TSTP Solution File: GEO172+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 03:48:09 EDT 2022
% Result : Theorem 20.47s 6.50s
% Output : Proof 28.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 00:39:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.64/0.63 ____ _
% 0.64/0.63 ___ / __ \_____(_)___ ________ __________
% 0.64/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.63
% 0.64/0.63 A Theorem Prover for First-Order Logic
% 0.64/0.63 (ePrincess v.1.0)
% 0.64/0.63
% 0.64/0.63 (c) Philipp Rümmer, 2009-2015
% 0.64/0.63 (c) Peter Backeman, 2014-2015
% 0.64/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.63 Bug reports to peter@backeman.se
% 0.64/0.63
% 0.64/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.63
% 0.64/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.04 Prover 0: Preprocessing ...
% 2.51/1.25 Prover 0: Warning: ignoring some quantifiers
% 2.51/1.27 Prover 0: Constructing countermodel ...
% 17.95/5.93 Prover 0: gave up
% 17.95/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.95/5.97 Prover 1: Preprocessing ...
% 18.45/6.08 Prover 1: Constructing countermodel ...
% 18.83/6.13 Prover 1: gave up
% 18.83/6.13 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.83/6.16 Prover 2: Preprocessing ...
% 19.99/6.34 Prover 2: Warning: ignoring some quantifiers
% 19.99/6.35 Prover 2: Constructing countermodel ...
% 20.47/6.50 Prover 2: proved (365ms)
% 20.47/6.50
% 20.47/6.50 No countermodel exists, formula is valid
% 20.47/6.50 % SZS status Theorem for theBenchmark
% 20.47/6.50
% 20.47/6.50 Generating proof ... Warning: ignoring some quantifiers
% 27.54/8.11 found it (size 282)
% 27.54/8.11
% 27.54/8.11 % SZS output start Proof for theBenchmark
% 27.54/8.11 Assumed formulas after preprocessing and simplification:
% 27.54/8.11 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & incident_point_and_line(v2, v1) = 0 & incident_point_and_line(v2, v0) = 0 & equal_points(v2, v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ? [v10] : ((v10 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v5, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v5, v7) = v9) | ~ (convergent_lines(v5, v6) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | unorthogonal_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v6) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v7) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_lines(v8, v7) = v6) | ~ (orthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (incident_point_and_line(v8, v7) = v6) | ~ (incident_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_lines(v8, v7) = v6) | ~ (parallel_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_lines(v8, v7) = v6) | ~ (equal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_points(v8, v7) = v6) | ~ (equal_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (unorthogonal_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = 0) | ~ (convergent_lines(v5, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (orthogonal_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (incident_point_and_line(v5, v6) = v7) | apart_point_and_line(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (parallel_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_lines(v5, v6) = v7) | distinct_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_points(v5, v6) = v7) | distinct_points(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | orthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v5, v6) = v7) | incident_point_and_line(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | parallel_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | equal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v5, v6) = v7) | equal_points(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (point(v7) = v6) | ~ (point(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (line(v7) = v6) | ~ (line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & point(v7) = 0) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v6) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & point(v5) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ( ~ (orthogonal_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unorthogonal_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (incident_point_and_line(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (parallel_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equal_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equal_points(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & orthogonal_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (apart_point_and_line(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & incident_point_and_line(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v5) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & point(v7) = 0 & intersection_point(v5, v6) = v7) | ( ~ (v7 = 0) & line(v6) = v7) | ( ~ (v7 = 0) & line(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & parallel_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equal_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & line(v7) = 0 & line_connecting(v5, v6) = v7) | ( ~ (v7 = 0) & point(v6) = v7) | ( ~ (v7 = 0) & point(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equal_points(v5, v6) = v7)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : orthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : incident_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : parallel_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equal_points(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : orthogonal_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7 & ? [v5] : ? [v6] : point(v5) = v6 & ? [v5] : ? [v6] : line(v5) = v6)
% 28.05/8.18 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 28.05/8.18 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_2_2, all_0_3_3) = 0 & incident_point_and_line(all_0_2_2, all_0_4_4) = 0 & equal_points(all_0_2_2, all_0_1_1) = all_0_0_0 & intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_4_4, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1
% 28.05/8.22 |
% 28.05/8.22 | Applying alpha-rule on (1) yields:
% 28.05/8.22 | (2) ! [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)))
% 28.05/8.22 | (3) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 28.05/8.22 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 28.05/8.22 | (5) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 28.05/8.22 | (6) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 28.05/8.22 | (7) ! [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))
