TSTP Solution File: GEO198+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO198+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 03:48:34 EDT 2022
% Result : Theorem 20.46s 6.03s
% Output : Proof 40.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO198+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 01:29:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.97 Prover 0: Preprocessing ...
% 2.47/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.51/1.21 Prover 0: Constructing countermodel ...
% 17.31/5.38 Prover 0: gave up
% 17.31/5.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.73/5.42 Prover 1: Preprocessing ...
% 18.27/5.54 Prover 1: Constructing countermodel ...
% 18.27/5.59 Prover 1: gave up
% 18.27/5.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.73/5.61 Prover 2: Preprocessing ...
% 19.14/5.77 Prover 2: Warning: ignoring some quantifiers
% 19.14/5.78 Prover 2: Constructing countermodel ...
% 20.46/6.03 Prover 2: proved (443ms)
% 20.46/6.03
% 20.46/6.03 No countermodel exists, formula is valid
% 20.46/6.03 % SZS status Theorem for theBenchmark
% 20.46/6.03
% 20.46/6.03 Generating proof ... Warning: ignoring some quantifiers
% 39.32/12.38 found it (size 525)
% 39.32/12.38
% 39.32/12.38 % SZS output start Proof for theBenchmark
% 39.32/12.38 Assumed formulas after preprocessing and simplification:
% 39.32/12.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v4, v1) = v5 & incident_point_and_line(v3, v2) = 0 & intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7)
% 39.62/12.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 39.62/12.47 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0 & incident_point_and_line(all_0_2_2, all_0_3_3) = 0 & intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & convergent_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 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
% 40.07/12.51 |
% 40.07/12.51 | Applying alpha-rule on (1) yields:
% 40.07/12.51 | (2) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 40.07/12.51 | (3) ! [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)))
% 40.07/12.51 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 40.07/12.51 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 40.07/12.51 | (6) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 40.07/12.51 | (7) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 40.07/12.51 | (8) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 40.07/12.51 | (9) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 40.07/12.51 | (10) ! [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)))
% 40.07/12.51 | (11) ! [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)))
% 40.07/12.51 | (12) ! [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)))
% 40.07/12.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 40.07/12.51 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 40.07/12.51 | (15) ! [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)))
% 40.07/12.51 | (16) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 40.07/12.51 | (17) ! [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)))
% 40.07/12.51 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 40.07/12.51 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 40.07/12.51 | (20) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 40.07/12.51 | (21) ! [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)))
% 40.07/12.51 | (22) ! [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)))
% 40.07/12.51 | (23) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 40.07/12.51 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 40.07/12.51 | (25) ! [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))
% 40.07/12.51 | (26) ! [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)
% 40.07/12.51 | (27) ! [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))
% 40.07/12.52 | (28) ! [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)))
% 40.07/12.52 | (29) ! [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)))
% 40.07/12.52 | (30) ! [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)))
% 40.07/12.52 | (31) ! [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)))
% 40.07/12.52 | (32) ! [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)))
% 40.07/12.52 | (33) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 40.07/12.52 | (34) ! [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)))
% 40.07/12.52 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 40.07/12.52 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 40.07/12.52 | (37) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 40.07/12.52 | (38) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 40.07/12.52 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 40.07/12.52 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 40.07/12.52 | (41) ! [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)
% 40.07/12.52 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 40.07/12.52 | (43) ! [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)))
% 40.07/12.52 | (44) ! [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)
% 40.07/12.52 | (45) ! [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))
% 40.07/12.52 | (46) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 40.07/12.52 | (47) ! [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)))
% 40.07/12.52 | (48) ! [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)))
% 40.07/12.52 | (49) ! [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)))
% 40.07/12.52 | (50) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 40.07/12.52 | (51) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 40.07/12.52 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 40.07/12.52 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 40.07/12.52 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 40.07/12.53 | (55) ! [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)))
% 40.07/12.53 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 40.07/12.53 | (57) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 40.07/12.53 | (58) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 40.07/12.53 | (59) ! [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)))
% 40.07/12.53 | (60) ! [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)))
% 40.07/12.53 | (61) ! [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)))
% 40.07/12.53 | (62) ? [v0] : ? [v1] : line(v0) = v1
% 40.07/12.53 | (63) intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1
% 40.07/12.53 | (64) ! [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)))
% 40.07/12.53 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 40.07/12.53 | (66) ! [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)))
% 40.07/12.53 | (67) ! [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)))
% 40.07/12.53 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 40.07/12.53 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 40.07/12.53 | (70) ? [v0] : ? [v1] : point(v0) = v1
% 40.07/12.53 | (71) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 40.07/12.53 | (72) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 40.07/12.53 | (73) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 40.07/12.53 | (74) ! [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)))
% 40.07/12.53 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 40.07/12.53 | (76) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 40.07/12.53 | (77) ! [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)))
% 40.07/12.53 | (78) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 40.07/12.53 | (79) ! [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)))
% 40.07/12.53 | (80) ! [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)))
% 40.07/12.53 | (81) ! [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)))
% 40.07/12.54 | (82) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 40.07/12.54 | (83) ! [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)))
% 40.07/12.54 | (84) ! [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))
% 40.07/12.54 | (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)))
% 40.07/12.54 | (86) incident_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0
% 40.07/12.54 | (87) ! [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)))
% 40.07/12.54 | (88) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 40.07/12.54 | (89) ! [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))
% 40.07/12.54 | (90) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 40.07/12.54 | (91) ! [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)))
% 40.07/12.54 | (92) ! [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))
% 40.07/12.54 | (93) ~ (all_0_0_0 = 0)
% 40.07/12.54 | (94) ! [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)))
% 40.07/12.54 | (95) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 40.07/12.54 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 40.07/12.54 | (97) incident_point_and_line(all_0_2_2, all_0_3_3) = 0
% 40.07/12.54 | (98) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 40.07/12.54 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 40.07/12.54 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 40.07/12.54 | (101) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 40.07/12.54 | (102) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 40.07/12.54 | (103) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 40.07/12.54 | (104) ! [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)))
