TSTP Solution File: SET797+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET797+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:22:08 EDT 2022
% Result : Theorem 4.93s 1.77s
% Output : Proof 7.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET797+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 : Sat Jul 9 23:03:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/0.95 Prover 0: Preprocessing ...
% 2.65/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.65/1.25 Prover 0: Constructing countermodel ...
% 3.83/1.49 Prover 0: gave up
% 3.83/1.49 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.83/1.53 Prover 1: Preprocessing ...
% 4.93/1.72 Prover 1: Constructing countermodel ...
% 4.93/1.77 Prover 1: proved (286ms)
% 4.93/1.77
% 4.93/1.77 No countermodel exists, formula is valid
% 4.93/1.77 % SZS status Theorem for theBenchmark
% 4.93/1.77
% 4.93/1.77 Generating proof ... found it (size 18)
% 6.56/2.08
% 6.56/2.08 % SZS output start Proof for theBenchmark
% 6.56/2.08 Assumed formulas after preprocessing and simplification:
% 6.56/2.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & upper_bound(v4, v0, v3) = 0 & upper_bound(v4, v0, v2) = v5 & order(v0, v1) = 0 & subset(v3, v1) = 0 & subset(v2, v3) = 0 & subset(v2, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (order(v6, v7) = 0) | ~ (apply(v6, v8, v10) = v11) | ~ (apply(v6, v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apply(v6, v9, v10) = v15 & member(v10, v7) = v14 & member(v9, v7) = v13 & member(v8, v7) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (greatest_lower_bound(v11, v10, v9, v8) = v7) | ~ (greatest_lower_bound(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (least_upper_bound(v11, v10, v9, v8) = v7) | ~ (least_upper_bound(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (greatest_lower_bound(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & ~ (v14 = 0) & lower_bound(v11, v8, v7) = 0 & apply(v8, v11, v6) = v14 & member(v11, v9) = 0) | (lower_bound(v6, v8, v7) = v12 & member(v6, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (least_upper_bound(v6, v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & ~ (v14 = 0) & upper_bound(v11, v8, v7) = 0 & apply(v8, v6, v11) = v14 & member(v11, v9) = 0) | (upper_bound(v6, v8, v7) = v12 & member(v6, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (least(v8, v6, v7) = 0) | ~ (apply(v6, v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (greatest(v8, v6, v7) = 0) | ~ (apply(v6, v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lower_bound(v8, v6, v7) = 0) | ~ (apply(v6, v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (upper_bound(v8, v6, v7) = 0) | ~ (apply(v6, v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (total_order(v6, v7) = 0) | ~ (apply(v6, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (apply(v6, v9, v8) = v13 & member(v9, v7) = v12 & member(v8, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 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] : ? [v12] : (member(v6, v8) = v11 & member(v6, v7) = v12 & ( ~ (v11 = 0) | v12 = 0))) & ! [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] : ? [v12] : (member(v6, v8) = v12 & member(v6, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [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 | ~ (min(v10, v9, v8) = v7) | ~ (min(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (max(v10, v9, v8) = v7) | ~ (max(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (least(v10, v9, v8) = v7) | ~ (least(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (greatest(v10, v9, v8) = v7) | ~ (greatest(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (lower_bound(v10, v9, v8) = v7) | ~ (lower_bound(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (upper_bound(v10, v9, v8) = v7) | ~ (upper_bound(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] : ( ~ (greatest_lower_bound(v6, v7, v8, v9) = 0) | ~ (lower_bound(v10, v8, v7) = 0) | ? [v11] : ? [v12] : (apply(v8, v10, v6) = v12 & member(v10, v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (least_upper_bound(v6, v7, v8, v9) = 0) | ~ (upper_bound(v10, v8, v7) = 0) | ? [v11] : ? [v12] : (apply(v8, v6, v10) = v12 & member(v10, v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (min(v8, v6, v7) = 0) | ~ (apply(v6, v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (max(v8, v6, v7) = 0) | ~ (apply(v6, v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (order(v6, v7) = 0) | ~ (apply(v6, v8, v9) = 0) | ? [v10] : ? [v11] : ? [v12] : (apply(v6, v9, v8) = v12 & member(v9, v7) = v11 & member(v8, v7) = v10 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (min(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & ~ (v10 = v8) & apply(v6, v10, v8) = 0 & member(v10, v7) = 0) | ( ~ (v10 = 0) & member(v8, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (max(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & ~ (v10 = v8) & apply(v6, v8, v10) = 0 & member(v10, v7) = 0) | ( ~ (v10 = 0) & member(v8, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (least(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & ~ (v12 = 0) & apply(v6, v8, v10) = v12 & member(v10, v7) = 0) | ( ~ (v10 = 0) & member(v8, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (greatest(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & ~ (v12 = 0) & apply(v6, v10, v8) = v12 & member(v10, v7) = 0) | ( ~ (v10 = 0) & member(v8, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (lower_bound(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & apply(v6, v8, v10) = v11 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (upper_bound(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & apply(v6, v10, v8) = v11 & member(v10, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (order(v6, v7) = 0) | ~ (apply(v6, v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10)) & ! [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] : (v8 = v6 | v7 = v6 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v6, v9) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (total_order(v9, v8) = v7) | ~ (total_order(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (order(v9, v8) = v7) | ~ (order(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] : ( ~ (greatest_lower_bound(v6, v7, v8, v9) = 0) | (lower_bound(v6, v8, v7) = 0 & member(v6, v7) = 0)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (least_upper_bound(v6, v7, v8, v9) = 0) | (upper_bound(v6, v8, v7) = 0 & member(v6, v7) = 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] : ? [v11] : (member(v6, v8) = v11 & member(v6, v7) = v10 & (v11 = 0 | v10 = 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 | ~ (total_order(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & apply(v6, v10, v9) = v14 & apply(v6, v9, v10) = v13 & member(v10, v7) = 0 & member(v9, v7) = 0) | ( ~ (v9 = 0) & order(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (order(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = 0) & apply(v6, v10, v11) = 0 & apply(v6, v9, v11) = v17 & apply(v6, v9, v10) = 0 & member(v11, v7) = 0 & member(v10, v7) = 0 & member(v9, v7) = 0) | (v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v10 = v9) & apply(v6, v10, v9) = 0 & apply(v6, v9, v10) = 0 & member(v10, v7) = 0 & member(v9, v7) = 0) | (v10 = 0 & ~ (v11 = 0) & apply(v6, v9, v9) = v11 & 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] : ? [v10] : (subset(v7, v6) = v10 & subset(v6, v7) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [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] : ( ~ (min(v8, v6, v7) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (max(v8, v6, v7) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (least(v8, v6, v7) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ( ~ (greatest(v8, v6, v7) = 0) | member(v8, v7) = 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(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : ( ~ (total_order(v6, v7) = 0) | order(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (equal_set(v6, v7) = 0) | (subset(v7, v6) = 0 & subset(v6, v7) = 0)) & ! [v6] : ~ (member(v6, empty_set) = 0))
