TSTP Solution File: GEO221+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:54 EDT 2022
% Result : Theorem 16.14s 4.43s
% Output : Proof 20.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jun 18 18:33:14 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.58/0.62 ____ _
% 0.58/0.62 ___ / __ \_____(_)___ ________ __________
% 0.58/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.62
% 0.58/0.62 A Theorem Prover for First-Order Logic
% 0.58/0.62 (ePrincess v.1.0)
% 0.58/0.62
% 0.58/0.62 (c) Philipp Rümmer, 2009-2015
% 0.58/0.62 (c) Peter Backeman, 2014-2015
% 0.58/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.62 Bug reports to peter@backeman.se
% 0.58/0.62
% 0.58/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.62
% 0.58/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.95/1.02 Prover 0: Preprocessing ...
% 2.56/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.56/1.27 Prover 0: Constructing countermodel ...
% 13.63/3.92 Prover 0: gave up
% 13.63/3.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 13.63/3.96 Prover 1: Preprocessing ...
% 14.40/4.08 Prover 1: Constructing countermodel ...
% 14.77/4.12 Prover 1: gave up
% 14.77/4.12 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.77/4.15 Prover 2: Preprocessing ...
% 15.69/4.33 Prover 2: Warning: ignoring some quantifiers
% 15.69/4.33 Prover 2: Constructing countermodel ...
% 16.14/4.43 Prover 2: proved (306ms)
% 16.14/4.43
% 16.14/4.43 No countermodel exists, formula is valid
% 16.14/4.43 % SZS status Theorem for theBenchmark
% 16.14/4.43
% 16.14/4.43 Generating proof ... Warning: ignoring some quantifiers
% 19.57/5.22 found it (size 167)
% 19.57/5.22
% 19.57/5.22 % SZS output start Proof for theBenchmark
% 19.57/5.22 Assumed formulas after preprocessing and simplification:
% 19.57/5.22 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v1, v3) = 0 & equal_lines(v3, v4) = v5 & orthogonal_through_point(v2, v1) = v4 & orthogonal_through_point(v2, v0) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7)
% 19.72/5.30 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 19.72/5.30 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_2_2) = 0 & equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_1_1 & orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 & ! [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
% 20.15/5.34 |
% 20.15/5.34 | Applying alpha-rule on (1) yields:
% 20.15/5.34 | (2) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 20.15/5.34 | (3) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 20.15/5.34 | (4) ! [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)))
% 20.15/5.34 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 20.15/5.34 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 20.15/5.34 | (7) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 20.15/5.34 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 20.15/5.34 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.15/5.34 | (10) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 20.15/5.34 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 20.15/5.34 | (12) equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 20.15/5.34 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 20.15/5.34 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 20.15/5.34 | (15) ! [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)))
% 20.15/5.34 | (16) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 20.15/5.34 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 20.15/5.34 | (18) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 20.15/5.34 | (19) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 20.15/5.34 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 20.15/5.34 | (21) ! [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)))
% 20.15/5.34 | (22) ! [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)))
% 20.15/5.34 | (23) ! [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)
% 20.15/5.34 | (24) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 20.15/5.34 | (25) ! [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)))
% 20.15/5.34 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 20.15/5.35 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 20.15/5.35 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 20.15/5.35 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 20.15/5.35 | (30) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 20.15/5.35 | (31) orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_1_1
% 20.15/5.35 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 20.15/5.35 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 20.15/5.35 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.15/5.35 | (35) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 20.15/5.35 | (36) ! [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)))
% 20.15/5.35 | (37) ! [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)))
% 20.15/5.35 | (38) ! [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)))
% 20.15/5.35 | (39) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 20.15/5.35 | (40) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 20.15/5.35 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 20.15/5.35 | (42) ! [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)
% 20.15/5.35 | (43) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 20.15/5.35 | (44) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 20.15/5.35 | (45) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2
% 20.15/5.35 | (46) ! [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)))
% 20.15/5.35 | (47) ! [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)))
% 20.15/5.35 | (48) ! [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)))
% 20.15/5.35 | (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)))
% 20.15/5.35 | (50) ! [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))
% 20.15/5.35 | (51) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 20.15/5.35 | (52) ! [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)))
% 20.15/5.35 | (53) ! [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))
% 20.15/5.35 | (54) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 20.15/5.35 | (55) ! [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)))
% 20.15/5.35 | (56) ? [v0] : ? [v1] : line(v0) = v1
% 20.15/5.35 | (57) ! [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)))
% 20.15/5.36 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 20.15/5.36 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 20.15/5.36 | (60) ! [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)))
% 20.15/5.36 | (61) ! [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)))
% 20.15/5.36 | (62) ! [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)))
% 20.15/5.36 | (63) ! [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)))
% 20.15/5.36 | (64) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 20.15/5.36 | (65) ! [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)))
