TSTP Solution File: GEO218+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:52 EDT 2022
% Result : Theorem 14.97s 4.12s
% Output : Proof 61.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 04:20:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.59 ____ _
% 0.21/0.59 ___ / __ \_____(_)___ ________ __________
% 0.21/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.21/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.21/0.59
% 0.21/0.59 A Theorem Prover for First-Order Logic
% 0.21/0.59 (ePrincess v.1.0)
% 0.21/0.59
% 0.21/0.59 (c) Philipp Rümmer, 2009-2015
% 0.21/0.59 (c) Peter Backeman, 2014-2015
% 0.21/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.21/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.21/0.59 Bug reports to peter@backeman.se
% 0.21/0.59
% 0.21/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.21/0.59
% 0.21/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.94 Prover 0: Preprocessing ...
% 2.16/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.16 Prover 0: Constructing countermodel ...
% 12.50/3.59 Prover 0: gave up
% 12.50/3.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.80/3.63 Prover 1: Preprocessing ...
% 13.48/3.74 Prover 1: Constructing countermodel ...
% 13.48/3.80 Prover 1: gave up
% 13.48/3.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 13.96/3.83 Prover 2: Preprocessing ...
% 14.66/3.99 Prover 2: Warning: ignoring some quantifiers
% 14.66/4.00 Prover 2: Constructing countermodel ...
% 14.97/4.12 Prover 2: proved (320ms)
% 14.97/4.12
% 14.97/4.12 No countermodel exists, formula is valid
% 14.97/4.12 % SZS status Theorem for theBenchmark
% 14.97/4.12
% 14.97/4.12 Generating proof ... Warning: ignoring some quantifiers
% 61.26/32.43 found it (size 161)
% 61.26/32.43
% 61.26/32.43 % SZS output start Proof for theBenchmark
% 61.26/32.43 Assumed formulas after preprocessing and simplification:
% 61.26/32.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & orthogonal_lines(v1, v2) = v3 & orthogonal_lines(v0, v2) = 0 & parallel_lines(v0, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_lines(v5, v6) = 0) | ? [v10] : ((v10 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v5) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (apart_point_and_line(v4, v5) = v8) | ? [v10] : ((v10 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ? [v10] : ((v10 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (apart_point_and_line(v4, v5) = v8) | ~ (distinct_lines(v5, v6) = 0) | ? [v10] : ((v10 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_points(v4, v5) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v4, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v4, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v9) | ~ (apart_point_and_line(v4, v7) = v8) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v4, v7) = v9) | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_points(v4, v5) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v6, v5) = v8) | ~ (distinct_points(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (apart_point_and_line(v4, v5) = v7) | ? [v9] : ((v9 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (distinct_lines(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v7) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v5) = v7) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (convergent_lines(v5, v6) = v8) | ~ (convergent_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (convergent_lines(v4, v6) = v8) | ~ (distinct_lines(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = v8) | ~ (distinct_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (distinct_points(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (unorthogonal_lines(v4, v6) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v4, v6) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v8) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v8) | ~ (convergent_lines(v4, v5) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v4, v5) = v7) | ~ (convergent_lines(v4, v6) = v8) | ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v5, v6) = v8) | ~ (convergent_lines(v4, v6) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v4, v6) = v8) | ~ (convergent_lines(v4, v5) = v7) | ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v7) | ~ (convergent_lines(v5, v6) = 0) | unorthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v4, v5) = v7) | ~ (convergent_lines(v5, v6) = 0) | unorthogonal_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v6, v5) = v7) | ~ (apart_point_and_line(v4, v5) = 0) | distinct_points(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v6) = v7) | ~ (apart_point_and_line(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v6) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v4, v5) = 0) | (v8 = 0 & convergent_lines(v5, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v4, v6) = 0) | (v8 = 0 & convergent_lines(v5, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | apart_point_and_line(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v4, v5) = 0) | ~ (distinct_points(v4, v6) = v7) | apart_point_and_line(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v4, v5) = 0) | ~ (distinct_lines(v5, v6) = v7) | convergent_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v5, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_lines(v7, v6) = v5) | ~ (orthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (incident_point_and_line(v7, v6) = v5) | ~ (incident_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_lines(v7, v6) = v5) | ~ (parallel_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_lines(v7, v6) = v5) | ~ (equal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_points(v7, v6) = v5) | ~ (equal_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (orthogonal_through_point(v7, v6) = v5) | ~ (orthogonal_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unorthogonal_lines(v7, v6) = v5) | ~ (unorthogonal_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_through_point(v7, v6) = v5) | ~ (parallel_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = v7) | ~ (unorthogonal_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (unorthogonal_lines(v4, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (unorthogonal_lines(v4, v5) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v4, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v4, v5) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (unorthogonal_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (convergent_lines(v5, v6) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = v7) | ~ (convergent_lines(v5, v6) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (convergent_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (convergent_lines(v4, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v5, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v5, v6) = 0) | ~ (convergent_lines(v4, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v5, v6) = 0) | ~ (convergent_lines(v4, v5) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v4, v6) = v7) | ~ (convergent_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v7) = 0) | (v8 = 0 & apart_point_and_line(v5, v6) = 0) | (v8 = 0 & apart_point_and_line(v4, v7) = 0) | (v8 = 0 & apart_point_and_line(v4, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (orthogonal_lines(v4, v5) = v6) | unorthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (incident_point_and_line(v4, v5) = v6) | apart_point_and_line(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (parallel_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_lines(v4, v5) = v6) | distinct_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_points(v4, v5) = v6) | distinct_points(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v6) | orthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v4, v5) = v6) | incident_point_and_line(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | parallel_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | unorthogonal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v4, v5) = v6) | equal_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v4, v5) = v6) | equal_points(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (point(v6) = v5) | ~ (point(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (line(v6) = v5) | ~ (line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & unorthogonal_lines(v6, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (orthogonal_through_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & point(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v6, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & point(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & point(v6) = 0) | ( ~ (v7 = 0) & line(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v5) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & point(v5) = v7) | ( ~ (v7 = 0) & point(v4) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v5, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ( ~ (orthogonal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unorthogonal_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (incident_point_and_line(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (parallel_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & convergent_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equal_points(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & distinct_points(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & orthogonal_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (apart_point_and_line(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & incident_point_and_line(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v5) = v7)) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v4) = v7)) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & point(v6) = 0 & intersection_point(v4, v5) = v6) | ( ~ (v6 = 0) & line(v5) = v6) | ( ~ (v6 = 0) & line(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & parallel_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & equal_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v5, v6) = v7)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & line(v6) = 0 & line_connecting(v4, v5) = v6) | ( ~ (v6 = 0) & point(v5) = v6) | ( ~ (v6 = 0) & point(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & equal_points(v4, v5) = v6)) & ! [v4] : ~ (convergent_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0) & ? [v4] : ? [v5] : ? [v6] : orthogonal_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : incident_point_and_line(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : parallel_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : equal_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : equal_points(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : orthogonal_through_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : unorthogonal_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : parallel_through_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : intersection_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : line_connecting(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : apart_point_and_line(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : convergent_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_points(v5, v4) = v6 & ? [v4] : ? [v5] : point(v4) = v5 & ? [v4] : ? [v5] : line(v4) = v5)
% 61.50/32.52 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 61.50/32.52 | (1) ~ (all_0_0_0 = 0) & orthogonal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & orthogonal_lines(all_0_3_3, all_0_1_1) = 0 & parallel_lines(all_0_3_3, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = 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 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = 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 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, 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] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = 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, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = 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(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = 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, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_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 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, 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 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(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) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [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) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = 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, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = 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] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(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] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = 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 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(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 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1
% 61.50/32.56 |
% 61.50/32.56 | Applying alpha-rule on (1) yields:
% 61.50/32.56 | (2) ! [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)))
% 61.50/32.56 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 61.50/32.56 | (4) ! [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))
% 61.50/32.56 | (5) ! [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)