% 6.56/2.15 | 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:
% 6.56/2.15 | (1) ~ (all_0_0_0 = 0) & upper_bound(all_0_1_1, all_0_5_5, all_0_2_2) = 0 & upper_bound(all_0_1_1, all_0_5_5, all_0_3_3) = all_0_0_0 & order(all_0_5_5, all_0_4_4) = 0 & subset(all_0_2_2, all_0_4_4) = 0 & subset(all_0_3_3, all_0_2_2) = 0 & subset(all_0_3_3, all_0_4_4) = 0 & ! [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)
% 6.92/2.18 |
% 6.92/2.18 | Applying alpha-rule on (1) yields:
% 6.92/2.18 | (2) ! [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)))
% 6.92/2.18 | (3) ~ (all_0_0_0 = 0)
% 6.92/2.18 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.92/2.18 | (5) ! [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)))))
% 6.92/2.18 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 6.92/2.18 | (7) ! [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)))
% 6.92/2.18 | (8) ! [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)))
% 6.92/2.18 | (9) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0)
% 6.92/2.18 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 6.92/2.18 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0))
% 6.92/2.18 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0))
% 6.92/2.18 | (13) ! [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))
% 6.92/2.18 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0))
% 6.92/2.18 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0))
% 6.92/2.18 | (16) ! [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)))
% 6.92/2.18 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.92/2.19 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.92/2.19 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0))
% 6.92/2.19 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0))
% 6.92/2.19 | (21) subset(all_0_3_3, all_0_2_2) = 0
% 6.92/2.19 | (22) upper_bound(all_0_1_1, all_0_5_5, all_0_3_3) = all_0_0_0
% 6.92/2.19 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.92/2.19 | (24) ! [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))
% 6.92/2.19 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.92/2.19 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 6.92/2.19 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.92/2.19 | (28) subset(all_0_2_2, all_0_4_4) = 0
% 6.92/2.19 | (29) order(all_0_5_5, all_0_4_4) = 0
% 6.92/2.19 | (30) ! [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))
% 6.92/2.19 | (31) ! [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))
% 6.92/2.19 | (32) ! [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)))
% 7.00/2.19 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 7.00/2.19 | (34) ! [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))
% 7.00/2.19 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 7.00/2.19 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 7.00/2.19 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 7.00/2.19 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 7.00/2.19 | (39) ! [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))
% 7.00/2.19 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 7.00/2.19 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.00/2.19 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 7.00/2.19 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 7.00/2.19 | (44) ! [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))))
% 7.00/2.19 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 7.00/2.19 | (46) ! [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))))
% 7.00/2.19 | (47) ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.00/2.19 | (48) ! [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)))
% 7.00/2.20 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 7.00/2.20 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 7.00/2.20 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 7.00/2.20 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.00/2.20 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 7.00/2.20 | (54) ! [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)))
% 7.00/2.20 | (55) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.00/2.20 | (56) ! [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)))))
% 7.00/2.20 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 7.00/2.20 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.00/2.20 | (59) subset(all_0_3_3, all_0_4_4) = 0
% 7.00/2.20 | (60) ! [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))
% 7.00/2.20 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0))
% 7.00/2.20 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 7.00/2.20 | (63) ! [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))
% 7.00/2.20 | (64) upper_bound(all_0_1_1, all_0_5_5, all_0_2_2) = 0
% 7.00/2.20 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.00/2.20 | (66) ! [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)))
% 7.00/2.20 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0))
% 7.00/2.20 | (68) ! [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)))
% 7.00/2.20 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 7.00/2.20 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 7.00/2.20 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 7.00/2.20 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 7.00/2.20 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0))
% 7.00/2.20 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 7.00/2.20 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 7.00/2.20 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.00/2.20 | (77) ! [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)))
% 7.00/2.20 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 7.00/2.20 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 7.00/2.20 | (80) ! [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))))
% 7.00/2.21 | (81) ! [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)))
% 7.00/2.21 |
% 7.00/2.21 | Instantiating formula (60) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms upper_bound(all_0_1_1, all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 7.00/2.21 | (82) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 7.00/2.21 |
% 7.00/2.21 +-Applying beta-rule and splitting (82), into two cases.
