TSTP Solution File: SET795+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET795+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 16.82s 6.29s
% Output : Proof 19.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET795+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 05:38:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.59 ____ _
% 0.46/0.59 ___ / __ \_____(_)___ ________ __________
% 0.46/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.59
% 0.46/0.59 A Theorem Prover for First-Order Logic
% 0.46/0.60 (ePrincess v.1.0)
% 0.46/0.60
% 0.46/0.60 (c) Philipp Rümmer, 2009-2015
% 0.46/0.60 (c) Peter Backeman, 2014-2015
% 0.46/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.60 Bug reports to peter@backeman.se
% 0.46/0.60
% 0.46/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.60
% 0.46/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.97 Prover 0: Preprocessing ...
% 2.49/1.25 Prover 0: Warning: ignoring some quantifiers
% 2.93/1.28 Prover 0: Constructing countermodel ...
% 15.39/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 15.39/6.00 Prover 1: Preprocessing ...
% 16.68/6.21 Prover 1: Constructing countermodel ...
% 16.82/6.28 Prover 1: proved (345ms)
% 16.82/6.29 Prover 0: stopped
% 16.82/6.29
% 16.82/6.29 No countermodel exists, formula is valid
% 16.82/6.29 % SZS status Theorem for theBenchmark
% 16.82/6.29
% 16.82/6.29 Generating proof ... found it (size 96)
% 18.48/6.66
% 18.48/6.66 % SZS output start Proof for theBenchmark
% 18.48/6.66 Assumed formulas after preprocessing and simplification:
% 18.48/6.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & least_upper_bound(v3, v4, v0, v1) = v5 & order(v0, v1) = 0 & apply(v0, v2, v3) = 0 & unordered_pair(v2, v3) = v4 & member(v3, v1) = 0 & member(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))
% 18.85/6.71 | 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:
% 18.85/6.71 | (1) ~ (all_0_0_0 = 0) & least_upper_bound(all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4) = all_0_0_0 & order(all_0_5_5, all_0_4_4) = 0 & apply(all_0_5_5, all_0_3_3, all_0_2_2) = 0 & unordered_pair(all_0_3_3, all_0_2_2) = all_0_1_1 & member(all_0_2_2, all_0_4_4) = 0 & member(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)
% 18.85/6.72 |
% 18.85/6.72 | Applying alpha-rule on (1) yields:
% 18.85/6.72 | (2) ! [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))
% 18.85/6.73 | (3) ! [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))))
% 18.85/6.73 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 18.85/6.73 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 18.85/6.73 | (6) ! [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)))
% 18.85/6.73 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0))
% 18.85/6.73 | (8) member(all_0_2_2, all_0_4_4) = 0
% 18.85/6.73 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 18.85/6.73 | (10) ! [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))
% 18.85/6.73 | (11) ! [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))
% 18.85/6.73 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 18.85/6.73 | (13) ! [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)))
% 18.85/6.73 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0))
% 18.85/6.73 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 18.85/6.73 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 18.85/6.73 | (17) ! [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)))
% 18.85/6.73 | (18) order(all_0_5_5, all_0_4_4) = 0
% 18.85/6.73 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 18.85/6.73 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 18.85/6.73 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0))
% 18.85/6.73 | (22) ! [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)))
% 18.85/6.73 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 18.85/6.73 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 18.85/6.73 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 18.85/6.73 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 18.85/6.73 | (27) ! [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)))
% 18.85/6.73 | (28) ! [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))
% 18.85/6.73 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0))
% 18.85/6.75 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 18.85/6.75 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0))
% 18.85/6.75 | (32) ! [v0] : ~ (member(v0, empty_set) = 0)
% 18.85/6.75 | (33) apply(all_0_5_5, all_0_3_3, all_0_2_2) = 0
% 18.85/6.75 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 18.85/6.75 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 18.85/6.75 | (36) ! [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))))
% 18.85/6.75 | (37) ! [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))
% 18.85/6.75 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 18.85/6.75 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 18.85/6.75 | (40) ! [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))
% 18.85/6.75 | (41) ! [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))))
% 18.85/6.75 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 18.85/6.75 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 18.85/6.75 | (44) ! [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)))