% 20.15/5.36 | (66) ! [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)))
% 20.15/5.36 | (67) ! [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)))
% 20.15/5.36 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 20.15/5.36 | (69) ~ (all_0_0_0 = 0)
% 20.15/5.36 | (70) ! [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)))
% 20.15/5.36 | (71) ! [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))
% 20.15/5.36 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 20.15/5.36 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 20.15/5.36 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 20.15/5.36 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 20.15/5.36 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 20.15/5.36 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 20.15/5.36 | (78) ! [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)))
% 20.15/5.36 | (79) ! [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)))
% 20.15/5.36 | (80) ! [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)))
% 20.15/5.36 | (81) ! [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)))
% 20.15/5.36 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 20.15/5.36 | (83) ! [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))
% 20.15/5.36 | (84) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 20.15/5.36 | (85) ! [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)))
% 20.15/5.36 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 20.15/5.36 | (87) ! [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)))
% 20.15/5.37 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 20.15/5.37 | (89) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 20.15/5.37 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 20.15/5.37 | (91) ! [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)))
% 20.15/5.37 | (92) ! [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)))
% 20.15/5.37 | (93) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 20.15/5.37 | (94) ! [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)))
% 20.15/5.37 | (95) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 20.15/5.37 | (96) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 20.15/5.37 | (97) ! [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)))
% 20.15/5.37 | (98) ! [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)))
% 20.15/5.37 | (99) ! [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)))
% 20.15/5.37 | (100) ! [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)))
% 20.15/5.37 | (101) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 20.15/5.37 | (102) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 20.15/5.37 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 20.15/5.37 | (104) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 20.15/5.37 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 20.15/5.37 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 20.15/5.37 | (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)))
% 20.15/5.37 | (108) ! [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)))
% 20.15/5.37 | (109) ! [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)))
% 20.15/5.37 | (110) ! [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)
% 20.15/5.37 | (111) ! [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)))
% 20.15/5.37 | (112) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 20.15/5.37 | (113) ! [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)))
% 20.15/5.37 | (114) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 20.15/5.37 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 20.15/5.37 | (116) ! [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))
% 20.15/5.37 | (117) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 20.15/5.37 | (118) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 20.15/5.37 | (119) ! [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)))
% 20.15/5.37 | (120) ! [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))
% 20.15/5.37 | (121) incident_point_and_line(all_0_4_4, all_0_2_2) = 0
% 20.15/5.38 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 20.15/5.38 | (123) ! [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)))
% 20.15/5.38 | (124) ! [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))
% 20.15/5.38 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 20.15/5.38 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 20.15/5.38 | (127) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 20.15/5.38 | (128) ! [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)
% 20.15/5.38 | (129) ! [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)))
% 20.15/5.38 | (130) ! [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)))
% 20.15/5.38 | (131) ! [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)))
% 20.15/5.38 | (132) ! [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)))
% 20.15/5.38 | (133) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 20.15/5.38 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 20.15/5.38 | (135) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 20.15/5.38 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 20.15/5.38 | (137) ! [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)))
% 20.15/5.38 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 20.15/5.38 | (139) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 20.15/5.38 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 20.15/5.38 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 20.15/5.38 | (142) ? [v0] : ? [v1] : point(v0) = v1
% 20.15/5.38 | (143) ! [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)))
% 20.15/5.38 | (144) ! [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)))
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (96) with all_0_2_2, all_0_4_4 and discharging atoms incident_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 20.15/5.38 | (145) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0)
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (14) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 20.15/5.38 | (146) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (68) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 20.15/5.38 | (147) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_1_1, all_0_3_3) = v0)
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (77) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 20.15/5.38 | (148) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = v0)
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (68) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 20.15/5.38 | (149) ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (77) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 20.15/5.38 | (150) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 20.15/5.38 |
% 20.15/5.38 | Instantiating (150) with all_41_0_53 yields:
% 20.15/5.38 | (151) ~ (all_41_0_53 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53