% 40.07/12.54 | (105) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 40.07/12.54 | (106) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 40.07/12.54 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 40.07/12.54 | (108) ! [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))
% 40.07/12.54 | (109) ! [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)))
% 40.07/12.54 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 40.07/12.54 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 40.07/12.54 | (112) ! [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)))
% 40.07/12.54 | (113) ! [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)))
% 40.07/12.54 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 40.07/12.54 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 40.07/12.54 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 40.07/12.55 | (117) ! [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)))
% 40.07/12.55 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 40.07/12.55 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 40.07/12.55 | (120) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 40.07/12.55 | (121) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 40.07/12.55 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 40.07/12.55 | (123) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 40.07/12.55 | (124) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 40.07/12.55 | (125) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2
% 40.07/12.55 | (126) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 40.07/12.55 | (127) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 40.07/12.55 | (128) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 40.07/12.55 | (129) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 40.07/12.55 | (130) ! [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)))
% 40.07/12.55 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 40.07/12.55 | (132) ! [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)))
% 40.07/12.55 | (133) ! [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)))
% 40.07/12.55 | (134) ! [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)))
% 40.07/12.55 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 40.07/12.55 | (136) convergent_lines(all_0_5_5, all_0_3_3) = 0
% 40.07/12.55 | (137) ! [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)))
% 40.07/12.55 | (138) ! [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)))
% 40.07/12.55 | (139) ! [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)))
% 40.07/12.55 | (140) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 40.07/12.55 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 40.07/12.55 | (142) ! [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)))
% 40.07/12.55 | (143) ! [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)))
% 40.07/12.55 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 40.07/12.55 | (145) ! [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)
% 40.07/12.55 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 40.07/12.55 | (147) ! [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)))
% 40.07/12.55 |
% 40.07/12.55 | Instantiating formula (54) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms incident_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 40.07/12.55 | (148) all_0_0_0 = 0 | apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 40.07/12.55 |
% 40.07/12.55 | 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:
% 40.07/12.55 | (149) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = v0)
% 40.07/12.55 |
% 40.07/12.55 | Instantiating formula (12) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 40.07/12.55 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 40.07/12.55 |
% 40.07/12.56 | Instantiating formula (137) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 40.07/12.56 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (12) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 40.07/12.56 | (152) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (137) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 40.07/12.56 | (153) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (124) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 40.07/12.56 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (16) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 40.07/12.56 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (124) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 40.07/12.56 | (156) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (16) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 40.07/12.56 | (157) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (124) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 40.07/12.56 | (158) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (16) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 40.07/12.56 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (159) with all_42_0_53, all_42_1_54 yields:
% 40.07/12.56 | (160) ~ (all_42_0_53 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54 & apart_point_and_line(all_42_1_54, all_0_5_5) = all_42_0_53
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (160) yields:
% 40.07/12.56 | (161) ~ (all_42_0_53 = 0)
% 40.07/12.56 | (162) intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54
% 40.07/12.56 | (163) apart_point_and_line(all_42_1_54, all_0_5_5) = all_42_0_53
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (158) with all_44_0_55, all_44_1_56 yields:
% 40.07/12.56 | (164) ~ (all_44_0_55 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_44_1_56 & apart_point_and_line(all_44_1_56, all_0_4_4) = all_44_0_55
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (164) yields:
% 40.07/12.56 | (165) ~ (all_44_0_55 = 0)
% 40.07/12.56 | (166) intersection_point(all_0_5_5, all_0_4_4) = all_44_1_56
% 40.07/12.56 | (167) apart_point_and_line(all_44_1_56, all_0_4_4) = all_44_0_55
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (157) with all_56_0_73, all_56_1_74 yields:
% 40.07/12.56 | (168) ~ (all_56_0_73 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_56_1_74 & apart_point_and_line(all_56_1_74, all_0_5_5) = all_56_0_73
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (168) yields:
% 40.07/12.56 | (169) ~ (all_56_0_73 = 0)
% 40.07/12.56 | (170) intersection_point(all_0_5_5, all_0_3_3) = all_56_1_74
% 40.07/12.56 | (171) apart_point_and_line(all_56_1_74, all_0_5_5) = all_56_0_73
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (156) with all_58_0_75, all_58_1_76 yields:
% 40.07/12.56 | (172) ~ (all_58_0_75 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_58_1_76 & apart_point_and_line(all_58_1_76, all_0_3_3) = all_58_0_75
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (172) yields:
% 40.07/12.56 | (173) ~ (all_58_0_75 = 0)
% 40.07/12.56 | (174) intersection_point(all_0_5_5, all_0_3_3) = all_58_1_76
% 40.07/12.56 | (175) apart_point_and_line(all_58_1_76, all_0_3_3) = all_58_0_75
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (155) with all_68_0_88, all_68_1_89 yields:
% 40.07/12.56 | (176) ~ (all_68_0_88 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_68_1_89 & apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (176) yields:
% 40.07/12.56 | (177) ~ (all_68_0_88 = 0)
% 40.07/12.56 | (178) intersection_point(all_0_3_3, all_0_4_4) = all_68_1_89
% 40.07/12.56 | (179) apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (153) with all_70_0_90 yields:
% 40.07/12.56 | (180) ( ~ (all_70_0_90 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_70_0_90) | ( ~ (all_70_0_90 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_70_0_90)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (152) with all_71_0_91 yields:
% 40.07/12.56 | (181) ( ~ (all_71_0_91 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_71_0_91) | ( ~ (all_71_0_91 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_71_0_91)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (154) with all_72_0_92, all_72_1_93 yields:
% 40.07/12.56 | (182) ~ (all_72_0_92 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_72_1_93 & apart_point_and_line(all_72_1_93, all_0_4_4) = all_72_0_92
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (182) yields:
% 40.07/12.56 | (183) ~ (all_72_0_92 = 0)
% 40.07/12.56 | (184) intersection_point(all_0_3_3, all_0_4_4) = all_72_1_93
% 40.07/12.56 | (185) apart_point_and_line(all_72_1_93, all_0_4_4) = all_72_0_92
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (150) with all_79_0_100 yields:
% 40.07/12.56 | (186) ( ~ (all_79_0_100 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_79_0_100) | ( ~ (all_79_0_100 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_79_0_100)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (151) with all_86_0_109 yields:
% 40.07/12.56 | (187) ( ~ (all_86_0_109 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_86_0_109) | ( ~ (all_86_0_109 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_86_0_109)
% 40.07/12.56 |
% 40.07/12.56 | Instantiating (149) with all_87_0_110 yields:
% 40.07/12.56 | (188) ~ (all_87_0_110 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (188) yields:
% 40.07/12.56 | (189) ~ (all_87_0_110 = 0)
% 40.07/12.56 | (190) apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110
% 40.07/12.56 |
% 40.07/12.56 +-Applying beta-rule and splitting (148), into two cases.
