TSTP Solution File: GEO219+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 17.04s 4.62s
% Output : Proof 21.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 10:08:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.59 ____ _
% 0.49/0.59 ___ / __ \_____(_)___ ________ __________
% 0.49/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.59
% 0.49/0.59 A Theorem Prover for First-Order Logic
% 0.49/0.59 (ePrincess v.1.0)
% 0.49/0.59
% 0.49/0.59 (c) Philipp Rümmer, 2009-2015
% 0.49/0.59 (c) Peter Backeman, 2014-2015
% 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59 Bug reports to peter@backeman.se
% 0.49/0.59
% 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59
% 0.49/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.84/0.97 Prover 0: Preprocessing ...
% 2.43/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.43/1.21 Prover 0: Constructing countermodel ...
% 14.14/4.03 Prover 0: gave up
% 14.14/4.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.51/4.07 Prover 1: Preprocessing ...
% 15.19/4.20 Prover 1: Constructing countermodel ...
% 15.59/4.28 Prover 1: gave up
% 15.59/4.28 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.59/4.31 Prover 2: Preprocessing ...
% 16.52/4.47 Prover 2: Warning: ignoring some quantifiers
% 16.66/4.49 Prover 2: Constructing countermodel ...
% 17.04/4.62 Prover 2: proved (340ms)
% 17.04/4.62
% 17.04/4.62 No countermodel exists, formula is valid
% 17.04/4.62 % SZS status Theorem for theBenchmark
% 17.04/4.62
% 17.04/4.62 Generating proof ... Warning: ignoring some quantifiers
% 20.39/5.35 found it (size 193)
% 20.39/5.35
% 20.39/5.35 % SZS output start Proof for theBenchmark
% 20.39/5.35 Assumed formulas after preprocessing and simplification:
% 20.39/5.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & orthogonal_lines(v1, v2) = v3 & orthogonal_lines(v0, v1) = 0 & parallel_lines(v0, v2) = 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)
% 20.63/5.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 20.63/5.42 | (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_2_2) = 0 & parallel_lines(all_0_3_3, all_0_1_1) = 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
% 20.96/5.46 |
% 20.96/5.46 | Applying alpha-rule on (1) yields:
% 20.96/5.46 | (2) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 20.96/5.46 | (3) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 20.96/5.46 | (4) ! [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)))
% 20.96/5.46 | (5) ! [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)))
% 20.96/5.46 | (6) ! [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)))
% 20.96/5.46 | (7) ! [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)))
% 21.04/5.46 | (8) ! [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)))
% 21.04/5.46 | (9) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 21.04/5.46 | (10) parallel_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.46 | (11) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 21.04/5.46 | (12) ! [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)))
% 21.04/5.46 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 21.04/5.47 | (14) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 21.04/5.47 | (15) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 21.04/5.47 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 21.04/5.47 | (17) ! [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)
% 21.04/5.47 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 21.04/5.47 | (19) ! [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)))
% 21.04/5.47 | (20) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 21.04/5.47 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 21.04/5.47 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 21.04/5.47 | (23) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 21.04/5.47 | (24) ! [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)))
% 21.04/5.47 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 21.04/5.47 | (26) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 21.04/5.47 | (27) ! [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)))
% 21.04/5.47 | (28) ! [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)))
% 21.04/5.47 | (29) ! [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)))
% 21.04/5.47 | (30) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 21.04/5.47 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 21.04/5.47 | (32) ! [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)))
% 21.04/5.47 | (33) ! [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)))
% 21.04/5.47 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 21.04/5.47 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 21.04/5.47 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 21.04/5.47 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 21.04/5.47 | (38) ! [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)))
% 21.04/5.47 | (39) ! [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))
% 21.04/5.47 | (40) ! [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)
% 21.04/5.47 | (41) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 21.04/5.47 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 21.04/5.47 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 21.04/5.47 | (44) ! [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))
% 21.04/5.47 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 21.04/5.47 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 21.04/5.47 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 21.04/5.47 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 21.04/5.47 | (49) ! [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)))
