TSTP Solution File: GEO219+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO219+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : Sat Jul 16 03:48:52 EDT 2022
% Result : Theorem 5.89s 2.00s
% Output : Proof 8.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO219+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.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 Jun 18 04:07:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.93 Prover 0: Preprocessing ...
% 2.13/1.08 Prover 0: Warning: ignoring some quantifiers
% 2.23/1.10 Prover 0: Constructing countermodel ...
% 3.96/1.57 Prover 0: gave up
% 3.96/1.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.96/1.60 Prover 1: Preprocessing ...
% 4.31/1.68 Prover 1: Constructing countermodel ...
% 4.52/1.75 Prover 1: gave up
% 4.52/1.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.93/1.77 Prover 2: Preprocessing ...
% 5.25/1.89 Prover 2: Warning: ignoring some quantifiers
% 5.25/1.90 Prover 2: Constructing countermodel ...
% 5.89/2.00 Prover 2: proved (247ms)
% 5.89/2.00
% 5.89/2.00 No countermodel exists, formula is valid
% 5.89/2.00 % SZS status Theorem for theBenchmark
% 5.89/2.00
% 5.89/2.00 Generating proof ... Warning: ignoring some quantifiers
% 7.98/2.46 found it (size 104)
% 7.98/2.46
% 7.98/2.46 % SZS output start Proof for theBenchmark
% 7.98/2.46 Assumed formulas after preprocessing and simplification:
% 7.98/2.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = 0 & unorthogonal_lines(v0, v1) = v3 & convergent_lines(v0, v2) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection_point(v5, v6) = v8) | ~ (distinct_points(v7, v8) = v9) | ? [v10] : ? [v11] : (( ~ (v11 = 0) & ~ (v10 = 0) & apart_point_and_line(v7, v6) = v11 & apart_point_and_line(v7, v5) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v5, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & distinct_points(v7, v6) = 0 & distinct_points(v7, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v5, v6) = 0) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7)
% 8.16/2.51 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 8.16/2.51 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.16/2.53 |
% 8.16/2.53 | Applying alpha-rule on (1) yields:
% 8.16/2.54 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 8.16/2.54 | (3) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 8.16/2.54 | (4) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 8.16/2.54 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 8.38/2.54 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 8.38/2.54 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 8.38/2.54 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 8.40/2.54 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 8.40/2.54 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 8.40/2.54 | (11) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 8.40/2.54 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 8.40/2.54 | (13) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 8.40/2.54 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 8.40/2.54 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 8.40/2.54 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 8.40/2.54 | (17) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 8.40/2.54 | (18) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 8.40/2.54 | (19) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.40/2.55 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 8.40/2.55 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 8.40/2.55 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 8.40/2.55 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 8.40/2.55 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 8.40/2.55 | (25) convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0
% 8.40/2.55 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 8.40/2.55 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 8.40/2.55 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 8.40/2.55 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 8.40/2.55 | (30) ~ (all_0_1_1 = 0)
% 8.40/2.55 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 8.40/2.55 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 8.40/2.55 | (33) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 8.40/2.55 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 8.40/2.55 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 8.40/2.55 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 8.40/2.55 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 8.40/2.55 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 8.40/2.55 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 8.40/2.55 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 8.40/2.55 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 8.40/2.56 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 8.40/2.56 | (43) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 8.40/2.56 | (44) ~ (all_0_0_0 = 0)
% 8.40/2.56 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 8.40/2.56 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 8.40/2.56 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.40/2.56 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 8.40/2.56 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 8.40/2.56 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 8.40/2.56 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 8.40/2.56 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 8.40/2.56 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 8.40/2.56 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 8.40/2.56 | (55) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 8.40/2.56 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 8.40/2.56 | (57) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 8.40/2.56 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 8.40/2.56 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 8.40/2.56 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 8.40/2.56 | (61) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 8.40/2.56 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 8.40/2.56 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 8.40/2.57 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 8.40/2.57 | (65) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 8.40/2.57 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (14) with 0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 8.40/2.57 | (67) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (24) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 8.40/2.57 | (68) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (38) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 8.40/2.57 | (69) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (22) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 8.40/2.57 | (70) all_0_1_1 = 0 | convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (36) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.40/2.57 | (71) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (64) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.40/2.57 | (72) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (63) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.40/2.57 | (73) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 8.40/2.57 |
% 8.40/2.57 | Instantiating (73) with all_22_0_26 yields:
% 8.40/2.57 | (74) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26) | ( ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating (68) with all_25_0_29, all_25_1_30 yields:
% 8.40/2.57 | (75) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating (67) with all_26_0_31, all_26_1_32 yields:
% 8.40/2.57 | (76) (all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_26_1_32 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating (72) with all_29_0_35, all_29_1_36 yields:
% 8.40/2.57 | (77) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36)
% 8.40/2.57 |
% 8.40/2.57 +-Applying beta-rule and splitting (70), into two cases.