% 40.07/12.56 |-Branch one:
% 40.07/12.56 | (191) apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 40.07/12.56 |
% 40.07/12.56 +-Applying beta-rule and splitting (186), into two cases.
% 40.07/12.56 |-Branch one:
% 40.07/12.56 | (192) ~ (all_79_0_100 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_79_0_100
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (192) yields:
% 40.07/12.56 | (193) ~ (all_79_0_100 = 0)
% 40.07/12.56 | (194) apart_point_and_line(all_0_1_1, all_0_3_3) = all_79_0_100
% 40.07/12.56 |
% 40.07/12.56 +-Applying beta-rule and splitting (187), into two cases.
% 40.07/12.56 |-Branch one:
% 40.07/12.56 | (195) ~ (all_86_0_109 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_86_0_109
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (195) yields:
% 40.07/12.56 | (196) ~ (all_86_0_109 = 0)
% 40.07/12.56 | (197) apart_point_and_line(all_0_1_1, all_0_5_5) = all_86_0_109
% 40.07/12.56 |
% 40.07/12.56 +-Applying beta-rule and splitting (180), into two cases.
% 40.07/12.56 |-Branch one:
% 40.07/12.56 | (198) ~ (all_70_0_90 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_70_0_90
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (198) yields:
% 40.07/12.56 | (199) ~ (all_70_0_90 = 0)
% 40.07/12.56 | (200) apart_point_and_line(all_0_2_2, all_0_5_5) = all_70_0_90
% 40.07/12.56 |
% 40.07/12.56 +-Applying beta-rule and splitting (181), into two cases.
% 40.07/12.56 |-Branch one:
% 40.07/12.56 | (201) ~ (all_71_0_91 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_71_0_91
% 40.07/12.56 |
% 40.07/12.56 | Applying alpha-rule on (201) yields:
% 40.07/12.56 | (202) ~ (all_71_0_91 = 0)
% 40.07/12.56 | (203) apart_point_and_line(all_0_2_2, all_0_4_4) = all_71_0_91
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (144) with all_0_3_3, all_0_4_4, all_68_1_89, all_72_1_93 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_72_1_93, intersection_point(all_0_3_3, all_0_4_4) = all_68_1_89, yields:
% 40.07/12.56 | (204) all_72_1_93 = all_68_1_89
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (144) with all_0_5_5, all_0_3_3, all_58_1_76, all_0_1_1 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_58_1_76, intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 40.07/12.56 | (205) all_58_1_76 = all_0_1_1
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (144) with all_0_5_5, all_0_3_3, all_56_1_74, all_58_1_76 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_58_1_76, intersection_point(all_0_5_5, all_0_3_3) = all_56_1_74, yields:
% 40.07/12.56 | (206) all_58_1_76 = all_56_1_74
% 40.07/12.56 |
% 40.07/12.56 | Instantiating formula (144) with all_0_5_5, all_0_4_4, all_44_1_56, all_0_2_2 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_44_1_56, intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 40.07/12.57 | (207) all_44_1_56 = all_0_2_2
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (144) with all_0_5_5, all_0_4_4, all_42_1_54, all_44_1_56 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_44_1_56, intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54, yields:
% 40.07/12.57 | (208) all_44_1_56 = all_42_1_54
% 40.07/12.57 |
% 40.07/12.57 | Combining equations (206,205) yields a new equation:
% 40.07/12.57 | (209) all_56_1_74 = all_0_1_1
% 40.07/12.57 |
% 40.07/12.57 | Simplifying 209 yields:
% 40.07/12.57 | (210) all_56_1_74 = all_0_1_1
% 40.07/12.57 |
% 40.07/12.57 | Combining equations (207,208) yields a new equation:
% 40.07/12.57 | (211) all_42_1_54 = all_0_2_2
% 40.07/12.57 |
% 40.07/12.57 | Combining equations (211,208) yields a new equation:
% 40.07/12.57 | (207) all_44_1_56 = all_0_2_2
% 40.07/12.57 |
% 40.07/12.57 | From (204) and (185) follows:
% 40.07/12.57 | (213) apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92
% 40.07/12.57 |
% 40.07/12.57 | From (205) and (175) follows:
% 40.07/12.57 | (214) apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75
% 40.07/12.57 |
% 40.07/12.57 | From (210) and (171) follows:
% 40.07/12.57 | (215) apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73
% 40.07/12.57 |
% 40.07/12.57 | From (207) and (167) follows:
% 40.07/12.57 | (216) apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55
% 40.07/12.57 |
% 40.07/12.57 | From (211) and (163) follows:
% 40.07/12.57 | (217) apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (114) with all_0_1_1, all_0_3_3, all_58_0_75, all_79_0_100 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_79_0_100, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (218) all_79_0_100 = all_58_0_75
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (114) with all_0_1_1, all_0_5_5, all_56_0_73, all_86_0_109 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_86_0_109, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.57 | (219) all_86_0_109 = all_56_0_73
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (114) with all_0_2_2, all_0_4_4, all_44_0_55, all_71_0_91 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_71_0_91, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.57 | (220) all_71_0_91 = all_44_0_55
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (114) with all_0_2_2, all_0_5_5, all_42_0_53, all_70_0_90 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_70_0_90, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.07/12.57 | (221) all_70_0_90 = all_42_0_53
% 40.07/12.57 |
% 40.07/12.57 | Equations (219) can reduce 196 to:
% 40.07/12.57 | (169) ~ (all_56_0_73 = 0)
% 40.07/12.57 |
% 40.07/12.57 | Equations (218) can reduce 193 to:
% 40.07/12.57 | (173) ~ (all_58_0_75 = 0)
% 40.07/12.57 |
% 40.07/12.57 | Equations (220) can reduce 202 to:
% 40.07/12.57 | (165) ~ (all_44_0_55 = 0)
% 40.07/12.57 |
% 40.07/12.57 | Equations (221) can reduce 199 to:
% 40.07/12.57 | (161) ~ (all_42_0_53 = 0)
% 40.07/12.57 |
% 40.07/12.57 | From (218) and (194) follows:
% 40.07/12.57 | (214) apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75
% 40.07/12.57 |
% 40.07/12.57 | From (219) and (197) follows:
% 40.07/12.57 | (215) apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73
% 40.07/12.57 |
% 40.07/12.57 | From (220) and (203) follows:
% 40.07/12.57 | (216) apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55
% 40.07/12.57 |
% 40.07/12.57 | From (221) and (200) follows:
% 40.07/12.57 | (217) apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (47) with all_68_0_88, all_68_0_88, all_0_3_3, all_0_3_3, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, yields:
% 40.07/12.57 | (230) all_68_0_88 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_68_0_88, all_68_0_88, all_0_3_3, all_0_3_3, all_68_1_89, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, yields:
% 40.07/12.57 | (231) all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (47) with all_72_0_92, all_68_0_88, all_0_4_4, all_0_3_3, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (232) all_72_0_92 = 0 | all_68_0_88 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (47) with all_68_0_88, all_72_0_92, all_0_3_3, all_0_4_4, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (233) all_72_0_92 = 0 | all_68_0_88 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_72_0_92, all_68_0_88, all_0_4_4, all_0_3_3, all_68_1_89, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (234) all_72_0_92 = 0 | all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_68_0_88, all_72_0_92, all_0_3_3, all_0_4_4, all_68_1_89, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (235) all_72_0_92 = 0 | all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (47) with all_72_0_92, all_72_0_92, all_0_4_4, all_0_4_4, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (236) all_72_0_92 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_72_0_92, all_72_0_92, all_0_4_4, all_0_4_4, all_68_1_89, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, yields:
% 40.07/12.57 | (237) all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_58_0_75, all_68_0_88, all_0_3_3, all_0_3_3, all_0_1_1, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (238) all_68_0_88 = 0 | all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89, all_0_1_1) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_68_0_88, all_58_0_75, all_0_3_3, all_0_3_3, all_68_1_89, all_0_1_1 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (239) all_68_0_88 = 0 | all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_58_0_75, all_72_0_92, all_0_3_3, all_0_4_4, all_0_1_1, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (240) all_72_0_92 = 0 | all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_72_0_92, all_58_0_75, all_0_4_4, all_0_3_3, all_68_1_89, all_0_1_1 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (241) all_72_0_92 = 0 | all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (94) with all_58_0_75, all_72_0_92, all_0_4_4, all_0_3_3, all_0_1_1, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, yields:
% 40.07/12.57 | (242) all_72_0_92 = 0 | all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (47) with all_58_0_75, all_58_0_75, 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_58_0_75, yields:
% 40.07/12.57 | (243) all_58_0_75 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_58_0_75, all_58_0_75, 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_58_0_75, yields:
% 40.07/12.57 | (244) all_58_0_75 = 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))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_56_0_73, all_68_0_88, all_0_5_5, all_0_3_3, all_0_1_1, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.57 | (245) all_68_0_88 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_1_1) = v0))
% 40.07/12.57 |
% 40.07/12.57 | Instantiating formula (59) with all_68_0_88, all_56_0_73, all_0_3_3, all_0_5_5, all_68_1_89, all_0_1_1 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (246) all_68_0_88 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_56_0_73, all_68_0_88, all_0_3_3, all_0_5_5, all_0_1_1, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (247) all_68_0_88 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_1_1) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_68_0_88, all_56_0_73, all_0_5_5, all_0_3_3, all_68_1_89, all_0_1_1 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (248) all_68_0_88 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (47) with all_56_0_73, all_58_0_75, all_0_5_5, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (249) all_58_0_75 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (47) with all_58_0_75, all_56_0_73, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (250) all_58_0_75 = 0 | all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_56_0_73, all_58_0_75, all_0_5_5, 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_58_0_75, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (251) all_58_0_75 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_58_0_75, all_56_0_73, all_0_3_3, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, yields:
% 40.07/12.58 | (252) all_58_0_75 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_87_0_110, all_68_0_88, all_0_3_3, all_0_3_3, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (253) all_87_0_110 = 0 | all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_68_0_88, all_87_0_110, all_0_3_3, all_0_3_3, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (254) all_87_0_110 = 0 | all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_87_0_110, all_72_0_92, all_0_3_3, all_0_4_4, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (255) all_87_0_110 = 0 | all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_72_0_92, all_87_0_110, all_0_4_4, all_0_3_3, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (256) all_87_0_110 = 0 | all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_87_0_110, all_72_0_92, all_0_4_4, all_0_3_3, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (257) all_87_0_110 = 0 | all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_72_0_92, all_87_0_110, all_0_3_3, all_0_4_4, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (258) all_87_0_110 = 0 | all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_87_0_110, all_58_0_75, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (259) all_87_0_110 = 0 | all_58_0_75 = 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))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_58_0_75, all_87_0_110, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (260) all_87_0_110 = 0 | all_58_0_75 = 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))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_87_0_110, all_56_0_73, all_0_3_3, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (261) all_87_0_110 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_56_0_73, all_87_0_110, all_0_5_5, 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_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (262) all_87_0_110 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_87_0_110, all_56_0_73, all_0_5_5, 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_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (263) all_87_0_110 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_56_0_73, all_87_0_110, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, yields:
% 40.07/12.58 | (264) all_87_0_110 = 0 | all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (47) with all_87_0_110, all_87_0_110, 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_87_0_110, yields:
% 40.07/12.58 | (265) all_87_0_110 = 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))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_87_0_110, all_87_0_110, 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_87_0_110, yields:
% 40.07/12.58 | (266) all_87_0_110 = 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))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_44_0_55, all_68_0_88, all_0_4_4, all_0_3_3, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.58 | (267) all_68_0_88 = 0 | all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_68_0_88, all_44_0_55, all_0_3_3, all_0_4_4, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.58 | (268) all_68_0_88 = 0 | all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_44_0_55, all_68_0_88, all_0_3_3, all_0_4_4, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.58 | (269) all_68_0_88 = 0 | all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (94) with all_68_0_88, all_44_0_55, all_0_4_4, all_0_3_3, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.58 | (270) all_68_0_88 = 0 | all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_44_0_55, all_58_0_75, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.58 | (271) all_58_0_75 = 0 | all_44_0_55 = 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))
% 40.07/12.58 |
% 40.07/12.58 | Instantiating formula (59) with all_58_0_75, all_44_0_55, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.59 | (272) all_58_0_75 = 0 | all_44_0_55 = 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))
% 40.07/12.59 |
% 40.07/12.59 | Instantiating formula (94) with all_44_0_55, all_58_0_75, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.59 | (273) all_58_0_75 = 0 | all_44_0_55 = 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))
% 40.07/12.59 |
% 40.07/12.59 | Instantiating formula (94) with all_58_0_75, all_44_0_55, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.59 | (274) all_58_0_75 = 0 | all_44_0_55 = 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))
% 40.07/12.59 |
% 40.07/12.59 | Instantiating formula (41) with all_44_0_55, all_0_2_2, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = 0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.59 | (275) all_44_0_55 = 0 | distinct_points(all_0_1_1, all_0_2_2) = 0
% 40.07/12.59 |
% 40.07/12.59 | Instantiating formula (59) with all_44_0_55, all_56_0_73, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.07/12.59 | (276) all_56_0_73 = 0 | all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_56_0_73, all_44_0_55, all_0_5_5, 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_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.50/12.59 | (277) all_56_0_73 = 0 | all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_44_0_55, all_56_0_73, all_0_5_5, 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_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.50/12.59 | (278) all_56_0_73 = 0 | all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_56_0_73, all_44_0_55, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.50/12.59 | (279) all_56_0_73 = 0 | all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (47) with all_44_0_55, all_87_0_110, 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_87_0_110, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.50/12.59 | (280) all_87_0_110 = 0 | all_44_0_55 = 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))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_87_0_110, all_44_0_55, 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_87_0_110, apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, yields:
% 40.50/12.59 | (281) all_87_0_110 = 0 | all_44_0_55 = 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))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (47) with all_44_0_55, all_44_0_55, 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_44_0_55, yields:
% 40.50/12.59 | (282) all_44_0_55 = 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))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_44_0_55, all_44_0_55, 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_44_0_55, yields:
% 40.50/12.59 | (283) all_44_0_55 = 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))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_42_0_53, all_68_0_88, all_0_5_5, all_0_3_3, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (284) all_68_0_88 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_68_0_88, all_42_0_53, all_0_3_3, all_0_5_5, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (285) all_68_0_88 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_42_0_53, all_68_0_88, all_0_3_3, all_0_5_5, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (286) all_68_0_88 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_68_0_88, all_42_0_53, all_0_5_5, all_0_3_3, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_3_3) = all_68_0_88, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (287) all_68_0_88 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_42_0_53, all_72_0_92, all_0_5_5, all_0_4_4, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (288) all_72_0_92 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_72_0_92, all_42_0_53, all_0_4_4, all_0_5_5, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (289) all_72_0_92 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_42_0_53, all_72_0_92, all_0_4_4, all_0_5_5, all_0_2_2, all_68_1_89 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (290) all_72_0_92 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_72_0_92, all_42_0_53, all_0_5_5, all_0_4_4, all_68_1_89, all_0_2_2 and discharging atoms apart_point_and_line(all_68_1_89, all_0_4_4) = all_72_0_92, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (291) all_72_0_92 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_42_0_53, all_58_0_75, all_0_5_5, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (292) all_58_0_75 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_58_0_75, all_42_0_53, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (293) all_58_0_75 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_42_0_53, all_58_0_75, all_0_3_3, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (294) all_58_0_75 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (94) with all_58_0_75, all_42_0_53, all_0_5_5, 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_58_0_75, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (295) all_58_0_75 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_42_0_53, all_56_0_73, all_0_5_5, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (296) all_56_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_56_0_73, all_42_0_53, all_0_5_5, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_73, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (297) all_56_0_73 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (47) with all_42_0_53, all_87_0_110, all_0_5_5, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (298) all_87_0_110 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (47) with all_87_0_110, all_42_0_53, all_0_3_3, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (299) all_87_0_110 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_42_0_53, all_87_0_110, all_0_5_5, 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_87_0_110, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (300) all_87_0_110 = 0 | all_42_0_53 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.59 |
% 40.50/12.59 | Instantiating formula (59) with all_87_0_110, all_42_0_53, all_0_3_3, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_87_0_110, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.59 | (301) all_87_0_110 = 0 | all_42_0_53 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (47) with all_42_0_53, all_44_0_55, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (302) all_44_0_55 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (47) with all_44_0_55, all_42_0_53, all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (303) all_44_0_55 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (59) with all_42_0_53, all_44_0_55, all_0_5_5, 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_44_0_55, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (304) all_44_0_55 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (59) with all_44_0_55, all_42_0_53, all_0_4_4, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_44_0_55, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (305) all_44_0_55 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (47) with all_42_0_53, all_42_0_53, all_0_5_5, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (306) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 40.50/12.60 |
% 40.50/12.60 | Instantiating formula (59) with all_42_0_53, all_42_0_53, all_0_5_5, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields:
% 40.50/12.60 | (307) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (306), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (308) all_42_0_53 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (308) can reduce 161 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.60 | (311) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (307), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (308) all_42_0_53 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (308) can reduce 161 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.60 | (315) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (236), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (316) all_72_0_92 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (316) can reduce 183 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.60 | (319) ? [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))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (237), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (316) all_72_0_92 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (316) can reduce 183 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.60 | (323) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (242), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (316) all_72_0_92 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (316) can reduce 183 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.60 | (327) all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (239), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (328) all_68_0_88 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (328) can reduce 177 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.60 | (331) all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (240), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (316) all_72_0_92 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (316) can reduce 183 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.60 | (335) all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (241), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (316) all_72_0_92 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (316) can reduce 183 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.60 | (339) all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (327), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (340) all_58_0_75 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (340) can reduce 173 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.60 | (343) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (331), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (340) all_58_0_75 