TSTP Solution File: GEO171+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 03:48:08 EDT 2022
% Result : Theorem 19.70s 5.91s
% Output : Proof 22.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 18:29:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.62 ____ _
% 0.56/0.62 ___ / __ \_____(_)___ ________ __________
% 0.56/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.62
% 0.56/0.62 A Theorem Prover for First-Order Logic
% 0.56/0.62 (ePrincess v.1.0)
% 0.56/0.62
% 0.56/0.62 (c) Philipp Rümmer, 2009-2015
% 0.56/0.62 (c) Peter Backeman, 2014-2015
% 0.56/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.62 Bug reports to peter@backeman.se
% 0.56/0.62
% 0.56/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.62
% 0.56/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.03 Prover 0: Preprocessing ...
% 2.48/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.48/1.27 Prover 0: Constructing countermodel ...
% 16.98/5.28 Prover 0: gave up
% 16.98/5.28 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.98/5.31 Prover 1: Preprocessing ...
% 17.88/5.44 Prover 1: Constructing countermodel ...
% 17.88/5.46 Prover 1: gave up
% 17.88/5.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.28/5.49 Prover 2: Preprocessing ...
% 18.80/5.66 Prover 2: Warning: ignoring some quantifiers
% 18.80/5.67 Prover 2: Constructing countermodel ...
% 19.70/5.91 Prover 2: proved (447ms)
% 19.70/5.91
% 19.70/5.91 No countermodel exists, formula is valid
% 19.70/5.91 % SZS status Theorem for theBenchmark
% 19.70/5.91
% 19.70/5.91 Generating proof ... Warning: ignoring some quantifiers
% 22.38/6.41 found it (size 39)
% 22.38/6.41
% 22.38/6.41 % SZS output start Proof for theBenchmark
% 22.38/6.41 Assumed formulas after preprocessing and simplification:
% 22.38/6.41 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v0, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (apart_point_and_line(v3, v5) = v7) | ~ (distinct_lines(v4, v5) = 0) | ? [v9] : ((v9 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v4) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (apart_point_and_line(v3, v4) = v7) | ? [v9] : ((v9 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v8) | ~ (apart_point_and_line(v3, v5) = v7) | ? [v9] : ((v9 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unorthogonal_lines(v4, v6) = v8) | ~ (apart_point_and_line(v3, v4) = v7) | ~ (distinct_lines(v4, v5) = 0) | ? [v9] : ((v9 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (apart_point_and_line(v4, v5) = v7) | ~ (distinct_points(v3, v4) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v3, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (apart_point_and_line(v3, v6) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v6) = v8) | ~ (apart_point_and_line(v3, v5) = v7) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | (v9 = 0 & apart_point_and_line(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v5) = v8) | ~ (apart_point_and_line(v3, v6) = v7) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v4, v5) = v8) | ~ (apart_point_and_line(v3, v5) = v7) | ~ (distinct_lines(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (apart_point_and_line(v3, v6) = v8) | ~ (apart_point_and_line(v3, v5) = v7) | ~ (distinct_points(v3, v4) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v3, v5) = v7) | ~ (unorthogonal_lines(v3, v4) = v6) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v5, v4) = v7) | ~ (distinct_points(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v3, v4) = v6) | ? [v8] : ((v8 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (distinct_lines(v4, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v6) | ~ (convergent_lines(v4, v5) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v6) | ~ (convergent_lines(v4, v5) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (convergent_lines(v4, v5) = v7) | ~ (convergent_lines(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (convergent_lines(v3, v5) = v7) | ~ (distinct_lines(v4, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = v7) | ~ (distinct_lines(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_points(v4, v5) = v7) | ~ (distinct_points(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = v7) | ~ (unorthogonal_lines(v3, v5) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = v7) | ~ (convergent_lines(v3, v5) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v7) | ~ (unorthogonal_lines(v3, v4) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v7) | ~ (convergent_lines(v3, v4) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v6) | ~ (convergent_lines(v4, v5) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v3, v4) = v6) | ~ (convergent_lines(v3, v5) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v4, v5) = v7) | ~ (convergent_lines(v3, v5) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (convergent_lines(v3, v5) = v7) | ~ (convergent_lines(v3, v4) = v6) | ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v3, v5) = v6) | ~ (convergent_lines(v4, v5) = 0) | unorthogonal_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unorthogonal_lines(v3, v4) = v6) | ~ (convergent_lines(v4, v5) = 0) | unorthogonal_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v5, v4) = v6) | ~ (apart_point_and_line(v3, v4) = 0) | distinct_points(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v3, v5) = v6) | ~ (apart_point_and_line(v3, v4) = 0) | distinct_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v3, v5) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v7] : ((v7 = 0 & apart_point_and_line(v3, v4) = 0) | (v7 = 0 & convergent_lines(v4, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v3, v4) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v7] : ((v7 = 0 & apart_point_and_line(v3, v5) = 0) | (v7 = 0 & convergent_lines(v4, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v3, v4) = 0) | ~ (distinct_lines(v4, v5) = v6) | apart_point_and_line(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v3, v4) = 0) | ~ (distinct_points(v3, v5) = v6) | apart_point_and_line(v5, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | convergent_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v3, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | convergent_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v3, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | distinct_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v3, v4) = 0) | ~ (distinct_lines(v4, v5) = v6) | convergent_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v4, v5) = v6) | ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v3, v5) = v6) | ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v4, v5) = v6) | ~ (distinct_points(v3, v4) = 0) | distinct_points(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v3, v5) = v6) | ~ (distinct_points(v3, v4) = 0) | distinct_points(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (orthogonal_lines(v6, v5) = v4) | ~ (orthogonal_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (incident_point_and_line(v6, v5) = v4) | ~ (incident_point_and_line(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (parallel_lines(v6, v5) = v4) | ~ (parallel_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_lines(v6, v5) = v4) | ~ (equal_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_points(v6, v5) = v4) | ~ (equal_points(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (orthogonal_through_point(v6, v5) = v4) | ~ (orthogonal_through_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unorthogonal_lines(v6, v5) = v4) | ~ (unorthogonal_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (parallel_through_point(v6, v5) = v4) | ~ (parallel_through_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection_point(v6, v5) = v4) | ~ (intersection_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (line_connecting(v6, v5) = v4) | ~ (line_connecting(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (apart_point_and_line(v6, v5) = v4) | ~ (apart_point_and_line(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (convergent_lines(v6, v5) = v4) | ~ (convergent_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (distinct_lines(v6, v5) = v4) | ~ (distinct_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (distinct_points(v6, v5) = v4) | ~ (distinct_points(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = v6) | ~ (unorthogonal_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (unorthogonal_lines(v3, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (unorthogonal_lines(v3, v4) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (convergent_lines(v3, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) | ~ (convergent_lines(v3, v4) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) | ~ (unorthogonal_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) | ~ (convergent_lines(v4, v5) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) | ~ (convergent_lines(v4, v5) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (convergent_lines(v4, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (convergent_lines(v3, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v4, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v4, v5) = 0) | ~ (convergent_lines(v3, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v4, v5) = 0) | ~ (convergent_lines(v3, v4) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v3, v5) = v6) | ~ (convergent_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) | ~ (distinct_points(v3, v4) = 0) | ? [v7] : ((v7 = 0 & apart_point_and_line(v4, v6) = 0) | (v7 = 0 & apart_point_and_line(v4, v5) = 0) | (v7 = 0 & apart_point_and_line(v3, v6) = 0) | (v7 = 0 & apart_point_and_line(v3, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (orthogonal_lines(v3, v4) = v5) | unorthogonal_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (incident_point_and_line(v3, v4) = v5) | apart_point_and_line(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (parallel_lines(v3, v4) = v5) | convergent_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_lines(v3, v4) = v5) | distinct_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_points(v3, v4) = v5) | distinct_points(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unorthogonal_lines(v3, v4) = v5) | orthogonal_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unorthogonal_lines(v3, v4) = v5) | convergent_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v3, v4) = v5) | incident_point_and_line(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | parallel_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | unorthogonal_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & distinct_lines(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | equal_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v3, v4) = v5) | equal_points(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (point(v5) = v4) | ~ (point(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (line(v5) = v4) | ~ (line(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (orthogonal_through_point(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & unorthogonal_lines(v5, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (orthogonal_through_point(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (orthogonal_through_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & convergent_lines(v5, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & point(v5) = 