TSTP Solution File: GEO261+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 03:49:18 EDT 2022
% Result : Theorem 21.51s 5.66s
% Output : Proof 31.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 : Sat Jun 18 18:35:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.93 Prover 0: Preprocessing ...
% 2.46/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.65/1.21 Prover 0: Constructing countermodel ...
% 3.77/1.50 Prover 0: gave up
% 3.77/1.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.10/1.55 Prover 1: Preprocessing ...
% 4.89/1.71 Prover 1: Constructing countermodel ...
% 5.26/1.80 Prover 1: gave up
% 5.26/1.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.45/1.84 Prover 2: Preprocessing ...
% 6.59/2.08 Prover 2: Warning: ignoring some quantifiers
% 6.59/2.10 Prover 2: Constructing countermodel ...
% 14.50/4.03 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.72/4.08 Prover 3: Preprocessing ...
% 14.98/4.12 Prover 3: Warning: ignoring some quantifiers
% 14.98/4.13 Prover 3: Constructing countermodel ...
% 15.19/4.22 Prover 3: gave up
% 15.19/4.22 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 15.19/4.24 Prover 4: Preprocessing ...
% 16.04/4.40 Prover 4: Warning: ignoring some quantifiers
% 16.34/4.41 Prover 4: Constructing countermodel ...
% 19.77/5.24 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.77/5.28 Prover 5: Preprocessing ...
% 20.49/5.42 Prover 5: Constructing countermodel ...
% 21.51/5.66 Prover 5: proved (417ms)
% 21.51/5.66 Prover 2: stopped
% 21.51/5.66 Prover 4: stopped
% 21.51/5.66
% 21.51/5.66 No countermodel exists, formula is valid
% 21.51/5.66 % SZS status Theorem for theBenchmark
% 21.51/5.66
% 21.51/5.66 Generating proof ... found it (size 155)
% 30.39/7.77
% 30.39/7.77 % SZS output start Proof for theBenchmark
% 30.39/7.77 Assumed formulas after preprocessing and simplification:
% 30.39/7.77 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (left_apart_point(v1, v5) = v7) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v4) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v4) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v4) = v14 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v6) = v15 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v4) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v4 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v6) = v15 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v11 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v5) = v13 & left_apart_point(v1, v3) = v12 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v5) = v14 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v11 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v11 & left_apart_point(v0, v3) = v9 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v11 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v3) = v10 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v5) = v12 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v15 & left_apart_point(v0, v3) = v10 & reverse_line(v2) = v12 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v5) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v15 & left_apart_point(v1, v3) = v11 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v9 & reverse_line(v2) = v12 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v6) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v6) = v11 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v3) = v10 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v6) = v14 & left_apart_point(v0, v3) = v9 & reverse_line(v2) = v11 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v3) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v3) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v3) = v8 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v3) = v8 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v3) = v9 & reverse_line(v3) = v13 & reverse_line(v2) = v10 & ( ~ (v7 = 0) | ~ (v6 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v3) = v9 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v13 & reverse_line(v2) = v10 & ( ~ (v7 = 0) | ~ (v6 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : (left_apart_point(v0, v1) = v6 & unequally_directed_lines(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v10 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v9 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v8 & left_apart_point(v0, v2) = v7 & reverse_line(v2) = v10 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v3) = v9 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v10 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v9 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v8 & reverse_line(v2) = v10 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v4) = v12 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v4) = v11 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v7 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v7 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v5 = 0)) & ( ~ (v6 = 0) | ~ (v4 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v2, v3) = v7 & before_on_line(v0, v2, v1) = v8 & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v2, v3) = v7 & before_on_line(v0, v1, v2) = v6 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v2, v3) = v8 & before_on_line(v0, v1, v2) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))) | (v5 = 0 & v4 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v1) = v7 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v1) = v8 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))) | (v5 = 0 & v4 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v1, v2) = v6 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v5 = 0)) & ( ~ (v6 = 0) | ~ (v4 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v3, v2) = v8 & before_on_line(v0, v1, v2) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (unequally_directed_lines(v1, v4) = v10 & unequally_directed_lines(v1, v2) = v9 & unequally_directed_lines(v0, v3) = v7 & unequally_directed_lines(v0, v2) = v8 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v3) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [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] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v8 & before_on_line(v0, v1, v2) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ? [v6] : (distinct_lines(v1, v2) = v6 & left_apart_point(v0, v1) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (line_connecting(v0, v1) = v4) | ~ (left_apart_point(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_convergent_lines(v4, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v1, v2) = v3) | ~ (incident_point_and_line(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v1, v0) = v6 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v1, v2) = v3) | ~ (incident_point_and_line(v1, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v6 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v2, v0) = v4) | ~ (incident_point_and_line(v1, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v2, v0) = v3) | ~ (line_connecting(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v1, v0) = v7 & equally_directed_lines(v0, v4) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v1, v0) = v3) | ~ (line_connecting(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v7 & equally_directed_lines(v0, v4) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v8 & incident_point_and_line(v1, v0) = v7 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & right_apart_point(v1, v2) = v6 & right_apart_point(v0, v2) = v7 & ( ~ (v5 = 0) | (v7 = 0 & v4 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (right_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v0, v2) = v5 & right_apart_point(v1, v2) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (right_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v0, v2) = v6 & right_apart_point(v1, v2) = v7 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v0, v2) = v3) | ~ (right_apart_point(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v1, v2) = v6 & right_apart_point(v0, v2) = v5 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v0, v2) = v3) | ~ (right_apart_point(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v1, v2) = v7 & right_apart_point(v0, v2) = v6 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (right_apart_point(v1, v2) = v3) | ~ (right_apart_point(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v5 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (right_apart_point(v1, v2) = v3) | ~ (right_apart_point(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v5 = 0) | (v7 = 0 & v4 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v4) = v7 & unequally_directed_lines(v0, v2) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v7 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v2) = v7 & unequally_directed_lines(v1, v7) = v10 & unequally_directed_lines(v1, v2) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v3) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v2) = v8 & reverse_line(v1) = v6 & unequally_directed_lines(v1, v8) = v10 & unequally_directed_lines(v0, v8) = v9 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 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(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v0, v5) = v6 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v2) = v4 & ( ~ (v4 = 0) | v6 = 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] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v5 & left_convergent_lines(v5, v2) = v6 & left_apart_point(v0, v2) = v4 & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v4 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v4 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v1) = v6 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v4 & line_connecting(v0, v1) = v5 & left_convergent_lines(v5, v2) = v6 & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [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 | ~ (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] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(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 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(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 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (left_apart_point(v1, v11) = v13 & left_apart_point(v1, v8) = v10 & left_apart_point(v1, v3) = v7 & left_apart_point(v1, v2) = v5 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v8) = v9 & left_apart_point(v0, v3) = v6 & left_apart_point(v0, v2) = v4 & reverse_line(v3) = v11 & reverse_line(v2) = v8 & (v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v3) = v5 & before_on_line(v0, v2, v1) = v7 & before_on_line(v0, v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (incident_point_and_line(v2, v0) = 0) | ~ (line_connecting(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v1, v0) = v5 & equally_directed_lines(v0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (incident_point_and_line(v1, v0) = 0) | ~ (line_connecting(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v2, v0) = v5 & equally_directed_lines(v0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v4 & left_convergent_lines(v3, v2) = v6 & left_apart_point(v1, v2) = v5 & ( ~ (v4 = 0) | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (distinct_lines(v1, v2) = v5 & left_apart_point(v0, v3) = v6 & unequally_directed_lines(v1, v2) = v4 & ( ~ (v4 = 0) | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v1) = v4 & unequally_directed_lines(v1, v3) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v3) = v7 & unequally_directed_lines(v0, v2) = v6 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v7 & reverse_line(v1) = v4 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v2) = v6 & ( ~ (v5 = 0) | (v9 = 0 & v3 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (unequally_directed_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v4) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v3 & right_apart_point(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v3 & left_apart_point(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4)) & ! [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] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0) & ! [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(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & line(v2) = v5 & line(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (point(v2) = v8 & line(v1) = v4 & line(v0) = v3 & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line(v0) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v3 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v1, v2) = 0) | ~ (incident_point_and_line(v2, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (before_on_line(v0, v1, v2) = v6 & incident_point_and_line(v1, v0) = v3 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v1, v2) = 0) | ~ (incident_point_and_line(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (before_on_line(v0, v1, v2) = v6 & incident_point_and_line(v2, v0) = v3 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (line_connecting(v0, v1) = v4 & left_convergent_lines(v4, v2) = v5 & left_apart_point(v1, v2) = v3 & (v5 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & line_connecting(v1, v2) = v3 & equally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (incident_point_and_line(v2, v0) = 0) | ~ (incident_point_and_line(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v1, v2) = v3 & before_on_line(v0, v1, v2) = v6 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v3 & line_connecting(v0, v1) = v4 & equally_directed_lines(v4, v5) = v6 & reverse_line(v2) = v5 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v3 & line_connecting(v1, v0) = v4 & equally_directed_lines(v2, v5) = v6 & reverse_line(v4) = v5 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (distinct_points(v0, v1) = v3 & apart_point_and_line(v1, v2) = v5 & apart_point_and_line(v0, v2) = v4 & ( ~ (v3 = 0) | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v3 & right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = v5 & ((v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v4 & right_apart_point(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (distinct_lines(v1, v2) = v3 & left_apart_point(v0, v4) = v5 & reverse_line(v2) = v4 & (v5 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v4 & left_apart_point(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v4 & line(v0) = v3 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (left_convergent_lines(v0, v2) = v5 & left_convergent_lines(v0, v1) = v4 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (convergent_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (convergent_lines(v0, v1) = v3 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & distinct_points(v0, v1) = v2 & line_connecting(v0, v1) = v3 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (parallel_through_point(v0, v1) = v2 & line(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & point(v5) = v6 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & unequally_directed_lines(v0, v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : (left_apart_point(v0, v1) = v2 & right_apart_point(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ? [v3] : (line(v1) = v3 & line(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v3 & line(v0) = v2 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & ( ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0))))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (left_convergent_lines(v0, v2) = v5 & left_convergent_lines(v0, v1) = v4 & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : (convergent_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ? [v3] : (convergent_lines(v0, v1) = v3 & unequally_directed_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) & ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & between_on_line(v0, v2, v3, v4) = 0 & incident_point_and_line(v3, v1) = 0 & divides_points(v1, v2, v4) = v5 & convergent_lines(v0, v1) = 0)
% 31.01/7.91 | Applying alpha-rule on (0) yields:
% 31.01/7.91 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v1, v2) = v3) | ~ (incident_point_and_line(v1, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v6 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0))))
% 31.01/7.91 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 31.01/7.91 | (3) ! [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))
% 31.01/7.91 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v4) = v7 & unequally_directed_lines(v0, v2) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v6 = 0))))
% 31.01/7.91 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v3 & line_connecting(v1, v0) = v4 & equally_directed_lines(v2, v5) = v6 & reverse_line(v4) = v5 & ( ~ (v3 = 0) | v6 = 0)))
% 31.01/7.91 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v4 & line_connecting(v0, v1) = v5 & left_convergent_lines(v5, v2) = v6 & ( ~ (v4 = 0) | v6 = 0)))
% 31.01/7.91 | (7) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 31.01/7.91 | (8) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 31.01/7.91 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 31.01/7.91 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v2, v3) = v8 & before_on_line(v0, v1, v2) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))) | (v5 = 0 & v4 = 0))
% 31.01/7.91 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 31.01/7.91 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v5) = v14 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v11 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.91 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v0, v2) = v3) | ~ (right_apart_point(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v1, v2) = v7 & right_apart_point(v0, v2) = v6 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0))) | (v4 = 0 & v3 = 0))
% 31.01/7.91 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & line_connecting(v1, v2) = v3 & equally_directed_lines(v0, v3) = 0))
% 31.01/7.91 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0))))
% 31.01/7.91 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (incident_point_and_line(v2, v0) = 0) | ~ (line_connecting(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v1, v0) = v5 & equally_directed_lines(v0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0)))
% 31.01/7.91 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (line_connecting(v0, v1) = v4 & left_convergent_lines(v4, v2) = v5 & left_apart_point(v1, v2) = v3 & (v5 = 0 | v3 = 0)))
% 31.01/7.91 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 31.01/7.91 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v3) = v8 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.91 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 31.01/7.91 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & between_on_line(v0, v2, v3, v4) = 0 & incident_point_and_line(v3, v1) = 0 & divides_points(v1, v2, v4) = v5 & convergent_lines(v0, v1) = 0)
% 31.01/7.91 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 31.01/7.91 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0)))))
% 31.01/7.92 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v3 & left_apart_point(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 31.01/7.92 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v3 & right_apart_point(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 31.01/7.92 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v7 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v4 = 0) | (v8 = 0 & v6 = 0))))
% 31.01/7.92 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 31.01/7.92 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 31.01/7.92 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v15 & left_apart_point(v0, v3) = v10 & reverse_line(v2) = v12 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 31.01/7.92 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (distinct_lines(v1, v2) = v3 & left_apart_point(v0, v4) = v5 & reverse_line(v2) = v4 & (v5 = 0 | v3 = 0)))
