TSTP Solution File: GEO202+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 03:48:38 EDT 2022
% Result : Theorem 22.01s 6.19s
% Output : Proof 35.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 16:58:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.57 (ePrincess v.1.0)
% 0.51/0.57
% 0.51/0.57 (c) Philipp Rümmer, 2009-2015
% 0.51/0.57 (c) Peter Backeman, 2014-2015
% 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.57 Bug reports to peter@backeman.se
% 0.51/0.57
% 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.57
% 0.51/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/0.97 Prover 0: Preprocessing ...
% 2.46/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.46/1.21 Prover 0: Constructing countermodel ...
% 19.23/5.58 Prover 0: gave up
% 19.23/5.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.39/5.62 Prover 1: Preprocessing ...
% 19.62/5.74 Prover 1: Constructing countermodel ...
% 20.12/5.78 Prover 1: gave up
% 20.12/5.78 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.45/5.82 Prover 2: Preprocessing ...
% 21.07/5.97 Prover 2: Warning: ignoring some quantifiers
% 21.07/5.98 Prover 2: Constructing countermodel ...
% 22.01/6.19 Prover 2: proved (404ms)
% 22.01/6.19
% 22.01/6.19 No countermodel exists, formula is valid
% 22.01/6.19 % SZS status Theorem for theBenchmark
% 22.01/6.19
% 22.01/6.19 Generating proof ... Warning: ignoring some quantifiers
% 34.74/9.70 found it (size 556)
% 34.74/9.70
% 34.74/9.70 % SZS output start Proof for theBenchmark
% 34.74/9.70 Assumed formulas after preprocessing and simplification:
% 34.74/9.70 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & equal_points(v5, v0) = v6 & intersection_point(v3, v4) = v5 & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & convergent_lines(v3, v4) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v9, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_lines(v8, v9) = 0) | ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v9, v10) = v12) | ~ (apart_point_and_line(v7, v8) = v11) | ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (apart_point_and_line(v7, v8) = v11) | ~ (distinct_lines(v8, v9) = 0) | ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v8, v9) = v11) | ~ (distinct_points(v7, v8) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v7, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v7, v10) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v9) = v12) | ~ (apart_point_and_line(v7, v10) = v11) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v9) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v7, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_points(v7, v8) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v9, v8) = v11) | ~ (distinct_points(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ? [v12] : ((v12 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_lines(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v10) | ~ (convergent_lines(v8, v9) = v11) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v10) | ~ (convergent_lines(v8, v9) = v11) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (convergent_lines(v8, v9) = v11) | ~ (convergent_lines(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (convergent_lines(v7, v9) = v11) | ~ (distinct_lines(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = v11) | ~ (distinct_lines(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_points(v8, v9) = v11) | ~ (distinct_points(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & distinct_points(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) | ~ (unorthogonal_lines(v7, v9) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) | ~ (convergent_lines(v7, v9) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) | ~ (convergent_lines(v7, v8) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (convergent_lines(v8, v9) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v7, v9) = v11) | ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v8, v9) = v11) | ~ (convergent_lines(v7, v9) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v7, v9) = v11) | ~ (convergent_lines(v7, v8) = v10) | ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v10) | ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v9, v8) = v10) | ~ (apart_point_and_line(v7, v8) = 0) | distinct_points(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v9) = v10) | ~ (apart_point_and_line(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v8) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v9) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v8, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v8, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v7, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v8, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v7, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_lines(v10, v9) = v8) | ~ (orthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (incident_point_and_line(v10, v9) = v8) | ~ (incident_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_lines(v10, v9) = v8) | ~ (parallel_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_lines(v10, v9) = v8) | ~ (equal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_points(v10, v9) = v8) | ~ (equal_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_through_point(v10, v9) = v8) | ~ (orthogonal_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unorthogonal_lines(v10, v9) = v8) | ~ (unorthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_through_point(v10, v9) = v8) | ~ (parallel_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection_point(v10, v9) = v8) | ~ (intersection_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (line_connecting(v10, v9) = v8) | ~ (line_connecting(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apart_point_and_line(v10, v9) = v8) | ~ (apart_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (convergent_lines(v10, v9) = v8) | ~ (convergent_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_lines(v10, v9) = v8) | ~ (distinct_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_points(v10, v9) = v8) | ~ (distinct_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) | ~ (unorthogonal_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (unorthogonal_lines(v7, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (convergent_lines(v7, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (unorthogonal_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (convergent_lines(v8, v9) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v8, v9) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v7, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v8, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) | ~ (convergent_lines(v7, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) | ~ (distinct_points(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v8, v10) = 0) | (v11 = 0 & apart_point_and_line(v8, v9) = 0) | (v11 = 0 & apart_point_and_line(v7, v10) = 0) | (v11 = 0 & apart_point_and_line(v7, v9) = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (orthogonal_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (incident_point_and_line(v7, v8) = v9) | apart_point_and_line(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (parallel_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_lines(v7, v8) = v9) | distinct_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_points(v7, v8) = v9) | distinct_points(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v9) | orthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v7, v8) = v9) | incident_point_and_line(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | parallel_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | equal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | equal_points(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (point(v9) = v8) | ~ (point(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (line(v9) = v8) | ~ (line(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & unorthogonal_lines(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v7, v8) = v9) | ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) | ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : ((v10 = 0 & point(v9) = 0) | ( ~ (v10 = 0) & line(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v8) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & point(v7) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v7] : ! [v8] : ( ~ (orthogonal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (incident_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (parallel_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_points(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & orthogonal_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & incident_point_and_line(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v8) = v10)) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v7) = v10)) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & point(v9) = 0 & intersection_point(v7, v8) = v9) | ( ~ (v9 = 0) & line(v8) = v9) | ( ~ (v9 = 0) & line(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & parallel_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & equal_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v8, v9) = v10)) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v7, v9) = v10)) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & line(v9) = 0 & line_connecting(v7, v8) = v9) | ( ~ (v9 = 0) & point(v8) = v9) | ( ~ (v9 = 0) & point(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & equal_points(v7, v8) = v9)) & ! [v7] : ~ (convergent_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_points(v7, v7) = 0) & ? [v7] : ? [v8] : ? [v9] : orthogonal_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : incident_point_and_line(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : parallel_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : equal_points(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : orthogonal_through_point(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : unorthogonal_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : parallel_through_point(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection_point(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : line_connecting(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : apart_point_and_line(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : convergent_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : distinct_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : distinct_points(v8, v7) = v9 & ? [v7] : ? [v8] : point(v7) = v8 & ? [v7] : ? [v8] : line(v7) = v8)