% 28.05/8.22 | (8) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 28.05/8.22 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 28.05/8.22 | (10) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 28.05/8.22 | (11) ~ (all_0_0_0 = 0)
% 28.05/8.22 | (12) ! [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)))
% 28.05/8.22 | (13) ! [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)))
% 28.05/8.22 | (14) ! [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)))
% 28.05/8.22 | (15) ! [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)))
% 28.05/8.22 | (16) ! [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)))
% 28.05/8.22 | (17) ! [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)))
% 28.05/8.22 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 28.05/8.22 | (19) ? [v0] : ? [v1] : point(v0) = v1
% 28.05/8.22 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 28.05/8.22 | (21) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 28.05/8.22 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 28.05/8.22 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 28.05/8.22 | (24) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 28.05/8.22 | (25) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 28.05/8.22 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 28.05/8.22 | (27) ! [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)
% 28.05/8.22 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 28.05/8.22 | (29) ! [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)))
% 28.05/8.22 | (30) ! [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)
% 28.05/8.22 | (31) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 28.05/8.22 | (32) ! [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))
% 28.05/8.22 | (33) ! [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))
% 28.05/8.22 | (34) incident_point_and_line(all_0_2_2, all_0_4_4) = 0
% 28.05/8.22 | (35) ! [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)))
% 28.05/8.22 | (36) ! [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)))
% 28.05/8.22 | (37) ! [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)))
% 28.05/8.23 | (38) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 28.05/8.23 | (39) ! [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)))
% 28.05/8.23 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 28.05/8.23 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 28.05/8.23 | (42) ! [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)
% 28.05/8.23 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 28.05/8.23 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 28.05/8.23 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 28.27/8.23 | (46) ! [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)))
% 28.27/8.23 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 28.27/8.23 | (48) ! [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))
% 28.27/8.23 | (49) ! [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)))
% 28.27/8.23 | (50) ! [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)))
% 28.27/8.23 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 28.27/8.23 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 28.27/8.23 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 28.27/8.23 | (54) ! [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)))
% 28.27/8.23 | (55) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 28.27/8.23 | (56) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 28.27/8.23 | (57) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 28.27/8.23 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 28.27/8.23 | (59) ! [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)))
% 28.27/8.23 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 28.27/8.23 | (61) ! [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)))
% 28.27/8.23 | (62) ! [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)))
% 28.27/8.23 | (63) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 28.27/8.23 | (64) ! [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)))
% 28.27/8.23 | (65) ! [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)))
% 28.27/8.23 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 28.27/8.23 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 28.27/8.23 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 28.27/8.23 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 28.27/8.23 | (70) ! [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)))
% 28.27/8.24 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 28.27/8.24 | (72) ! [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)))
% 28.27/8.24 | (73) ! [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)))
% 28.27/8.24 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 28.27/8.24 | (75) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 28.27/8.24 | (76) ! [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)))
% 28.27/8.24 | (77) equal_points(all_0_2_2, all_0_1_1) = all_0_0_0
% 28.27/8.24 | (78) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 28.27/8.24 | (79) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 28.27/8.24 | (80) ! [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)))
% 28.27/8.24 | (81) ! [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)))
% 28.27/8.24 | (82) ! [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)))
% 28.27/8.24 | (83) ! [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)))
% 28.27/8.24 | (84) ! [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)))
% 28.27/8.24 | (85) ! [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)))
% 28.27/8.24 | (86) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 28.27/8.24 | (87) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 28.27/8.24 | (88) ! [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)))
% 28.27/8.24 | (89) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 28.27/8.24 | (90) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 28.27/8.24 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 28.27/8.24 | (92) intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1
% 28.27/8.24 | (93) ! [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)))
% 28.34/8.24 | (94) ! [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)))
% 28.34/8.24 | (95) ! [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)))
% 28.34/8.24 | (96) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 28.34/8.24 | (97) ! [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)))
% 28.34/8.24 | (98) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 28.34/8.24 | (99) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 28.34/8.24 | (100) ! [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)))