% 21.04/5.47 | (50) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 21.04/5.47 | (51) ! [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)))
% 21.04/5.47 | (52) ! [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))
% 21.04/5.47 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 21.04/5.47 | (54) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 21.04/5.47 | (55) ! [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))
% 21.04/5.47 | (56) ! [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)))
% 21.04/5.47 | (57) ! [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)))
% 21.04/5.48 | (58) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 21.04/5.48 | (59) ! [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)))
% 21.04/5.48 | (60) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 21.04/5.48 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 21.04/5.48 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 21.04/5.48 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 21.04/5.48 | (64) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 21.04/5.48 | (65) ~ (all_0_0_0 = 0)
% 21.04/5.48 | (66) ! [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)))
% 21.04/5.48 | (67) ! [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)
% 21.04/5.48 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 21.04/5.48 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 21.04/5.48 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 21.04/5.48 | (71) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 21.04/5.48 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 21.04/5.48 | (73) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 21.04/5.48 | (74) ! [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)))
% 21.04/5.48 | (75) ! [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)))
% 21.04/5.48 | (76) ! [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)))
% 21.04/5.48 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 21.04/5.48 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 21.04/5.48 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 21.04/5.48 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 21.04/5.48 | (81) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 21.04/5.48 | (82) ! [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)))
% 21.04/5.48 | (83) ? [v0] : ? [v1] : point(v0) = v1
% 21.04/5.48 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 21.04/5.48 | (85) ! [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)))
% 21.04/5.48 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 21.04/5.48 | (87) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 21.04/5.48 | (88) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 21.04/5.48 | (89) ! [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)))
% 21.04/5.48 | (90) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 21.04/5.48 | (91) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 21.04/5.48 | (92) ! [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)))
% 21.04/5.48 | (93) orthogonal_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 21.04/5.48 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 21.04/5.48 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 21.04/5.48 | (96) ! [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)))
% 21.04/5.48 | (97) ! [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)))
% 21.04/5.48 | (98) ! [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)))
% 21.04/5.48 | (99) ! [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)))
% 21.04/5.48 | (100) ! [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)))
% 21.04/5.48 | (101) ! [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)))
% 21.04/5.48 | (102) ! [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)))
% 21.04/5.49 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 21.04/5.49 | (104) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 21.04/5.49 | (105) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 21.04/5.49 | (106) ! [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)))
% 21.04/5.49 | (107) ! [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))
% 21.04/5.49 | (108) ! [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)))
% 21.04/5.49 | (109) ! [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)))
% 21.04/5.49 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 21.04/5.49 | (111) ! [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)))
% 21.04/5.49 | (112) ! [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)))
% 21.04/5.49 | (113) ! [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)))
% 21.04/5.49 | (114) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 21.04/5.49 | (115) ? [v0] : ? [v1] : line(v0) = v1
% 21.04/5.49 | (116) ! [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)
% 21.04/5.49 | (117) orthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.49 | (118) ! [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))
% 21.04/5.49 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 21.04/5.49 | (120) ! [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)))
% 21.04/5.49 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 21.04/5.49 | (122) ! [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)))
% 21.04/5.49 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 21.04/5.49 | (124) ! [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)))
% 21.04/5.49 | (125) ! [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)))