% 61.50/32.56 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 61.50/32.56 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 61.50/32.56 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 61.50/32.56 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 61.50/32.56 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 61.50/32.56 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 61.50/32.56 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 61.50/32.56 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 61.50/32.56 | (14) ! [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)))
% 61.50/32.56 | (15) ! [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)))
% 61.50/32.56 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 61.50/32.56 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 61.50/32.56 | (18) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 61.50/32.56 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 61.50/32.56 | (20) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 61.50/32.56 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 61.50/32.56 | (22) ! [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)))
% 61.50/32.57 | (23) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 61.50/32.57 | (24) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 61.50/32.57 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 61.50/32.57 | (26) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 61.50/32.57 | (27) ! [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)))
% 61.50/32.57 | (28) ! [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)
% 61.50/32.57 | (29) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 61.50/32.57 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 61.50/32.57 | (31) ! [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)))
% 61.50/32.57 | (32) ! [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)))
% 61.50/32.57 | (33) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 61.50/32.57 | (34) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 61.50/32.57 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 61.50/32.57 | (36) ! [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)))
% 61.50/32.57 | (37) ! [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)))
% 61.50/32.57 | (38) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 61.50/32.57 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 61.50/32.57 | (40) ? [v0] : ? [v1] : line(v0) = v1
% 61.50/32.57 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 61.50/32.57 | (42) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 61.50/32.57 | (43) ! [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))
% 61.50/32.57 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 61.50/32.57 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 61.84/32.57 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 61.84/32.57 | (47) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 61.84/32.57 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 61.84/32.57 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 61.84/32.57 | (50) ! [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)))
% 61.84/32.57 | (51) ! [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)
% 61.84/32.57 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 61.84/32.57 | (53) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 61.84/32.57 | (54) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 61.84/32.57 | (55) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 61.84/32.57 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 61.84/32.57 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 61.84/32.58 | (58) ! [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)))
% 61.84/32.58 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 61.84/32.58 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 61.84/32.58 | (61) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 61.84/32.58 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 61.84/32.58 | (63) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 61.84/32.58 | (64) ~ (all_0_0_0 = 0)
% 61.84/32.58 | (65) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 61.84/32.58 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 61.84/32.58 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 61.84/32.58 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 61.84/32.58 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 61.84/32.58 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 61.84/32.58 | (71) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 61.84/32.58 | (72) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 61.84/32.58 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 61.84/32.58 | (74) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 61.84/32.58 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 61.84/32.58 | (76) ! [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)))
% 61.84/32.58 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 61.84/32.58 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 61.84/32.58 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 61.84/32.58 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 61.84/32.58 | (81) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 61.84/32.58 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 61.84/32.58 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 61.84/32.58 | (84) ! [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)))
% 61.84/32.58 | (85) orthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.58 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 61.84/32.58 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 61.84/32.58 | (88) ! [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)))
% 61.84/32.58 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 61.84/32.58 | (90) ? [v0] : ? [v1] : point(v0) = v1
% 61.84/32.58 | (91) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 61.84/32.58 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 61.84/32.58 | (93) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 61.84/32.58 | (94) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 61.84/32.59 | (95) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 61.84/32.59 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 61.84/32.59 | (97) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 61.84/32.59 | (98) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 61.84/32.59 | (99) ! [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))
% 61.84/32.59 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 61.84/32.59 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 61.84/32.59 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 61.84/32.59 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 61.84/32.59 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 61.84/32.59 | (105) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 61.84/32.59 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 61.84/32.59 | (107) ! [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)))