% 7.00/2.21 |-Branch one:
% 7.00/2.21 | (83) all_0_0_0 = 0
% 7.00/2.21 |
% 7.00/2.21 | Equations (83) can reduce 3 to:
% 7.00/2.21 | (84) $false
% 7.00/2.21 |
% 7.00/2.21 |-The branch is then unsatisfiable
% 7.00/2.21 |-Branch two:
% 7.00/2.21 | (3) ~ (all_0_0_0 = 0)
% 7.00/2.21 | (86) ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 7.00/2.21 |
% 7.00/2.21 | Instantiating (86) with all_14_0_6, all_14_1_7 yields:
% 7.00/2.21 | (87) ~ (all_14_0_6 = 0) & apply(all_0_5_5, all_14_1_7, all_0_1_1) = all_14_0_6 & member(all_14_1_7, all_0_3_3) = 0
% 7.00/2.21 |
% 7.00/2.21 | Applying alpha-rule on (87) yields:
% 7.00/2.21 | (88) ~ (all_14_0_6 = 0)
% 7.00/2.21 | (89) apply(all_0_5_5, all_14_1_7, all_0_1_1) = all_14_0_6
% 7.00/2.21 | (90) member(all_14_1_7, all_0_3_3) = 0
% 7.00/2.21 |
% 7.00/2.21 | Instantiating formula (30) with all_14_0_6, all_14_1_7, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms upper_bound(all_0_1_1, all_0_5_5, all_0_2_2) = 0, apply(all_0_5_5, all_14_1_7, all_0_1_1) = all_14_0_6, yields:
% 7.00/2.21 | (91) all_14_0_6 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_14_1_7, all_0_2_2) = v0)
% 7.00/2.21 |
% 7.00/2.21 | Instantiating formula (62) with all_14_1_7, all_0_2_2, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_2_2) = 0, member(all_14_1_7, all_0_3_3) = 0, yields:
% 7.00/2.21 | (92) member(all_14_1_7, all_0_2_2) = 0
% 7.00/2.21 |
% 7.00/2.21 +-Applying beta-rule and splitting (91), into two cases.
% 7.00/2.21 |-Branch one:
% 7.00/2.21 | (93) all_14_0_6 = 0
% 7.00/2.21 |
% 7.00/2.21 | Equations (93) can reduce 88 to:
% 7.00/2.21 | (84) $false
% 7.00/2.21 |
% 7.00/2.21 |-The branch is then unsatisfiable
% 7.00/2.21 |-Branch two:
% 7.00/2.21 | (88) ~ (all_14_0_6 = 0)
% 7.00/2.21 | (96) ? [v0] : ( ~ (v0 = 0) & member(all_14_1_7, all_0_2_2) = v0)
% 7.00/2.21 |
% 7.00/2.21 | Instantiating (96) with all_34_0_8 yields:
% 7.00/2.21 | (97) ~ (all_34_0_8 = 0) & member(all_14_1_7, all_0_2_2) = all_34_0_8
% 7.00/2.21 |
% 7.00/2.21 | Applying alpha-rule on (97) yields:
% 7.00/2.21 | (98) ~ (all_34_0_8 = 0)
% 7.00/2.21 | (99) member(all_14_1_7, all_0_2_2) = all_34_0_8
% 7.00/2.21 |
% 7.00/2.21 | Instantiating formula (65) with all_14_1_7, all_0_2_2, 0, all_34_0_8 and discharging atoms member(all_14_1_7, all_0_2_2) = all_34_0_8, member(all_14_1_7, all_0_2_2) = 0, yields:
% 7.00/2.21 | (100) all_34_0_8 = 0
% 7.00/2.21 |
% 7.00/2.21 | Equations (100) can reduce 98 to:
% 7.00/2.21 | (84) $false
% 7.00/2.21 |
% 7.00/2.21 |-The branch is then unsatisfiable
% 7.00/2.21 % SZS output end Proof for theBenchmark
% 7.10/2.21
% 7.10/2.21 1630ms
%------------------------------------------------------------------------------