% 35.18/9.79 | 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, all_0_6_6 yields:
% 35.18/9.79 | (1) ~ (all_0_0_0 = 0) & equal_points(all_0_1_1, all_0_6_6) = all_0_0_0 & intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1 & line_connecting(all_0_6_6, all_0_4_4) = all_0_2_2 & line_connecting(all_0_6_6, all_0_5_5) = all_0_3_3 & convergent_lines(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_6_6, all_0_4_4) = 0 & distinct_points(all_0_6_6, all_0_5_5) = 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
% 35.18/9.82 |
% 35.18/9.82 | Applying alpha-rule on (1) yields:
% 35.18/9.82 | (2) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 35.18/9.82 | (3) ! [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)))
% 35.18/9.82 | (4) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 35.18/9.82 | (5) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 35.18/9.83 | (6) ! [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)))
% 35.18/9.83 | (7) ! [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)))
% 35.18/9.83 | (8) ! [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)))
% 35.18/9.83 | (9) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 35.18/9.83 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 35.18/9.83 | (11) ? [v0] : ? [v1] : point(v0) = v1
% 35.18/9.83 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 35.18/9.83 | (13) ! [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)
% 35.18/9.83 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 35.18/9.83 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 35.18/9.83 | (16) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 35.18/9.83 | (17) ! [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)))
% 35.18/9.83 | (18) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 35.18/9.83 | (19) ! [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)))
% 35.18/9.83 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 35.18/9.83 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 35.18/9.83 | (22) ! [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)))
% 35.18/9.83 | (23) ! [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)))
% 35.18/9.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 35.18/9.83 | (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))
% 35.18/9.83 | (26) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 35.18/9.83 | (27) ! [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)))
% 35.18/9.83 | (28) ? [v0] : ? [v1] : line(v0) = v1
% 35.18/9.83 | (29) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 35.18/9.83 | (30) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 35.18/9.83 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 35.43/9.83 | (32) ! [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)))
% 35.43/9.83 | (33) ! [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))
% 35.43/9.84 | (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)))
% 35.43/9.84 | (35) ! [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)))
% 35.43/9.84 | (36) ! [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))
% 35.43/9.84 | (37) ! [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))
% 35.43/9.84 | (38) ! [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)))
% 35.43/9.84 | (39) ! [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))
% 35.43/9.84 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 35.43/9.84 | (41) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 35.43/9.84 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 35.43/9.84 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 35.43/9.84 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 35.43/9.84 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 35.43/9.84 | (46) ! [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)))
% 35.43/9.84 | (47) ! [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)))
% 35.43/9.84 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 35.43/9.84 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 35.43/9.84 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 35.43/9.84 | (51) ! [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)))
% 35.43/9.84 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 35.43/9.84 | (53) ! [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)))
% 35.43/9.84 | (54) ! [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)))
% 35.43/9.85 | (55) ! [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)))
% 35.43/9.85 | (56) ! [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)))
% 35.43/9.85 | (57) ! [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)))
% 35.43/9.85 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 35.43/9.85 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 35.43/9.85 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 35.43/9.85 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 35.43/9.85 | (62) ! [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))
% 35.43/9.85 | (63) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 35.43/9.85 | (64) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 35.43/9.85 | (65) ! [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)))
% 35.43/9.85 | (66) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 35.43/9.85 | (67) ! [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)))
% 35.43/9.85 | (68) ~ (all_0_0_0 = 0)
% 35.43/9.85 | (69) ! [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)))
% 35.43/9.85 | (70) ! [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)))
% 35.43/9.85 | (71) ! [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)))
% 35.50/9.85 | (72) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 35.50/9.85 | (73) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 35.50/9.85 | (74) ! [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)))
% 35.50/9.85 | (75) ! [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)))
% 35.50/9.85 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 35.50/9.85 | (77) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 35.50/9.85 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 35.50/9.85 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 35.50/9.85 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 35.50/9.85 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 35.50/9.85 | (82) ! [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)))
% 35.50/9.85 | (83) ! [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))
% 35.50/9.85 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 35.50/9.85 | (85) ! [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)))
% 35.50/9.85 | (86) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 35.50/9.85 | (87) ! [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)
% 35.50/9.85 | (88) ! [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)))
% 35.50/9.85 | (89) distinct_points(all_0_6_6, all_0_5_5) = 0
% 35.50/9.85 | (90) line_connecting(all_0_6_6, all_0_4_4) = all_0_2_2
% 35.50/9.85 | (91) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 35.50/9.85 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 35.50/9.86 | (93) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 35.50/9.86 | (94) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 35.50/9.86 | (95) ! [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)))
% 35.50/9.86 | (96) ! [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)))
% 35.50/9.86 | (97) ! [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)))
% 35.50/9.86 | (98) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 35.50/9.86 | (99) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 35.50/9.86 | (100) distinct_points(all_0_6_6, all_0_4_4) = 0
% 35.50/9.86 | (101) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 35.50/9.86 | (102) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 35.50/9.86 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 35.50/9.86 | (104) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 35.50/9.86 | (105) ! [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)))
% 35.50/9.86 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 35.50/9.86 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 35.50/9.86 | (108) ! [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)))
% 35.50/9.86 | (109) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 35.50/9.86 | (110) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 35.50/9.86 | (111) ! [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)))
% 35.50/9.86 | (112) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 35.50/9.86 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 35.50/9.86 | (114) ! [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)))
% 35.50/9.86 | (115) ! [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)))
% 35.50/9.86 | (116) ! [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)))
% 35.50/9.86 | (117) ! [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)
% 35.50/9.86 | (118) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 35.50/9.86 | (119) ! [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)))
% 35.50/9.86 | (120) ! [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)
% 35.50/9.86 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 35.50/9.86 | (122) ! [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)))
% 35.50/9.86 | (123) equal_points(all_0_1_1, all_0_6_6) = all_0_0_0
% 35.50/9.86 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 35.50/9.86 | (125) ! [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)))
% 35.50/9.86 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 35.50/9.86 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 35.50/9.86 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 35.50/9.86 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 35.50/9.86 | (130) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 35.50/9.86 | (131) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 35.50/9.86 | (132) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 35.50/9.86 | (133) ! [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)))