% 20.15/5.38 |
% 20.15/5.38 | Applying alpha-rule on (151) yields:
% 20.15/5.38 | (152) ~ (all_41_0_53 = 0)
% 20.15/5.38 | (153) apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53
% 20.15/5.38 |
% 20.15/5.38 | Instantiating (149) with all_43_0_54 yields:
% 20.15/5.38 | (154) ~ (all_43_0_54 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54
% 20.15/5.38 |
% 20.15/5.38 | Applying alpha-rule on (154) yields:
% 20.15/5.38 | (155) ~ (all_43_0_54 = 0)
% 20.15/5.38 | (156) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54
% 20.15/5.38 |
% 20.15/5.38 | Instantiating (148) with all_46_0_56 yields:
% 20.15/5.38 | (157) ~ (all_46_0_56 = 0) & apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56
% 20.15/5.38 |
% 20.15/5.38 | Applying alpha-rule on (157) yields:
% 20.15/5.38 | (158) ~ (all_46_0_56 = 0)
% 20.15/5.38 | (159) apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56
% 20.15/5.38 |
% 20.15/5.38 | Instantiating (145) with all_48_0_57 yields:
% 20.15/5.38 | (160) ~ (all_48_0_57 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57
% 20.15/5.38 |
% 20.15/5.38 | Applying alpha-rule on (160) yields:
% 20.15/5.38 | (161) ~ (all_48_0_57 = 0)
% 20.15/5.38 | (162) apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57
% 20.15/5.38 |
% 20.15/5.38 | Instantiating (147) with all_50_0_58 yields:
% 20.15/5.38 | (163) ~ (all_50_0_58 = 0) & unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58
% 20.15/5.38 |
% 20.15/5.38 | Applying alpha-rule on (163) yields:
% 20.15/5.38 | (164) ~ (all_50_0_58 = 0)
% 20.15/5.38 | (165) unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58
% 20.15/5.38 |
% 20.15/5.38 +-Applying beta-rule and splitting (146), into two cases.
% 20.15/5.38 |-Branch one:
% 20.15/5.38 | (166) distinct_lines(all_0_2_2, all_0_1_1) = 0
% 20.15/5.38 |
% 20.15/5.38 | Instantiating formula (116) with all_50_0_58, all_50_0_58, all_0_3_3, all_0_3_3, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58, yields:
% 20.15/5.38 | (167) all_50_0_58 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 20.15/5.39 |
% 20.15/5.39 | Instantiating formula (65) with all_50_0_58, all_46_0_56, all_0_3_3, all_0_1_1, all_0_1_1, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58, apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, yields:
% 20.15/5.39 | (168) all_50_0_58 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 20.15/5.39 |
% 20.42/5.39 | Instantiating formula (65) with all_43_0_54, all_46_0_56, all_0_3_3, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, yields:
% 20.42/5.39 | (169) all_46_0_56 = 0 | all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (65) with all_50_0_58, all_48_0_57, all_0_3_3, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (170) all_50_0_58 = 0 | all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (80) with all_50_0_58, all_48_0_57, all_0_3_3, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (171) all_50_0_58 = 0 | all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (65) with all_43_0_54, all_48_0_57, all_0_3_3, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (172) all_48_0_57 = 0 | all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (92) with all_48_0_57, all_46_0_56, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (173) all_48_0_57 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_48_0_57, all_46_0_56, all_0_2_2, all_0_1_1, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (174) all_48_0_57 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_46_0_56, all_48_0_57, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (175) all_48_0_57 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (92) with all_48_0_57, all_48_0_57, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (176) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_48_0_57, all_48_0_57, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, yields:
% 20.42/5.39 | (177) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (65) with all_43_0_54, all_41_0_53, all_0_3_3, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (178) all_43_0_54 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_41_0_53, all_46_0_56, all_0_2_2, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (179) all_46_0_56 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_46_0_56, all_41_0_53, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (180) all_46_0_56 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (15) with all_41_0_53, all_46_0_56, all_0_1_1, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (181) all_46_0_56 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (15) with all_46_0_56, all_41_0_53, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (182) all_46_0_56 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_41_0_53, all_48_0_57, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (183) all_48_0_57 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (62) with all_48_0_57, all_41_0_53, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, yields:
% 20.42/5.39 | (184) all_48_0_57 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (48) with all_50_0_58, all_46_0_56, all_0_3_3, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_3_3) = all_50_0_58, apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (185) all_50_0_58 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (81) with all_43_0_54, all_48_0_57, all_0_3_3, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (186) all_48_0_57 = 0 | all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (81) with all_43_0_54, all_41_0_53, all_0_3_3, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (187) all_43_0_54 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (38) with all_46_0_56, all_46_0_56, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = all_46_0_56, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (188) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (100) with all_48_0_57, all_48_0_57, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (189) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (100) with all_48_0_57, all_41_0_53, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (190) all_48_0_57 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.39 |