% 21.04/5.49 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 21.04/5.49 | (127) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 21.04/5.49 | (128) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 21.04/5.49 | (129) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 21.04/5.49 | (130) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 21.04/5.49 | (131) ! [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))
% 21.04/5.49 | (132) ! [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)))
% 21.04/5.49 | (133) ! [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)))
% 21.04/5.49 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 21.04/5.49 | (135) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 21.04/5.49 | (136) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 21.04/5.49 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 21.04/5.49 | (138) ! [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)))
% 21.04/5.49 | (139) ! [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)))
% 21.04/5.49 | (140) ! [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)))
% 21.04/5.49 | (141) ! [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)))
% 21.04/5.49 | (142) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 21.04/5.49 | (143) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 21.04/5.49 |
% 21.04/5.50 | Instantiating formula (47) 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:
% 21.04/5.50 | (144) all_0_0_0 = 0 | unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (105) with all_0_2_2, all_0_3_3 and discharging atoms orthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.04/5.50 | (145) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (88) with all_0_1_1, all_0_3_3 and discharging atoms parallel_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 21.04/5.50 | (146) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_1_1) = v0)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (146) with all_40_0_50 yields:
% 21.04/5.50 | (147) ~ (all_40_0_50 = 0) & convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (147) yields:
% 21.04/5.50 | (148) ~ (all_40_0_50 = 0)
% 21.04/5.50 | (149) convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (145) with all_42_0_51 yields:
% 21.04/5.50 | (150) ~ (all_42_0_51 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (150) yields:
% 21.04/5.50 | (151) ~ (all_42_0_51 = 0)
% 21.04/5.50 | (152) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (144), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (153) unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (33) with 0, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.04/5.50 | (154) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 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))
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (125) 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_2_2) = all_42_0_51, yields:
% 21.04/5.50 | (155) ? [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_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (131) with all_42_0_51, all_42_0_51, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, yields:
% 21.04/5.50 | (156) all_42_0_51 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (35) with all_42_0_51, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, yields:
% 21.04/5.50 | (157) all_42_0_51 = 0 | convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (39) with all_40_0_50, all_40_0_50, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, yields:
% 21.04/5.50 | (158) all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (96) 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_1_1) = all_40_0_50, yields:
% 21.04/5.50 | (159) ? [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_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (108) with 0, 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_1_1) = all_40_0_50, yields:
% 21.04/5.50 | (160) ? [v0] : ((v0 = 0 & all_40_0_50 = 0 & unorthogonal_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))
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (12) with all_40_0_50, all_42_0_51, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, yields:
% 21.04/5.50 | (161) ? [v0] : ((v0 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 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))
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (129) with all_40_0_50, all_0_1_1, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, yields:
% 21.04/5.50 | (162) all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_1_1) = v0)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (161) with all_53_0_52 yields:
% 21.04/5.50 | (163) (all_53_0_52 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_53_0_52 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_53_0_52 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_53_0_52) | ( ~ (all_53_0_52 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (160) with all_56_0_55 yields:
% 21.04/5.50 | (164) (all_56_0_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | (all_56_0_55 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_56_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55) | ( ~ (all_56_0_55 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_56_0_55)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (159) with all_57_0_56, all_57_1_57 yields:
% 21.04/5.50 | (165) (all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_57_1_57 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (154) with all_61_0_61, all_61_1_62 yields:
% 21.04/5.50 | (166) (all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_61_1_62 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_61_1_62 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62)
% 21.04/5.50 |
% 21.04/5.50 | Instantiating (155) with all_62_0_63, all_62_1_64 yields:
% 21.04/5.50 | (167) (all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_62_1_64 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (157), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (163), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (169) (all_53_0_52 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_53_0_52 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_53_0_52 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_53_0_52)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (169), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (170) (all_53_0_52 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_53_0_52 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (170), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (171) all_53_0_52 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (171) yields:
% 21.04/5.50 | (172) all_53_0_52 = 0
% 21.04/5.50 | (173) all_42_0_51 = 0
% 21.04/5.50 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.50 |
% 21.04/5.50 | Equations (173) can reduce 151 to:
% 21.04/5.50 | (175) $false
% 21.04/5.50 |
% 21.04/5.50 |-The branch is then unsatisfiable
% 21.04/5.50 |-Branch two:
% 21.04/5.50 | (176) all_53_0_52 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (176) yields:
% 21.04/5.50 | (172) all_53_0_52 = 0
% 21.04/5.50 | (178) all_40_0_50 = 0
% 21.04/5.50 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.50 |
% 21.04/5.50 | Equations (178) can reduce 148 to:
% 21.04/5.50 | (175) $false
% 21.04/5.50 |
% 21.04/5.50 |-The branch is then unsatisfiable
% 21.04/5.50 |-Branch two:
% 21.04/5.50 | (181) ~ (all_53_0_52 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_53_0_52
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (181) yields:
% 21.04/5.50 | (182) ~ (all_53_0_52 = 0)
% 21.04/5.50 | (183) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_53_0_52
% 21.04/5.50 |
% 21.04/5.50 | Instantiating formula (80) with all_0_2_2, all_0_1_1, all_53_0_52, 0 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_53_0_52, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.04/5.50 | (172) all_53_0_52 = 0
% 21.04/5.50 |
% 21.04/5.50 | Equations (172) can reduce 182 to:
% 21.04/5.50 | (175) $false
% 21.04/5.50 |
% 21.04/5.50 |-The branch is then unsatisfiable
% 21.04/5.50 |-Branch two:
% 21.04/5.50 | (186) ~ (all_53_0_52 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52
% 21.04/5.50 |
% 21.04/5.50 | Applying alpha-rule on (186) yields:
% 21.04/5.50 | (182) ~ (all_53_0_52 = 0)
% 21.04/5.50 | (188) convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (158), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (178) all_40_0_50 = 0
% 21.04/5.50 |
% 21.04/5.50 | Equations (178) can reduce 148 to:
% 21.04/5.50 | (175) $false
% 21.04/5.50 |
% 21.04/5.50 |-The branch is then unsatisfiable
% 21.04/5.50 |-Branch two:
% 21.04/5.50 | (148) ~ (all_40_0_50 = 0)
% 21.04/5.50 | (192) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (164), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (193) (all_56_0_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | (all_56_0_55 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_56_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (193), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.50 | (194) (all_56_0_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0) | (all_56_0_55 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 21.04/5.50 |
% 21.04/5.50 +-Applying beta-rule and splitting (194), into two cases.
% 21.04/5.50 |-Branch one:
% 21.04/5.51 | (195) all_56_0_55 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (195) yields:
% 21.04/5.51 | (196) all_56_0_55 = 0
% 21.04/5.51 | (178) all_40_0_50 = 0
% 21.04/5.51 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (178) can reduce 148 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (200) all_56_0_55 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (200) yields:
% 21.04/5.51 | (196) all_56_0_55 = 0
% 21.04/5.51 | (202) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (156), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (173) all_42_0_51 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (173) can reduce 151 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (151) ~ (all_42_0_51 = 0)
% 21.04/5.51 | (206) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (162), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (178) all_40_0_50 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (178) can reduce 148 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (148) ~ (all_40_0_50 = 0)
% 21.04/5.51 | (210) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_1_1) = v0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (165), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (211) (all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (211), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (212) all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (212) yields:
% 21.04/5.51 | (213) all_57_0_56 = 0
% 21.04/5.51 | (214) all_57_1_57 = 0
% 21.04/5.51 | (215) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.51 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.51 |