% 31.01/7.92 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v1, v2) = v3) | ~ (incident_point_and_line(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v1, v0) = v6 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0))))
% 31.01/7.92 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 31.01/7.92 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))
% 31.01/7.92 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v4) = v14 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v6) = v15 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.92 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v3 = 0))))
% 31.01/7.92 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v1, v2) = v6 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v5 = 0)) & ( ~ (v6 = 0) | ~ (v4 = 0))))))
% 31.01/7.92 | (37) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ? [v3] : (convergent_lines(v0, v1) = v3 & unequally_directed_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.01/7.92 | (38) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : (convergent_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.01/7.92 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ? [v6] : (distinct_lines(v1, v2) = v6 & left_apart_point(v0, v1) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 31.01/7.92 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v4 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v6) = v15 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.92 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v6) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v6) = v11 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 31.01/7.92 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v8 & incident_point_and_line(v1, v0) = v7 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v4 = 0))))
% 31.01/7.92 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v1) = v4 & unequally_directed_lines(v1, v3) = v9 & unequally_directed_lines(v1, v2) = v8 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v3) = v7 & unequally_directed_lines(v0, v2) = v6 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v6 = 0))))
% 31.01/7.92 | (44) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : (parallel_through_point(v0, v1) = v2 & line(v2) = 0))
% 31.01/7.92 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v3) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v3) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.92 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 31.01/7.92 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 31.01/7.92 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 31.01/7.92 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (incident_point_and_line(v2, v0) = 0) | ~ (incident_point_and_line(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v1, v2) = v3 & before_on_line(v0, v1, v2) = v6 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 31.01/7.92 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 31.01/7.92 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 31.01/7.93 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 31.01/7.93 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 31.01/7.93 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (incident_point_and_line(v1, v0) = 0) | ~ (line_connecting(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v2, v0) = v5 & equally_directed_lines(v0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0)))
% 31.01/7.93 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 31.01/7.93 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v3) = v10 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.93 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v5 & left_convergent_lines(v5, v2) = v6 & left_apart_point(v0, v2) = v4 & ( ~ (v4 = 0) | v6 = 0)))
% 31.01/7.93 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4))
% 31.01/7.93 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))))
% 31.01/7.93 | (60) ! [v0] : ! [v1] : ( ~ (point(v1) = 0) | ~ (point(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (line(v3) = v4 & distinct_points(v0, v1) = v2 & line_connecting(v0, v1) = v3 & ( ~ (v2 = 0) | v4 = 0)))
% 31.01/7.93 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (right_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v0, v2) = v5 & right_apart_point(v1, v2) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = 0) | ~ (v3 = 0))))))
% 31.01/7.93 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v3) = v9 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v10 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.93 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : (left_apart_point(v0, v1) = v6 & unequally_directed_lines(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 31.01/7.93 | (64) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 31.01/7.93 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 31.01/7.93 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 31.01/7.93 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4))
% 31.01/7.93 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 31.01/7.93 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.93 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 31.01/7.93 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 31.01/7.93 | (72) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0)))
% 31.01/7.93 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v4 & left_convergent_lines(v3, v2) = v6 & left_apart_point(v1, v2) = v5 & ( ~ (v4 = 0) | v6 = 0 | v5 = 0)))
% 31.01/7.93 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v4 & line(v0) = v3 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0)))
% 31.01/7.93 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v1, v2) = 0) | ~ (incident_point_and_line(v2, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (before_on_line(v0, v1, v2) = v6 & incident_point_and_line(v1, v0) = v3 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 31.01/7.93 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 31.01/7.93 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v4 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 31.01/7.93 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v2, v3) = v7 & before_on_line(v0, v1, v2) = v6 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0))))))
% 31.01/7.93 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (left_convergent_lines(v0, v2) = v5 & left_convergent_lines(v0, v1) = v4 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)))