0) | ( ~ (v6 = 0) & line(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v5, v4) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v5, v3) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & point(v3) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v4, v5) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ( ~ (orthogonal_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & unorthogonal_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (parallel_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (equal_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (equal_points(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & orthogonal_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & intersection_point(v3, v4) = v5 & apart_point_and_line(v5, v4) = v6)) & ! [v3] : ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & intersection_point(v3, v4) = v5 & apart_point_and_line(v5, v3) = v6)) & ! [v3] : ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & point(v5) = 0 & intersection_point(v3, v4) = v5) | ( ~ (v5 = 0) & line(v4) = v5) | ( ~ (v5 = 0) & line(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & parallel_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (distinct_lines(v3, v4) = 0) | convergent_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (distinct_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & equal_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & line_connecting(v3, v4) = v5 & apart_point_and_line(v4, v5) = v6)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & line_connecting(v3, v4) = v5 & apart_point_and_line(v3, v5) = v6)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & line(v5) = 0 & line_connecting(v3, v4) = v5) | ( ~ (v5 = 0) & point(v4) = v5) | ( ~ (v5 = 0) & point(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & equal_points(v3, v4) = v5)) & ! [v3] : ~ (convergent_lines(v3, v3) = 0) & ! [v3] : ~ (distinct_lines(v3, v3) = 0) & ! [v3] : ~ (distinct_points(v3, v3) = 0) & ? [v3] : ? [v4] : ? [v5] : orthogonal_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : incident_point_and_line(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : parallel_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : equal_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : equal_points(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : orthogonal_through_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : unorthogonal_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : parallel_through_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : intersection_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : line_connecting(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : apart_point_and_line(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : convergent_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : distinct_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : distinct_points(v4, v3) = v5 & ? [v3] : ? [v4] : point(v3) = v4 & ? [v3] : ? [v4] : line(v3) = v4)
% 22.38/6.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 22.38/6.47 | (1) ~ (all_0_0_0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = 0 & distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_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
% 22.80/6.50 |
% 22.80/6.50 | Applying alpha-rule on (1) yields:
% 22.80/6.50 | (2) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 22.80/6.50 | (3) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 22.80/6.50 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 22.80/6.50 | (5) ! [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)
% 22.80/6.50 | (6) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 22.80/6.50 | (7) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 22.80/6.50 | (8) ? [v0] : ? [v1] : line(v0) = v1
% 22.80/6.50 | (9) ! [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)
% 22.80/6.50 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 22.80/6.50 | (11) ! [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)))
% 22.80/6.50 | (12) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 22.80/6.50 | (13) ! [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)
% 22.80/6.50 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 22.80/6.50 | (15) ! [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)))
% 22.80/6.50 | (16) ! [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)))
% 22.80/6.50 | (17) ! [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)))
% 22.80/6.50 | (18) ! [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)))
% 22.80/6.50 | (19) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 22.80/6.50 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 22.80/6.50 | (21) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.80/6.50 | (22) ! [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)))
% 22.80/6.50 | (23) ! [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)))
% 22.80/6.50 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 22.80/6.50 | (25) ! [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)))
% 22.80/6.50 | (26) ! [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)))
% 22.80/6.50 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 22.80/6.50 | (28) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 22.80/6.50 | (29) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 22.80/6.50 | (30) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 22.80/6.50 | (31) ! [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)))
% 22.80/6.50 | (32) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 22.80/6.50 | (33) ! [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)))