% 35.50/9.86 | (134) ! [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)))
% 35.50/9.87 | (135) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 35.50/9.87 | (136) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 35.50/9.87 | (137) ! [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)))
% 35.50/9.87 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 35.50/9.87 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 35.50/9.87 | (140) intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1
% 35.50/9.87 | (141) line_connecting(all_0_6_6, all_0_5_5) = all_0_3_3
% 35.50/9.87 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 35.50/9.87 | (143) ! [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)))
% 35.50/9.87 | (144) ! [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)))
% 35.50/9.87 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 35.50/9.87 | (146) ! [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)))
% 35.50/9.87 | (147) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (60) with all_0_0_0, all_0_6_6, all_0_1_1 and discharging atoms equal_points(all_0_1_1, all_0_6_6) = all_0_0_0, yields:
% 35.50/9.87 | (148) all_0_0_0 = 0 | distinct_points(all_0_1_1, all_0_6_6) = 0
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (144) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 35.50/9.87 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (95) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 35.50/9.87 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (85) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 35.50/9.87 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (115) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 35.50/9.87 | (152) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (85) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 35.50/9.87 | (153) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (115) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 35.50/9.87 | (154) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (118) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 35.50/9.87 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (98) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 35.50/9.87 | (156) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (16) with all_0_4_4, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.87 | (157) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_6_6, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (102) with all_0_4_4, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.87 | (158) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_6_6, all_0_4_4) = v0 & apart_point_and_line(all_0_6_6, v0) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (16) with all_0_5_5, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.87 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_6_6, all_0_5_5) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating formula (102) with all_0_5_5, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.87 | (160) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_6_6, all_0_5_5) = v0 & apart_point_and_line(all_0_6_6, v0) = v1)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (160) with all_42_0_54, all_42_1_55 yields:
% 35.50/9.87 | (161) ~ (all_42_0_54 = 0) & line_connecting(all_0_6_6, all_0_5_5) = all_42_1_55 & apart_point_and_line(all_0_6_6, all_42_1_55) = all_42_0_54
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (161) yields:
% 35.50/9.87 | (162) ~ (all_42_0_54 = 0)
% 35.50/9.87 | (163) line_connecting(all_0_6_6, all_0_5_5) = all_42_1_55
% 35.50/9.87 | (164) apart_point_and_line(all_0_6_6, all_42_1_55) = all_42_0_54
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (159) with all_44_0_56, all_44_1_57 yields:
% 35.50/9.87 | (165) ~ (all_44_0_56 = 0) & line_connecting(all_0_6_6, all_0_5_5) = all_44_1_57 & apart_point_and_line(all_0_5_5, all_44_1_57) = all_44_0_56
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (165) yields:
% 35.50/9.87 | (166) ~ (all_44_0_56 = 0)
% 35.50/9.87 | (167) line_connecting(all_0_6_6, all_0_5_5) = all_44_1_57
% 35.50/9.87 | (168) apart_point_and_line(all_0_5_5, all_44_1_57) = all_44_0_56
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (156) with all_49_0_61, all_49_1_62 yields:
% 35.50/9.87 | (169) ~ (all_49_0_61 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_49_1_62 & apart_point_and_line(all_49_1_62, all_0_3_3) = all_49_0_61
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (169) yields:
% 35.50/9.87 | (170) ~ (all_49_0_61 = 0)
% 35.50/9.87 | (171) intersection_point(all_0_3_3, all_0_2_2) = all_49_1_62
% 35.50/9.87 | (172) apart_point_and_line(all_49_1_62, all_0_3_3) = all_49_0_61
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (155) with all_51_0_63, all_51_1_64 yields:
% 35.50/9.87 | (173) ~ (all_51_0_63 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_51_1_64 & apart_point_and_line(all_51_1_64, all_0_2_2) = all_51_0_63
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (173) yields:
% 35.50/9.87 | (174) ~ (all_51_0_63 = 0)
% 35.50/9.87 | (175) intersection_point(all_0_3_3, all_0_2_2) = all_51_1_64
% 35.50/9.87 | (176) apart_point_and_line(all_51_1_64, all_0_2_2) = all_51_0_63
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (154) with all_54_0_67 yields:
% 35.50/9.87 | (177) ( ~ (all_54_0_67 = 0) & apart_point_and_line(all_0_6_6, all_0_3_3) = all_54_0_67) | ( ~ (all_54_0_67 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_54_0_67)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (153) with all_55_0_68 yields:
% 35.50/9.87 | (178) ( ~ (all_55_0_68 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_55_0_68) | ( ~ (all_55_0_68 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_55_0_68)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (158) with all_59_0_73, all_59_1_74 yields:
% 35.50/9.87 | (179) ~ (all_59_0_73 = 0) & line_connecting(all_0_6_6, all_0_4_4) = all_59_1_74 & apart_point_and_line(all_0_6_6, all_59_1_74) = all_59_0_73
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (179) yields:
% 35.50/9.87 | (180) ~ (all_59_0_73 = 0)
% 35.50/9.87 | (181) line_connecting(all_0_6_6, all_0_4_4) = all_59_1_74
% 35.50/9.87 | (182) apart_point_and_line(all_0_6_6, all_59_1_74) = all_59_0_73
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (157) with all_61_0_75, all_61_1_76 yields:
% 35.50/9.87 | (183) ~ (all_61_0_75 = 0) & line_connecting(all_0_6_6, all_0_4_4) = all_61_1_76 & apart_point_and_line(all_0_4_4, all_61_1_76) = all_61_0_75
% 35.50/9.87 |
% 35.50/9.87 | Applying alpha-rule on (183) yields:
% 35.50/9.87 | (184) ~ (all_61_0_75 = 0)
% 35.50/9.87 | (185) line_connecting(all_0_6_6, all_0_4_4) = all_61_1_76
% 35.50/9.87 | (186) apart_point_and_line(all_0_4_4, all_61_1_76) = all_61_0_75
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (152) with all_67_0_81 yields:
% 35.50/9.87 | (187) ( ~ (all_67_0_81 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = all_67_0_81) | ( ~ (all_67_0_81 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_67_0_81)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (150) with all_68_0_82 yields:
% 35.50/9.87 | (188) ( ~ (all_68_0_82 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_68_0_82) | ( ~ (all_68_0_82 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_68_0_82)
% 35.50/9.87 |
% 35.50/9.87 | Instantiating (149) with all_69_0_83 yields:
% 35.50/9.87 | (189) ( ~ (all_69_0_83 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_69_0_83) | ( ~ (all_69_0_83 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_69_0_83)
% 35.50/9.88 |
% 35.50/9.88 | Instantiating (151) with all_70_0_84 yields:
% 35.50/9.88 | (190) ( ~ (all_70_0_84 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_70_0_84) | ( ~ (all_70_0_84 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_70_0_84)
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (148), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (191) distinct_points(all_0_1_1, all_0_6_6) = 0
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (187), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (192) ~ (all_67_0_81 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = all_67_0_81
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (192) yields:
% 35.50/9.88 | (193) ~ (all_67_0_81 = 0)
% 35.50/9.88 | (194) apart_point_and_line(all_0_6_6, all_0_2_2) = all_67_0_81
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (188), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (195) ~ (all_68_0_82 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_68_0_82
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (195) yields:
% 35.50/9.88 | (196) ~ (all_68_0_82 = 0)
% 35.50/9.88 | (197) apart_point_and_line(all_0_1_1, all_0_3_3) = all_68_0_82
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (177), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (198) ~ (all_54_0_67 = 0) & apart_point_and_line(all_0_6_6, all_0_3_3) = all_54_0_67
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (198) yields:
% 35.50/9.88 | (199) ~ (all_54_0_67 = 0)
% 35.50/9.88 | (200) apart_point_and_line(all_0_6_6, all_0_3_3) = all_54_0_67
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (178), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (201) ~ (all_55_0_68 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_55_0_68
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (201) yields:
% 35.50/9.88 | (202) ~ (all_55_0_68 = 0)
% 35.50/9.88 | (203) apart_point_and_line(all_0_5_5, all_0_3_3) = all_55_0_68
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (189), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (204) ~ (all_69_0_83 = 0) & apart_point_and_line(all_0_1_1, all_0_2_2) = all_69_0_83
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (204) yields:
% 35.50/9.88 | (205) ~ (all_69_0_83 = 0)
% 35.50/9.88 | (206) apart_point_and_line(all_0_1_1, all_0_2_2) = all_69_0_83
% 35.50/9.88 |
% 35.50/9.88 +-Applying beta-rule and splitting (190), into two cases.
