TSTP Solution File: GEO217+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO217+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 03:48:51 EDT 2022
% Result : Theorem 6.27s 2.10s
% Output : Proof 30.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO217+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 11:38:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.59 ____ _
% 0.60/0.59 ___ / __ \_____(_)___ ________ __________
% 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.97 Prover 0: Preprocessing ...
% 2.06/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.06/1.14 Prover 0: Constructing countermodel ...
% 3.83/1.58 Prover 0: gave up
% 3.83/1.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.83/1.61 Prover 1: Preprocessing ...
% 4.22/1.69 Prover 1: Constructing countermodel ...
% 4.55/1.72 Prover 1: gave up
% 4.55/1.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.55/1.74 Prover 2: Preprocessing ...
% 5.09/1.87 Prover 2: Warning: ignoring some quantifiers
% 5.09/1.88 Prover 2: Constructing countermodel ...
% 6.27/2.10 Prover 2: proved (383ms)
% 6.27/2.10
% 6.27/2.10 No countermodel exists, formula is valid
% 6.27/2.10 % SZS status Theorem for theBenchmark
% 6.27/2.10
% 6.27/2.10 Generating proof ... Warning: ignoring some quantifiers
% 30.02/10.71 found it (size 264)
% 30.02/10.71
% 30.02/10.71 % SZS output start Proof for theBenchmark
% 30.02/10.71 Assumed formulas after preprocessing and simplification:
% 30.02/10.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & convergent_lines(v1, v2) = 0 & convergent_lines(v0, v2) = v4 & convergent_lines(v0, v1) = v3 & ! [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)
% 30.40/10.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 30.40/10.78 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0 & convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & ! [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
% 30.54/10.80 |
% 30.54/10.80 | Applying alpha-rule on (1) yields:
% 30.54/10.80 | (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))
% 30.54/10.80 | (3) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 30.54/10.80 | (4) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 30.54/10.80 | (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)))
% 30.54/10.80 | (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)))
% 30.54/10.80 | (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)))
% 30.54/10.81 | (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)))
% 30.54/10.81 | (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)))
% 30.54/10.81 | (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)))
% 30.54/10.81 | (11) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 30.54/10.81 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 30.54/10.81 | (13) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 30.54/10.81 | (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)))
% 30.54/10.81 | (15) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 30.54/10.81 | (16) ! [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))
% 30.54/10.81 | (17) ! [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)))
% 30.54/10.81 | (18) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 30.54/10.81 | (19) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 30.54/10.81 | (20) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 30.54/10.81 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 30.54/10.81 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 30.54/10.81 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 30.54/10.81 | (24) ! [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)))
% 30.54/10.81 | (25) ! [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)))
% 30.54/10.81 | (26) convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0
% 30.54/10.81 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 30.54/10.81 | (28) ! [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))
% 30.54/10.81 | (29) ! [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)))
% 30.54/10.81 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 30.54/10.82 | (31) ~ (all_0_1_1 = 0)
% 30.54/10.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 30.54/10.82 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 30.54/10.82 | (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))
% 30.54/10.82 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 30.54/10.82 | (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))
% 30.54/10.82 | (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)))
% 30.54/10.82 | (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))
% 30.54/10.82 | (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)))
% 30.54/10.82 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 30.54/10.82 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 30.54/10.82 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 30.54/10.82 | (43) ~ (all_0_0_0 = 0)
% 30.54/10.82 | (44) ! [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)))
% 30.54/10.82 | (45) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 30.54/10.82 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 30.54/10.82 | (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)
% 30.54/10.82 | (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)
% 30.54/10.82 | (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)
% 30.54/10.82 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 30.54/10.82 | (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)))
% 30.54/10.82 | (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)))
% 30.54/10.82 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 30.54/10.82 | (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)))
% 30.54/10.82 | (55) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 30.54/10.82 | (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)
% 30.54/10.82 | (57) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 30.54/10.83 | (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)))
% 30.54/10.83 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 30.54/10.83 | (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)))
% 30.54/10.83 | (61) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 30.54/10.83 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 30.54/10.83 | (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)))
% 30.54/10.83 | (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)))
% 30.54/10.83 | (65) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 30.54/10.83 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 30.54/10.83 |
% 30.54/10.83 | Instantiating formula (37) with 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) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 30.54/10.83 | (67) ? [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) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0))
% 30.54/10.83 |
% 30.54/10.83 | 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:
% 30.54/10.83 | (68) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 30.54/10.83 |
% 30.54/10.83 | Instantiating formula (39) with all_0_1_1, 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) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.54/10.83 | (69) ? [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 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0))
% 30.54/10.83 |
% 30.54/10.83 | Instantiating formula (7) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 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_3_3) = all_0_1_1, yields:
% 30.54/10.83 | (70) ? [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 & unorthogonal_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))
% 30.54/10.83 |
% 30.54/10.83 | Instantiating formula (7) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.54/10.83 | (71) ? [v0] : ((v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 30.54/10.83 |
% 30.54/10.83 | Instantiating formula (22) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.54/10.83 | (72) all_0_1_1 = 0 | unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.83 |
% 30.54/10.83 | Instantiating (71) with all_23_0_26 yields:
% 30.54/10.83 | (73) (all_23_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_23_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_23_0_26) | ( ~ (all_23_0_26 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26)
% 30.54/10.83 |
% 30.54/10.83 | Instantiating (70) with all_24_0_27 yields:
% 30.54/10.83 | (74) (all_24_0_27 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_24_0_27 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_24_0_27 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27) | ( ~ (all_24_0_27 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_24_0_27)
% 30.54/10.83 |
% 30.54/10.83 | Instantiating (69) with all_27_0_30, all_27_1_31 yields:
% 30.54/10.83 | (75) (all_27_0_30 = 0 & all_27_1_31 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_27_1_31 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_27_1_31 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_27_1_31)
% 30.54/10.83 |
% 30.54/10.83 | Instantiating (67) with all_28_0_32, all_28_1_33 yields:
% 30.54/10.83 | (76) (all_28_0_32 = 0 & all_28_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_28_1_33 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_28_1_33 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_1_33)
% 30.54/10.83 |
% 30.54/10.83 +-Applying beta-rule and splitting (74), into two cases.