% 21.04/5.51 | Instantiating formula (80) with all_0_3_3, all_0_2_2, 0, all_42_0_51 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.04/5.51 | (173) all_42_0_51 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (173) can reduce 151 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (219) all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (219) yields:
% 21.04/5.51 | (214) all_57_1_57 = 0
% 21.04/5.51 | (178) all_40_0_50 = 0
% 21.04/5.51 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (178) can reduce 148 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (224) ~ (all_57_1_57 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (224) yields:
% 21.04/5.51 | (225) ~ (all_57_1_57 = 0)
% 21.04/5.51 | (226) convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (167), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (227) (all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (227), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (228) all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (228) yields:
% 21.04/5.51 | (229) all_62_0_63 = 0
% 21.04/5.51 | (230) all_62_1_64 = 0
% 21.04/5.51 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 | (232) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.04/5.51 |
% 21.04/5.51 | Instantiating formula (68) with all_0_3_3, all_0_1_1, 0, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, convergent_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 21.04/5.51 | (178) all_40_0_50 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (178) can reduce 148 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (235) all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (235) yields:
% 21.04/5.51 | (230) all_62_1_64 = 0
% 21.04/5.51 | (173) all_42_0_51 = 0
% 21.04/5.51 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (173) can reduce 151 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (240) ~ (all_62_1_64 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (240) yields:
% 21.04/5.51 | (241) ~ (all_62_1_64 = 0)
% 21.04/5.51 | (242) convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.04/5.51 |
% 21.04/5.51 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_57_1_57, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57, yields:
% 21.04/5.51 | (243) all_62_1_64 = all_57_1_57
% 21.04/5.51 |
% 21.04/5.51 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_53_0_52, all_57_1_57 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57, convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, yields:
% 21.04/5.51 | (244) all_57_1_57 = all_53_0_52
% 21.04/5.51 |
% 21.04/5.51 | Instantiating formula (68) with all_0_2_2, all_0_1_1, 0, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.04/5.51 | (230) all_62_1_64 = 0
% 21.04/5.51 |
% 21.04/5.51 | Combining equations (243,230) yields a new equation:
% 21.04/5.51 | (246) all_57_1_57 = 0
% 21.04/5.51 |
% 21.04/5.51 | Simplifying 246 yields:
% 21.04/5.51 | (214) all_57_1_57 = 0
% 21.04/5.51 |
% 21.04/5.51 | Combining equations (214,244) yields a new equation:
% 21.04/5.51 | (172) all_53_0_52 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (172) can reduce 182 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (250) ~ (all_56_0_55 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (250) yields:
% 21.04/5.51 | (251) ~ (all_56_0_55 = 0)
% 21.04/5.51 | (252) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (156), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (173) all_42_0_51 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (173) can reduce 151 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (151) ~ (all_42_0_51 = 0)
% 21.04/5.51 | (206) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (162), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (178) all_40_0_50 = 0
% 21.04/5.51 |
% 21.04/5.51 | Equations (178) can reduce 148 to:
% 21.04/5.51 | (175) $false
% 21.04/5.51 |
% 21.04/5.51 |-The branch is then unsatisfiable
% 21.04/5.51 |-Branch two:
% 21.04/5.51 | (148) ~ (all_40_0_50 = 0)
% 21.04/5.51 | (210) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_1_1) = v0)
% 21.04/5.51 |
% 21.04/5.51 | Instantiating (210) with all_94_0_79 yields:
% 21.04/5.51 | (261) ~ (all_94_0_79 = 0) & distinct_lines(all_0_3_3, all_0_1_1) = all_94_0_79
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (261) yields:
% 21.04/5.51 | (262) ~ (all_94_0_79 = 0)
% 21.04/5.51 | (263) distinct_lines(all_0_3_3, all_0_1_1) = all_94_0_79
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (166), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (264) (all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_61_1_62 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 21.04/5.51 |
% 21.04/5.51 +-Applying beta-rule and splitting (264), into two cases.
% 21.04/5.51 |-Branch one:
% 21.04/5.51 | (265) all_61_0_61 = 0 & all_61_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 21.04/5.51 |
% 21.04/5.51 | Applying alpha-rule on (265) yields:
% 21.04/5.51 | (266) all_61_0_61 = 0
% 21.25/5.51 | (267) all_61_1_62 = 0
% 21.25/5.51 | (268) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 21.25/5.51 | (269) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 21.25/5.51 |
% 21.25/5.51 | Instantiating formula (90) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 21.25/5.51 | (270) $false
% 21.25/5.51 |
% 21.25/5.51 |-The branch is then unsatisfiable
% 21.25/5.51 |-Branch two:
% 21.25/5.51 | (271) all_61_1_62 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.25/5.51 |
% 21.25/5.51 | Applying alpha-rule on (271) yields:
% 21.25/5.51 | (267) all_61_1_62 = 0
% 21.25/5.51 | (202) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.25/5.51 |
% 21.25/5.51 +-Applying beta-rule and splitting (165), into two cases.