% 22.80/6.51 | (34) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 22.80/6.51 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 22.80/6.51 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.51 | (37) ! [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)))
% 22.80/6.51 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 22.80/6.51 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.80/6.51 | (40) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 22.80/6.51 | (41) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 22.80/6.51 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 22.80/6.51 | (43) ! [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))
% 22.80/6.51 | (44) ! [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)))
% 22.80/6.51 | (45) ! [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)))
% 22.80/6.51 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.80/6.51 | (47) ! [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)))
% 22.80/6.51 | (48) ! [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))
% 22.80/6.51 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 22.80/6.51 | (50) ! [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)))
% 22.80/6.51 | (51) ! [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)))
% 22.80/6.51 | (52) ! [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)))
% 22.80/6.51 | (53) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 22.80/6.51 | (54) ! [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)))
% 22.80/6.51 | (55) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 22.80/6.51 | (56) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 22.80/6.51 | (57) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 22.80/6.51 | (58) ! [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))
% 22.80/6.51 | (59) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 22.80/6.51 | (60) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 22.80/6.51 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 22.80/6.51 | (62) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 22.80/6.51 | (63) ! [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)))
% 22.80/6.51 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.80/6.51 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 22.80/6.51 | (66) ! [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)))
% 22.80/6.51 | (67) ! [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)))
% 22.80/6.51 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 22.80/6.51 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 22.80/6.51 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 22.80/6.51 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 22.80/6.51 | (72) ! [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))
% 22.80/6.51 | (73) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 22.80/6.51 | (74) ! [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)))
% 22.80/6.51 | (75) ! [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)))
% 22.80/6.51 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 22.80/6.51 | (77) ! [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)))
% 22.80/6.51 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 22.80/6.51 | (79) ! [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)))
% 22.80/6.52 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.80/6.52 | (81) ! [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))
% 22.80/6.52 | (82) ! [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)))
% 22.80/6.52 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.80/6.52 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 22.80/6.52 | (85) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 22.80/6.52 | (86) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 22.80/6.52 | (87) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 22.80/6.52 | (88) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 22.80/6.52 | (89) ! [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)))
% 22.80/6.52 | (90) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 22.80/6.52 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 22.80/6.52 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.52 | (93) ! [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)))
% 22.80/6.52 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.80/6.52 | (95) ! [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)))
% 22.80/6.52 | (96) ! [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)))
% 22.80/6.52 | (97) ! [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)))
% 22.80/6.52 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 22.80/6.52 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 22.80/6.52 | (100) ! [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)))
% 22.80/6.52 | (101) ! [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)
% 22.80/6.52 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.52 | (103) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.80/6.52 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 22.80/6.52 | (105) ! [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)))
% 22.80/6.52 | (106) ! [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)))
% 22.80/6.52 | (107) ! [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)))
% 22.80/6.52 | (108) ! [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)))
% 22.80/6.52 | (109) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 22.80/6.52 | (110) ? [v0] : ? [v1] : point(v0) = v1
% 22.80/6.52 | (111) ! [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))
% 22.80/6.52 | (112) ~ (all_0_0_0 = 0)