% 30.54/10.83 |-Branch one:
% 30.54/10.83 | (77) (all_24_0_27 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_24_0_27 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_24_0_27 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27)
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (77), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (78) (all_24_0_27 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_24_0_27 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (78), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (79) all_24_0_27 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (79) yields:
% 30.54/10.84 | (80) all_24_0_27 = 0
% 30.54/10.84 | (81) all_0_0_0 = 0
% 30.54/10.84 | (82) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (81) can reduce 43 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (84) all_24_0_27 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (84) yields:
% 30.54/10.84 | (80) all_24_0_27 = 0
% 30.54/10.84 | (86) all_0_1_1 = 0
% 30.54/10.84 | (87) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (86) can reduce 31 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (89) ~ (all_24_0_27 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (89) yields:
% 30.54/10.84 | (90) ~ (all_24_0_27 = 0)
% 30.54/10.84 | (91) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (72), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (87) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (75), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (93) (all_27_0_30 = 0 & all_27_1_31 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_27_1_31 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (93), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (94) all_27_0_30 = 0 & all_27_1_31 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (94) yields:
% 30.54/10.84 | (95) all_27_0_30 = 0
% 30.54/10.84 | (96) all_27_1_31 = 0
% 30.54/10.84 | (82) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 30.54/10.84 | (98) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (68), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (81) all_0_0_0 = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (81) can reduce 43 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (43) ~ (all_0_0_0 = 0)
% 30.54/10.84 | (102) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 30.54/10.84 |
% 30.54/10.84 | Instantiating formula (33) 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:
% 30.54/10.84 | (81) all_0_0_0 = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (81) can reduce 43 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (105) all_27_1_31 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (105) yields:
% 30.54/10.84 | (96) all_27_1_31 = 0
% 30.54/10.84 | (86) all_0_1_1 = 0
% 30.54/10.84 | (87) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (86) can reduce 31 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (110) ~ (all_27_1_31 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_27_1_31
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (110) yields:
% 30.54/10.84 | (111) ~ (all_27_1_31 = 0)
% 30.54/10.84 | (112) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_27_1_31
% 30.54/10.84 |
% 30.54/10.84 +-Applying beta-rule and splitting (68), into two cases.
% 30.54/10.84 |-Branch one:
% 30.54/10.84 | (81) all_0_0_0 = 0
% 30.54/10.84 |
% 30.54/10.84 | Equations (81) can reduce 43 to:
% 30.54/10.84 | (83) $false
% 30.54/10.84 |
% 30.54/10.84 |-The branch is then unsatisfiable
% 30.54/10.84 |-Branch two:
% 30.54/10.84 | (43) ~ (all_0_0_0 = 0)
% 30.54/10.84 | (102) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 30.54/10.84 |
% 30.54/10.84 | Instantiating (102) with all_50_0_38 yields:
% 30.54/10.84 | (117) ~ (all_50_0_38 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38
% 30.54/10.84 |
% 30.54/10.84 | Applying alpha-rule on (117) yields:
% 30.54/10.84 | (118) ~ (all_50_0_38 = 0)
% 30.54/10.84 | (119) convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38
% 30.82/10.84 |
% 30.82/10.84 +-Applying beta-rule and splitting (76), into two cases.
% 30.82/10.84 |-Branch one:
% 30.82/10.84 | (120) (all_28_0_32 = 0 & all_28_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | (all_28_1_33 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 30.82/10.84 |
% 30.82/10.84 +-Applying beta-rule and splitting (120), into two cases.