% 21.25/5.51 |-Branch one:
% 21.25/5.51 | (211) (all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0)
% 21.25/5.51 |
% 21.25/5.51 +-Applying beta-rule and splitting (211), into two cases.
% 21.25/5.51 |-Branch one:
% 21.25/5.51 | (212) all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.51 |
% 21.25/5.51 | Applying alpha-rule on (212) yields:
% 21.25/5.51 | (213) all_57_0_56 = 0
% 21.25/5.51 | (214) all_57_1_57 = 0
% 21.25/5.51 | (215) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.51 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.51 |
% 21.25/5.51 | Instantiating formula (80) with all_0_3_3, all_0_2_2, all_56_0_55, all_42_0_51 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, yields:
% 21.25/5.51 | (280) all_56_0_55 = all_42_0_51
% 21.25/5.51 |
% 21.25/5.51 | Instantiating formula (80) with all_0_3_3, all_0_2_2, 0, all_56_0_55 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.25/5.51 | (196) all_56_0_55 = 0
% 21.25/5.51 |
% 21.25/5.51 | Combining equations (196,280) yields a new equation:
% 21.25/5.51 | (173) all_42_0_51 = 0
% 21.25/5.51 |
% 21.25/5.52 | Equations (173) can reduce 151 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (219) all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (219) yields:
% 21.25/5.52 | (214) all_57_1_57 = 0
% 21.25/5.52 | (178) all_40_0_50 = 0
% 21.25/5.52 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (178) can reduce 148 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (224) ~ (all_57_1_57 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (224) yields:
% 21.25/5.52 | (225) ~ (all_57_1_57 = 0)
% 21.25/5.52 | (226) convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (167), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (227) (all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (227), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (228) all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (228) yields:
% 21.25/5.52 | (229) all_62_0_63 = 0
% 21.25/5.52 | (230) all_62_1_64 = 0
% 21.25/5.52 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 | (232) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_3_3, all_0_1_1, 0, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, convergent_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 21.25/5.52 | (178) all_40_0_50 = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (178) can reduce 148 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (235) all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (235) yields:
% 21.25/5.52 | (230) all_62_1_64 = 0
% 21.25/5.52 | (173) all_42_0_51 = 0
% 21.25/5.52 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (173) can reduce 151 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (240) ~ (all_62_1_64 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (240) yields:
% 21.25/5.52 | (241) ~ (all_62_1_64 = 0)
% 21.25/5.52 | (242) convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_57_1_57, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57, yields:
% 21.25/5.52 | (243) all_62_1_64 = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_53_0_52, all_57_1_57 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57, convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, yields:
% 21.25/5.52 | (244) all_57_1_57 = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, 0, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.25/5.52 | (230) all_62_1_64 = 0
% 21.25/5.52 |
% 21.25/5.52 | Combining equations (243,230) yields a new equation:
% 21.25/5.52 | (246) all_57_1_57 = 0
% 21.25/5.52 |
% 21.25/5.52 | Simplifying 246 yields:
% 21.25/5.52 | (214) all_57_1_57 = 0
% 21.25/5.52 |
% 21.25/5.52 | Combining equations (244,214) yields a new equation:
% 21.25/5.52 | (313) all_53_0_52 = 0
% 21.25/5.52 |
% 21.25/5.52 | Simplifying 313 yields:
% 21.25/5.52 | (172) all_53_0_52 = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (172) can reduce 182 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (316) ~ (all_61_1_62 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (316) yields:
% 21.25/5.52 | (317) ~ (all_61_1_62 = 0)
% 21.25/5.52 | (318) convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (165), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (211) (all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0)
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (211), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (212) all_57_0_56 = 0 & all_57_1_57 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (212) yields:
% 21.25/5.52 | (213) all_57_0_56 = 0
% 21.25/5.52 | (214) all_57_1_57 = 0
% 21.25/5.52 | (215) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (80) with all_0_3_3, all_0_2_2, all_56_0_55, all_42_0_51 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_42_0_51, yields:
% 21.25/5.52 | (280) all_56_0_55 = all_42_0_51