% 61.84/32.59 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 61.84/32.59 | (109) parallel_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.59 | (110) orthogonal_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 61.84/32.59 | (111) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 61.84/32.59 | (112) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 61.84/32.59 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 61.84/32.59 | (114) ! [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))
% 61.84/32.59 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 61.84/32.59 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 61.84/32.59 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 61.84/32.59 | (118) ! [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)))
% 61.84/32.59 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 61.84/32.59 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 61.84/32.59 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 61.84/32.59 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 61.84/32.59 | (123) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 61.84/32.59 | (124) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 61.84/32.59 | (125) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 61.84/32.59 | (126) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 61.84/32.59 | (127) ! [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)))
% 61.84/32.59 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 61.84/32.59 | (129) ! [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))
% 61.84/32.59 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 61.84/32.59 | (131) ! [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))
% 61.84/32.60 | (132) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 61.84/32.60 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 61.84/32.60 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 61.84/32.60 | (135) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 61.84/32.60 | (136) ! [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)))
% 61.84/32.60 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 61.84/32.60 | (138) ! [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)
% 61.84/32.60 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 61.84/32.60 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 61.84/32.60 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 61.84/32.60 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 61.84/32.60 | (143) ! [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)))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (98) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms orthogonal_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 61.84/32.60 | (144) all_0_0_0 = 0 | unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (112) with all_0_1_1, all_0_3_3 and discharging atoms orthogonal_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 61.84/32.60 | (145) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_1_1) = v0)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (47) with all_0_2_2, all_0_3_3 and discharging atoms parallel_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 61.84/32.60 | (146) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating (146) with all_40_0_50 yields:
% 61.84/32.60 | (147) ~ (all_40_0_50 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50
% 61.84/32.60 |
% 61.84/32.60 | Applying alpha-rule on (147) yields:
% 61.84/32.60 | (148) ~ (all_40_0_50 = 0)
% 61.84/32.60 | (149) convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50
% 61.84/32.60 |
% 61.84/32.60 | Instantiating (145) with all_42_0_51 yields:
% 61.84/32.60 | (150) ~ (all_42_0_51 = 0) & unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51
% 61.84/32.60 |
% 61.84/32.60 | Applying alpha-rule on (150) yields:
% 61.84/32.60 | (151) ~ (all_42_0_51 = 0)
% 61.84/32.60 | (152) unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51
% 61.84/32.60 |
% 61.84/32.60 +-Applying beta-rule and splitting (144), into two cases.
% 61.84/32.60 |-Branch one:
% 61.84/32.60 | (153) unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (116) with 0, all_0_1_1, all_0_1_1, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 61.84/32.60 | (154) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (22) with all_42_0_51, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, yields:
% 61.84/32.60 | (155) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (59) with 0, all_42_0_51, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, yields:
% 61.84/32.60 | (156) ? [v0] : ((v0 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 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))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (129) with all_42_0_51, all_42_0_51, all_0_1_1, all_0_1_1, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, yields:
% 61.84/32.60 | (157) all_42_0_51 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_1_1) = v0)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (134) with all_42_0_51, all_0_1_1, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, yields:
% 61.84/32.60 | (158) all_42_0_51 = 0 | convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (114) with all_40_0_50, all_40_0_50, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.60 | (159) all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (2) with all_40_0_50, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.60 | (160) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (36) with all_42_0_51, all_40_0_50, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.60 | (161) ? [v0] : ((v0 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (133) with all_40_0_50, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.60 | (162) all_40_0_50 = 0 | unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.60 |
% 61.84/32.60 | Instantiating formula (105) with all_40_0_50, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.60 | (163) all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating (161) with all_54_0_53 yields:
% 61.84/32.60 | (164) (all_54_0_53 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_54_0_53 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_54_0_53 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_54_0_53) | ( ~ (all_54_0_53 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating (160) with all_55_0_54, all_55_1_55 yields:
% 61.84/32.60 | (165) (all_55_0_54 = 0 & all_55_1_55 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_55_1_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_55_1_55 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55)
% 61.84/32.60 |
% 61.84/32.60 | Instantiating (156) with all_57_0_57 yields:
% 61.84/32.60 | (166) (all_57_0_57 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_57_0_57 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_57_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_57_0_57) | ( ~ (all_57_0_57 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57)
% 61.84/32.61 |
% 61.84/32.61 | Instantiating (155) with all_61_0_61, all_61_1_62 yields:
% 61.84/32.61 | (167) (all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_61_1_62 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_61_1_62 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62)
% 61.84/32.61 |
% 61.84/32.61 | Instantiating (154) with all_65_0_67, all_65_1_68 yields:
% 61.84/32.61 | (168) (all_65_0_67 = 0 & all_65_1_68 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_65_1_68 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_65_1_68 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_65_1_68)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (158), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (162), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (170) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (165), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (171) (all_55_0_54 = 0 & all_55_1_55 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_55_1_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (171), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (172) all_55_0_54 = 0 & all_55_1_55 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (172) yields:
% 61.84/32.61 | (173) all_55_0_54 = 0
% 61.84/32.61 | (174) all_55_1_55 = 0
% 61.84/32.61 | (175) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (157), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (177) all_42_0_51 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (177) can reduce 151 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (151) ~ (all_42_0_51 = 0)
% 61.84/32.61 | (180) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_1_1) = v0)
% 61.84/32.61 |
% 61.84/32.61 | Instantiating formula (96) with all_0_3_3, all_0_1_1, 0, all_42_0_51 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_1_1) = all_42_0_51, unorthogonal_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 61.84/32.61 | (177) all_42_0_51 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (177) can reduce 151 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (183) all_55_1_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (183) yields:
% 61.84/32.61 | (174) all_55_1_55 = 0
% 61.84/32.61 | (185) all_40_0_50 = 0
% 61.84/32.61 | (170) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (185) can reduce 148 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (188) ~ (all_55_1_55 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (188) yields:
% 61.84/32.61 | (189) ~ (all_55_1_55 = 0)
% 61.84/32.61 | (190) convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (157), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (177) all_42_0_51 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (177) can reduce 151 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (151) ~ (all_42_0_51 = 0)
% 61.84/32.61 | (180) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_1_1) = v0)
% 61.84/32.61 |
% 61.84/32.61 | Instantiating (180) with all_80_0_73 yields:
% 61.84/32.61 | (195) ~ (all_80_0_73 = 0) & convergent_lines(all_0_1_1, all_0_1_1) = all_80_0_73
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (195) yields:
% 61.84/32.61 | (196) ~ (all_80_0_73 = 0)
% 61.84/32.61 | (197) convergent_lines(all_0_1_1, all_0_1_1) = all_80_0_73
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (163), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (185) all_40_0_50 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (185) can reduce 148 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (148) ~ (all_40_0_50 = 0)
% 61.84/32.61 | (201) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (164), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (202) (all_54_0_53 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_54_0_53 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_54_0_53 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_54_0_53)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (202), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (203) (all_54_0_53 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_54_0_53 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (203), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (204) all_54_0_53 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (204) yields:
% 61.84/32.61 | (205) all_54_0_53 = 0
% 61.84/32.61 | (177) all_42_0_51 = 0
% 61.84/32.61 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (177) can reduce 151 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (209) all_54_0_53 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (209) yields:
% 61.84/32.61 | (205) all_54_0_53 = 0
% 61.84/32.61 | (185) all_40_0_50 = 0
% 61.84/32.61 | (170) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (185) can reduce 148 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (214) ~ (all_54_0_53 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_54_0_53
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (214) yields:
% 61.84/32.61 | (215) ~ (all_54_0_53 = 0)
% 61.84/32.61 | (216) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_54_0_53
% 61.84/32.61 |
% 61.84/32.61 | Instantiating formula (96) with all_0_2_2, all_0_1_1, all_54_0_53, 0 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_54_0_53, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 61.84/32.61 | (205) all_54_0_53 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (205) can reduce 215 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (219) ~ (all_54_0_53 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (219) yields:
% 61.84/32.61 | (215) ~ (all_54_0_53 = 0)
% 61.84/32.61 | (221) convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (159), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (185) all_40_0_50 = 0
% 61.84/32.61 |
% 61.84/32.61 | Equations (185) can reduce 148 to:
% 61.84/32.61 | (178) $false
% 61.84/32.61 |
% 61.84/32.61 |-The branch is then unsatisfiable
% 61.84/32.61 |-Branch two:
% 61.84/32.61 | (148) ~ (all_40_0_50 = 0)
% 61.84/32.61 | (225) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (166), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (226) (all_57_0_57 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_57_0_57 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_57_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_57_0_57)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (226), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (227) (all_57_0_57 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_57_0_57 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 61.84/32.61 |
% 61.84/32.61 +-Applying beta-rule and splitting (227), into two cases.