% 18.85/6.75 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 18.85/6.75 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 18.85/6.75 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0))
% 18.85/6.75 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 18.85/6.75 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 18.85/6.76 | (50) least_upper_bound(all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4) = all_0_0_0
% 18.85/6.76 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 18.85/6.76 | (52) ! [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)))
% 18.85/6.76 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 18.85/6.76 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 18.85/6.76 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 18.85/6.76 | (56) ! [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)))
% 18.85/6.76 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 18.85/6.76 | (58) ! [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))
% 18.85/6.76 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0))
% 18.85/6.76 | (60) ! [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)))
% 18.85/6.76 | (61) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 18.85/6.76 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 18.85/6.76 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 18.85/6.76 | (64) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0)
% 18.85/6.76 | (65) ! [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)))
% 18.85/6.76 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0))
% 18.85/6.76 | (67) ! [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)))
% 18.85/6.76 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0))
% 18.85/6.76 | (69) ~ (all_0_0_0 = 0)
% 18.85/6.76 | (70) ! [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)))))
% 18.85/6.76 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 18.85/6.76 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 18.85/6.76 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 18.85/6.77 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 18.85/6.77 | (75) unordered_pair(all_0_3_3, all_0_2_2) = all_0_1_1
% 18.85/6.77 | (76) member(all_0_3_3, all_0_4_4) = 0
% 18.85/6.77 | (77) ! [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)))))
% 18.85/6.77 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 18.85/6.77 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 18.85/6.77 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 18.85/6.77 | (81) ! [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))
% 18.85/6.77 |
% 18.85/6.77 | Instantiating formula (70) with all_0_0_0, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms least_upper_bound(all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4) = all_0_0_0, yields:
% 18.85/6.77 | (82) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & upper_bound(v0, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, v0) = v3 & member(v0, all_0_4_4) = 0) | (upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = v1 & member(all_0_2_2, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 18.85/6.77 |
% 18.85/6.77 | Instantiating formula (41) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms order(all_0_5_5, all_0_4_4) = 0, apply(all_0_5_5, all_0_3_3, all_0_2_2) = 0, yields:
% 18.85/6.77 | (83) all_0_2_2 = all_0_3_3 | ? [v0] : ? [v1] : ? [v2] : (apply(all_0_5_5, all_0_2_2, all_0_3_3) = v2 & member(all_0_2_2, all_0_4_4) = v1 & member(all_0_3_3, all_0_4_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 18.85/6.77 |
% 18.85/6.77 +-Applying beta-rule and splitting (83), into two cases.
% 18.85/6.77 |-Branch one:
% 18.85/6.77 | (84) all_0_2_2 = all_0_3_3
% 18.85/6.77 |
% 18.85/6.77 | From (84) and (33) follows:
% 18.85/6.77 | (85) apply(all_0_5_5, all_0_3_3, all_0_3_3) = 0
% 18.85/6.77 |
% 18.85/6.77 | From (84) and (75) follows:
% 18.85/6.77 | (86) unordered_pair(all_0_3_3, all_0_3_3) = all_0_1_1
% 18.85/6.77 |
% 18.85/6.77 +-Applying beta-rule and splitting (82), into two cases.
% 18.85/6.77 |-Branch one:
% 18.85/6.77 | (87) all_0_0_0 = 0
% 18.85/6.77 |
% 18.85/6.77 | Equations (87) can reduce 69 to:
% 18.85/6.77 | (88) $false
% 18.85/6.77 |
% 18.85/6.77 |-The branch is then unsatisfiable
% 18.85/6.77 |-Branch two:
% 18.85/6.77 | (69) ~ (all_0_0_0 = 0)
% 18.85/6.77 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & upper_bound(v0, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, v0) = v3 & member(v0, all_0_4_4) = 0) | (upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = v1 & member(all_0_2_2, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 18.85/6.78 |
% 18.85/6.78 | Instantiating (90) with all_22_0_6, all_22_1_7, all_22_2_8, all_22_3_9 yields:
% 18.85/6.78 | (91) (all_22_1_7 = 0 & all_22_2_8 = 0 & ~ (all_22_0_6 = 0) & upper_bound(all_22_3_9, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, all_22_3_9) = all_22_0_6 & member(all_22_3_9, all_0_4_4) = 0) | (upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_22_2_8 & member(all_0_2_2, all_0_1_1) = all_22_3_9 & ( ~ (all_22_2_8 = 0) | ~ (all_22_3_9 = 0)))
% 18.85/6.78 |
% 18.85/6.78 +-Applying beta-rule and splitting (91), into two cases.