% 35.50/9.88 |-Branch one:
% 35.50/9.88 | (207) ~ (all_70_0_84 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_70_0_84
% 35.50/9.88 |
% 35.50/9.88 | Applying alpha-rule on (207) yields:
% 35.50/9.88 | (208) ~ (all_70_0_84 = 0)
% 35.50/9.88 | (209) apart_point_and_line(all_0_4_4, all_0_2_2) = all_70_0_84
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (44) with all_0_3_3, all_0_2_2, all_51_1_64, all_0_1_1 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_51_1_64, intersection_point(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 35.50/9.88 | (210) all_51_1_64 = all_0_1_1
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (44) with all_0_3_3, all_0_2_2, all_49_1_62, all_51_1_64 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_51_1_64, intersection_point(all_0_3_3, all_0_2_2) = all_49_1_62, yields:
% 35.50/9.88 | (211) all_51_1_64 = all_49_1_62
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (142) with all_0_6_6, all_0_4_4, all_61_1_76, all_0_2_2 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_61_1_76, line_connecting(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 35.50/9.88 | (212) all_61_1_76 = all_0_2_2
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (142) with all_0_6_6, all_0_4_4, all_59_1_74, all_61_1_76 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_61_1_76, line_connecting(all_0_6_6, all_0_4_4) = all_59_1_74, yields:
% 35.50/9.88 | (213) all_61_1_76 = all_59_1_74
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (142) with all_0_6_6, all_0_5_5, all_44_1_57, all_0_3_3 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_44_1_57, line_connecting(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 35.50/9.88 | (214) all_44_1_57 = all_0_3_3
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (142) with all_0_6_6, all_0_5_5, all_42_1_55, all_44_1_57 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_44_1_57, line_connecting(all_0_6_6, all_0_5_5) = all_42_1_55, yields:
% 35.50/9.88 | (215) all_44_1_57 = all_42_1_55
% 35.50/9.88 |
% 35.50/9.88 | Combining equations (212,213) yields a new equation:
% 35.50/9.88 | (216) all_59_1_74 = all_0_2_2
% 35.50/9.88 |
% 35.50/9.88 | Combining equations (211,210) yields a new equation:
% 35.50/9.88 | (217) all_49_1_62 = all_0_1_1
% 35.50/9.88 |
% 35.50/9.88 | Simplifying 217 yields:
% 35.50/9.88 | (218) all_49_1_62 = all_0_1_1
% 35.50/9.88 |
% 35.50/9.88 | Combining equations (215,214) yields a new equation:
% 35.50/9.88 | (219) all_42_1_55 = all_0_3_3
% 35.50/9.88 |
% 35.50/9.88 | Simplifying 219 yields:
% 35.50/9.88 | (220) all_42_1_55 = all_0_3_3
% 35.50/9.88 |
% 35.50/9.88 | Combining equations (216,213) yields a new equation:
% 35.50/9.88 | (212) all_61_1_76 = all_0_2_2
% 35.50/9.88 |
% 35.50/9.88 | From (210) and (176) follows:
% 35.50/9.88 | (222) apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63
% 35.50/9.88 |
% 35.50/9.88 | From (218) and (172) follows:
% 35.50/9.88 | (223) apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61
% 35.50/9.88 |
% 35.50/9.88 | From (212) and (186) follows:
% 35.50/9.88 | (224) apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75
% 35.50/9.88 |
% 35.50/9.88 | From (214) and (168) follows:
% 35.50/9.88 | (225) apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56
% 35.50/9.88 |
% 35.50/9.88 | From (216) and (182) follows:
% 35.50/9.88 | (226) apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73
% 35.50/9.88 |
% 35.50/9.88 | From (220) and (164) follows:
% 35.50/9.88 | (227) apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_1_1, all_0_2_2, all_51_0_63, all_69_0_83 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_69_0_83, apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, yields:
% 35.50/9.88 | (228) all_69_0_83 = all_51_0_63
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_1_1, all_0_3_3, all_49_0_61, all_68_0_82 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_68_0_82, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, yields:
% 35.50/9.88 | (229) all_68_0_82 = all_49_0_61
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_4_4, all_0_2_2, all_61_0_75, all_70_0_84 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_70_0_84, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.88 | (230) all_70_0_84 = all_61_0_75
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_5_5, all_0_3_3, all_44_0_56, all_55_0_68 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_55_0_68, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.88 | (231) all_55_0_68 = all_44_0_56
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_6_6, all_0_2_2, all_59_0_73, all_67_0_81 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_67_0_81, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.88 | (232) all_67_0_81 = all_59_0_73
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (61) with all_0_6_6, all_0_3_3, all_42_0_54, all_54_0_67 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_54_0_67, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.88 | (233) all_54_0_67 = all_42_0_54
% 35.50/9.88 |
% 35.50/9.88 | Equations (230) can reduce 208 to:
% 35.50/9.88 | (184) ~ (all_61_0_75 = 0)
% 35.50/9.88 |
% 35.50/9.88 | Equations (228) can reduce 205 to:
% 35.50/9.88 | (174) ~ (all_51_0_63 = 0)
% 35.50/9.88 |
% 35.50/9.88 | Equations (229) can reduce 196 to:
% 35.50/9.88 | (170) ~ (all_49_0_61 = 0)
% 35.50/9.88 |
% 35.50/9.88 | Equations (232) can reduce 193 to:
% 35.50/9.88 | (180) ~ (all_59_0_73 = 0)
% 35.50/9.88 |
% 35.50/9.88 | Equations (231) can reduce 202 to:
% 35.50/9.88 | (166) ~ (all_44_0_56 = 0)
% 35.50/9.88 |
% 35.50/9.88 | Equations (233) can reduce 199 to:
% 35.50/9.88 | (162) ~ (all_42_0_54 = 0)
% 35.50/9.88 |
% 35.50/9.88 | From (228) and (206) follows:
% 35.50/9.88 | (222) apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63
% 35.50/9.88 |
% 35.50/9.88 | From (229) and (197) follows:
% 35.50/9.88 | (223) apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61
% 35.50/9.88 |
% 35.50/9.88 | From (230) and (209) follows:
% 35.50/9.88 | (224) apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75
% 35.50/9.88 |
% 35.50/9.88 | From (231) and (203) follows:
% 35.50/9.88 | (225) apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56
% 35.50/9.88 |
% 35.50/9.88 | From (232) and (194) follows:
% 35.50/9.88 | (226) apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73
% 35.50/9.88 |
% 35.50/9.88 | From (233) and (200) follows:
% 35.50/9.88 | (227) apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (6) with all_51_0_63, all_51_0_63, all_0_2_2, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, yields:
% 35.50/9.88 | (246) all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (32) with all_51_0_63, all_51_0_63, all_0_2_2, all_0_2_2, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, yields:
% 35.50/9.88 | (247) all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (6) with all_49_0_61, all_51_0_63, 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_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, yields:
% 35.50/9.88 | (248) all_51_0_63 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (6) with all_51_0_63, all_49_0_61, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, yields:
% 35.50/9.88 | (249) all_51_0_63 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (32) with all_49_0_61, all_51_0_63, all_0_3_3, all_0_2_2, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, yields:
% 35.50/9.88 | (250) all_51_0_63 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.50/9.88 |
% 35.50/9.88 | Instantiating formula (32) with all_51_0_63, all_49_0_61, all_0_2_2, 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_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, yields:
% 35.50/9.89 | (251) all_51_0_63 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (6) with all_49_0_61, all_49_0_61, 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_49_0_61, yields:
% 35.50/9.89 | (252) all_49_0_61 = 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))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_49_0_61, all_49_0_61, 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_49_0_61, yields:
% 35.50/9.89 | (253) all_49_0_61 = 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))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_61_0_75, all_51_0_63, all_0_2_2, 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_2_2) = all_51_0_63, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (254) all_61_0_75 = 0 | all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_51_0_63, all_61_0_75, all_0_2_2, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (255) all_61_0_75 = 0 | all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_61_0_75, all_49_0_61, all_0_2_2, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (256) all_61_0_75 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_49_0_61, all_61_0_75, all_0_3_3, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (257) all_61_0_75 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_61_0_75, all_49_0_61, all_0_3_3, 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_3_3) = all_49_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (258) all_61_0_75 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_49_0_61, all_61_0_75, all_0_2_2, all_0_3_3, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (259) all_61_0_75 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (56) with all_61_0_75, all_61_0_75, all_0_2_2, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.89 | (260) all_61_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (6) with all_61_0_75, all_61_0_75, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (261) all_61_0_75 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_61_0_75, all_61_0_75, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, yields:
% 35.50/9.89 | (262) all_61_0_75 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_44_0_56, all_51_0_63, all_0_3_3, all_0_2_2, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (263) all_51_0_63 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_51_0_63, all_44_0_56, all_0_2_2, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (264) all_51_0_63 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_44_0_56, all_51_0_63, all_0_2_2, 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_2_2) = all_51_0_63, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (265) all_51_0_63 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_51_0_63, all_44_0_56, all_0_3_3, all_0_2_2, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (266) all_51_0_63 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_44_0_56, all_49_0_61, all_0_3_3, 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_49_0_61, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (267) all_49_0_61 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, 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_5_5) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_49_0_61, all_44_0_56, all_0_3_3, all_0_3_3, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (268) all_49_0_61 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_44_0_56, all_61_0_75, all_0_3_3, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (269) all_61_0_75 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_61_0_75, all_44_0_56, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (270) all_61_0_75 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_44_0_56, all_61_0_75, all_0_2_2, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (271) all_61_0_75 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_61_0_75, all_44_0_56, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (272) all_61_0_75 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (6) with all_44_0_56, all_44_0_56, all_0_3_3, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, yields:
% 35.50/9.89 | (273) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_51_0_63, all_59_0_73, all_0_2_2, all_0_2_2, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.89 | (274) all_59_0_73 = 0 | all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (32) with all_49_0_61, all_59_0_73, all_0_3_3, all_0_2_2, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.89 | (275) all_59_0_73 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.89 |
% 35.50/9.89 | Instantiating formula (108) with all_59_0_73, all_49_0_61, all_0_3_3, all_0_2_2, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.89 | (276) all_59_0_73 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_49_0_61, all_59_0_73, all_0_2_2, all_0_3_3, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (277) all_59_0_73 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_59_0_73, all_61_0_75, all_0_2_2, all_0_2_2, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (278) all_61_0_75 = 0 | all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_59_0_73, all_44_0_56, all_0_2_2, all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (279) all_59_0_73 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_44_0_56, all_59_0_73, all_0_3_3, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (280) all_59_0_73 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_59_0_73, all_44_0_56, all_0_3_3, all_0_2_2, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (281) all_59_0_73 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_44_0_56, all_59_0_73, all_0_2_2, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (282) all_59_0_73 = 0 | all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (122) with all_59_0_73, all_59_0_73, all_0_2_2, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.90 | (283) all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (6) with all_59_0_73, all_59_0_73, all_0_2_2, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (284) all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_59_0_73, all_59_0_73, all_0_2_2, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, yields:
% 35.50/9.90 | (285) all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_42_0_54, all_51_0_63, all_0_3_3, all_0_2_2, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (286) all_51_0_63 = 0 | all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_51_0_63, all_42_0_54, all_0_2_2, all_0_3_3, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (287) all_51_0_63 = 0 | all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_51_0_63, all_42_0_54, all_0_3_3, all_0_2_2, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (288) all_51_0_63 = 0 | all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_42_0_54, all_49_0_61, all_0_3_3, all_0_3_3, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (289) all_49_0_61 = 0 | all_42_0_54 = 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_6_6, 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_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_49_0_61, all_42_0_54, all_0_3_3, all_0_3_3, all_0_1_1, all_0_6_6 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (290) all_49_0_61 = 0 | all_42_0_54 = 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_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_42_0_54, all_61_0_75, all_0_3_3, all_0_2_2, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (291) all_61_0_75 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_61_0_75, all_42_0_54, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (292) all_61_0_75 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_42_0_54, all_61_0_75, all_0_2_2, all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (293) all_61_0_75 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (108) with all_61_0_75, all_42_0_54, all_0_3_3, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_61_0_75, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (294) all_61_0_75 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_42_0_54, all_44_0_56, all_0_3_3, all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_44_0_56, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (295) all_44_0_56 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (122) with all_42_0_54, all_59_0_73, all_0_3_3, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.90 | (296) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (122) with all_59_0_73, all_42_0_54, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.90 | (297) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (122) with all_42_0_54, all_59_0_73, all_0_3_3, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.90 | (298) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (122) with all_59_0_73, all_42_0_54, all_0_2_2, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.90 | (299) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (6) with all_42_0_54, all_59_0_73, all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (300) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (6) with all_59_0_73, all_42_0_54, all_0_2_2, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (301) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_42_0_54, all_59_0_73, all_0_3_3, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (302) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.50/9.90 |
% 35.50/9.90 | Instantiating formula (32) with all_59_0_73, all_42_0_54, all_0_2_2, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.90 | (303) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (122) with all_42_0_54, all_42_0_54, all_0_3_3, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.50/9.91 | (304) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (122) with all_42_0_54, all_42_0_54, all_0_3_3, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.50/9.91 | (305) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (6) with all_42_0_54, all_42_0_54, all_0_3_3, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.91 | (306) all_42_0_54 = 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))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (32) with all_42_0_54, all_42_0_54, all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, yields:
% 35.50/9.91 | (307) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (122) with all_49_0_61, all_51_0_63, all_0_3_3, all_0_2_2, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (308) all_51_0_63 = 0 | all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (122) with all_49_0_61, all_49_0_61, all_0_3_3, all_0_3_3, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (309) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (56) with all_59_0_73, all_59_0_73, all_0_2_2, all_0_2_2, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (310) all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (56) with all_59_0_73, all_42_0_54, all_0_2_2, all_0_3_3, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (311) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (56) with all_42_0_54, all_59_0_73, all_0_3_3, all_0_2_2, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (312) all_59_0_73 = 0 | all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.50/9.91 |
% 35.50/9.91 | Instantiating formula (56) with all_42_0_54, all_42_0_54, all_0_3_3, all_0_3_3, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.50/9.91 | (313) all_42_0_54 = 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))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (306), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (314) all_42_0_54 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (314) can reduce 162 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (162) ~ (all_42_0_54 = 0)
% 35.50/9.91 | (317) ? [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))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (284), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (318) all_59_0_73 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (318) can reduce 180 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (180) ~ (all_59_0_73 = 0)
% 35.50/9.91 | (321) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (246), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (322) all_51_0_63 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (322) can reduce 174 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (174) ~ (all_51_0_63 = 0)
% 35.50/9.91 | (321) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (252), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (326) all_49_0_61 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (326) can reduce 170 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (170) ~ (all_49_0_61 = 0)
% 35.50/9.91 | (317) ? [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))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (261), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (330) all_61_0_75 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (330) can reduce 184 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (184) ~ (all_61_0_75 = 0)
% 35.50/9.91 | (321) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (273), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (334) all_44_0_56 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (334) can reduce 166 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (166) ~ (all_44_0_56 = 0)
% 35.50/9.91 | (317) ? [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))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (310), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (318) all_59_0_73 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (318) can reduce 180 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (180) ~ (all_59_0_73 = 0)
% 35.50/9.91 | (341) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (260), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (330) all_61_0_75 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (330) can reduce 184 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (184) ~ (all_61_0_75 = 0)
% 35.50/9.91 | (345) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.50/9.91 |
% 35.50/9.91 +-Applying beta-rule and splitting (313), into two cases.
% 35.50/9.91 |-Branch one:
% 35.50/9.91 | (314) all_42_0_54 = 0
% 35.50/9.91 |
% 35.50/9.91 | Equations (314) can reduce 162 to:
% 35.50/9.91 | (315) $false
% 35.50/9.91 |
% 35.50/9.91 |-The branch is then unsatisfiable
% 35.50/9.91 |-Branch two:
% 35.50/9.91 | (162) ~ (all_42_0_54 = 0)
% 35.50/9.91 | (349) ? [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))
% 35.50/9.91 |
% 35.79/9.91 +-Applying beta-rule and splitting (311), into two cases.
% 35.79/9.91 |-Branch one:
% 35.79/9.91 | (318) all_59_0_73 = 0
% 35.79/9.91 |
% 35.79/9.91 | Equations (318) can reduce 180 to:
% 35.79/9.91 | (315) $false
% 35.79/9.91 |
% 35.79/9.91 |-The branch is then unsatisfiable
% 35.79/9.91 |-Branch two:
% 35.79/9.91 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.91 | (353) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0))
% 35.79/9.91 |
% 35.79/9.91 +-Applying beta-rule and splitting (312), into two cases.
% 35.79/9.91 |-Branch one:
% 35.79/9.91 | (318) all_59_0_73 = 0
% 35.79/9.91 |
% 35.79/9.91 | Equations (318) can reduce 180 to:
% 35.79/9.91 | (315) $false
% 35.79/9.91 |
% 35.79/9.91 |-The branch is then unsatisfiable
% 35.79/9.91 |-Branch two:
% 35.79/9.91 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.91 | (357) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.91 |
% 35.79/9.91 +-Applying beta-rule and splitting (263), into two cases.