% 28.34/8.24 | (101) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 28.34/8.24 | (102) ! [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)))
% 28.34/8.24 | (103) ? [v0] : ? [v1] : line(v0) = v1
% 28.34/8.24 | (104) ! [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)))
% 28.34/8.24 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 28.34/8.25 | (106) ! [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)))
% 28.34/8.25 | (107) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 28.34/8.25 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 28.34/8.25 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 28.34/8.25 | (110) ! [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))
% 28.34/8.25 | (111) ! [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)))
% 28.34/8.25 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 28.34/8.25 | (113) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 28.34/8.25 | (114) ! [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)))
% 28.34/8.25 | (115) ! [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))
% 28.34/8.25 | (116) ! [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)))
% 28.34/8.25 | (117) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 28.34/8.25 | (118) ! [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)
% 28.34/8.25 | (119) ! [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)))
% 28.34/8.25 | (120) ! [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)))
% 28.34/8.25 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 28.34/8.25 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 28.34/8.25 | (123) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 28.34/8.25 | (124) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 28.34/8.25 | (125) incident_point_and_line(all_0_2_2, all_0_3_3) = 0
% 28.34/8.25 | (126) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 28.34/8.25 | (127) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 28.34/8.25 | (128) ! [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)))
% 28.34/8.25 | (129) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 28.34/8.25 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 28.34/8.25 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 28.34/8.25 | (132) ! [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)))
% 28.34/8.25 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 28.34/8.25 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 28.34/8.25 | (135) ! [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))
% 28.34/8.25 | (136) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 28.34/8.25 | (137) ! [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)))
% 28.34/8.25 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 28.34/8.25 | (139) ! [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)))
% 28.34/8.25 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 28.34/8.25 | (141) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 28.34/8.25 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 28.34/8.26 | (143) ! [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)))
% 28.34/8.26 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 28.34/8.26 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (127) with all_0_3_3, all_0_2_2 and discharging atoms incident_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 28.34/8.26 | (146) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = v0)
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (127) with all_0_4_4, all_0_2_2 and discharging atoms incident_point_and_line(all_0_2_2, all_0_4_4) = 0, yields:
% 28.34/8.26 | (147) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0)
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (69) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_points(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 28.34/8.26 | (148) all_0_0_0 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (29) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 28.34/8.26 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (61) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 28.34/8.26 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (141) with all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 28.34/8.26 | (151) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (86) with all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 28.34/8.26 | (152) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (152) with all_42_0_52, all_42_1_53 yields:
% 28.34/8.26 | (153) ~ (all_42_0_52 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_42_1_53 & apart_point_and_line(all_42_1_53, all_0_4_4) = all_42_0_52
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (153) yields:
% 28.34/8.26 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.26 | (155) intersection_point(all_0_4_4, all_0_3_3) = all_42_1_53
% 28.34/8.26 | (156) apart_point_and_line(all_42_1_53, all_0_4_4) = all_42_0_52
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (151) with all_46_0_56, all_46_1_57 yields:
% 28.34/8.26 | (157) ~ (all_46_0_56 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_46_1_57 & apart_point_and_line(all_46_1_57, all_0_3_3) = all_46_0_56
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (157) yields:
% 28.34/8.26 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.26 | (159) intersection_point(all_0_4_4, all_0_3_3) = all_46_1_57
% 28.34/8.26 | (160) apart_point_and_line(all_46_1_57, all_0_3_3) = all_46_0_56
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (147) with all_52_0_65 yields:
% 28.34/8.26 | (161) ~ (all_52_0_65 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (161) yields:
% 28.34/8.26 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.26 | (163) apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (146) with all_54_0_66 yields:
% 28.34/8.26 | (164) ~ (all_54_0_66 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (164) yields:
% 28.34/8.26 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.26 | (166) apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (150) with all_56_0_67 yields:
% 28.34/8.26 | (167) ( ~ (all_56_0_67 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_56_0_67) | ( ~ (all_56_0_67 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_56_0_67)
% 28.34/8.26 |
% 28.34/8.26 | Instantiating (149) with all_57_0_68 yields:
% 28.34/8.26 | (168) ( ~ (all_57_0_68 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_57_0_68) | ( ~ (all_57_0_68 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_57_0_68)
% 28.34/8.26 |
% 28.34/8.26 +-Applying beta-rule and splitting (148), into two cases.