% 18.85/6.78 |-Branch one:
% 18.85/6.78 | (92) all_22_1_7 = 0 & all_22_2_8 = 0 & ~ (all_22_0_6 = 0) & upper_bound(all_22_3_9, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, all_22_3_9) = all_22_0_6 & member(all_22_3_9, all_0_4_4) = 0
% 18.85/6.78 |
% 18.85/6.78 | Applying alpha-rule on (92) yields:
% 18.85/6.78 | (93) upper_bound(all_22_3_9, all_0_5_5, all_0_1_1) = 0
% 18.85/6.78 | (94) member(all_22_3_9, all_0_4_4) = 0
% 18.85/6.78 | (95) ~ (all_22_0_6 = 0)
% 18.85/6.78 | (96) apply(all_0_5_5, all_0_2_2, all_22_3_9) = all_22_0_6
% 18.85/6.78 | (97) all_22_2_8 = 0
% 18.85/6.78 | (98) all_22_1_7 = 0
% 18.85/6.78 |
% 18.85/6.78 | From (84) and (96) follows:
% 18.85/6.78 | (99) apply(all_0_5_5, all_0_3_3, all_22_3_9) = all_22_0_6
% 18.85/6.78 |
% 18.85/6.78 | Instantiating formula (81) with all_22_0_6, all_0_3_3, all_22_3_9, all_0_1_1, all_0_5_5 and discharging atoms upper_bound(all_22_3_9, all_0_5_5, all_0_1_1) = 0, apply(all_0_5_5, all_0_3_3, all_22_3_9) = all_22_0_6, yields:
% 18.85/6.78 | (100) all_22_0_6 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_1_1) = v0)
% 18.85/6.78 |
% 18.85/6.78 +-Applying beta-rule and splitting (100), into two cases.
% 18.85/6.78 |-Branch one:
% 18.85/6.78 | (101) all_22_0_6 = 0
% 19.31/6.78 |
% 19.31/6.78 | Equations (101) can reduce 95 to:
% 19.31/6.78 | (88) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (95) ~ (all_22_0_6 = 0)
% 19.31/6.78 | (104) ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_1_1) = v0)
% 19.31/6.78 |
% 19.31/6.78 | Instantiating (104) with all_41_0_10 yields:
% 19.31/6.78 | (105) ~ (all_41_0_10 = 0) & member(all_0_3_3, all_0_1_1) = all_41_0_10
% 19.31/6.78 |
% 19.31/6.78 | Applying alpha-rule on (105) yields:
% 19.31/6.78 | (106) ~ (all_41_0_10 = 0)
% 19.31/6.78 | (107) member(all_0_3_3, all_0_1_1) = all_41_0_10
% 19.31/6.78 |
% 19.31/6.78 | Instantiating formula (51) with all_41_0_10, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms unordered_pair(all_0_3_3, all_0_3_3) = all_0_1_1, member(all_0_3_3, all_0_1_1) = all_41_0_10, yields:
% 19.31/6.78 | (108) all_41_0_10 = 0
% 19.31/6.78 |
% 19.31/6.78 | Equations (108) can reduce 106 to:
% 19.31/6.78 | (88) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (110) upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_22_2_8 & member(all_0_2_2, all_0_1_1) = all_22_3_9 & ( ~ (all_22_2_8 = 0) | ~ (all_22_3_9 = 0))
% 19.31/6.78 |
% 19.31/6.78 | Applying alpha-rule on (110) yields:
% 19.31/6.78 | (111) upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_22_2_8
% 19.31/6.78 | (112) member(all_0_2_2, all_0_1_1) = all_22_3_9
% 19.31/6.78 | (113) ~ (all_22_2_8 = 0) | ~ (all_22_3_9 = 0)
% 19.31/6.78 |
% 19.31/6.78 | From (84) and (111) follows:
% 19.31/6.78 | (114) upper_bound(all_0_3_3, all_0_5_5, all_0_1_1) = all_22_2_8
% 19.31/6.78 |
% 19.31/6.78 | From (84) and (112) follows:
% 19.31/6.78 | (115) member(all_0_3_3, all_0_1_1) = all_22_3_9
% 19.31/6.78 |
% 19.31/6.78 | Instantiating formula (51) with all_22_3_9, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms unordered_pair(all_0_3_3, all_0_3_3) = all_0_1_1, member(all_0_3_3, all_0_1_1) = all_22_3_9, yields:
% 19.31/6.78 | (116) all_22_3_9 = 0
% 19.31/6.78 |
% 19.31/6.78 +-Applying beta-rule and splitting (113), into two cases.