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (340) can reduce 173 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.60 | (347) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (339), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (340) all_58_0_75 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (340) can reduce 173 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.60 | (351) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (243), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (340) all_58_0_75 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (340) can reduce 173 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.60 | (355) ? [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))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (282), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (356) all_44_0_55 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (356) can reduce 165 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.60 | (319) ? [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))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (231), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (328) all_68_0_88 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (328) can reduce 177 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.60 | (363) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (238), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (328) all_68_0_88 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (328) can reduce 177 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.60 | (367) all_58_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89, all_0_1_1) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (335), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (340) all_58_0_75 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (340) can reduce 173 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.60 | (371) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_1_1) = v0))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (265), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (372) all_87_0_110 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (372) can reduce 189 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.60 | (355) ? [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))
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (275), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (376) distinct_points(all_0_1_1, all_0_2_2) = 0
% 40.50/12.60 |
% 40.50/12.60 +-Applying beta-rule and splitting (230), into two cases.
% 40.50/12.60 |-Branch one:
% 40.50/12.60 | (328) all_68_0_88 = 0
% 40.50/12.60 |
% 40.50/12.60 | Equations (328) can reduce 177 to:
% 40.50/12.60 | (309) $false
% 40.50/12.60 |
% 40.50/12.60 |-The branch is then unsatisfiable
% 40.50/12.60 |-Branch two:
% 40.50/12.60 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.60 | (355) ? [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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (283), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (356) all_44_0_55 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (356) can reduce 165 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.61 | (384) ? [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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (244), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (340) all_58_0_75 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (340) can reduce 173 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.61 | (388) ? [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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (298), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (392) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (303), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (356) all_44_0_55 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (356) can reduce 165 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.61 | (396) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (280), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (400) all_44_0_55 = 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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (232), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (404) all_68_0_88 = 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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (233), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (408) all_68_0_88 = 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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (299), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (412) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (302), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (356) all_44_0_55 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (356) can reduce 165 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.61 | (416) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (290), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (420) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (279), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (421) all_56_0_73 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (421) can reduce 169 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.61 | (424) all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (305), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (356) all_44_0_55 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (356) can reduce 165 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.61 | (428) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (288), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (432) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (301), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (436) all_42_0_53 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (278), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (421) all_56_0_73 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (421) can reduce 169 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.61 | (440) all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (304), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (356) all_44_0_55 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (356) can reduce 165 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (165) ~ (all_44_0_55 = 0)
% 40.50/12.61 | (444) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (286), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (328) all_68_0_88 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (328) can reduce 177 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.61 | (448) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (300), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (452) all_42_0_53 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (235), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (456) all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (277), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (421) all_56_0_73 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (421) can reduce 169 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.61 | (460) all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (291), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (464) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (281), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (372) all_87_0_110 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (372) can reduce 189 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.61 | (468) all_44_0_55 = 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))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (234), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.61 | (472) all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (287), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (328) all_68_0_88 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (328) can reduce 177 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.61 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.61 | (476) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.61 |
% 40.50/12.61 +-Applying beta-rule and splitting (289), into two cases.