% 61.84/32.61 |-Branch one:
% 61.84/32.61 | (228) all_57_0_57 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.61 |
% 61.84/32.61 | Applying alpha-rule on (228) yields:
% 61.84/32.61 | (229) all_57_0_57 = 0
% 61.84/32.62 | (177) all_42_0_51 = 0
% 61.84/32.62 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (177) can reduce 151 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (233) all_57_0_57 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (233) yields:
% 61.84/32.62 | (229) all_57_0_57 = 0
% 61.84/32.62 | (235) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (167), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (236) (all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_61_1_62 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0)
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (236), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (237) all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (237) yields:
% 61.84/32.62 | (238) all_61_0_61 = 0
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.62 | (170) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 | (241) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_3_3, all_0_2_2, 0, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 61.84/32.62 | (185) all_40_0_50 = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (185) can reduce 148 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (244) all_61_1_62 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (244) yields:
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.62 | (177) all_42_0_51 = 0
% 61.84/32.62 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (177) can reduce 151 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (249) ~ (all_61_1_62 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (249) yields:
% 61.84/32.62 | (250) ~ (all_61_1_62 = 0)
% 61.84/32.62 | (251) convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_55_1_55, all_61_1_62 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55, yields:
% 61.84/32.62 | (252) all_61_1_62 = all_55_1_55
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_54_0_53, all_55_1_55 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55, convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53, yields:
% 61.84/32.62 | (253) all_55_1_55 = all_54_0_53
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, 0, all_61_1_62 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.62 |
% 61.84/32.62 | Combining equations (252,239) yields a new equation:
% 61.84/32.62 | (255) all_55_1_55 = 0
% 61.84/32.62 |
% 61.84/32.62 | Simplifying 255 yields:
% 61.84/32.62 | (174) all_55_1_55 = 0
% 61.84/32.62 |
% 61.84/32.62 | Combining equations (253,174) yields a new equation:
% 61.84/32.62 | (257) all_54_0_53 = 0
% 61.84/32.62 |
% 61.84/32.62 | Simplifying 257 yields:
% 61.84/32.62 | (205) all_54_0_53 = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (205) can reduce 215 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (260) ~ (all_57_0_57 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_57_0_57
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (260) yields:
% 61.84/32.62 | (261) ~ (all_57_0_57 = 0)
% 61.84/32.62 | (262) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_57_0_57
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (96) with all_0_3_3, all_0_2_2, 0, all_57_0_57 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_57_0_57, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 61.84/32.62 | (229) all_57_0_57 = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (229) can reduce 261 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (265) ~ (all_57_0_57 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (265) yields:
% 61.84/32.62 | (261) ~ (all_57_0_57 = 0)
% 61.84/32.62 | (267) convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (167), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (236) (all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_61_1_62 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0)
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (236), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (237) all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (237) yields:
% 61.84/32.62 | (238) all_61_0_61 = 0
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.62 | (170) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 | (241) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_3_3, all_0_2_2, all_57_0_57, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57, convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.62 | (274) all_57_0_57 = all_40_0_50
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_3_3, all_0_2_2, 0, all_57_0_57 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 61.84/32.62 | (229) all_57_0_57 = 0
% 61.84/32.62 |
% 61.84/32.62 | Combining equations (274,229) yields a new equation:
% 61.84/32.62 | (276) all_40_0_50 = 0
% 61.84/32.62 |
% 61.84/32.62 | Simplifying 276 yields:
% 61.84/32.62 | (185) all_40_0_50 = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (185) can reduce 148 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (244) all_61_1_62 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (244) yields:
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.62 | (177) all_42_0_51 = 0
% 61.84/32.62 | (169) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Equations (177) can reduce 151 to:
% 61.84/32.62 | (178) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (249) ~ (all_61_1_62 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (249) yields:
% 61.84/32.62 | (250) ~ (all_61_1_62 = 0)
% 61.84/32.62 | (251) convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (168), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (287) (all_65_0_67 = 0 & all_65_1_68 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_65_1_68 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 61.84/32.62 |
% 61.84/32.62 +-Applying beta-rule and splitting (287), into two cases.