% 28.34/8.26 |-Branch one:
% 28.34/8.26 | (169) distinct_points(all_0_2_2, all_0_1_1) = 0
% 28.34/8.26 |
% 28.34/8.26 +-Applying beta-rule and splitting (168), into two cases.
% 28.34/8.26 |-Branch one:
% 28.34/8.26 | (170) ~ (all_57_0_68 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_57_0_68
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (170) yields:
% 28.34/8.26 | (171) ~ (all_57_0_68 = 0)
% 28.34/8.26 | (172) apart_point_and_line(all_0_1_1, all_0_3_3) = all_57_0_68
% 28.34/8.26 |
% 28.34/8.26 +-Applying beta-rule and splitting (167), into two cases.
% 28.34/8.26 |-Branch one:
% 28.34/8.26 | (173) ~ (all_56_0_67 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_56_0_67
% 28.34/8.26 |
% 28.34/8.26 | Applying alpha-rule on (173) yields:
% 28.34/8.26 | (174) ~ (all_56_0_67 = 0)
% 28.34/8.26 | (175) apart_point_and_line(all_0_1_1, all_0_4_4) = all_56_0_67
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_46_1_57, all_0_1_1 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_46_1_57, intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 28.34/8.26 | (176) all_46_1_57 = all_0_1_1
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (47) with all_0_4_4, all_0_3_3, all_42_1_53, all_46_1_57 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_46_1_57, intersection_point(all_0_4_4, all_0_3_3) = all_42_1_53, yields:
% 28.34/8.26 | (177) all_46_1_57 = all_42_1_53
% 28.34/8.26 |
% 28.34/8.26 | Combining equations (176,177) yields a new equation:
% 28.34/8.26 | (178) all_42_1_53 = all_0_1_1
% 28.34/8.26 |
% 28.34/8.26 | Combining equations (178,177) yields a new equation:
% 28.34/8.26 | (176) all_46_1_57 = all_0_1_1
% 28.34/8.26 |
% 28.34/8.26 | From (176) and (160) follows:
% 28.34/8.26 | (180) apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56
% 28.34/8.26 |
% 28.34/8.26 | From (178) and (156) follows:
% 28.34/8.26 | (181) apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (9) with all_0_1_1, all_0_3_3, all_46_0_56, all_57_0_68 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_57_0_68, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, yields:
% 28.34/8.26 | (182) all_57_0_68 = all_46_0_56
% 28.34/8.26 |
% 28.34/8.26 | Instantiating formula (9) with all_0_1_1, all_0_4_4, all_42_0_52, all_56_0_67 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_56_0_67, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.26 | (183) all_56_0_67 = all_42_0_52
% 28.34/8.26 |
% 28.34/8.26 | Equations (182) can reduce 171 to:
% 28.34/8.26 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.26 |
% 28.34/8.27 | Equations (183) can reduce 174 to:
% 28.34/8.27 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.27 |
% 28.34/8.27 | From (182) and (172) follows:
% 28.34/8.27 | (180) apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56
% 28.34/8.27 |
% 28.34/8.27 | From (183) and (175) follows:
% 28.34/8.27 | (181) apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_46_0_56, all_46_0_56, all_0_3_3, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, yields:
% 28.34/8.27 | (188) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_46_0_56, all_46_0_56, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, yields:
% 28.34/8.27 | (189) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_42_0_52, all_46_0_56, all_0_4_4, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (190) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_46_0_56, all_42_0_52, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (191) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_42_0_52, all_46_0_56, all_0_4_4, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (192) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_46_0_56, all_42_0_52, all_0_3_3, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (193) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_42_0_52, all_42_0_52, all_0_4_4, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (194) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_42_0_52, all_42_0_52, all_0_4_4, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, yields:
% 28.34/8.27 | (195) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_54_0_66, all_46_0_56, all_0_3_3, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (196) all_54_0_66 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_46_0_56, all_54_0_66, all_0_3_3, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (197) all_54_0_66 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_54_0_66, all_42_0_52, all_0_3_3, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (198) all_54_0_66 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_42_0_52, all_54_0_66, all_0_4_4, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (199) all_54_0_66 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (111) with all_54_0_66, all_42_0_52, all_0_4_4, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (200) all_54_0_66 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (111) with all_42_0_52, all_54_0_66, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (201) all_54_0_66 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_54_0_66, all_54_0_66, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (202) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_54_0_66, all_54_0_66, all_0_3_3, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, yields:
% 28.34/8.27 | (203) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_52_0_65, all_46_0_56, all_0_4_4, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (204) all_52_0_65 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_46_0_56, all_52_0_65, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (205) all_52_0_65 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (111) with all_52_0_65, all_46_0_56, all_0_3_3, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (206) all_52_0_65 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (111) with all_46_0_56, all_52_0_65, all_0_4_4, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (207) all_52_0_65 = 0 | all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_52_0_65, all_42_0_52, all_0_4_4, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (208) all_52_0_65 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (104) with all_42_0_52, all_52_0_65, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.27 | (209) all_52_0_65 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.27 |
% 28.34/8.27 | Instantiating formula (137) with all_52_0_65, all_54_0_66, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (210) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (137) with all_54_0_66, all_52_0_65, all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (211) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (104) with all_52_0_65, all_54_0_66, all_0_4_4, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (212) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (104) with all_54_0_66, all_52_0_65, all_0_3_3, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (213) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (137) with all_52_0_65, all_52_0_65, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (214) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (104) with all_52_0_65, all_52_0_65, all_0_4_4, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, yields:
% 28.34/8.28 | (215) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (132) with all_46_0_56, all_46_0_56, all_0_3_3, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (216) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (132) with all_46_0_56, all_42_0_52, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (217) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (132) with all_42_0_52, all_46_0_56, all_0_4_4, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (218) all_46_0_56 = 0 | all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (132) with all_42_0_52, all_42_0_52, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_42_0_52, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (219) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (70) with all_54_0_66, all_54_0_66, all_0_3_3, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (220) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (70) with all_54_0_66, all_52_0_65, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (221) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (70) with all_52_0_65, all_54_0_66, all_0_4_4, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (222) all_54_0_66 = 0 | all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 | Instantiating formula (70) with all_52_0_65, all_52_0_65, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.34/8.28 | (223) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (188), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (224) all_46_0_56 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (224) can reduce 158 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.28 | (227) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (194), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (228) all_42_0_52 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (228) can reduce 154 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.28 | (231) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (191), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (224) all_46_0_56 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (224) can reduce 158 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.28 | (235) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (192), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (224) all_46_0_56 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (224) can reduce 158 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.28 | (239) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (202), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (240) all_54_0_66 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (240) can reduce 165 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.28 | (227) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (214), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (244) all_52_0_65 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (244) can reduce 162 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.28 | (231) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (215), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (244) all_52_0_65 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (244) can reduce 162 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.28 | (251) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (189), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (224) all_46_0_56 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (224) can reduce 158 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.28 | (255) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (210), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (240) all_54_0_66 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (240) can reduce 165 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.28 | (259) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.28 |
% 28.34/8.28 +-Applying beta-rule and splitting (211), into two cases.
% 28.34/8.28 |-Branch one:
% 28.34/8.28 | (240) all_54_0_66 = 0
% 28.34/8.28 |
% 28.34/8.28 | Equations (240) can reduce 165 to:
% 28.34/8.28 | (225) $false
% 28.34/8.28 |
% 28.34/8.28 |-The branch is then unsatisfiable
% 28.34/8.28 |-Branch two:
% 28.34/8.28 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.28 | (263) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (193), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (224) all_46_0_56 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (224) can reduce 158 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.29 | (267) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (212), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (271) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (213), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (275) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (195), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (228) all_42_0_52 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (228) can reduce 154 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.29 | (279) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (219), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (228) all_42_0_52 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (228) can reduce 154 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.29 | (283) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (220), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (287) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (203), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (291) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (216), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (224) all_46_0_56 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (224) can reduce 158 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.29 | (295) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (223), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (299) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (190), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (224) all_46_0_56 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (224) can reduce 158 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.29 | (303) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (208), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (307) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (196), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (311) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (197), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (315) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (204), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (319) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (205), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (323) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (221), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (327) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (222), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (331) all_52_0_65 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (207), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (335) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (217), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (224) all_46_0_56 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (224) can reduce 158 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.29 | (339) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (206), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (343) all_46_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (209), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (244) all_52_0_65 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (244) can reduce 162 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.29 | (347) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.29 |
% 28.34/8.29 +-Applying beta-rule and splitting (198), into two cases.