% 31.01/7.93 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v1) = v7 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0))))))
% 31.01/7.93 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v3) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v11 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.94 | (82) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & ( ~ (v3 = 0) | ( ~ (v6 = 0) & ~ (v5 = 0)))))
% 31.01/7.94 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.94 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 31.01/7.94 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 31.01/7.94 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 31.01/7.94 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v2, v0) = v3) | ~ (line_connecting(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v1, v0) = v7 & equally_directed_lines(v0, v4) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v3 = 0))))
% 31.01/7.94 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 31.01/7.94 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 31.01/7.94 | (90) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 31.01/7.94 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (convergent_lines(v0, v1) = v3 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 31.01/7.94 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (convergent_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 31.01/7.94 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 31.01/7.94 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (distinct_points(v0, v1) = v3 & apart_point_and_line(v1, v2) = v5 & apart_point_and_line(v0, v2) = v4 & ( ~ (v3 = 0) | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 31.01/7.94 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v7) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v7) = v15 & left_apart_point(v1, v5) = v13 & left_apart_point(v1, v3) = v12 & left_apart_point(v0, v7) = v14 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.94 | (96) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 31.01/7.94 | (97) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 31.01/7.94 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 31.01/7.94 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (unequally_directed_lines(v1, v4) = v10 & unequally_directed_lines(v1, v2) = v9 & unequally_directed_lines(v0, v3) = v7 & unequally_directed_lines(v0, v2) = v8 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v5 = 0))))
% 31.01/7.94 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (distinct_lines(v1, v2) = v5 & left_apart_point(v0, v3) = v6 & unequally_directed_lines(v1, v2) = v4 & ( ~ (v4 = 0) | v6 = 0 | v5 = 0)))
% 31.01/7.94 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v15 & left_apart_point(v1, v3) = v11 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v9 & reverse_line(v2) = v12 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 31.01/7.94 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 31.01/7.94 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v8 & before_on_line(v0, v1, v2) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 31.01/7.94 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 31.01/7.94 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v5) = v11 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v10 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.94 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v3 & right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = v5 & ((v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 31.01/7.94 | (107) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 31.01/7.94 | (108) ! [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))
% 31.01/7.94 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (right_apart_point(v1, v2) = v3) | ~ (right_apart_point(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v5 = 0) | (v7 = 0 & v4 = 0) | (v6 = 0 & v3 = 0))))
% 31.01/7.94 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & right_apart_point(v1, v2) = v6 & right_apart_point(v0, v2) = v7 & ( ~ (v5 = 0) | (v7 = 0 & v4 = 0) | (v6 = 0 & v3 = 0))))
% 31.01/7.94 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v11 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.94 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 31.01/7.94 | (113) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (left_convergent_lines(v0, v2) = v5 & left_convergent_lines(v0, v1) = v4 & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)))
% 31.01/7.94 | (114) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 31.01/7.95 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v5) = v11 & left_apart_point(v0, v3) = v9 & reverse_line(v3) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.95 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))
% 31.01/7.95 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v1) = v8 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))) | (v5 = 0 & v4 = 0))
% 31.01/7.95 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3))
% 31.01/7.95 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (reverse_line(v2) = v7 & reverse_line(v1) = v4 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v2) = v6 & ( ~ (v5 = 0) | (v9 = 0 & v3 = 0) | (v8 = 0 & v6 = 0))))
% 31.01/7.95 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 31.01/7.95 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v2, v0) = v4) | ~ (incident_point_and_line(v1, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & line_connecting(v1, v2) = v7 & equally_directed_lines(v0, v7) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v6 = 0 & v4 = 0 & v3 = 0))))
% 31.01/7.95 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v4 & left_apart_point(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0)))))
% 31.01/7.95 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : (apart_point_and_line(v0, v1) = v4 & right_apart_point(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0)))))
% 31.01/7.95 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4))
% 31.01/7.95 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v5) = v12 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v3) = v11 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 31.01/7.95 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v5) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.01/7.95 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 31.01/7.95 | (128) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4))