% 19.31/6.78 |-Branch one:
% 19.31/6.78 | (117) ~ (all_22_2_8 = 0)
% 19.31/6.78 |
% 19.31/6.78 | Instantiating formula (37) with all_22_2_8, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms upper_bound(all_0_3_3, all_0_5_5, all_0_1_1) = all_22_2_8, yields:
% 19.31/6.78 | (118) all_22_2_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_3_3) = v1 & member(v0, all_0_1_1) = 0)
% 19.31/6.78 |
% 19.31/6.78 +-Applying beta-rule and splitting (118), into two cases.
% 19.31/6.78 |-Branch one:
% 19.31/6.78 | (97) all_22_2_8 = 0
% 19.31/6.78 |
% 19.31/6.78 | Equations (97) can reduce 117 to:
% 19.31/6.78 | (88) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (117) ~ (all_22_2_8 = 0)
% 19.31/6.78 | (122) ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_3_3) = v1 & member(v0, all_0_1_1) = 0)
% 19.31/6.78 |
% 19.31/6.78 | Instantiating (122) with all_53_0_11, all_53_1_12 yields:
% 19.31/6.78 | (123) ~ (all_53_0_11 = 0) & apply(all_0_5_5, all_53_1_12, all_0_3_3) = all_53_0_11 & member(all_53_1_12, all_0_1_1) = 0
% 19.31/6.78 |
% 19.31/6.78 | Applying alpha-rule on (123) yields:
% 19.31/6.78 | (124) ~ (all_53_0_11 = 0)
% 19.31/6.78 | (125) apply(all_0_5_5, all_53_1_12, all_0_3_3) = all_53_0_11
% 19.31/6.78 | (126) member(all_53_1_12, all_0_1_1) = 0
% 19.31/6.78 |
% 19.31/6.78 | Instantiating formula (53) with all_0_5_5, all_0_3_3, all_0_3_3, all_53_0_11, 0 and discharging atoms apply(all_0_5_5, all_0_3_3, all_0_3_3) = 0, yields:
% 19.31/6.78 | (127) all_53_0_11 = 0 | ~ (apply(all_0_5_5, all_0_3_3, all_0_3_3) = all_53_0_11)
% 19.31/6.78 |
% 19.31/6.78 | Instantiating formula (19) with all_0_1_1, all_0_3_3, all_0_3_3, all_53_1_12 and discharging atoms unordered_pair(all_0_3_3, all_0_3_3) = all_0_1_1, member(all_53_1_12, all_0_1_1) = 0, yields:
% 19.31/6.78 | (128) all_53_1_12 = all_0_3_3
% 19.31/6.78 |
% 19.31/6.78 | From (128) and (125) follows:
% 19.31/6.78 | (129) apply(all_0_5_5, all_0_3_3, all_0_3_3) = all_53_0_11
% 19.31/6.78 |
% 19.31/6.78 +-Applying beta-rule and splitting (127), into two cases.