% 28.34/8.29 |-Branch one:
% 28.34/8.29 | (240) all_54_0_66 = 0
% 28.34/8.29 |
% 28.34/8.29 | Equations (240) can reduce 165 to:
% 28.34/8.29 | (225) $false
% 28.34/8.29 |
% 28.34/8.29 |-The branch is then unsatisfiable
% 28.34/8.29 |-Branch two:
% 28.34/8.29 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.29 | (351) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (199), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (240) all_54_0_66 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (240) can reduce 165 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.30 | (355) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (218), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (224) all_46_0_56 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (224) can reduce 158 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.30 | (359) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (200), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (240) all_54_0_66 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (240) can reduce 165 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.30 | (363) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (201), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (240) all_54_0_66 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (240) can reduce 165 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (165) ~ (all_54_0_66 = 0)
% 28.34/8.30 | (367) all_42_0_52 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (235), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (371) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (239), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (375) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (259), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (244) all_52_0_65 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (244) can reduce 162 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.30 | (379) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (263), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (244) all_52_0_65 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (244) can reduce 162 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.30 | (371) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (267), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (387) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (271), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (244) all_52_0_65 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (244) can reduce 162 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.30 | (391) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (275), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (244) all_52_0_65 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (244) can reduce 162 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.30 | (395) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (303), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (379) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (307), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (403) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (311), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (224) all_46_0_56 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (224) can reduce 158 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.30 | (407) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (319), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (224) all_46_0_56 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (224) can reduce 158 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.30 | (411) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (323), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (224) all_46_0_56 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (224) can reduce 158 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.30 | (415) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (343), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (224) all_46_0_56 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (224) can reduce 158 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (158) ~ (all_46_0_56 = 0)
% 28.34/8.30 | (419) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (347), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (423) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (351), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (427) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (355), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (431) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 28.34/8.30 |
% 28.34/8.30 | Instantiating (431) with all_288_0_151 yields:
% 28.34/8.30 | (432) (all_288_0_151 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_288_0_151 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_288_0_151 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151) | ( ~ (all_288_0_151 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_288_0_151)
% 28.34/8.30 |
% 28.34/8.30 +-Applying beta-rule and splitting (359), into two cases.
% 28.34/8.30 |-Branch one:
% 28.34/8.30 | (228) all_42_0_52 = 0
% 28.34/8.30 |
% 28.34/8.30 | Equations (228) can reduce 154 to:
% 28.34/8.30 | (225) $false
% 28.34/8.30 |
% 28.34/8.30 |-The branch is then unsatisfiable
% 28.34/8.30 |-Branch two:
% 28.34/8.30 | (154) ~ (all_42_0_52 = 0)
% 28.34/8.30 | (436) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.30 |
% 28.34/8.31 | Instantiating (436) with all_292_0_152 yields:
% 28.34/8.31 | (437) (all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_292_0_152 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_292_0_152)
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (437), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (438) (all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0)
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (438), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (439) all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (439) yields:
% 28.34/8.31 | (440) all_292_0_152 = 0
% 28.34/8.31 | (441) apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 28.34/8.31 |
% 28.34/8.31 | Instantiating formula (9) with all_0_2_2, all_0_3_3, 0, all_54_0_66 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_54_0_66, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 28.34/8.31 | (240) all_54_0_66 = 0
% 28.34/8.31 |
% 28.34/8.31 | Equations (240) can reduce 165 to:
% 28.34/8.31 | (225) $false
% 28.34/8.31 |
% 28.34/8.31 |-The branch is then unsatisfiable
% 28.34/8.31 |-Branch two:
% 28.34/8.31 | (444) all_292_0_152 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (444) yields:
% 28.34/8.31 | (440) all_292_0_152 = 0
% 28.34/8.31 | (446) apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (331), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (244) all_52_0_65 = 0
% 28.34/8.31 |
% 28.34/8.31 | Equations (244) can reduce 162 to:
% 28.34/8.31 | (225) $false
% 28.34/8.31 |
% 28.34/8.31 |-The branch is then unsatisfiable
% 28.34/8.31 |-Branch two:
% 28.34/8.31 | (162) ~ (all_52_0_65 = 0)
% 28.34/8.31 | (450) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 28.34/8.31 |
% 28.34/8.31 | Instantiating formula (9) with all_0_2_2, all_0_4_4, 0, all_52_0_65 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields:
% 28.34/8.31 | (244) all_52_0_65 = 0
% 28.34/8.31 |
% 28.34/8.31 | Equations (244) can reduce 162 to:
% 28.34/8.31 | (225) $false
% 28.34/8.31 |
% 28.34/8.31 |-The branch is then unsatisfiable
% 28.34/8.31 |-Branch two:
% 28.34/8.31 | (453) ~ (all_292_0_152 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_292_0_152
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (453) yields:
% 28.34/8.31 | (454) ~ (all_292_0_152 = 0)
% 28.34/8.31 | (455) distinct_lines(all_0_3_3, all_0_4_4) = all_292_0_152
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (432), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (456) (all_288_0_151 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_288_0_151 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_288_0_151 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151)
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (456), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (457) (all_288_0_151 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_288_0_151 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0)
% 28.34/8.31 |
% 28.34/8.31 +-Applying beta-rule and splitting (457), into two cases.
% 28.34/8.31 |-Branch one:
% 28.34/8.31 | (458) all_288_0_151 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (458) yields:
% 28.34/8.31 | (459) all_288_0_151 = 0
% 28.34/8.31 | (460) apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 28.34/8.31 |
% 28.34/8.31 | Instantiating formula (9) with all_0_1_1, all_0_3_3, 0, all_46_0_56 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_56, apart_point_and_line(all_0_1_1, all_0_3_3) = 0, yields:
% 28.34/8.31 | (224) all_46_0_56 = 0
% 28.34/8.31 |
% 28.34/8.31 | Equations (224) can reduce 158 to:
% 28.34/8.31 | (225) $false
% 28.34/8.31 |
% 28.34/8.31 |-The branch is then unsatisfiable
% 28.34/8.31 |-Branch two:
% 28.34/8.31 | (463) all_288_0_151 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (463) yields:
% 28.34/8.31 | (459) all_288_0_151 = 0
% 28.34/8.31 | (446) apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 28.34/8.31 |
% 28.34/8.31 | Instantiating formula (9) with all_0_2_2, all_0_4_4, 0, all_52_0_65 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_65, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields:
% 28.34/8.31 | (244) all_52_0_65 = 0
% 28.34/8.31 |
% 28.34/8.31 | Equations (244) can reduce 162 to:
% 28.34/8.31 | (225) $false
% 28.34/8.31 |
% 28.34/8.31 |-The branch is then unsatisfiable
% 28.34/8.31 |-Branch two:
% 28.34/8.31 | (468) ~ (all_288_0_151 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151
% 28.34/8.31 |
% 28.34/8.31 | Applying alpha-rule on (468) yields:
% 28.34/8.31 | (469) ~ (all_288_0_151 = 0)
% 28.34/8.31 | (470) distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151
% 28.34/8.31 |
% 28.34/8.31 | Instantiating formula (140) with all_0_3_3, all_0_4_4, all_288_0_151, all_292_0_152 and discharging atoms distinct_lines(all_0_3_3, all_0_4_4) = all_292_0_152, distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151, yields:
% 28.67/8.31 | (471) all_292_0_152 = all_288_0_151
% 28.67/8.31 |
% 28.67/8.31 | Equations (471) can reduce 454 to:
% 28.67/8.31 | (469) ~ (all_288_0_151 = 0)
% 28.67/8.31 |
% 28.67/8.31 | From (471) and (455) follows:
% 28.67/8.31 | (470) distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151
% 28.67/8.31 |
% 28.67/8.31 | Instantiating formula (144) with all_288_0_151, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_4_4) = all_288_0_151, yields:
% 28.67/8.31 | (474) all_288_0_151 = 0 | convergent_lines(all_0_4_4, all_0_4_4) = 0
% 28.67/8.31 |
% 28.67/8.31 +-Applying beta-rule and splitting (474), into two cases.