% 40.50/12.61 |-Branch one:
% 40.50/12.61 | (316) all_72_0_92 = 0
% 40.50/12.61 |
% 40.50/12.61 | Equations (316) can reduce 183 to:
% 40.50/12.61 | (309) $false
% 40.50/12.61 |
% 40.50/12.61 |-The branch is then unsatisfiable
% 40.50/12.61 |-Branch two:
% 40.50/12.62 | (183) ~ (all_72_0_92 = 0)
% 40.50/12.62 | (480) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (292), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (484) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (293), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (488) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (271), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (492) all_44_0_55 = 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))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (296), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (421) all_56_0_73 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (421) can reduce 169 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.62 | (496) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (294), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (500) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (295), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (504) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (297), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (421) all_56_0_73 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (421) can reduce 169 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.62 | (508) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (272), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (512) all_44_0_55 = 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))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (276), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (421) all_56_0_73 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (421) can reduce 169 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.62 | (516) all_44_0_55 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (273), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (520) all_44_0_55 = 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))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (263), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (372) all_87_0_110 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (372) can reduce 189 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.62 | (524) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (264), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (372) all_87_0_110 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (372) can reduce 189 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.62 | (528) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (274), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (532) all_44_0_55 = 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))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (367), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (340) all_58_0_75 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (340) can reduce 173 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.62 | (536) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (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_68_1_89, all_0_1_1) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (404), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (328) all_68_0_88 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (328) can reduce 177 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.62 | (540) ? [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))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (420), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (308) can reduce 161 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.62 | (544) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (428), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (308) can reduce 161 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.62 | (548) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (432), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (308) can reduce 161 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.62 | (552) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (436), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (308) can reduce 161 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.62 | (556) ? [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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (456), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (328) all_68_0_88 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (328) can reduce 177 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.62 | (560) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_68_1_89, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_68_1_89) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (480), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.62 |
% 40.50/12.62 | Equations (308) can reduce 161 to:
% 40.50/12.62 | (309) $false
% 40.50/12.62 |
% 40.50/12.62 |-The branch is then unsatisfiable
% 40.50/12.62 |-Branch two:
% 40.50/12.62 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.62 | (564) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.62 |
% 40.50/12.62 +-Applying beta-rule and splitting (508), into two cases.
% 40.50/12.62 |-Branch one:
% 40.50/12.62 | (308) all_42_0_53 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (308) can reduce 161 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.63 | (568) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (524), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (421) all_56_0_73 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (421) can reduce 169 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (169) ~ (all_56_0_73 = 0)
% 40.50/12.63 | (572) ? [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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.63 |
% 40.50/12.63 | Instantiating (572) with all_403_0_143 yields:
% 40.50/12.63 | (573) (all_403_0_143 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_403_0_143 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_403_0_143 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_403_0_143) | ( ~ (all_403_0_143 = 0) & distinct_points(all_0_1_1, all_0_2_2) = all_403_0_143)
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (573), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (574) (all_403_0_143 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_403_0_143 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_403_0_143 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_403_0_143)
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (574), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (575) (all_403_0_143 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_403_0_143 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0)
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (575), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (576) all_403_0_143 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 40.50/12.63 |
% 40.50/12.63 | Applying alpha-rule on (576) yields:
% 40.50/12.63 | (577) all_403_0_143 = 0
% 40.50/12.63 | (578) apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (266), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (582) ? [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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (259), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (586) all_58_0_75 = 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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (251), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (590) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (252), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (594) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (260), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (598) all_58_0_75 = 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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (249), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (602) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (250), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (606) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (598), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (610) ? [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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (586), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (173) ~ (all_58_0_75 = 0)
% 40.50/12.63 | (614) ? [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))
% 40.50/12.63 |
% 40.50/12.63 | Instantiating formula (114) with all_0_1_1, all_0_3_3, 0, all_58_0_75 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_58_0_75, apart_point_and_line(all_0_1_1, all_0_3_3) = 0, yields:
% 40.50/12.63 | (340) all_58_0_75 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (340) can reduce 173 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (617) all_403_0_143 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 40.50/12.63 |
% 40.50/12.63 | Applying alpha-rule on (617) yields:
% 40.50/12.63 | (577) all_403_0_143 = 0
% 40.50/12.63 | (619) apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (266), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (582) ? [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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (260), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (598) all_58_0_75 = 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))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (255), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (631) all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (256), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (635) all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (257), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (639) all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (258), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (643) all_72_0_92 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.63 |
% 40.50/12.63 +-Applying beta-rule and splitting (261), into two cases.
% 40.50/12.63 |-Branch one:
% 40.50/12.63 | (372) all_87_0_110 = 0
% 40.50/12.63 |
% 40.50/12.63 | Equations (372) can reduce 189 to:
% 40.50/12.63 | (309) $false
% 40.50/12.63 |
% 40.50/12.63 |-The branch is then unsatisfiable
% 40.50/12.63 |-Branch two:
% 40.50/12.63 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.63 | (647) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (262), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (372) all_87_0_110 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (372) can reduce 189 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.64 | (651) all_56_0_73 = 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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (253), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (372) all_87_0_110 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (372) can reduce 189 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.64 | (655) all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (254), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (372) all_87_0_110 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (372) can reduce 189 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (189) ~ (all_87_0_110 = 0)
% 40.50/12.64 | (659) all_68_0_88 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (267), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (663) all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (268), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (667) all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (269), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (671) all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (270), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (675) all_44_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (245), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (679) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_1_1) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (247), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (683) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_1_1) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (248), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (687) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (246), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (691) all_56_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (416), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (695) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (444), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (699) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (448), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (703) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (488), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (707) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (659), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (711) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, 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_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (284), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (715) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (285), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (328) all_68_0_88 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (328) can reduce 177 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (177) ~ (all_68_0_88 = 0)
% 40.50/12.64 | (719) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (392), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (723) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (396), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (727) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (412), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (731) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (452), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (735) ? [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_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 40.50/12.64 |
% 40.50/12.64 +-Applying beta-rule and splitting (464), into two cases.