% 35.79/9.91 |-Branch one:
% 35.79/9.91 | (322) all_51_0_63 = 0
% 35.79/9.91 |
% 35.79/9.91 | Equations (322) can reduce 174 to:
% 35.79/9.91 | (315) $false
% 35.79/9.91 |
% 35.79/9.91 |-The branch is then unsatisfiable
% 35.79/9.91 |-Branch two:
% 35.79/9.91 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.91 | (361) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.79/9.91 |
% 35.79/9.91 +-Applying beta-rule and splitting (266), into two cases.
% 35.79/9.91 |-Branch one:
% 35.79/9.91 | (322) all_51_0_63 = 0
% 35.79/9.91 |
% 35.79/9.91 | Equations (322) can reduce 174 to:
% 35.79/9.91 | (315) $false
% 35.79/9.91 |
% 35.79/9.91 |-The branch is then unsatisfiable
% 35.79/9.91 |-Branch two:
% 35.79/9.91 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.91 | (365) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (264), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (369) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (265), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (373) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (353), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (314) all_42_0_54 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (314) can reduce 162 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.92 | (377) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (361), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (334) all_44_0_56 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (334) can reduce 166 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (166) ~ (all_44_0_56 = 0)
% 35.79/9.92 | (381) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (369), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (334) all_44_0_56 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (334) can reduce 166 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (166) ~ (all_44_0_56 = 0)
% 35.79/9.92 | (385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (373), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (334) all_44_0_56 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (334) can reduce 166 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (166) ~ (all_44_0_56 = 0)
% 35.79/9.92 | (389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_5_5) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (248), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (393) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (253), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (326) all_49_0_61 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (326) can reduce 170 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.92 | (397) ? [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))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (262), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (330) all_61_0_75 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (330) can reduce 184 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.92 | (401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (272), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (330) all_61_0_75 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (330) can reduce 184 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.92 | (405) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (271), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (330) all_61_0_75 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (330) can reduce 184 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.92 | (409) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (285), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (318) all_59_0_73 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (318) can reduce 180 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.92 | (413) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (307), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (314) all_42_0_54 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (314) can reduce 162 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.92 | (417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (304), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (314) all_42_0_54 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (314) can reduce 162 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.92 | (421) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (305), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (314) all_42_0_54 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (314) can reduce 162 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.92 | (425) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (309), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (326) all_49_0_61 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (326) can reduce 170 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.92 | (429) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (247), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (433) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (249), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (437) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (300), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (318) all_59_0_73 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (318) can reduce 180 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.92 | (441) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (301), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (318) all_59_0_73 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (318) can reduce 180 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.92 | (445) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.92 |
% 35.79/9.92 +-Applying beta-rule and splitting (251), into two cases.
% 35.79/9.92 |-Branch one:
% 35.79/9.92 | (322) all_51_0_63 = 0
% 35.79/9.92 |
% 35.79/9.92 | Equations (322) can reduce 174 to:
% 35.79/9.92 | (315) $false
% 35.79/9.92 |
% 35.79/9.92 |-The branch is then unsatisfiable
% 35.79/9.92 |-Branch two:
% 35.79/9.92 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.92 | (449) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (255), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (453) all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (297), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (318) can reduce 180 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.93 | (457) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (299), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (318) can reduce 180 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.93 | (461) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (259), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (465) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (294), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (469) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (258), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (473) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (295), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (334) all_44_0_56 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (334) can reduce 166 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (166) ~ (all_44_0_56 = 0)
% 35.79/9.93 | (477) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (302), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (318) can reduce 180 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.93 | (481) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (290), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (326) all_49_0_61 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (326) can reduce 170 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.93 | (485) all_42_0_54 = 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_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (298), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (318) can reduce 180 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.93 | (489) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (250), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (322) all_51_0_63 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (322) can reduce 174 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.93 | (493) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (254), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (497) all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (291), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (501) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (287), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (322) all_51_0_63 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (322) can reduce 174 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.93 | (505) all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (288), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (322) all_51_0_63 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (322) can reduce 174 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.93 | (509) all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (292), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (513) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (293), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (330) all_61_0_75 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (330) can reduce 184 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.93 | (517) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (289), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (326) all_49_0_61 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (326) can reduce 170 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.93 | (521) all_42_0_54 = 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_6_6, 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_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (303), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.93 | Equations (318) can reduce 180 to:
% 35.79/9.93 | (315) $false
% 35.79/9.93 |
% 35.79/9.93 |-The branch is then unsatisfiable
% 35.79/9.93 |-Branch two:
% 35.79/9.93 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.93 | (525) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.93 |
% 35.79/9.93 +-Applying beta-rule and splitting (296), into two cases.
% 35.79/9.93 |-Branch one:
% 35.79/9.93 | (318) all_59_0_73 = 0
% 35.79/9.93 |
% 35.79/9.94 | Equations (318) can reduce 180 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.94 | (529) all_42_0_54 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (308), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (322) all_51_0_63 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (322) can reduce 174 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.94 | (533) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (286), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (322) all_51_0_63 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (322) can reduce 174 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.94 | (537) all_42_0_54 = 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_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (283), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (318) all_59_0_73 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (318) can reduce 180 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.94 | (541) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (281), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (318) all_59_0_73 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (318) can reduce 180 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.94 | (545) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (274), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (318) all_59_0_73 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (318) can reduce 180 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.94 | (549) all_51_0_63 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (282), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (318) all_59_0_73 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (318) can reduce 180 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.94 | (553) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (256), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (330) all_61_0_75 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (330) can reduce 184 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.94 | (557) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (257), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (330) all_61_0_75 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (330) can reduce 184 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.94 | (561) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (393), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (326) all_49_0_61 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (326) can reduce 170 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.94 | (565) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (437), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (326) all_49_0_61 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (326) can reduce 170 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.94 | (569) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (445), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (314) all_42_0_54 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (314) can reduce 162 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.94 | (569) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (449), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (326) all_49_0_61 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (326) can reduce 170 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.94 | (577) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 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_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (457), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (314) all_42_0_54 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (314) can reduce 162 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.94 | (581) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (461), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (314) all_42_0_54 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (314) can reduce 162 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.94 | (585) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (465), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (326) all_49_0_61 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (326) can reduce 170 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.94 | (589) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (469), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (314) all_42_0_54 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (314) can reduce 162 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.94 | (593) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (473), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (326) all_49_0_61 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (326) can reduce 170 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.94 | (597) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.79/9.94 |
% 35.79/9.94 +-Applying beta-rule and splitting (481), into two cases.
% 35.79/9.94 |-Branch one:
% 35.79/9.94 | (314) all_42_0_54 = 0
% 35.79/9.94 |
% 35.79/9.94 | Equations (314) can reduce 162 to:
% 35.79/9.94 | (315) $false
% 35.79/9.94 |
% 35.79/9.94 |-The branch is then unsatisfiable
% 35.79/9.94 |-Branch two:
% 35.79/9.94 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (601) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (485), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (605) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (489), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (609) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (493), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (326) all_49_0_61 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (326) can reduce 170 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.95 | (613) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (497), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (322) all_51_0_63 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (322) can reduce 174 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.95 | (617) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (501), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (621) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (505), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (625) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (509), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (629) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (513), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (633) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (517), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (637) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (525), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (641) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (529), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (314) all_42_0_54 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (314) can reduce 162 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.95 | (645) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (267), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (326) all_49_0_61 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (326) can reduce 170 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.95 | (649) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, 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_5_5) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (268), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (326) all_49_0_61 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (326) can reduce 170 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (170) ~ (all_49_0_61 = 0)
% 35.79/9.95 | (653) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (269), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (330) all_61_0_75 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (330) can reduce 184 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.95 | (657) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (270), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (330) all_61_0_75 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (330) can reduce 184 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.95 | (661) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (275), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (318) all_59_0_73 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (318) can reduce 180 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.95 | (665) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.95 |
% 35.79/9.95 +-Applying beta-rule and splitting (279), into two cases.