% 30.82/10.84 |-Branch one:
% 30.82/10.84 | (121) all_28_0_32 = 0 & all_28_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.82/10.84 |
% 30.82/10.84 | Applying alpha-rule on (121) yields:
% 30.82/10.84 | (122) all_28_0_32 = 0
% 30.82/10.84 | (123) all_28_1_33 = 0
% 30.82/10.84 | (87) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.82/10.84 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.82/10.84 |
% 30.82/10.84 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.82/10.84 | (86) all_0_1_1 = 0
% 30.82/10.84 |
% 30.82/10.84 | Equations (86) can reduce 31 to:
% 30.82/10.84 | (83) $false
% 30.82/10.84 |
% 30.82/10.84 |-The branch is then unsatisfiable
% 30.82/10.84 |-Branch two:
% 30.82/10.84 | (128) all_28_1_33 = 0 & all_0_0_0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 30.82/10.84 |
% 30.82/10.84 | Applying alpha-rule on (128) yields:
% 30.82/10.84 | (123) all_28_1_33 = 0
% 30.82/10.84 | (81) all_0_0_0 = 0
% 30.82/10.84 | (82) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 30.82/10.84 |
% 30.82/10.84 | Equations (81) can reduce 43 to:
% 30.82/10.84 | (83) $false
% 30.82/10.84 |
% 30.82/10.84 |-The branch is then unsatisfiable
% 30.82/10.84 |-Branch two:
% 30.82/10.84 | (133) ~ (all_28_1_33 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_1_33
% 30.82/10.84 |
% 30.82/10.84 | Applying alpha-rule on (133) yields:
% 30.82/10.84 | (134) ~ (all_28_1_33 = 0)
% 30.82/10.84 | (135) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_1_33
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (42) with all_0_3_3, all_0_2_2, all_27_1_31, all_28_1_33 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_1_33, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_27_1_31, yields:
% 30.82/10.85 | (136) all_28_1_33 = all_27_1_31
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (42) with all_0_3_3, all_0_2_2, all_24_0_27, all_28_1_33 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_28_1_33, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27, yields:
% 30.82/10.85 | (137) all_28_1_33 = all_24_0_27
% 30.82/10.85 |
% 30.82/10.85 | Combining equations (136,137) yields a new equation:
% 30.82/10.85 | (138) all_27_1_31 = all_24_0_27
% 30.82/10.85 |
% 30.82/10.85 | Simplifying 138 yields:
% 30.82/10.85 | (139) all_27_1_31 = all_24_0_27
% 30.82/10.85 |
% 30.82/10.85 | Equations (139) can reduce 111 to:
% 30.82/10.85 | (90) ~ (all_24_0_27 = 0)
% 30.82/10.85 |
% 30.82/10.85 | From (139) and (112) follows:
% 30.82/10.85 | (91) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (38) with all_24_0_27, all_24_0_27, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_24_0_27, yields:
% 30.82/10.85 | (142) all_24_0_27 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (32) with all_24_0_27, 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) = all_24_0_27, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 30.82/10.85 | (143) all_24_0_27 = 0 | unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (9) with 0, 0, 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) = 0, yields:
% 30.82/10.85 | (144) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (54) with 0, 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) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.82/10.85 | (145) ? [v0] : ((v0 = 0 & all_0_1_1 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0))
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (7) with all_50_0_38, all_50_0_38, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38, yields:
% 30.82/10.85 | (146) ? [v0] : ((v0 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (63) with all_50_0_38, 0, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38, yields:
% 30.82/10.85 | (147) ? [v0] : ((v0 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0))
% 30.82/10.85 |
% 30.82/10.85 | Instantiating formula (22) with all_50_0_38, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38, yields:
% 30.82/10.85 | (148) all_50_0_38 = 0 | unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.82/10.85 |
% 30.82/10.85 | Instantiating (147) with all_65_0_39 yields:
% 30.82/10.85 | (149) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39) | ( ~ (all_65_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39)
% 30.82/10.85 |
% 30.82/10.85 | Instantiating (146) with all_67_0_41 yields:
% 30.82/10.85 | (150) (all_67_0_41 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_67_0_41 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_41) | ( ~ (all_67_0_41 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_41)
% 30.82/10.85 |
% 30.82/10.85 | Instantiating (144) with all_70_0_44 yields:
% 30.82/10.85 | (151) (all_70_0_44 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_70_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_70_0_44) | ( ~ (all_70_0_44 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_70_0_44)
% 30.82/10.85 |
% 30.82/10.85 | Instantiating (145) with all_73_0_48 yields:
% 30.82/10.85 | (152) (all_73_0_48 = 0 & all_0_1_1 = 0) | (all_73_0_48 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_73_0_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_73_0_48) | ( ~ (all_73_0_48 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_73_0_48)
% 30.82/10.85 |
% 30.82/10.85 +-Applying beta-rule and splitting (73), into two cases.