% 40.50/12.64 |-Branch one:
% 40.50/12.64 | (308) all_42_0_53 = 0
% 40.50/12.64 |
% 40.50/12.64 | Equations (308) can reduce 161 to:
% 40.50/12.64 | (309) $false
% 40.50/12.64 |
% 40.50/12.64 |-The branch is then unsatisfiable
% 40.50/12.64 |-Branch two:
% 40.50/12.64 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.64 | (739) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (476), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (743) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (484), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (747) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (496), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (751) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (500), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (755) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (504), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (759) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (715), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (763) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_68_1_89, all_0_2_2) = v0))
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (719), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (161) ~ (all_42_0_53 = 0)
% 40.50/12.65 | (767) ? [v0] : ((v0 = 0 & apart_point_and_line(all_68_1_89, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_68_1_89) = v0))
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (114) with all_0_2_2, all_0_5_5, 0, all_42_0_53 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, apart_point_and_line(all_0_2_2, all_0_5_5) = 0, yields:
% 40.50/12.65 | (308) all_42_0_53 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (308) can reduce 161 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (770) ~ (all_403_0_143 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_403_0_143
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (770) yields:
% 40.50/12.65 | (771) ~ (all_403_0_143 = 0)
% 40.50/12.65 | (772) distinct_lines(all_0_3_3, all_0_5_5) = all_403_0_143
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (111) with all_403_0_143, all_0_5_5, all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_5_5) = all_403_0_143, yields:
% 40.50/12.65 | (773) all_403_0_143 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0
% 40.50/12.65 |
% 40.50/12.65 +-Applying beta-rule and splitting (773), into two cases.
% 40.50/12.65 |-Branch one:
% 40.50/12.65 | (774) convergent_lines(all_0_5_5, all_0_5_5) = 0
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (106) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields:
% 40.50/12.65 | (775) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (776) ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0)
% 40.50/12.65 | (577) all_403_0_143 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (577) can reduce 771 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (779) ~ (all_403_0_143 = 0) & distinct_points(all_0_1_1, all_0_2_2) = all_403_0_143
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (779) yields:
% 40.50/12.65 | (771) ~ (all_403_0_143 = 0)
% 40.50/12.65 | (781) distinct_points(all_0_1_1, all_0_2_2) = all_403_0_143
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (36) with all_0_1_1, all_0_2_2, 0, all_403_0_143 and discharging atoms distinct_points(all_0_1_1, all_0_2_2) = all_403_0_143, distinct_points(all_0_1_1, all_0_2_2) = 0, yields:
% 40.50/12.65 | (577) all_403_0_143 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (577) can reduce 771 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (784) ~ (distinct_points(all_0_1_1, all_0_2_2) = 0)
% 40.50/12.65 | (356) all_44_0_55 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (356) can reduce 165 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (787) ~ (all_71_0_91 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_71_0_91
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (787) yields:
% 40.50/12.65 | (202) ~ (all_71_0_91 = 0)
% 40.50/12.65 | (789) convergent_lines(all_0_5_5, all_0_4_4) = all_71_0_91
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (115) with all_0_5_5, all_0_4_4, all_71_0_91, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_71_0_91, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 40.50/12.65 | (790) all_71_0_91 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (790) can reduce 202 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (792) ~ (all_70_0_90 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_70_0_90
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (792) yields:
% 40.50/12.65 | (199) ~ (all_70_0_90 = 0)
% 40.50/12.65 | (794) convergent_lines(all_0_5_5, all_0_4_4) = all_70_0_90
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (115) with all_0_5_5, all_0_4_4, all_70_0_90, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_70_0_90, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 40.50/12.65 | (795) all_70_0_90 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (795) can reduce 199 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (797) ~ (all_86_0_109 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_86_0_109
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (797) yields:
% 40.50/12.65 | (196) ~ (all_86_0_109 = 0)
% 40.50/12.65 | (799) convergent_lines(all_0_5_5, all_0_3_3) = all_86_0_109
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (115) with all_0_5_5, all_0_3_3, all_86_0_109, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_86_0_109, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 40.50/12.65 | (800) all_86_0_109 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (800) can reduce 196 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (802) ~ (all_79_0_100 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_79_0_100
% 40.50/12.65 |
% 40.50/12.65 | Applying alpha-rule on (802) yields:
% 40.50/12.65 | (193) ~ (all_79_0_100 = 0)
% 40.50/12.65 | (804) convergent_lines(all_0_5_5, all_0_3_3) = all_79_0_100
% 40.50/12.65 |
% 40.50/12.65 | Instantiating formula (115) with all_0_5_5, all_0_3_3, all_79_0_100, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_79_0_100, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 40.50/12.65 | (805) all_79_0_100 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (805) can reduce 193 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 |-Branch two:
% 40.50/12.65 | (807) ~ (apart_point_and_line(all_0_1_1, all_0_4_4) = 0)
% 40.50/12.65 | (808) all_0_0_0 = 0
% 40.50/12.65 |
% 40.50/12.65 | Equations (808) can reduce 93 to:
% 40.50/12.65 | (309) $false
% 40.50/12.65 |
% 40.50/12.65 |-The branch is then unsatisfiable
% 40.50/12.65 % SZS output end Proof for theBenchmark
% 40.50/12.65
% 40.50/12.65 12056ms
%------------------------------------------------------------------------------