% 19.31/6.78 |-Branch one:
% 19.31/6.78 | (130) ~ (apply(all_0_5_5, all_0_3_3, all_0_3_3) = all_53_0_11)
% 19.31/6.78 |
% 19.31/6.78 | Using (129) and (130) yields:
% 19.31/6.78 | (131) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (129) apply(all_0_5_5, all_0_3_3, all_0_3_3) = all_53_0_11
% 19.31/6.78 | (133) all_53_0_11 = 0
% 19.31/6.78 |
% 19.31/6.78 | Equations (133) can reduce 124 to:
% 19.31/6.78 | (88) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (97) all_22_2_8 = 0
% 19.31/6.78 | (136) ~ (all_22_3_9 = 0)
% 19.31/6.78 |
% 19.31/6.78 | Equations (116) can reduce 136 to:
% 19.31/6.78 | (88) $false
% 19.31/6.78 |
% 19.31/6.78 |-The branch is then unsatisfiable
% 19.31/6.78 |-Branch two:
% 19.31/6.78 | (138) ~ (all_0_2_2 = all_0_3_3)
% 19.31/6.78 | (139) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_5_5, all_0_2_2, all_0_3_3) = v2 & member(all_0_2_2, all_0_4_4) = v1 & member(all_0_3_3, all_0_4_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.31/6.78 |
% 19.31/6.78 | Instantiating (139) with all_18_0_13, all_18_1_14, all_18_2_15 yields:
% 19.31/6.78 | (140) apply(all_0_5_5, all_0_2_2, all_0_3_3) = all_18_0_13 & member(all_0_2_2, all_0_4_4) = all_18_1_14 & member(all_0_3_3, all_0_4_4) = all_18_2_15 & ( ~ (all_18_0_13 = 0) | ~ (all_18_1_14 = 0) | ~ (all_18_2_15 = 0))
% 19.31/6.79 |
% 19.31/6.79 | Applying alpha-rule on (140) yields:
% 19.31/6.79 | (141) apply(all_0_5_5, all_0_2_2, all_0_3_3) = all_18_0_13
% 19.31/6.79 | (142) member(all_0_2_2, all_0_4_4) = all_18_1_14
% 19.31/6.79 | (143) member(all_0_3_3, all_0_4_4) = all_18_2_15
% 19.31/6.79 | (144) ~ (all_18_0_13 = 0) | ~ (all_18_1_14 = 0) | ~ (all_18_2_15 = 0)
% 19.31/6.79 |
% 19.31/6.79 +-Applying beta-rule and splitting (82), into two cases.
% 19.31/6.79 |-Branch one:
% 19.31/6.79 | (87) all_0_0_0 = 0
% 19.31/6.79 |
% 19.31/6.79 | Equations (87) can reduce 69 to:
% 19.31/6.79 | (88) $false
% 19.31/6.79 |
% 19.31/6.79 |-The branch is then unsatisfiable
% 19.31/6.79 |-Branch two:
% 19.31/6.79 | (69) ~ (all_0_0_0 = 0)
% 19.31/6.79 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & v1 = 0 & ~ (v3 = 0) & upper_bound(v0, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, v0) = v3 & member(v0, all_0_4_4) = 0) | (upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = v1 & member(all_0_2_2, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 19.31/6.79 |
% 19.31/6.79 | Instantiating (90) with all_24_0_16, all_24_1_17, all_24_2_18, all_24_3_19 yields:
% 19.31/6.79 | (149) (all_24_1_17 = 0 & all_24_2_18 = 0 & ~ (all_24_0_16 = 0) & upper_bound(all_24_3_19, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, all_24_3_19) = all_24_0_16 & member(all_24_3_19, all_0_4_4) = 0) | (upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_24_2_18 & member(all_0_2_2, all_0_1_1) = all_24_3_19 & ( ~ (all_24_2_18 = 0) | ~ (all_24_3_19 = 0)))
% 19.31/6.79 |
% 19.31/6.79 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_18_1_14, 0 and discharging atoms member(all_0_2_2, all_0_4_4) = all_18_1_14, member(all_0_2_2, all_0_4_4) = 0, yields:
% 19.31/6.79 | (150) all_18_1_14 = 0
% 19.31/6.79 |
% 19.31/6.79 | From (150) and (142) follows:
% 19.31/6.79 | (8) member(all_0_2_2, all_0_4_4) = 0
% 19.31/6.79 |
% 19.31/6.79 +-Applying beta-rule and splitting (149), into two cases.