% 20.42/5.39 | Instantiating formula (100) with all_41_0_53, all_48_0_57, all_0_1_1, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_41_0_53, distinct_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 20.42/5.39 | (191) all_48_0_57 = 0 | all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (189), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (195) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (184), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (199) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (179), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (203) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (180), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (207) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (181), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (211) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (182), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (215) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (183), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (219) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (190), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (223) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (176), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (227) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (167), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (228) all_50_0_58 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (228) can reduce 164 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.40 | (231) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (185), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (228) all_50_0_58 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (228) can reduce 164 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.40 | (235) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (188), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (239) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (235), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (243) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 20.42/5.40 |
% 20.42/5.40 | Instantiating (243) with all_150_0_73 yields:
% 20.42/5.40 | (244) (all_150_0_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_150_0_73 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (244), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (245) all_150_0_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 20.42/5.40 |
% 20.42/5.40 | Applying alpha-rule on (245) yields:
% 20.42/5.40 | (246) all_150_0_73 = 0
% 20.42/5.40 | (247) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (168), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (228) all_50_0_58 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (228) can reduce 164 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.40 | (251) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (169), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (200) all_46_0_56 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (200) can reduce 158 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (158) ~ (all_46_0_56 = 0)
% 20.42/5.40 | (255) all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.40 |
% 20.42/5.40 +-Applying beta-rule and splitting (191), into two cases.
% 20.42/5.40 |-Branch one:
% 20.42/5.40 | (192) all_48_0_57 = 0
% 20.42/5.40 |
% 20.42/5.40 | Equations (192) can reduce 161 to:
% 20.42/5.40 | (193) $false
% 20.42/5.40 |
% 20.42/5.40 |-The branch is then unsatisfiable
% 20.42/5.40 |-Branch two:
% 20.42/5.40 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.40 | (259) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.40 |
% 20.42/5.41 +-Applying beta-rule and splitting (187), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (260) all_43_0_54 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (260) can reduce 155 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (155) ~ (all_43_0_54 = 0)
% 20.42/5.41 | (263) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (173), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (267) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (171), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (228) all_50_0_58 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (228) can reduce 164 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.41 | (271) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (271), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (275) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (177), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (279) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (172), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (283) all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (178), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (260) all_43_0_54 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (260) can reduce 155 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (155) ~ (all_43_0_54 = 0)
% 20.42/5.41 | (287) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (283), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (260) all_43_0_54 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (260) can reduce 155 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (155) ~ (all_43_0_54 = 0)
% 20.42/5.41 | (291) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (255), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (260) all_43_0_54 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (260) can reduce 155 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (155) ~ (all_43_0_54 = 0)
% 20.42/5.41 | (295) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 | Instantiating formula (76) with all_0_2_2, all_0_3_3, 0, all_43_0_54 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_43_0_54, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields:
% 20.42/5.41 | (260) all_43_0_54 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (260) can reduce 155 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (298) all_150_0_73 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 20.42/5.41 |
% 20.42/5.41 | Applying alpha-rule on (298) yields:
% 20.42/5.41 | (246) all_150_0_73 = 0
% 20.42/5.41 | (300) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (168), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (228) all_50_0_58 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (228) can reduce 164 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.41 | (251) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (191), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (259) all_41_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (170), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (228) all_50_0_58 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (228) can reduce 164 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.41 | (312) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (173), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (267) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (171), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (228) all_50_0_58 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (228) can reduce 164 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (164) ~ (all_50_0_58 = 0)
% 20.42/5.41 | (271) all_48_0_57 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (174), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (324) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (186), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (328) all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (172), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.41 | (283) all_43_0_54 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 20.42/5.41 |
% 20.42/5.41 +-Applying beta-rule and splitting (312), into two cases.