% 61.84/32.62 |-Branch one:
% 61.84/32.62 | (288) all_65_0_67 = 0 & all_65_1_68 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (288) yields:
% 61.84/32.62 | (289) all_65_0_67 = 0
% 61.84/32.62 | (290) all_65_1_68 = 0
% 61.84/32.62 | (291) unorthogonal_lines(all_0_1_1, all_0_1_1) = 0
% 61.84/32.62 | (292) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (132) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 61.84/32.62 | (293) $false
% 61.84/32.62 |
% 61.84/32.62 |-The branch is then unsatisfiable
% 61.84/32.62 |-Branch two:
% 61.84/32.62 | (294) all_65_1_68 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Applying alpha-rule on (294) yields:
% 61.84/32.62 | (290) all_65_1_68 = 0
% 61.84/32.62 | (235) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_55_1_55, all_61_1_62 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55, yields:
% 61.84/32.62 | (252) all_61_1_62 = all_55_1_55
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_54_0_53, all_55_1_55 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55, convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53, yields:
% 61.84/32.62 | (253) all_55_1_55 = all_54_0_53
% 61.84/32.62 |
% 61.84/32.62 | Instantiating formula (60) with all_0_2_2, all_0_1_1, 0, all_61_1_62 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 61.84/32.62 | (239) all_61_1_62 = 0
% 61.84/32.63 |
% 61.84/32.63 | Combining equations (252,239) yields a new equation:
% 61.84/32.63 | (255) all_55_1_55 = 0
% 61.84/32.63 |
% 61.84/32.63 | Simplifying 255 yields:
% 61.84/32.63 | (174) all_55_1_55 = 0
% 61.84/32.63 |
% 61.84/32.63 | Combining equations (174,253) yields a new equation:
% 61.84/32.63 | (205) all_54_0_53 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (205) can reduce 215 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (304) ~ (all_65_1_68 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_65_1_68
% 61.84/32.63 |
% 61.84/32.63 | Applying alpha-rule on (304) yields:
% 61.84/32.63 | (305) ~ (all_65_1_68 = 0)
% 61.84/32.63 | (306) convergent_lines(all_0_2_2, all_0_1_1) = all_65_1_68
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_61_1_62, all_65_1_68 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_65_1_68, convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, yields:
% 61.84/32.63 | (307) all_65_1_68 = all_61_1_62
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_55_1_55, all_61_1_62 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, convergent_lines(all_0_2_2, all_0_1_1) = all_55_1_55, yields:
% 61.84/32.63 | (252) all_61_1_62 = all_55_1_55
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (60) with all_0_2_2, all_0_1_1, all_54_0_53, all_65_1_68 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_65_1_68, convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53, yields:
% 61.84/32.63 | (309) all_65_1_68 = all_54_0_53
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (60) with all_0_3_3, all_0_2_2, all_57_0_57, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_57_0_57, convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.63 | (274) all_57_0_57 = all_40_0_50
% 61.84/32.63 |
% 61.84/32.63 | Combining equations (307,309) yields a new equation:
% 61.84/32.63 | (311) all_61_1_62 = all_54_0_53
% 61.84/32.63 |
% 61.84/32.63 | Simplifying 311 yields:
% 61.84/32.63 | (312) all_61_1_62 = all_54_0_53
% 61.84/32.63 |
% 61.84/32.63 | Combining equations (312,252) yields a new equation:
% 61.84/32.63 | (253) all_55_1_55 = all_54_0_53
% 61.84/32.63 |
% 61.84/32.63 | Equations (274) can reduce 261 to:
% 61.84/32.63 | (148) ~ (all_40_0_50 = 0)
% 61.84/32.63 |
% 61.84/32.63 | Equations (253) can reduce 189 to:
% 61.84/32.63 | (215) ~ (all_54_0_53 = 0)
% 61.84/32.63 |
% 61.84/32.63 | From (253) and (190) follows:
% 61.84/32.63 | (221) convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53
% 61.84/32.63 |
% 61.84/32.63 | From (274) and (267) follows:
% 61.84/32.63 | (149) convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (114) with all_54_0_53, all_80_0_73, all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = all_80_0_73, convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53, yields:
% 61.84/32.63 | (318) all_80_0_73 = 0 | all_54_0_53 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_2_2) = v0)
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (114) with all_54_0_53, all_54_0_53, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_54_0_53, yields:
% 61.84/32.63 | (319) all_54_0_53 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (83) with all_40_0_50, all_0_2_2, all_0_1_1, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = 0, convergent_lines(all_0_3_3, all_0_2_2) = all_40_0_50, yields:
% 61.84/32.63 | (320) all_40_0_50 = 0 | convergent_lines(all_0_1_1, all_0_2_2) = 0
% 61.84/32.63 |
% 61.84/32.63 +-Applying beta-rule and splitting (320), into two cases.