% 19.31/6.79 |-Branch one:
% 19.31/6.79 | (152) all_24_1_17 = 0 & all_24_2_18 = 0 & ~ (all_24_0_16 = 0) & upper_bound(all_24_3_19, all_0_5_5, all_0_1_1) = 0 & apply(all_0_5_5, all_0_2_2, all_24_3_19) = all_24_0_16 & member(all_24_3_19, all_0_4_4) = 0
% 19.31/6.79 |
% 19.31/6.79 | Applying alpha-rule on (152) yields:
% 19.31/6.79 | (153) member(all_24_3_19, all_0_4_4) = 0
% 19.31/6.79 | (154) ~ (all_24_0_16 = 0)
% 19.31/6.79 | (155) all_24_2_18 = 0
% 19.31/6.79 | (156) apply(all_0_5_5, all_0_2_2, all_24_3_19) = all_24_0_16
% 19.31/6.79 | (157) all_24_1_17 = 0
% 19.31/6.79 | (158) upper_bound(all_24_3_19, all_0_5_5, all_0_1_1) = 0
% 19.31/6.79 |
% 19.31/6.79 | Instantiating formula (81) with all_24_0_16, all_0_2_2, all_24_3_19, all_0_1_1, all_0_5_5 and discharging atoms upper_bound(all_24_3_19, all_0_5_5, all_0_1_1) = 0, apply(all_0_5_5, all_0_2_2, all_24_3_19) = all_24_0_16, yields:
% 19.31/6.79 | (159) all_24_0_16 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_2_2, all_0_1_1) = v0)
% 19.31/6.79 |
% 19.31/6.79 +-Applying beta-rule and splitting (159), into two cases.
% 19.31/6.79 |-Branch one:
% 19.31/6.79 | (160) all_24_0_16 = 0
% 19.31/6.79 |
% 19.31/6.79 | Equations (160) can reduce 154 to:
% 19.31/6.79 | (88) $false
% 19.31/6.79 |
% 19.31/6.79 |-The branch is then unsatisfiable
% 19.31/6.79 |-Branch two:
% 19.31/6.79 | (154) ~ (all_24_0_16 = 0)
% 19.31/6.79 | (163) ? [v0] : ( ~ (v0 = 0) & member(all_0_2_2, all_0_1_1) = v0)
% 19.37/6.79 |
% 19.37/6.79 | Instantiating (163) with all_54_0_20 yields:
% 19.37/6.79 | (164) ~ (all_54_0_20 = 0) & member(all_0_2_2, all_0_1_1) = all_54_0_20
% 19.37/6.79 |
% 19.37/6.79 | Applying alpha-rule on (164) yields:
% 19.37/6.79 | (165) ~ (all_54_0_20 = 0)
% 19.37/6.79 | (166) member(all_0_2_2, all_0_1_1) = all_54_0_20
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (51) with all_54_0_20, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms unordered_pair(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_0_2_2, all_0_1_1) = all_54_0_20, yields:
% 19.37/6.79 | (167) all_54_0_20 = 0
% 19.37/6.79 |
% 19.37/6.79 | Equations (167) can reduce 165 to:
% 19.37/6.79 | (88) $false
% 19.37/6.79 |
% 19.37/6.79 |-The branch is then unsatisfiable
% 19.37/6.79 |-Branch two:
% 19.37/6.79 | (169) upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_24_2_18 & member(all_0_2_2, all_0_1_1) = all_24_3_19 & ( ~ (all_24_2_18 = 0) | ~ (all_24_3_19 = 0))
% 19.37/6.79 |
% 19.37/6.79 | Applying alpha-rule on (169) yields:
% 19.37/6.79 | (170) upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_24_2_18
% 19.37/6.79 | (171) member(all_0_2_2, all_0_1_1) = all_24_3_19
% 19.37/6.79 | (172) ~ (all_24_2_18 = 0) | ~ (all_24_3_19 = 0)
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (51) with all_24_3_19, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms unordered_pair(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_0_2_2, all_0_1_1) = all_24_3_19, yields:
% 19.37/6.79 | (173) all_24_3_19 = 0
% 19.37/6.79 |
% 19.37/6.79 +-Applying beta-rule and splitting (172), into two cases.