% 20.42/5.41 |-Branch one:
% 20.42/5.41 | (192) all_48_0_57 = 0
% 20.42/5.41 |
% 20.42/5.41 | Equations (192) can reduce 161 to:
% 20.42/5.41 | (193) $false
% 20.42/5.41 |
% 20.42/5.41 |-The branch is then unsatisfiable
% 20.42/5.41 |-Branch two:
% 20.42/5.41 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.42 | (336) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 20.42/5.42 |
% 20.42/5.42 +-Applying beta-rule and splitting (271), into two cases.
% 20.42/5.42 |-Branch one:
% 20.42/5.42 | (192) all_48_0_57 = 0
% 20.42/5.42 |
% 20.42/5.42 | Equations (192) can reduce 161 to:
% 20.42/5.42 | (193) $false
% 20.42/5.42 |
% 20.42/5.42 |-The branch is then unsatisfiable
% 20.42/5.42 |-Branch two:
% 20.42/5.42 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.42 | (275) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 20.42/5.42 |
% 20.42/5.42 +-Applying beta-rule and splitting (177), into two cases.
% 20.42/5.42 |-Branch one:
% 20.42/5.42 | (192) all_48_0_57 = 0
% 20.42/5.42 |
% 20.42/5.42 | Equations (192) can reduce 161 to:
% 20.42/5.42 | (193) $false
% 20.42/5.42 |
% 20.42/5.42 |-The branch is then unsatisfiable
% 20.42/5.42 |-Branch two:
% 20.42/5.42 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.42 | (279) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.42 |
% 20.42/5.42 +-Applying beta-rule and splitting (175), into two cases.
% 20.42/5.42 |-Branch one:
% 20.42/5.42 | (192) all_48_0_57 = 0
% 20.42/5.42 |
% 20.42/5.42 | Equations (192) can reduce 161 to:
% 20.42/5.42 | (193) $false
% 20.42/5.42 |
% 20.42/5.42 |-The branch is then unsatisfiable
% 20.42/5.42 |-Branch two:
% 20.42/5.42 | (161) ~ (all_48_0_57 = 0)
% 20.42/5.42 | (348) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 20.42/5.42 |
% 20.42/5.42 | Instantiating formula (26) with all_0_4_4, all_0_2_2, 0, all_48_0_57 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_48_0_57, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 20.42/5.42 | (192) all_48_0_57 = 0
% 20.42/5.42 |
% 20.42/5.42 | Equations (192) can reduce 161 to:
% 20.42/5.42 | (193) $false
% 20.42/5.42 |
% 20.42/5.42 |-The branch is then unsatisfiable
% 20.42/5.42 |-Branch two:
% 20.42/5.42 | (351) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0)
% 20.42/5.42 | (352) all_0_0_0 = 0
% 20.42/5.42 |
% 20.42/5.42 | Equations (352) can reduce 69 to:
% 20.42/5.42 | (193) $false
% 20.42/5.42 |
% 20.42/5.42 |-The branch is then unsatisfiable
% 20.42/5.42 % SZS output end Proof for theBenchmark
% 20.42/5.42
% 20.42/5.42 4791ms
%------------------------------------------------------------------------------