% 30.82/10.85 |-Branch one:
% 30.82/10.85 | (153) (all_23_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_23_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_23_0_26)
% 30.82/10.85 |
% 30.82/10.85 +-Applying beta-rule and splitting (153), into two cases.
% 30.82/10.85 |-Branch one:
% 30.82/10.85 | (154) all_23_0_26 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.82/10.85 |
% 30.82/10.85 | Applying alpha-rule on (154) yields:
% 30.82/10.85 | (155) all_23_0_26 = 0
% 30.82/10.85 | (86) all_0_1_1 = 0
% 30.82/10.85 | (87) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 30.82/10.85 |
% 30.82/10.85 | Equations (86) can reduce 31 to:
% 30.82/10.85 | (83) $false
% 30.82/10.85 |
% 30.82/10.85 |-The branch is then unsatisfiable
% 30.82/10.85 |-Branch two:
% 30.82/10.85 | (159) ~ (all_23_0_26 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_23_0_26
% 30.82/10.85 |
% 30.82/10.85 | Applying alpha-rule on (159) yields:
% 30.82/10.85 | (160) ~ (all_23_0_26 = 0)
% 30.82/10.85 | (161) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_23_0_26
% 30.82/10.85 |
% 30.82/10.85 +-Applying beta-rule and splitting (142), into two cases.
% 30.82/10.85 |-Branch one:
% 30.82/10.85 | (80) all_24_0_27 = 0
% 30.88/10.85 |
% 30.88/10.85 | Equations (80) can reduce 90 to:
% 30.88/10.85 | (83) $false
% 30.88/10.85 |
% 30.88/10.85 |-The branch is then unsatisfiable
% 30.88/10.85 |-Branch two:
% 30.88/10.85 | (90) ~ (all_24_0_27 = 0)
% 30.88/10.85 | (165) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 30.88/10.85 |
% 30.88/10.86 +-Applying beta-rule and splitting (143), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (166) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.86 |
% 30.88/10.86 | Instantiating formula (42) with all_0_3_3, all_0_3_3, 0, all_23_0_26 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_23_0_26, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 30.88/10.86 | (155) all_23_0_26 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (155) can reduce 160 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (169) ~ (unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 30.88/10.86 | (80) all_24_0_27 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (80) can reduce 90 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (172) ~ (all_23_0_26 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (172) yields:
% 30.88/10.86 | (160) ~ (all_23_0_26 = 0)
% 30.88/10.86 | (174) convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (142), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (80) all_24_0_27 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (80) can reduce 90 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (90) ~ (all_24_0_27 = 0)
% 30.88/10.86 | (165) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 30.88/10.86 |
% 30.88/10.86 | Instantiating (165) with all_91_0_62 yields:
% 30.88/10.86 | (179) ~ (all_91_0_62 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_91_0_62
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (179) yields:
% 30.88/10.86 | (180) ~ (all_91_0_62 = 0)
% 30.88/10.86 | (181) convergent_lines(all_0_2_2, all_0_2_2) = all_91_0_62
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (143), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (166) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (152), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (183) (all_73_0_48 = 0 & all_0_1_1 = 0) | (all_73_0_48 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_73_0_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_73_0_48)
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (183), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (184) (all_73_0_48 = 0 & all_0_1_1 = 0) | (all_73_0_48 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (184), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (185) all_73_0_48 = 0 & all_0_1_1 = 0
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (185) yields:
% 30.88/10.86 | (186) all_73_0_48 = 0
% 30.88/10.86 | (86) all_0_1_1 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (86) can reduce 31 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (189) all_73_0_48 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (189) yields:
% 30.88/10.86 | (186) all_73_0_48 = 0
% 30.88/10.86 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.86 |
% 30.88/10.86 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.86 | (86) all_0_1_1 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (86) can reduce 31 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (194) ~ (all_73_0_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_73_0_48
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (194) yields:
% 30.88/10.86 | (195) ~ (all_73_0_48 = 0)
% 30.88/10.86 | (196) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_73_0_48
% 30.88/10.86 |
% 30.88/10.86 | Instantiating formula (42) with all_0_3_3, all_0_3_3, 0, all_73_0_48 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_73_0_48, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 30.88/10.86 | (186) all_73_0_48 = 0
% 30.88/10.86 |
% 30.88/10.86 | Equations (186) can reduce 195 to:
% 30.88/10.86 | (83) $false
% 30.88/10.86 |
% 30.88/10.86 |-The branch is then unsatisfiable
% 30.88/10.86 |-Branch two:
% 30.88/10.86 | (199) ~ (all_73_0_48 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_73_0_48
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (199) yields:
% 30.88/10.86 | (195) ~ (all_73_0_48 = 0)
% 30.88/10.86 | (201) convergent_lines(all_0_3_3, all_0_3_3) = all_73_0_48
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (148), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (202) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (150), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (203) (all_67_0_41 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_67_0_41 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_41)
% 30.88/10.86 |
% 30.88/10.86 +-Applying beta-rule and splitting (203), into two cases.