% 19.37/6.79 |-Branch one:
% 19.37/6.79 | (174) ~ (all_24_2_18 = 0)
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (37) with all_24_2_18, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms upper_bound(all_0_2_2, all_0_5_5, all_0_1_1) = all_24_2_18, yields:
% 19.37/6.79 | (175) all_24_2_18 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_2_2) = v1 & member(v0, all_0_1_1) = 0)
% 19.37/6.79 |
% 19.37/6.79 +-Applying beta-rule and splitting (175), into two cases.
% 19.37/6.79 |-Branch one:
% 19.37/6.79 | (155) all_24_2_18 = 0
% 19.37/6.79 |
% 19.37/6.79 | Equations (155) can reduce 174 to:
% 19.37/6.79 | (88) $false
% 19.37/6.79 |
% 19.37/6.79 |-The branch is then unsatisfiable
% 19.37/6.79 |-Branch two:
% 19.37/6.79 | (174) ~ (all_24_2_18 = 0)
% 19.37/6.79 | (179) ? [v0] : ? [v1] : ( ~ (v1 = 0) & apply(all_0_5_5, v0, all_0_2_2) = v1 & member(v0, all_0_1_1) = 0)
% 19.37/6.79 |
% 19.37/6.79 | Instantiating (179) with all_63_0_21, all_63_1_22 yields:
% 19.37/6.79 | (180) ~ (all_63_0_21 = 0) & apply(all_0_5_5, all_63_1_22, all_0_2_2) = all_63_0_21 & member(all_63_1_22, all_0_1_1) = 0
% 19.37/6.79 |
% 19.37/6.79 | Applying alpha-rule on (180) yields:
% 19.37/6.79 | (181) ~ (all_63_0_21 = 0)
% 19.37/6.79 | (182) apply(all_0_5_5, all_63_1_22, all_0_2_2) = all_63_0_21
% 19.37/6.79 | (183) member(all_63_1_22, all_0_1_1) = 0
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (53) with all_0_5_5, all_0_3_3, all_0_2_2, all_63_0_21, 0 and discharging atoms apply(all_0_5_5, all_0_3_3, all_0_2_2) = 0, yields:
% 19.37/6.79 | (184) all_63_0_21 = 0 | ~ (apply(all_0_5_5, all_0_3_3, all_0_2_2) = all_63_0_21)
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (19) with all_0_1_1, all_0_2_2, all_0_3_3, all_63_1_22 and discharging atoms unordered_pair(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_63_1_22, all_0_1_1) = 0, yields:
% 19.37/6.79 | (185) all_63_1_22 = all_0_2_2 | all_63_1_22 = all_0_3_3
% 19.37/6.79 |
% 19.37/6.79 | Instantiating formula (55) with all_63_0_21, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms order(all_0_5_5, all_0_4_4) = 0, yields:
% 19.37/6.79 | (186) all_63_0_21 = 0 | ~ (apply(all_0_5_5, all_0_2_2, all_0_2_2) = all_63_0_21) | ? [v0] : ( ~ (v0 = 0) & member(all_0_2_2, all_0_4_4) = v0)
% 19.37/6.79 |
% 19.37/6.79 +-Applying beta-rule and splitting (186), into two cases.
% 19.37/6.79 |-Branch one:
% 19.37/6.79 | (187) ~ (apply(all_0_5_5, all_0_2_2, all_0_2_2) = all_63_0_21)
% 19.37/6.79 |
% 19.37/6.79 | Using (182) and (187) yields:
% 19.37/6.79 | (188) ~ (all_63_1_22 = all_0_2_2)
% 19.37/6.79 |
% 19.37/6.79 +-Applying beta-rule and splitting (185), into two cases.