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (80) with all_0_3_3, all_0_2_2, 0, all_56_0_55 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_56_0_55, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.25/5.52 | (196) all_56_0_55 = 0
% 21.25/5.52 |
% 21.25/5.52 | Combining equations (196,280) yields a new equation:
% 21.25/5.52 | (173) all_42_0_51 = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (173) can reduce 151 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (219) all_57_1_57 = 0 & all_40_0_50 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (219) yields:
% 21.25/5.52 | (214) all_57_1_57 = 0
% 21.25/5.52 | (178) all_40_0_50 = 0
% 21.25/5.52 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (178) can reduce 148 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (224) ~ (all_57_1_57 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (224) yields:
% 21.25/5.52 | (225) ~ (all_57_1_57 = 0)
% 21.25/5.52 | (226) convergent_lines(all_0_2_2, all_0_1_1) = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (167), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (227) (all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0) | (all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (227), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (228) all_62_0_63 = 0 & all_62_1_64 = 0 & unorthogonal_lines(all_0_3_3, all_0_1_1) = 0 & convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (228) yields:
% 21.25/5.52 | (229) all_62_0_63 = 0
% 21.25/5.52 | (230) all_62_1_64 = 0
% 21.25/5.52 | (179) unorthogonal_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 | (232) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_3_3, all_0_1_1, 0, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, convergent_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 21.25/5.52 | (178) all_40_0_50 = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (178) can reduce 148 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (235) all_62_1_64 = 0 & all_42_0_51 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (235) yields:
% 21.25/5.52 | (230) all_62_1_64 = 0
% 21.25/5.52 | (173) all_42_0_51 = 0
% 21.25/5.52 | (168) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 21.25/5.52 |
% 21.25/5.52 | Equations (173) can reduce 151 to:
% 21.25/5.52 | (175) $false
% 21.25/5.52 |
% 21.25/5.52 |-The branch is then unsatisfiable
% 21.25/5.52 |-Branch two:
% 21.25/5.52 | (240) ~ (all_62_1_64 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.25/5.52 |
% 21.25/5.52 | Applying alpha-rule on (240) yields:
% 21.25/5.52 | (241) ~ (all_62_1_64 = 0)
% 21.25/5.52 | (242) convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_61_1_62, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = all_61_1_62, yields:
% 21.25/5.52 | (353) all_62_1_64 = all_61_1_62
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_57_1_57, 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_57_1_57, yields:
% 21.25/5.52 | (354) all_61_1_62 = all_57_1_57
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (68) with all_0_2_2, all_0_1_1, all_53_0_52, all_62_1_64 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_62_1_64, convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, yields:
% 21.25/5.52 | (355) all_62_1_64 = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Combining equations (353,355) yields a new equation:
% 21.25/5.52 | (356) all_61_1_62 = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Simplifying 356 yields:
% 21.25/5.52 | (357) all_61_1_62 = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Combining equations (357,354) yields a new equation:
% 21.25/5.52 | (244) all_57_1_57 = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Equations (244) can reduce 225 to:
% 21.25/5.52 | (182) ~ (all_53_0_52 = 0)
% 21.25/5.52 |
% 21.25/5.52 | From (244) and (226) follows:
% 21.25/5.52 | (188) convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (39) with all_53_0_52, all_40_0_50, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, yields:
% 21.25/5.52 | (361) all_53_0_52 = 0 | all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (129) with all_53_0_52, all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, yields:
% 21.25/5.52 | (362) all_53_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (69) with all_53_0_52, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.25/5.52 | (363) all_53_0_52 = 0 | convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 | Instantiating formula (107) with all_53_0_52, all_94_0_79, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_53_0_52, distinct_lines(all_0_3_3, all_0_1_1) = all_94_0_79, yields:
% 21.25/5.52 | (364) all_94_0_79 = 0 | all_53_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0)
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (363), into two cases.