% 8.40/2.57 |-Branch one:
% 8.40/2.57 | (78) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.57 |
% 8.40/2.57 +-Applying beta-rule and splitting (77), into two cases.
% 8.40/2.57 |-Branch one:
% 8.40/2.57 | (79) (all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 8.40/2.57 |
% 8.40/2.57 +-Applying beta-rule and splitting (79), into two cases.
% 8.40/2.57 |-Branch one:
% 8.40/2.57 | (80) all_29_0_35 = 0 & all_29_1_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.57 |
% 8.40/2.57 | Applying alpha-rule on (80) yields:
% 8.40/2.57 | (81) all_29_0_35 = 0
% 8.40/2.57 | (82) all_29_1_36 = 0
% 8.40/2.57 | (83) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.57 | (78) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.57 |
% 8.40/2.57 +-Applying beta-rule and splitting (69), into two cases.
% 8.40/2.57 |-Branch one:
% 8.40/2.57 | (85) all_0_1_1 = 0
% 8.40/2.57 |
% 8.40/2.57 | Equations (85) can reduce 30 to:
% 8.40/2.57 | (86) $false
% 8.40/2.57 |
% 8.40/2.57 |-The branch is then unsatisfiable
% 8.40/2.57 |-Branch two:
% 8.40/2.57 | (30) ~ (all_0_1_1 = 0)
% 8.40/2.57 | (88) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 8.40/2.57 |
% 8.40/2.57 | Instantiating formula (42) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_0_1_1, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 8.40/2.58 | (85) all_0_1_1 = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (85) can reduce 30 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (91) all_29_1_36 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (91) yields:
% 8.40/2.58 | (82) all_29_1_36 = 0
% 8.40/2.58 | (93) all_0_0_0 = 0
% 8.40/2.58 | (94) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (93) can reduce 44 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (96) ~ (all_29_1_36 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (96) yields:
% 8.40/2.58 | (97) ~ (all_29_1_36 = 0)
% 8.40/2.58 | (98) convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (75), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (99) (all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (99), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (100) all_25_0_29 = 0 & all_25_1_30 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (100) yields:
% 8.40/2.58 | (101) all_25_0_29 = 0
% 8.40/2.58 | (102) all_25_1_30 = 0
% 8.40/2.58 | (94) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 | (104) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (71), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (93) all_0_0_0 = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (93) can reduce 44 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (44) ~ (all_0_0_0 = 0)
% 8.40/2.58 | (108) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 8.40/2.58 |
% 8.40/2.58 | Instantiating formula (32) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 8.40/2.58 | (93) all_0_0_0 = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (93) can reduce 44 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (111) all_25_1_30 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (111) yields:
% 8.40/2.58 | (102) all_25_1_30 = 0
% 8.40/2.58 | (85) all_0_1_1 = 0
% 8.40/2.58 | (78) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (85) can reduce 30 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (116) ~ (all_25_1_30 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (116) yields:
% 8.40/2.58 | (117) ~ (all_25_1_30 = 0)
% 8.40/2.58 | (118) convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (71), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (93) all_0_0_0 = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (93) can reduce 44 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (44) ~ (all_0_0_0 = 0)
% 8.40/2.58 | (108) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (74), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (123) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26)
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (123), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (124) (all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (124), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (125) all_22_0_26 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (125) yields:
% 8.40/2.58 | (126) all_22_0_26 = 0
% 8.40/2.58 | (93) all_0_0_0 = 0
% 8.40/2.58 | (94) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (93) can reduce 44 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (130) all_22_0_26 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (130) yields:
% 8.40/2.58 | (126) all_22_0_26 = 0
% 8.40/2.58 | (85) all_0_1_1 = 0
% 8.40/2.58 | (78) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (85) can reduce 30 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (135) ~ (all_22_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (135) yields:
% 8.40/2.58 | (136) ~ (all_22_0_26 = 0)
% 8.40/2.58 | (137) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26
% 8.40/2.58 |
% 8.40/2.58 | Instantiating formula (42) with all_0_3_3, all_0_2_2, all_22_0_26, 0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_22_0_26, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 8.40/2.58 | (126) all_22_0_26 = 0
% 8.40/2.58 |
% 8.40/2.58 | Equations (126) can reduce 136 to:
% 8.40/2.58 | (86) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (140) ~ (all_22_0_26 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (140) yields:
% 8.40/2.58 | (136) ~ (all_22_0_26 = 0)
% 8.40/2.58 | (142) convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (76), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (143) (all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 8.40/2.58 |
% 8.40/2.58 +-Applying beta-rule and splitting (143), into two cases.
% 8.40/2.58 |-Branch one:
% 8.40/2.58 | (144) all_26_0_31 = 0 & all_26_1_32 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (144) yields:
% 8.40/2.58 | (145) all_26_0_31 = 0
% 8.40/2.58 | (146) all_26_1_32 = 0
% 8.40/2.58 | (147) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 8.40/2.58 | (148) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 8.40/2.58 |
% 8.40/2.58 | Instantiating formula (18) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 8.40/2.58 | (149) $false
% 8.40/2.58 |
% 8.40/2.58 |-The branch is then unsatisfiable
% 8.40/2.58 |-Branch two:
% 8.40/2.58 | (150) all_26_1_32 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Applying alpha-rule on (150) yields:
% 8.40/2.58 | (146) all_26_1_32 = 0
% 8.40/2.58 | (152) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 8.40/2.58 |
% 8.40/2.58 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_25_1_30, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields:
% 8.40/2.58 | (153) all_29_1_36 = all_25_1_30
% 8.40/2.58 |
% 8.40/2.58 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_22_0_26, all_25_1_30 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, yields:
% 8.40/2.59 | (154) all_25_1_30 = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (32) with all_0_3_3, all_0_2_2, 0, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 8.40/2.59 | (82) all_29_1_36 = 0
% 8.40/2.59 |
% 8.40/2.59 | Combining equations (153,82) yields a new equation:
% 8.40/2.59 | (156) all_25_1_30 = 0
% 8.40/2.59 |
% 8.40/2.59 | Simplifying 156 yields:
% 8.40/2.59 | (102) all_25_1_30 = 0
% 8.40/2.59 |
% 8.40/2.59 | Combining equations (154,102) yields a new equation:
% 8.40/2.59 | (158) all_22_0_26 = 0
% 8.40/2.59 |
% 8.40/2.59 | Simplifying 158 yields:
% 8.40/2.59 | (126) all_22_0_26 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (126) can reduce 136 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (161) ~ (all_26_1_32 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32
% 8.40/2.59 |
% 8.40/2.59 | Applying alpha-rule on (161) yields:
% 8.40/2.59 | (162) ~ (all_26_1_32 = 0)
% 8.40/2.59 | (163) convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_26_1_32, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32, yields:
% 8.40/2.59 | (164) all_29_1_36 = all_26_1_32
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_25_1_30, all_26_1_32 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_26_1_32, convergent_lines(all_0_3_3, all_0_2_2) = all_25_1_30, yields:
% 8.40/2.59 | (165) all_26_1_32 = all_25_1_30
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (32) with all_0_3_3, all_0_2_2, all_22_0_26, all_29_1_36 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_29_1_36, convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, yields:
% 8.40/2.59 | (166) all_29_1_36 = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Combining equations (164,166) yields a new equation:
% 8.40/2.59 | (167) all_26_1_32 = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Simplifying 167 yields:
% 8.40/2.59 | (168) all_26_1_32 = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Combining equations (168,165) yields a new equation:
% 8.40/2.59 | (154) all_25_1_30 = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Equations (154) can reduce 117 to:
% 8.40/2.59 | (136) ~ (all_22_0_26 = 0)
% 8.40/2.59 |
% 8.40/2.59 | From (154) and (118) follows:
% 8.40/2.59 | (142) convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (36) with all_22_0_26, all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.40/2.59 | (172) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (36) with all_0_0_0, all_22_0_26, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 8.40/2.59 | (173) all_22_0_26 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (62) with all_22_0_26, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_22_0_26, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 8.40/2.59 | (174) all_22_0_26 = 0 | convergent_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.59 |
% 8.40/2.59 +-Applying beta-rule and splitting (174), into two cases.
% 8.40/2.59 |-Branch one:
% 8.40/2.59 | (104) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 8.40/2.59 |
% 8.40/2.59 +-Applying beta-rule and splitting (173), into two cases.
% 8.40/2.59 |-Branch one:
% 8.40/2.59 | (126) all_22_0_26 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (126) can reduce 136 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (136) ~ (all_22_0_26 = 0)
% 8.40/2.59 | (179) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 8.40/2.59 |
% 8.40/2.59 +-Applying beta-rule and splitting (179), into two cases.
% 8.40/2.59 |-Branch one:
% 8.40/2.59 | (93) all_0_0_0 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (93) can reduce 44 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (44) ~ (all_0_0_0 = 0)
% 8.40/2.59 | (183) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 8.40/2.59 |
% 8.40/2.59 +-Applying beta-rule and splitting (172), into two cases.
% 8.40/2.59 |-Branch one:
% 8.40/2.59 | (126) all_22_0_26 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (126) can reduce 136 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (136) ~ (all_22_0_26 = 0)
% 8.40/2.59 | (187) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)
% 8.40/2.59 |
% 8.40/2.59 +-Applying beta-rule and splitting (187), into two cases.
% 8.40/2.59 |-Branch one:
% 8.40/2.59 | (93) all_0_0_0 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (93) can reduce 44 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (44) ~ (all_0_0_0 = 0)
% 8.40/2.59 | (191) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)
% 8.40/2.59 |
% 8.40/2.59 | Instantiating formula (32) with all_0_4_4, all_0_2_2, 0, all_0_0_0 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 8.40/2.59 | (93) all_0_0_0 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (93) can reduce 44 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (194) ~ (convergent_lines(all_0_4_4, all_0_2_2) = 0)
% 8.40/2.59 | (126) all_22_0_26 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (126) can reduce 136 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 |-Branch two:
% 8.40/2.59 | (197) ~ (convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 8.40/2.59 | (85) all_0_1_1 = 0
% 8.40/2.59 |
% 8.40/2.59 | Equations (85) can reduce 30 to:
% 8.40/2.59 | (86) $false
% 8.40/2.59 |
% 8.40/2.59 |-The branch is then unsatisfiable
% 8.40/2.59 % SZS output end Proof for theBenchmark
% 8.40/2.59
% 8.40/2.59 2006ms
%------------------------------------------------------------------------------