% 19.37/6.79 |-Branch one:
% 19.37/6.79 | (189) all_63_1_22 = all_0_2_2
% 19.37/6.79 |
% 19.37/6.79 | Equations (189) can reduce 188 to:
% 19.37/6.79 | (88) $false
% 19.37/6.79 |
% 19.37/6.79 |-The branch is then unsatisfiable
% 19.37/6.79 |-Branch two:
% 19.37/6.79 | (188) ~ (all_63_1_22 = all_0_2_2)
% 19.37/6.79 | (192) all_63_1_22 = all_0_3_3
% 19.37/6.79 |
% 19.37/6.79 | From (192) and (182) follows:
% 19.37/6.79 | (193) apply(all_0_5_5, all_0_3_3, all_0_2_2) = all_63_0_21
% 19.37/6.80 |
% 19.37/6.80 +-Applying beta-rule and splitting (184), into two cases.
% 19.37/6.80 |-Branch one:
% 19.37/6.80 | (194) ~ (apply(all_0_5_5, all_0_3_3, all_0_2_2) = all_63_0_21)
% 19.37/6.80 |
% 19.37/6.80 | Using (193) and (194) yields:
% 19.37/6.80 | (131) $false
% 19.37/6.80 |
% 19.37/6.80 |-The branch is then unsatisfiable
% 19.37/6.80 |-Branch two:
% 19.37/6.80 | (193) apply(all_0_5_5, all_0_3_3, all_0_2_2) = all_63_0_21
% 19.37/6.80 | (197) all_63_0_21 = 0
% 19.37/6.80 |
% 19.37/6.80 | Equations (197) can reduce 181 to:
% 19.37/6.80 | (88) $false
% 19.37/6.80 |
% 19.37/6.80 |-The branch is then unsatisfiable
% 19.37/6.80 |-Branch two:
% 19.37/6.80 | (199) apply(all_0_5_5, all_0_2_2, all_0_2_2) = all_63_0_21
% 19.37/6.80 | (200) all_63_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_2_2, all_0_4_4) = v0)
% 19.37/6.80 |
% 19.37/6.80 +-Applying beta-rule and splitting (200), into two cases.
% 19.37/6.80 |-Branch one:
% 19.37/6.80 | (197) all_63_0_21 = 0
% 19.37/6.80 |
% 19.37/6.80 | Equations (197) can reduce 181 to:
% 19.37/6.80 | (88) $false
% 19.37/6.80 |
% 19.37/6.80 |-The branch is then unsatisfiable
% 19.37/6.80 |-Branch two:
% 19.37/6.80 | (181) ~ (all_63_0_21 = 0)
% 19.37/6.80 | (204) ? [v0] : ( ~ (v0 = 0) & member(all_0_2_2, all_0_4_4) = v0)
% 19.37/6.80 |
% 19.37/6.80 | Instantiating (204) with all_84_0_23 yields:
% 19.37/6.80 | (205) ~ (all_84_0_23 = 0) & member(all_0_2_2, all_0_4_4) = all_84_0_23
% 19.37/6.80 |
% 19.37/6.80 | Applying alpha-rule on (205) yields:
% 19.37/6.80 | (206) ~ (all_84_0_23 = 0)
% 19.37/6.80 | (207) member(all_0_2_2, all_0_4_4) = all_84_0_23
% 19.37/6.80 |
% 19.37/6.80 | Instantiating formula (4) with all_0_2_2, all_0_4_4, all_84_0_23, 0 and discharging atoms member(all_0_2_2, all_0_4_4) = all_84_0_23, member(all_0_2_2, all_0_4_4) = 0, yields:
% 19.37/6.80 | (208) all_84_0_23 = 0
% 19.37/6.80 |
% 19.37/6.80 | Equations (208) can reduce 206 to:
% 19.37/6.80 | (88) $false
% 19.37/6.80 |
% 19.37/6.80 |-The branch is then unsatisfiable
% 19.37/6.80 |-Branch two:
% 19.37/6.80 | (155) all_24_2_18 = 0
% 19.37/6.80 | (211) ~ (all_24_3_19 = 0)
% 19.37/6.80 |
% 19.37/6.80 | Equations (173) can reduce 211 to:
% 19.37/6.80 | (88) $false
% 19.37/6.80 |
% 19.37/6.80 |-The branch is then unsatisfiable
% 19.37/6.80 % SZS output end Proof for theBenchmark
% 19.37/6.80
% 19.37/6.80 6193ms
%------------------------------------------------------------------------------