% 30.88/10.86 |-Branch one:
% 30.88/10.86 | (204) all_67_0_41 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.86 |
% 30.88/10.86 | Applying alpha-rule on (204) yields:
% 30.88/10.86 | (205) all_67_0_41 = 0
% 30.88/10.86 | (206) all_50_0_38 = 0
% 30.88/10.87 | (202) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.87 |
% 30.88/10.87 | Equations (206) can reduce 118 to:
% 30.88/10.87 | (83) $false
% 30.88/10.87 |
% 30.88/10.87 |-The branch is then unsatisfiable
% 30.88/10.87 |-Branch two:
% 30.88/10.87 | (209) ~ (all_67_0_41 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_41
% 30.88/10.87 |
% 30.88/10.87 | Applying alpha-rule on (209) yields:
% 30.88/10.87 | (210) ~ (all_67_0_41 = 0)
% 30.88/10.87 | (211) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_41
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (42) with all_0_4_4, all_0_4_4, 0, all_67_0_41 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_67_0_41, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 30.88/10.87 | (205) all_67_0_41 = 0
% 30.88/10.87 |
% 30.88/10.87 | Equations (205) can reduce 210 to:
% 30.88/10.87 | (83) $false
% 30.88/10.87 |
% 30.88/10.87 |-The branch is then unsatisfiable
% 30.88/10.87 |-Branch two:
% 30.88/10.87 | (214) ~ (all_67_0_41 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_41
% 30.88/10.87 |
% 30.88/10.87 | Applying alpha-rule on (214) yields:
% 30.88/10.87 | (210) ~ (all_67_0_41 = 0)
% 30.88/10.87 | (216) convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_41
% 30.88/10.87 |
% 30.88/10.87 +-Applying beta-rule and splitting (151), into two cases.
% 30.88/10.87 |-Branch one:
% 30.88/10.87 | (217) (all_70_0_44 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_70_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_70_0_44)
% 30.88/10.87 |
% 30.88/10.87 +-Applying beta-rule and splitting (217), into two cases.
% 30.88/10.87 |-Branch one:
% 30.88/10.87 | (218) all_70_0_44 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.87 |
% 30.88/10.87 | Applying alpha-rule on (218) yields:
% 30.88/10.87 | (219) all_70_0_44 = 0
% 30.88/10.87 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.87 | (86) all_0_1_1 = 0
% 30.88/10.87 |
% 30.88/10.87 | Equations (86) can reduce 31 to:
% 30.88/10.87 | (83) $false
% 30.88/10.87 |
% 30.88/10.87 |-The branch is then unsatisfiable
% 30.88/10.87 |-Branch two:
% 30.88/10.87 | (223) ~ (all_70_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_70_0_44
% 30.88/10.87 |
% 30.88/10.87 | Applying alpha-rule on (223) yields:
% 30.88/10.87 | (224) ~ (all_70_0_44 = 0)
% 30.88/10.87 | (225) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_70_0_44
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (42) with all_0_3_3, all_0_3_3, 0, all_70_0_44 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_70_0_44, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 30.88/10.87 | (219) all_70_0_44 = 0
% 30.88/10.87 |
% 30.88/10.87 | Equations (219) can reduce 224 to:
% 30.88/10.87 | (83) $false
% 30.88/10.87 |
% 30.88/10.87 |-The branch is then unsatisfiable
% 30.88/10.87 |-Branch two:
% 30.88/10.87 | (228) ~ (all_70_0_44 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_70_0_44
% 30.88/10.87 |
% 30.88/10.87 | Applying alpha-rule on (228) yields:
% 30.88/10.87 | (224) ~ (all_70_0_44 = 0)
% 30.88/10.87 | (230) convergent_lines(all_0_3_3, all_0_3_3) = all_70_0_44
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (33) with all_0_3_3, all_0_3_3, all_70_0_44, all_73_0_48 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_73_0_48, convergent_lines(all_0_3_3, all_0_3_3) = all_70_0_44, yields:
% 30.88/10.87 | (231) all_73_0_48 = all_70_0_44
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (33) with all_0_3_3, all_0_3_3, all_23_0_26, all_73_0_48 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_73_0_48, convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26, yields:
% 30.88/10.87 | (232) all_73_0_48 = all_23_0_26
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (33) with all_0_4_4, all_0_4_4, all_67_0_41, all_50_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_67_0_41, convergent_lines(all_0_4_4, all_0_4_4) = all_50_0_38, yields:
% 30.88/10.87 | (233) all_67_0_41 = all_50_0_38
% 30.88/10.87 |
% 30.88/10.87 | Combining equations (231,232) yields a new equation:
% 30.88/10.87 | (234) all_70_0_44 = all_23_0_26
% 30.88/10.87 |
% 30.88/10.87 | Simplifying 234 yields:
% 30.88/10.87 | (235) all_70_0_44 = all_23_0_26
% 30.88/10.87 |
% 30.88/10.87 | Equations (235) can reduce 224 to:
% 30.88/10.87 | (160) ~ (all_23_0_26 = 0)
% 30.88/10.87 |
% 30.88/10.87 | Equations (233) can reduce 210 to:
% 30.88/10.87 | (118) ~ (all_50_0_38 = 0)
% 30.88/10.87 |
% 30.88/10.87 | From (235) and (230) follows:
% 30.88/10.87 | (174) convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (14) with 0, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.87 | (239) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (36) with all_0_0_0, all_91_0_62, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = all_91_0_62, convergent_lines(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 30.88/10.87 | (240) all_91_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (59) with all_23_0_26, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26, yields:
% 30.88/10.87 | (241) all_23_0_26 = 0 | convergent_lines(all_0_2_2, all_0_3_3) = 0
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (36) with all_0_1_1, all_23_0_26, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.88/10.87 | (242) all_23_0_26 = 0 | all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 30.88/10.87 |
% 30.88/10.87 | Instantiating formula (64) with all_23_0_26, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_3_3) = all_23_0_26, yields:
% 30.88/10.87 | (243) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & all_23_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 30.88/10.87 |
% 30.88/10.87 | Instantiating (243) with all_126_0_63, all_126_1_64 yields:
% 30.88/10.87 | (244) (all_126_0_63 = 0 & all_126_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_126_1_64 = 0 & all_23_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_126_1_64 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_126_1_64)
% 30.88/10.87 |
% 30.88/10.88 | Instantiating (239) with all_137_0_77, all_137_1_78 yields:
% 30.88/10.88 | (245) (all_137_0_77 = 0 & all_137_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_137_1_78 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_137_1_78 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (241), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (246) convergent_lines(all_0_2_2, all_0_3_3) = 0
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (240), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (247) all_91_0_62 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (247) can reduce 180 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (180) ~ (all_91_0_62 = 0)
% 30.88/10.88 | (250) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (250), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (81) all_0_0_0 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (81) can reduce 43 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (43) ~ (all_0_0_0 = 0)
% 30.88/10.88 | (254) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)
% 30.88/10.88 |
% 30.88/10.88 | Instantiating (254) with all_187_0_206 yields:
% 30.88/10.88 | (255) ~ (all_187_0_206 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_187_0_206
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (255) yields:
% 30.88/10.88 | (256) ~ (all_187_0_206 = 0)
% 30.88/10.88 | (257) convergent_lines(all_0_2_2, all_0_4_4) = all_187_0_206
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (242), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (155) all_23_0_26 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (155) can reduce 160 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (160) ~ (all_23_0_26 = 0)
% 30.88/10.88 | (261) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (261), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (86) all_0_1_1 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (86) can reduce 31 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (31) ~ (all_0_1_1 = 0)
% 30.88/10.88 | (265) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)
% 30.88/10.88 |
% 30.88/10.88 | Instantiating (265) with all_228_0_270 yields:
% 30.88/10.88 | (266) ~ (all_228_0_270 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (266) yields:
% 30.88/10.88 | (267) ~ (all_228_0_270 = 0)
% 30.88/10.88 | (268) convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (245), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (269) (all_137_0_77 = 0 & all_137_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_137_1_78 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (269), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (270) all_137_0_77 = 0 & all_137_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (270) yields:
% 30.88/10.88 | (271) all_137_0_77 = 0
% 30.88/10.88 | (272) all_137_1_78 = 0
% 30.88/10.88 | (273) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 | (274) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (149), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (275) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (275), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (276) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (276), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (277) all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (277) yields:
% 30.88/10.88 | (278) all_65_0_39 = 0
% 30.88/10.88 | (206) all_50_0_38 = 0
% 30.88/10.88 | (202) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (206) can reduce 118 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (282) all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (282) yields:
% 30.88/10.88 | (278) all_65_0_39 = 0
% 30.88/10.88 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.88 |
% 30.88/10.88 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.88 | (86) all_0_1_1 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (86) can reduce 31 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (287) ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (287) yields:
% 30.88/10.88 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.88 | (289) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.88 |
% 30.88/10.88 | Instantiating formula (42) with all_0_3_3, all_0_4_4, 0, all_65_0_39 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.88 | (278) all_65_0_39 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (278) can reduce 288 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (292) ~ (all_65_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (292) yields:
% 30.88/10.88 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.88 | (294) convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.88 |
% 30.88/10.88 | Instantiating formula (33) with all_0_3_3, all_0_4_4, all_65_0_39, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39, yields:
% 30.88/10.88 | (295) all_228_0_270 = all_65_0_39
% 30.88/10.88 |
% 30.88/10.88 | Instantiating formula (33) with all_0_3_3, all_0_4_4, 0, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.88 | (296) all_228_0_270 = 0
% 30.88/10.88 |
% 30.88/10.88 | Combining equations (295,296) yields a new equation:
% 30.88/10.88 | (297) all_65_0_39 = 0
% 30.88/10.88 |
% 30.88/10.88 | Simplifying 297 yields:
% 30.88/10.88 | (278) all_65_0_39 = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (278) can reduce 288 to:
% 30.88/10.88 | (83) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (300) all_137_1_78 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (300) yields:
% 30.88/10.88 | (272) all_137_1_78 = 0
% 30.88/10.88 | (302) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.88 |
% 30.88/10.88 | Instantiating formula (19) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 30.88/10.88 | (303) $false
% 30.88/10.88 |
% 30.88/10.88 |-The branch is then unsatisfiable
% 30.88/10.88 |-Branch two:
% 30.88/10.88 | (304) ~ (all_137_1_78 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (304) yields:
% 30.88/10.88 | (305) ~ (all_137_1_78 = 0)
% 30.88/10.88 | (306) convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (244), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (307) (all_126_0_63 = 0 & all_126_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_126_1_64 = 0 & all_23_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (307), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (308) all_126_0_63 = 0 & all_126_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (308) yields:
% 30.88/10.88 | (309) all_126_0_63 = 0
% 30.88/10.88 | (310) all_126_1_64 = 0
% 30.88/10.88 | (273) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 | (274) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (149), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (275) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (275), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (276) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 30.88/10.88 |
% 30.88/10.88 +-Applying beta-rule and splitting (276), into two cases.
% 30.88/10.88 |-Branch one:
% 30.88/10.88 | (277) all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Applying alpha-rule on (277) yields:
% 30.88/10.88 | (278) all_65_0_39 = 0
% 30.88/10.88 | (206) all_50_0_38 = 0
% 30.88/10.88 | (202) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.88 |
% 30.88/10.88 | Equations (206) can reduce 118 to:
% 30.88/10.88 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (282) all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (282) yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_4_4, all_0_3_3, all_137_1_78, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.88/10.89 | (323) all_137_1_78 = all_0_1_1
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_137_1_78 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.89 | (272) all_137_1_78 = 0
% 30.88/10.89 |
% 30.88/10.89 | Combining equations (272,323) yields a new equation:
% 30.88/10.89 | (86) all_0_1_1 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (86) can reduce 31 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (287) ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (287) yields:
% 30.88/10.89 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.89 | (289) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (42) with all_0_3_3, all_0_4_4, 0, all_65_0_39 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (278) can reduce 288 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (292) ~ (all_65_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (292) yields:
% 30.88/10.89 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.89 | (294) convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_3_3, all_0_4_4, all_65_0_39, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39, yields:
% 30.88/10.89 | (295) all_228_0_270 = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_3_3, all_0_4_4, 0, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.89 | (296) all_228_0_270 = 0
% 30.88/10.89 |
% 30.88/10.89 | Combining equations (295,296) yields a new equation:
% 30.88/10.89 | (297) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Simplifying 297 yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (278) can reduce 288 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (340) all_126_1_64 = 0 & all_23_0_26 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (340) yields:
% 30.88/10.89 | (310) all_126_1_64 = 0
% 30.88/10.89 | (155) all_23_0_26 = 0
% 30.88/10.89 | (166) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (155) can reduce 160 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (345) ~ (all_126_1_64 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_126_1_64
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (345) yields:
% 30.88/10.89 | (346) ~ (all_126_1_64 = 0)
% 30.88/10.89 | (347) convergent_lines(all_0_4_4, all_0_3_3) = all_126_1_64
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_4_4, all_0_3_3, all_137_1_78, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 30.88/10.89 | (323) all_137_1_78 = all_0_1_1
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_4_4, all_0_3_3, all_126_1_64, all_137_1_78 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_137_1_78, convergent_lines(all_0_4_4, all_0_3_3) = all_126_1_64, yields:
% 30.88/10.89 | (349) all_137_1_78 = all_126_1_64
% 30.88/10.89 |
% 30.88/10.89 | Combining equations (349,323) yields a new equation:
% 30.88/10.89 | (350) all_126_1_64 = all_0_1_1
% 30.88/10.89 |
% 30.88/10.89 | Simplifying 350 yields:
% 30.88/10.89 | (351) all_126_1_64 = all_0_1_1
% 30.88/10.89 |
% 30.88/10.89 | Equations (351) can reduce 346 to:
% 30.88/10.89 | (31) ~ (all_0_1_1 = 0)
% 30.88/10.89 |
% 30.88/10.89 | From (351) and (347) follows:
% 30.88/10.89 | (15) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (59) with all_187_0_206, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, convergent_lines(all_0_2_2, all_0_4_4) = all_187_0_206, yields:
% 30.88/10.89 | (354) all_187_0_206 = 0 | convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (22) with all_228_0_270, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, yields:
% 30.88/10.89 | (355) all_228_0_270 = 0 | unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 +-Applying beta-rule and splitting (354), into two cases.