% 22.80/6.52 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 22.80/6.52 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.80/6.52 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 22.80/6.52 | (116) ! [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)))
% 22.80/6.52 | (117) ! [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)))
% 22.80/6.52 | (118) ! [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)))
% 22.80/6.52 | (119) ! [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)))
% 22.80/6.52 | (120) ! [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)))
% 22.80/6.53 | (121) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 22.80/6.53 | (122) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 22.80/6.53 | (123) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 22.80/6.53 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 22.80/6.53 | (125) ! [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)))
% 22.80/6.53 | (126) ! [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)))
% 22.80/6.53 | (127) ! [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)))
% 22.80/6.53 | (128) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 22.80/6.53 | (129) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 22.80/6.53 | (130) ! [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)))
% 22.80/6.53 | (131) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 22.80/6.53 | (132) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 22.80/6.53 | (133) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 22.80/6.53 | (134) ! [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)))
% 22.80/6.53 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 22.80/6.53 | (136) distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 22.80/6.53 | (137) ! [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))
% 22.80/6.53 | (138) ! [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)))
% 22.80/6.53 | (139) ! [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)))
% 22.80/6.53 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 22.80/6.53 | (141) ! [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)))
% 22.80/6.53 | (142) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 22.80/6.53 |
% 22.80/6.53 | Instantiating formula (21) with all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 22.80/6.53 | (143) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(v0, all_0_1_1) = v1)
% 22.80/6.53 |
% 22.80/6.53 | Instantiating formula (40) with all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 22.80/6.53 | (144) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 22.80/6.53 |
% 22.80/6.53 | Instantiating formula (48) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.80/6.53 | (145) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)
% 22.80/6.53 |
% 22.80/6.53 | Instantiating (144) with all_42_0_50, all_42_1_51 yields:
% 22.80/6.53 | (146) ~ (all_42_0_50 = 0) & intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51 & apart_point_and_line(all_42_1_51, all_0_2_2) = all_42_0_50
% 22.80/6.53 |
% 22.80/6.53 | Applying alpha-rule on (146) yields:
% 22.80/6.53 | (147) ~ (all_42_0_50 = 0)
% 22.80/6.53 | (148) intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51
% 22.80/6.53 | (149) apart_point_and_line(all_42_1_51, all_0_2_2) = all_42_0_50
% 22.80/6.53 |
% 22.80/6.53 | Instantiating (143) with all_44_0_52, all_44_1_53 yields:
% 22.80/6.53 | (150) ~ (all_44_0_52 = 0) & intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53 & apart_point_and_line(all_44_1_53, all_0_1_1) = all_44_0_52
% 22.80/6.53 |
% 22.80/6.53 | Applying alpha-rule on (150) yields:
% 22.80/6.53 | (151) ~ (all_44_0_52 = 0)
% 22.80/6.53 | (152) intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53
% 22.80/6.53 | (153) apart_point_and_line(all_44_1_53, all_0_1_1) = all_44_0_52
% 22.80/6.53 |
% 22.80/6.53 +-Applying beta-rule and splitting (145), into two cases.
% 22.80/6.53 |-Branch one:
% 22.80/6.53 | (154) all_0_0_0 = 0
% 22.80/6.53 |
% 22.80/6.53 | Equations (154) can reduce 112 to:
% 22.80/6.53 | (155) $false
% 22.80/6.53 |
% 22.80/6.53 |-The branch is then unsatisfiable
% 22.80/6.53 |-Branch two:
% 22.80/6.53 | (112) ~ (all_0_0_0 = 0)
% 22.80/6.53 | (157) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)
% 22.80/6.53 |
% 22.80/6.53 | Instantiating formula (42) with all_0_2_2, all_0_1_1, all_42_1_51, all_44_1_53 and discharging atoms intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53, intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51, yields:
% 22.80/6.53 | (158) all_44_1_53 = all_42_1_51
% 22.80/6.53 |
% 22.80/6.53 | From (158) and (153) follows:
% 22.80/6.53 | (159) apart_point_and_line(all_42_1_51, all_0_1_1) = all_44_0_52
% 22.80/6.53 |
% 22.80/6.53 | Instantiating formula (125) with all_44_0_52, all_44_0_52, all_0_1_1, all_0_1_1, all_42_1_51 and discharging atoms apart_point_and_line(all_42_1_51, all_0_1_1) = all_44_0_52, yields:
% 22.80/6.53 | (160) all_44_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 22.80/6.53 |
% 22.80/6.53 +-Applying beta-rule and splitting (160), into two cases.
% 22.80/6.53 |-Branch one:
% 22.80/6.53 | (161) all_44_0_52 = 0
% 22.80/6.53 |
% 22.80/6.53 | Equations (161) can reduce 151 to:
% 22.80/6.53 | (155) $false
% 22.80/6.53 |
% 22.80/6.53 |-The branch is then unsatisfiable
% 22.80/6.53 |-Branch two:
% 22.80/6.53 | (151) ~ (all_44_0_52 = 0)
% 22.80/6.54 | (164) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 22.80/6.54 |
% 22.80/6.54 | Instantiating (164) with all_100_0_81 yields:
% 22.80/6.54 | (165) (all_100_0_81 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (all_100_0_81 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81)
% 22.80/6.54 |
% 22.80/6.54 +-Applying beta-rule and splitting (165), into two cases.