% 28.67/8.31 |-Branch one:
% 28.67/8.31 | (475) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 28.67/8.31 |
% 28.67/8.31 | Instantiating formula (78) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 28.67/8.31 | (476) $false
% 28.67/8.31 |
% 28.67/8.31 |-The branch is then unsatisfiable
% 28.67/8.31 |-Branch two:
% 28.67/8.31 | (477) ~ (convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 28.67/8.31 | (459) all_288_0_151 = 0
% 28.67/8.31 |
% 28.67/8.31 | Equations (459) can reduce 469 to:
% 28.67/8.31 | (225) $false
% 28.67/8.31 |
% 28.67/8.31 |-The branch is then unsatisfiable
% 28.67/8.31 |-Branch two:
% 28.67/8.31 | (480) ~ (all_288_0_151 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_288_0_151
% 28.67/8.31 |
% 28.67/8.31 | Applying alpha-rule on (480) yields:
% 28.67/8.31 | (469) ~ (all_288_0_151 = 0)
% 28.67/8.31 | (482) distinct_points(all_0_2_2, all_0_1_1) = all_288_0_151
% 28.67/8.31 |
% 28.67/8.31 | Instantiating formula (18) with all_0_2_2, all_0_1_1, all_288_0_151, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_288_0_151, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 28.67/8.31 | (459) all_288_0_151 = 0
% 28.67/8.31 |
% 28.67/8.31 | Equations (459) can reduce 469 to:
% 28.67/8.31 | (225) $false
% 28.67/8.31 |
% 28.67/8.31 |-The branch is then unsatisfiable
% 28.67/8.32 |-Branch two:
% 28.67/8.32 | (485) ~ (all_56_0_67 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_56_0_67
% 28.67/8.32 |
% 28.67/8.32 | Applying alpha-rule on (485) yields:
% 28.67/8.32 | (174) ~ (all_56_0_67 = 0)
% 28.67/8.32 | (487) convergent_lines(all_0_4_4, all_0_3_3) = all_56_0_67
% 28.67/8.32 |
% 28.67/8.32 | Instantiating formula (105) with all_0_4_4, all_0_3_3, all_56_0_67, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_56_0_67, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 28.67/8.32 | (488) all_56_0_67 = 0
% 28.67/8.32 |
% 28.67/8.32 | Equations (488) can reduce 174 to:
% 28.67/8.32 | (225) $false
% 28.67/8.32 |
% 28.67/8.32 |-The branch is then unsatisfiable
% 28.67/8.32 |-Branch two:
% 28.67/8.32 | (490) ~ (all_57_0_68 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_57_0_68
% 28.67/8.32 |
% 28.67/8.32 | Applying alpha-rule on (490) yields:
% 28.67/8.32 | (171) ~ (all_57_0_68 = 0)
% 28.67/8.32 | (492) convergent_lines(all_0_4_4, all_0_3_3) = all_57_0_68
% 28.67/8.32 |
% 28.67/8.32 | Instantiating formula (105) with all_0_4_4, all_0_3_3, all_57_0_68, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_57_0_68, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 28.67/8.32 | (493) all_57_0_68 = 0
% 28.67/8.32 |
% 28.67/8.32 | Equations (493) can reduce 171 to:
% 28.67/8.32 | (225) $false
% 28.67/8.32 |
% 28.67/8.32 |-The branch is then unsatisfiable
% 28.67/8.32 |-Branch two:
% 28.67/8.32 | (495) ~ (distinct_points(all_0_2_2, all_0_1_1) = 0)
% 28.67/8.32 | (496) all_0_0_0 = 0
% 28.67/8.32 |
% 28.67/8.32 | Equations (496) can reduce 11 to:
% 28.67/8.32 | (225) $false
% 28.67/8.32 |
% 28.67/8.32 |-The branch is then unsatisfiable
% 28.67/8.32 % SZS output end Proof for theBenchmark
% 28.67/8.32
% 28.67/8.32 7667ms
%------------------------------------------------------------------------------