% 35.79/9.95 |-Branch one:
% 35.79/9.95 | (318) all_59_0_73 = 0
% 35.79/9.95 |
% 35.79/9.95 | Equations (318) can reduce 180 to:
% 35.79/9.95 | (315) $false
% 35.79/9.95 |
% 35.79/9.95 |-The branch is then unsatisfiable
% 35.79/9.95 |-Branch two:
% 35.79/9.95 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.95 | (669) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (278), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (330) all_61_0_75 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (330) can reduce 184 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (184) ~ (all_61_0_75 = 0)
% 35.79/9.96 | (673) all_59_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (280), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (318) all_59_0_73 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (318) can reduce 180 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.96 | (677) all_44_0_56 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (276), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (318) all_59_0_73 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (318) can reduce 180 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.96 | (681) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (277), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (318) all_59_0_73 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (318) can reduce 180 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (180) ~ (all_59_0_73 = 0)
% 35.79/9.96 | (685) all_49_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (357), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (314) all_42_0_54 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (314) can reduce 162 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.96 | (689) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.96 |
% 35.79/9.96 | Instantiating (689) with all_509_0_1848 yields:
% 35.79/9.96 | (690) (all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (all_509_0_1848 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848)
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (441), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (314) all_42_0_54 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (314) can reduce 162 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.96 | (565) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (453), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (322) all_51_0_63 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (322) can reduce 174 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (174) ~ (all_51_0_63 = 0)
% 35.79/9.96 | (698) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.79/9.96 |
% 35.79/9.96 +-Applying beta-rule and splitting (477), into two cases.
% 35.79/9.96 |-Branch one:
% 35.79/9.96 | (314) all_42_0_54 = 0
% 35.79/9.96 |
% 35.79/9.96 | Equations (314) can reduce 162 to:
% 35.79/9.96 | (315) $false
% 35.79/9.96 |
% 35.79/9.96 |-The branch is then unsatisfiable
% 35.79/9.96 |-Branch two:
% 35.79/9.96 | (162) ~ (all_42_0_54 = 0)
% 35.79/9.96 | (702) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (533), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (326) all_49_0_61 = 0
% 35.99/9.96 |
% 35.99/9.96 | Equations (326) can reduce 170 to:
% 35.99/9.96 | (315) $false
% 35.99/9.96 |
% 35.99/9.96 |-The branch is then unsatisfiable
% 35.99/9.96 |-Branch two:
% 35.99/9.96 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.96 | (706) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 35.99/9.96 |
% 35.99/9.96 | Instantiating (706) with all_529_0_1853 yields:
% 35.99/9.96 | (707) (all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (all_529_0_1853 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_529_0_1853)
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (537), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (314) all_42_0_54 = 0
% 35.99/9.96 |
% 35.99/9.96 | Equations (314) can reduce 162 to:
% 35.99/9.96 | (315) $false
% 35.99/9.96 |
% 35.99/9.96 |-The branch is then unsatisfiable
% 35.99/9.96 |-Branch two:
% 35.99/9.96 | (162) ~ (all_42_0_54 = 0)
% 35.99/9.96 | (711) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.99/9.96 |
% 35.99/9.96 | Instantiating (711) with all_533_0_1854 yields:
% 35.99/9.96 | (712) (all_533_0_1854 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_533_0_1854 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (all_533_0_1854 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854) | ( ~ (all_533_0_1854 = 0) & distinct_points(all_0_1_1, all_0_6_6) = all_533_0_1854)
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (549), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (322) all_51_0_63 = 0
% 35.99/9.96 |
% 35.99/9.96 | Equations (322) can reduce 174 to:
% 35.99/9.96 | (315) $false
% 35.99/9.96 |
% 35.99/9.96 |-The branch is then unsatisfiable
% 35.99/9.96 |-Branch two:
% 35.99/9.96 | (174) ~ (all_51_0_63 = 0)
% 35.99/9.96 | (716) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (557), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (326) all_49_0_61 = 0
% 35.99/9.96 |
% 35.99/9.96 | Equations (326) can reduce 170 to:
% 35.99/9.96 | (315) $false
% 35.99/9.96 |
% 35.99/9.96 |-The branch is then unsatisfiable
% 35.99/9.96 |-Branch two:
% 35.99/9.96 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.96 | (720) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_4_4) = v0))
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (561), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (326) all_49_0_61 = 0
% 35.99/9.96 |
% 35.99/9.96 | Equations (326) can reduce 170 to:
% 35.99/9.96 | (315) $false
% 35.99/9.96 |
% 35.99/9.96 |-The branch is then unsatisfiable
% 35.99/9.96 |-Branch two:
% 35.99/9.96 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.96 | (724) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_1_1) = v0))
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (712), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (725) (all_533_0_1854 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_533_0_1854 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (all_533_0_1854 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854)
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (725), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (726) (all_533_0_1854 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (all_533_0_1854 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0)
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (726), into two cases.
% 35.99/9.96 |-Branch one:
% 35.99/9.96 | (727) all_533_0_1854 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 35.99/9.96 |
% 35.99/9.96 | Applying alpha-rule on (727) yields:
% 35.99/9.96 | (728) all_533_0_1854 = 0
% 35.99/9.96 | (729) apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 35.99/9.96 |
% 35.99/9.96 +-Applying beta-rule and splitting (665), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (326) can reduce 170 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.97 | (733) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (681), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (326) can reduce 170 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.97 | (737) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_6_6) = v0))
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (685), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (326) can reduce 170 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.97 | (741) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.99/9.97 |
% 35.99/9.97 | Instantiating formula (61) with all_0_1_1, all_0_3_3, 0, all_49_0_61 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_1_1, all_0_3_3) = 0, yields:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (326) can reduce 170 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (744) all_533_0_1854 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (744) yields:
% 35.99/9.97 | (728) all_533_0_1854 = 0
% 35.99/9.97 | (746) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (673), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (318) all_59_0_73 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (318) can reduce 180 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (180) ~ (all_59_0_73 = 0)
% 35.99/9.97 | (750) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.99/9.97 |
% 35.99/9.97 | Instantiating formula (61) with all_0_6_6, all_0_2_2, 0, all_59_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 35.99/9.97 | (318) all_59_0_73 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (318) can reduce 180 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (753) ~ (all_533_0_1854 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (753) yields:
% 35.99/9.97 | (754) ~ (all_533_0_1854 = 0)
% 35.99/9.97 | (755) distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (707), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (756) (all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0)
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (756), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (757) all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (757) yields:
% 35.99/9.97 | (758) all_529_0_1853 = 0
% 35.99/9.97 | (746) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (673), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (318) all_59_0_73 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (318) can reduce 180 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (180) ~ (all_59_0_73 = 0)
% 35.99/9.97 | (750) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 35.99/9.97 |
% 35.99/9.97 | Instantiating formula (61) with all_0_6_6, all_0_2_2, 0, all_59_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_59_0_73, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 35.99/9.97 | (318) all_59_0_73 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (318) can reduce 180 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (766) all_529_0_1853 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (766) yields:
% 35.99/9.97 | (758) all_529_0_1853 = 0
% 35.99/9.97 | (768) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 35.99/9.97 |
% 35.99/9.97 | Instantiating formula (61) with all_0_6_6, all_0_3_3, 0, all_42_0_54 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_42_0_54, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 35.99/9.97 | (314) all_42_0_54 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (314) can reduce 162 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (771) ~ (all_529_0_1853 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_529_0_1853
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (771) yields:
% 35.99/9.97 | (772) ~ (all_529_0_1853 = 0)
% 35.99/9.97 | (773) distinct_lines(all_0_2_2, all_0_3_3) = all_529_0_1853
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (690), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (774) (all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0)
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (774), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (775) all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (775) yields:
% 35.99/9.97 | (776) all_509_0_1848 = 0
% 35.99/9.97 | (777) apart_point_and_line(all_0_1_1, all_0_2_2) = 0
% 35.99/9.97 |
% 35.99/9.97 | Instantiating formula (61) with all_0_1_1, all_0_2_2, 0, all_51_0_63 and discharging atoms apart_point_and_line(all_0_1_1, all_0_2_2) = all_51_0_63, apart_point_and_line(all_0_1_1, all_0_2_2) = 0, yields:
% 35.99/9.97 | (322) all_51_0_63 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (322) can reduce 174 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (780) all_509_0_1848 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 35.99/9.97 |
% 35.99/9.97 | Applying alpha-rule on (780) yields:
% 35.99/9.97 | (776) all_509_0_1848 = 0
% 35.99/9.97 | (729) apart_point_and_line(all_0_1_1, all_0_3_3) = 0
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (685), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.97 |
% 35.99/9.97 | Equations (326) can reduce 170 to:
% 35.99/9.97 | (315) $false
% 35.99/9.97 |
% 35.99/9.97 |-The branch is then unsatisfiable
% 35.99/9.97 |-Branch two:
% 35.99/9.97 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.97 | (741) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.99/9.97 |
% 35.99/9.97 +-Applying beta-rule and splitting (665), into two cases.