% 21.25/5.52 |-Branch one:
% 21.25/5.52 | (232) convergent_lines(all_0_3_3, all_0_1_1) = 0
% 21.25/5.52 |
% 21.25/5.52 +-Applying beta-rule and splitting (364), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (366) all_94_0_79 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (366) can reduce 262 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (262) ~ (all_94_0_79 = 0)
% 21.25/5.53 | (369) all_53_0_52 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0)
% 21.25/5.53 |
% 21.25/5.53 +-Applying beta-rule and splitting (369), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (172) all_53_0_52 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (172) can reduce 182 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (182) ~ (all_53_0_52 = 0)
% 21.25/5.53 | (373) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0)
% 21.25/5.53 |
% 21.25/5.53 +-Applying beta-rule and splitting (362), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (172) all_53_0_52 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (172) can reduce 182 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (182) ~ (all_53_0_52 = 0)
% 21.25/5.53 | (377) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0)
% 21.25/5.53 |
% 21.25/5.53 +-Applying beta-rule and splitting (361), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (172) all_53_0_52 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (172) can reduce 182 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (182) ~ (all_53_0_52 = 0)
% 21.25/5.53 | (381) all_40_0_50 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)
% 21.25/5.53 |
% 21.25/5.53 +-Applying beta-rule and splitting (381), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (178) all_40_0_50 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (178) can reduce 148 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (148) ~ (all_40_0_50 = 0)
% 21.25/5.53 | (385) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)
% 21.25/5.53 |
% 21.25/5.53 | Instantiating formula (68) with all_0_3_3, all_0_1_1, 0, all_40_0_50 and discharging atoms convergent_lines(all_0_3_3, all_0_1_1) = all_40_0_50, convergent_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 21.25/5.53 | (178) all_40_0_50 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (178) can reduce 148 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (388) ~ (convergent_lines(all_0_3_3, all_0_1_1) = 0)
% 21.25/5.53 | (172) all_53_0_52 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (172) can reduce 182 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (391) ~ (all_56_0_55 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_56_0_55
% 21.25/5.53 |
% 21.25/5.53 | Applying alpha-rule on (391) yields:
% 21.25/5.53 | (251) ~ (all_56_0_55 = 0)
% 21.25/5.53 | (393) convergent_lines(all_0_3_3, all_0_2_2) = all_56_0_55
% 21.25/5.53 |
% 21.25/5.53 | Instantiating formula (68) with all_0_3_3, all_0_2_2, 0, all_56_0_55 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_56_0_55, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 21.25/5.53 | (196) all_56_0_55 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (196) can reduce 251 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (396) ~ (convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 21.25/5.53 | (173) all_42_0_51 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (173) can reduce 151 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 |-Branch two:
% 21.25/5.53 | (399) ~ (unorthogonal_lines(all_0_2_2, all_0_1_1) = 0)
% 21.25/5.53 | (400) all_0_0_0 = 0
% 21.25/5.53 |
% 21.25/5.53 | Equations (400) can reduce 65 to:
% 21.25/5.53 | (175) $false
% 21.25/5.53 |
% 21.25/5.53 |-The branch is then unsatisfiable
% 21.25/5.53 % SZS output end Proof for theBenchmark
% 21.25/5.53
% 21.25/5.53 4924ms
%------------------------------------------------------------------------------