% 61.84/32.63 |-Branch one:
% 61.84/32.63 | (321) convergent_lines(all_0_1_1, all_0_2_2) = 0
% 61.84/32.63 |
% 61.84/32.63 +-Applying beta-rule and splitting (319), into two cases.
% 61.84/32.63 |-Branch one:
% 61.84/32.63 | (205) all_54_0_53 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (205) can reduce 215 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (215) ~ (all_54_0_53 = 0)
% 61.84/32.63 | (325) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 61.84/32.63 |
% 61.84/32.63 +-Applying beta-rule and splitting (318), into two cases.
% 61.84/32.63 |-Branch one:
% 61.84/32.63 | (326) all_80_0_73 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (326) can reduce 196 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (196) ~ (all_80_0_73 = 0)
% 61.84/32.63 | (329) all_54_0_53 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_2_2) = v0)
% 61.84/32.63 |
% 61.84/32.63 +-Applying beta-rule and splitting (329), into two cases.
% 61.84/32.63 |-Branch one:
% 61.84/32.63 | (205) all_54_0_53 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (205) can reduce 215 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (215) ~ (all_54_0_53 = 0)
% 61.84/32.63 | (333) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_1_1, all_0_2_2) = v0)
% 61.84/32.63 |
% 61.84/32.63 | Instantiating (333) with all_307_0_2097 yields:
% 61.84/32.63 | (334) ~ (all_307_0_2097 = 0) & convergent_lines(all_0_1_1, all_0_2_2) = all_307_0_2097
% 61.84/32.63 |
% 61.84/32.63 | Applying alpha-rule on (334) yields:
% 61.84/32.63 | (335) ~ (all_307_0_2097 = 0)
% 61.84/32.63 | (336) convergent_lines(all_0_1_1, all_0_2_2) = all_307_0_2097
% 61.84/32.63 |
% 61.84/32.63 | Instantiating formula (60) with all_0_1_1, all_0_2_2, 0, all_307_0_2097 and discharging atoms convergent_lines(all_0_1_1, all_0_2_2) = all_307_0_2097, convergent_lines(all_0_1_1, all_0_2_2) = 0, yields:
% 61.84/32.63 | (337) all_307_0_2097 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (337) can reduce 335 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (339) ~ (convergent_lines(all_0_1_1, all_0_2_2) = 0)
% 61.84/32.63 | (185) all_40_0_50 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (185) can reduce 148 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (342) ~ (unorthogonal_lines(all_0_3_3, all_0_2_2) = 0)
% 61.84/32.63 | (185) all_40_0_50 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (185) can reduce 148 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (345) ~ (convergent_lines(all_0_3_3, all_0_1_1) = 0)
% 61.84/32.63 | (177) all_42_0_51 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (177) can reduce 151 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 |-Branch two:
% 61.84/32.63 | (348) ~ (unorthogonal_lines(all_0_2_2, all_0_1_1) = 0)
% 61.84/32.63 | (349) all_0_0_0 = 0
% 61.84/32.63 |
% 61.84/32.63 | Equations (349) can reduce 64 to:
% 61.84/32.63 | (178) $false
% 61.84/32.63 |
% 61.84/32.63 |-The branch is then unsatisfiable
% 61.84/32.63 % SZS output end Proof for theBenchmark
% 61.84/32.63
% 61.84/32.63 32035ms
%------------------------------------------------------------------------------