4_4) = 0)
% 15.49/4.23 |
% 15.49/4.23 | Instantiating (161) with all_70_0_18, all_70_1_19 yields:
% 15.49/4.23 | (162) ~ (all_70_0_18 = 0) & apply(all_0_6_6, all_0_3_3, all_70_1_19) = all_70_0_18 & member(all_70_1_19, all_0_4_4) = 0
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (162) yields:
% 15.49/4.23 | (163) ~ (all_70_0_18 = 0)
% 15.49/4.23 | (164) apply(all_0_6_6, all_0_3_3, all_70_1_19) = all_70_0_18
% 15.49/4.23 | (165) member(all_70_1_19, all_0_4_4) = 0
% 15.49/4.23 |
% 15.49/4.23 | Instantiating formula (49) with all_70_0_18, all_70_1_19, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms least(all_0_3_3, all_0_6_6, all_0_4_4) = 0, apply(all_0_6_6, all_0_3_3, all_70_1_19) = all_70_0_18, yields:
% 15.49/4.23 | (166) all_70_0_18 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_70_1_19, all_0_4_4) = v0)
% 15.49/4.23 |
% 15.49/4.23 +-Applying beta-rule and splitting (166), into two cases.
% 15.49/4.23 |-Branch one:
% 15.49/4.23 | (167) all_70_0_18 = 0
% 15.49/4.23 |
% 15.49/4.23 | Equations (167) can reduce 163 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (163) ~ (all_70_0_18 = 0)
% 15.49/4.23 | (170) ? [v0] : ( ~ (v0 = 0) & member(all_70_1_19, all_0_4_4) = v0)
% 15.49/4.23 |
% 15.49/4.23 | Instantiating (170) with all_82_0_20 yields:
% 15.49/4.23 | (171) ~ (all_82_0_20 = 0) & member(all_70_1_19, all_0_4_4) = all_82_0_20
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (171) yields:
% 15.49/4.23 | (172) ~ (all_82_0_20 = 0)
% 15.49/4.23 | (173) member(all_70_1_19, all_0_4_4) = all_82_0_20
% 15.49/4.23 |
% 15.49/4.23 | Instantiating formula (53) with all_70_1_19, all_0_4_4, all_82_0_20, 0 and discharging atoms member(all_70_1_19, all_0_4_4) = all_82_0_20, member(all_70_1_19, all_0_4_4) = 0, yields:
% 15.49/4.23 | (174) all_82_0_20 = 0
% 15.49/4.23 |
% 15.49/4.23 | Equations (174) can reduce 172 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (137) all_43_2_15 = 0
% 15.49/4.23 | (177) ~ (all_43_3_16 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Equations (155) can reduce 177 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (89) all_0_0_0 = 0
% 15.49/4.23 | (180) ~ (all_0_1_1 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Equations (86) can reduce 180 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (182) ~ (member(all_0_3_3, all_0_4_4) = 0)
% 15.49/4.23 | (183) ~ (least(all_0_3_3, all_0_6_6, all_0_4_4) = 0)
% 15.49/4.23 |
% 15.49/4.23 | Using (26) and (183) yields:
% 15.49/4.23 | (91) ~ (all_0_2_2 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Using (66) and (182) yields:
% 15.49/4.23 | (180) ~ (all_0_1_1 = 0)
% 15.49/4.23 |
% 15.49/4.23 +-Applying beta-rule and splitting (7), into two cases.
% 15.49/4.23 |-Branch one:
% 15.49/4.23 | (88) all_0_0_0 = 0 & all_0_1_1 = 0 & ~ (all_0_2_2 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (88) yields:
% 15.49/4.23 | (89) all_0_0_0 = 0
% 15.49/4.23 | (86) all_0_1_1 = 0
% 15.49/4.23 | (91) ~ (all_0_2_2 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Equations (86) can reduce 180 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 |-Branch two:
% 15.49/4.23 | (124) all_0_2_2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 15.49/4.23 |
% 15.49/4.23 | Applying alpha-rule on (124) yields:
% 15.49/4.23 | (99) all_0_2_2 = 0
% 15.49/4.23 | (126) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 15.49/4.23 |
% 15.49/4.23 | Equations (99) can reduce 91 to:
% 15.49/4.23 | (100) $false
% 15.49/4.23 |
% 15.49/4.23 |-The branch is then unsatisfiable
% 15.49/4.23 % SZS output end Proof for theBenchmark
% 15.49/4.23
% 15.49/4.23 3631ms
%------------------------------------------------------------------------------