% 22.80/6.54 |-Branch one:
% 22.80/6.54 | (166) all_100_0_81 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 22.80/6.54 |
% 22.80/6.54 | Applying alpha-rule on (166) yields:
% 22.80/6.54 | (167) all_100_0_81 = 0
% 22.80/6.54 | (168) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 22.80/6.54 |
% 22.80/6.54 | Instantiating formula (34) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 22.80/6.54 | (169) $false
% 22.80/6.54 |
% 22.80/6.54 |-The branch is then unsatisfiable
% 22.80/6.54 |-Branch two:
% 22.80/6.54 | (170) ~ (all_100_0_81 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81
% 22.80/6.54 |
% 22.80/6.54 | Applying alpha-rule on (170) yields:
% 22.80/6.54 | (171) ~ (all_100_0_81 = 0)
% 22.80/6.54 | (172) distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81
% 22.80/6.54 |
% 22.80/6.54 | Instantiating formula (48) with all_0_0_0, all_100_0_81, all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81, distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.80/6.54 | (173) all_100_0_81 = 0 | all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54 |
% 22.80/6.54 +-Applying beta-rule and splitting (173), into two cases.
% 22.80/6.54 |-Branch one:
% 22.80/6.54 | (167) all_100_0_81 = 0
% 22.80/6.54 |
% 22.80/6.54 | Equations (167) can reduce 171 to:
% 22.80/6.54 | (155) $false
% 22.80/6.54 |
% 22.80/6.54 |-The branch is then unsatisfiable
% 22.80/6.54 |-Branch two:
% 22.80/6.54 | (171) ~ (all_100_0_81 = 0)
% 22.80/6.54 | (177) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54 |
% 22.80/6.54 +-Applying beta-rule and splitting (177), into two cases.
% 22.80/6.54 |-Branch one:
% 22.80/6.54 | (154) all_0_0_0 = 0
% 22.80/6.54 |
% 22.80/6.54 | Equations (154) can reduce 112 to:
% 22.80/6.54 | (155) $false
% 22.80/6.54 |
% 22.80/6.54 |-The branch is then unsatisfiable
% 22.80/6.54 |-Branch two:
% 22.80/6.54 | (112) ~ (all_0_0_0 = 0)
% 22.80/6.54 | (181) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54 |
% 22.80/6.54 | Instantiating (181) with all_211_0_94 yields:
% 22.80/6.54 | (182) ~ (all_211_0_94 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94
% 22.80/6.54 |
% 22.80/6.54 | Applying alpha-rule on (182) yields:
% 22.80/6.54 | (183) ~ (all_211_0_94 = 0)
% 22.80/6.54 | (184) distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94
% 22.80/6.54 |
% 22.80/6.54 | Instantiating formula (114) with all_211_0_94, all_0_2_2, all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94, yields:
% 22.80/6.54 | (185) all_211_0_94 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 22.80/6.54 |
% 22.80/6.54 +-Applying beta-rule and splitting (185), into two cases.
% 22.80/6.54 |-Branch one:
% 22.80/6.54 | (186) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 22.80/6.54 |
% 22.80/6.54 | Instantiating formula (34) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 22.80/6.54 | (169) $false
% 22.80/6.54 |
% 22.80/6.54 |-The branch is then unsatisfiable
% 22.80/6.54 |-Branch two:
% 22.80/6.54 | (188) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 22.80/6.54 | (189) all_211_0_94 = 0
% 22.80/6.54 |
% 22.80/6.54 | Equations (189) can reduce 183 to:
% 22.80/6.54 | (155) $false
% 22.80/6.54 |
% 22.80/6.54 |-The branch is then unsatisfiable
% 22.80/6.54 % SZS output end Proof for theBenchmark
% 22.80/6.54
% 22.80/6.54 5900ms
%------------------------------------------------------------------------------