% 35.99/9.97 |-Branch one:
% 35.99/9.97 | (326) all_49_0_61 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (326) can reduce 170 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (170) ~ (all_49_0_61 = 0)
% 35.99/9.98 | (733) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_1_1) = v0))
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (61) with all_0_1_1, all_0_3_3, 0, all_49_0_61 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_49_0_61, apart_point_and_line(all_0_1_1, all_0_3_3) = 0, yields:
% 35.99/9.98 | (326) all_49_0_61 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (326) can reduce 170 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (793) ~ (all_509_0_1848 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (793) yields:
% 35.99/9.98 | (794) ~ (all_509_0_1848 = 0)
% 35.99/9.98 | (795) distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (128) with all_0_2_2, all_0_3_3, all_529_0_1853, all_533_0_1854 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854, distinct_lines(all_0_2_2, all_0_3_3) = all_529_0_1853, yields:
% 35.99/9.98 | (796) all_533_0_1854 = all_529_0_1853
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (128) with all_0_2_2, all_0_3_3, all_509_0_1848, all_533_0_1854 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_533_0_1854, distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848, yields:
% 35.99/9.98 | (797) all_533_0_1854 = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Combining equations (796,797) yields a new equation:
% 35.99/9.98 | (798) all_529_0_1853 = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Simplifying 798 yields:
% 35.99/9.98 | (799) all_529_0_1853 = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Equations (799) can reduce 772 to:
% 35.99/9.98 | (794) ~ (all_509_0_1848 = 0)
% 35.99/9.98 |
% 35.99/9.98 | From (799) and (773) follows:
% 35.99/9.98 | (795) distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (40) with all_509_0_1848, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, distinct_lines(all_0_2_2, all_0_3_3) = all_509_0_1848, yields:
% 35.99/9.98 | (802) all_509_0_1848 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 35.99/9.98 |
% 35.99/9.98 +-Applying beta-rule and splitting (802), into two cases.
% 35.99/9.98 |-Branch one:
% 35.99/9.98 | (803) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (91) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 35.99/9.98 | (804) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (805) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 35.99/9.98 | (776) all_509_0_1848 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (776) can reduce 794 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (808) ~ (all_533_0_1854 = 0) & distinct_points(all_0_1_1, all_0_6_6) = all_533_0_1854
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (808) yields:
% 35.99/9.98 | (754) ~ (all_533_0_1854 = 0)
% 35.99/9.98 | (810) distinct_points(all_0_1_1, all_0_6_6) = all_533_0_1854
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (126) with all_0_1_1, all_0_6_6, all_533_0_1854, 0 and discharging atoms distinct_points(all_0_1_1, all_0_6_6) = all_533_0_1854, distinct_points(all_0_1_1, all_0_6_6) = 0, yields:
% 35.99/9.98 | (728) all_533_0_1854 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (728) can reduce 754 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (813) ~ (all_70_0_84 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_70_0_84
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (813) yields:
% 35.99/9.98 | (208) ~ (all_70_0_84 = 0)
% 35.99/9.98 | (815) distinct_points(all_0_6_6, all_0_4_4) = all_70_0_84
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (126) with all_0_6_6, all_0_4_4, all_70_0_84, 0 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_70_0_84, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.99/9.98 | (816) all_70_0_84 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (816) can reduce 208 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (818) ~ (all_69_0_83 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_69_0_83
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (818) yields:
% 35.99/9.98 | (205) ~ (all_69_0_83 = 0)
% 35.99/9.98 | (820) convergent_lines(all_0_3_3, all_0_2_2) = all_69_0_83
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (145) with all_0_3_3, all_0_2_2, all_69_0_83, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_69_0_83, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 35.99/9.98 | (821) all_69_0_83 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (821) can reduce 205 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (823) ~ (all_55_0_68 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_55_0_68
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (823) yields:
% 35.99/9.98 | (202) ~ (all_55_0_68 = 0)
% 35.99/9.98 | (825) distinct_points(all_0_6_6, all_0_5_5) = all_55_0_68
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (126) with all_0_6_6, all_0_5_5, all_55_0_68, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_55_0_68, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.99/9.98 | (826) all_55_0_68 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (826) can reduce 202 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (828) ~ (all_54_0_67 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_54_0_67
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (828) yields:
% 35.99/9.98 | (199) ~ (all_54_0_67 = 0)
% 35.99/9.98 | (830) distinct_points(all_0_6_6, all_0_5_5) = all_54_0_67
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (126) with all_0_6_6, all_0_5_5, all_54_0_67, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_54_0_67, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 35.99/9.98 | (831) all_54_0_67 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (831) can reduce 199 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (833) ~ (all_68_0_82 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_68_0_82
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (833) yields:
% 35.99/9.98 | (196) ~ (all_68_0_82 = 0)
% 35.99/9.98 | (835) convergent_lines(all_0_3_3, all_0_2_2) = all_68_0_82
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (145) with all_0_3_3, all_0_2_2, all_68_0_82, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_68_0_82, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 35.99/9.98 | (836) all_68_0_82 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (836) can reduce 196 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (838) ~ (all_67_0_81 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_67_0_81
% 35.99/9.98 |
% 35.99/9.98 | Applying alpha-rule on (838) yields:
% 35.99/9.98 | (193) ~ (all_67_0_81 = 0)
% 35.99/9.98 | (840) distinct_points(all_0_6_6, all_0_4_4) = all_67_0_81
% 35.99/9.98 |
% 35.99/9.98 | Instantiating formula (126) with all_0_6_6, all_0_4_4, all_67_0_81, 0 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_67_0_81, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 35.99/9.98 | (841) all_67_0_81 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (841) can reduce 193 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 |-Branch two:
% 35.99/9.98 | (843) ~ (distinct_points(all_0_1_1, all_0_6_6) = 0)
% 35.99/9.98 | (844) all_0_0_0 = 0
% 35.99/9.98 |
% 35.99/9.98 | Equations (844) can reduce 68 to:
% 35.99/9.98 | (315) $false
% 35.99/9.98 |
% 35.99/9.98 |-The branch is then unsatisfiable
% 35.99/9.98 % SZS output end Proof for theBenchmark
% 35.99/9.98
% 35.99/9.98 9401ms
%------------------------------------------------------------------------------