% 30.88/10.89 |-Branch one:
% 30.88/10.89 | (274) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 +-Applying beta-rule and splitting (355), into two cases.
% 30.88/10.89 |-Branch one:
% 30.88/10.89 | (273) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 +-Applying beta-rule and splitting (149), into two cases.
% 30.88/10.89 |-Branch one:
% 30.88/10.89 | (275) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39)
% 30.88/10.89 |
% 30.88/10.89 +-Applying beta-rule and splitting (275), into two cases.
% 30.88/10.89 |-Branch one:
% 30.88/10.89 | (276) (all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | (all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 30.88/10.89 |
% 30.88/10.89 +-Applying beta-rule and splitting (276), into two cases.
% 30.88/10.89 |-Branch one:
% 30.88/10.89 | (277) all_65_0_39 = 0 & all_50_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (277) yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 | (206) all_50_0_38 = 0
% 30.88/10.89 | (202) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (206) can reduce 118 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (282) all_65_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (282) yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 | (125) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_4_4, all_0_3_3, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 30.88/10.89 | (86) all_0_1_1 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (86) can reduce 31 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (287) ~ (all_65_0_39 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (287) yields:
% 30.88/10.89 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.89 | (289) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (42) with all_0_3_3, all_0_4_4, 0, all_65_0_39 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_65_0_39, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (278) can reduce 288 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (292) ~ (all_65_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (292) yields:
% 30.88/10.89 | (288) ~ (all_65_0_39 = 0)
% 30.88/10.89 | (294) convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_3_3, all_0_4_4, all_65_0_39, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = all_65_0_39, yields:
% 30.88/10.89 | (295) all_228_0_270 = all_65_0_39
% 30.88/10.89 |
% 30.88/10.89 | Instantiating formula (33) with all_0_3_3, all_0_4_4, 0, all_228_0_270 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_228_0_270, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 30.88/10.89 | (296) all_228_0_270 = 0
% 30.88/10.89 |
% 30.88/10.89 | Combining equations (295,296) yields a new equation:
% 30.88/10.89 | (297) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Simplifying 297 yields:
% 30.88/10.89 | (278) all_65_0_39 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (278) can reduce 288 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (383) ~ (unorthogonal_lines(all_0_3_3, all_0_4_4) = 0)
% 30.88/10.89 | (296) all_228_0_270 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (296) can reduce 267 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (386) ~ (convergent_lines(all_0_3_3, all_0_4_4) = 0)
% 30.88/10.89 | (387) all_187_0_206 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (387) can reduce 256 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (389) ~ (convergent_lines(all_0_2_2, all_0_3_3) = 0)
% 30.88/10.89 | (155) all_23_0_26 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (155) can reduce 160 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (392) ~ (unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 30.88/10.89 | (206) all_50_0_38 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (206) can reduce 118 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (169) ~ (unorthogonal_lines(all_0_3_3, all_0_3_3) = 0)
% 30.88/10.89 | (80) all_24_0_27 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (80) can reduce 90 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (398) ~ (unorthogonal_lines(all_0_4_4, all_0_3_3) = 0)
% 30.88/10.89 | (86) all_0_1_1 = 0
% 30.88/10.89 |
% 30.88/10.89 | Equations (86) can reduce 31 to:
% 30.88/10.89 | (83) $false
% 30.88/10.89 |
% 30.88/10.89 |-The branch is then unsatisfiable
% 30.88/10.89 |-Branch two:
% 30.88/10.89 | (401) ~ (all_24_0_27 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_24_0_27
% 30.88/10.89 |
% 30.88/10.89 | Applying alpha-rule on (401) yields:
% 30.88/10.89 | (90) ~ (all_24_0_27 = 0)
% 30.88/10.90 | (403) convergent_lines(all_0_3_3, all_0_2_2) = all_24_0_27
% 30.88/10.90 |
% 30.88/10.90 | Instantiating formula (33) with all_0_3_3, all_0_2_2, all_24_0_27, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_24_0_27, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 30.88/10.90 | (80) all_24_0_27 = 0
% 30.88/10.90 |
% 30.88/10.90 | Equations (80) can reduce 90 to:
% 30.88/10.90 | (83) $false
% 30.88/10.90 |
% 30.88/10.90 |-The branch is then unsatisfiable
% 30.88/10.90 % SZS output end Proof for theBenchmark
% 30.88/10.90
% 30.88/10.90 10294ms
%------------------------------------------------------------------------------