% 31.01/7.95 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 31.01/7.95 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v0, v2) = v3) | ~ (right_apart_point(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v1, v2) = v6 & right_apart_point(v0, v2) = v5 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = 0) | ~ (v3 = 0))))))
% 31.01/7.95 | (131) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 31.01/7.95 | (132) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 31.01/7.95 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 31.01/7.95 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 31.01/7.95 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 31.01/7.95 | (136) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v4) = v6 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & unequally_directed_lines(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 31.01/7.95 | (137) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (unequally_directed_lines(v0, v1) = v3 & unequally_directed_opposite_lines(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 31.01/7.95 | (138) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 31.01/7.95 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v2, v3) = v7 & before_on_line(v0, v2, v1) = v8 & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0) | (v7 = 0 & v4 = 0))))
% 31.01/7.95 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v7 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v9 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v3) = v10 & left_apart_point(v0, v2) = v8 & reverse_line(v2) = v12 & ( ~ (v7 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.95 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5))
% 31.01/7.95 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.01/7.95 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v1, v2) = v4) | ~ (right_apart_point(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v5 & left_apart_point(v0, v2) = v6 & right_apart_point(v1, v2) = v7 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0))) | (v4 = 0 & v3 = 0))
% 31.01/7.95 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v2, v3) = v4) | ~ (before_on_line(v0, v2, v1) = v5) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v6 & before_on_line(v0, v3, v2) = v8 & before_on_line(v0, v1, v2) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v5 = 0) | (v7 = 0 & v4 = 0))))
% 31.01/7.95 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v3) = v9 & reverse_line(v3) = v13 & reverse_line(v2) = v10 & ( ~ (v7 = 0) | ~ (v6 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0)))
% 31.01/7.95 | (146) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 31.01/7.95 | (147) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 31.01/7.95 | (148) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 31.01/7.95 | (149) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 31.01/7.95 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v2) = v8 & reverse_line(v1) = v6 & unequally_directed_lines(v1, v8) = v10 & unequally_directed_lines(v0, v8) = v9 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0))))
% 31.01/7.96 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v9 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v8 & left_apart_point(v0, v2) = v7 & reverse_line(v2) = v10 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.96 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_points(v0, v1) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & left_apart_point(v0, v2) = v7 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.96 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (distinct_points(v1, v2) = 0) | ~ (incident_point_and_line(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (before_on_line(v0, v1, v2) = v6 & incident_point_and_line(v2, v0) = v3 & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 31.01/7.96 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (left_apart_point(v0, v5) = v6 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v2) = v4 & ( ~ (v4 = 0) | v6 = 0)))
% 31.01/7.96 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v12) = v14 & left_apart_point(v1, v9) = v11 & left_apart_point(v1, v3) = v8 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v12) = v13 & left_apart_point(v0, v9) = v10 & reverse_line(v3) = v12 & reverse_line(v2) = v9 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v11 = 0 | v10 = 0 | v8 = 0 | v7 = 0)))
% 31.01/7.96 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4))
% 31.01/7.96 | (157) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 31.01/7.96 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v11) = v13 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v3) = v10 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v6) = v14 & left_apart_point(v0, v3) = v9 & reverse_line(v2) = v11 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0)))
% 31.01/7.96 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v3 = 0))))
% 31.01/7.96 | (160) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v3 & line(v0) = v2 & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5 & ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v7 = 0)))
% 31.01/7.96 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (right_apart_point(v1, v2) = v3) | ~ (right_apart_point(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : (divides_points(v2, v0, v1) = v7 & left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v5 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))))
% 31.01/7.96 | (162) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ? [v3] : (line(v1) = v3 & line(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.01/7.96 | (163) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3))
% 31.01/7.96 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (line_connecting(v0, v1) = v4) | ~ (left_apart_point(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : (distinct_points(v0, v1) = v5 & left_convergent_lines(v4, v2) = v7 & left_apart_point(v0, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 31.01/7.96 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 31.01/7.96 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v4 & right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 31.01/7.96 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v3) = v9 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v2) = v8 & reverse_line(v3) = v13 & reverse_line(v2) = v10 & ( ~ (v7 = 0) | ~ (v6 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0)))
% 31.40/7.96 | (168) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 31.40/7.96 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 31.40/7.96 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v10) = v12 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v3) = v9 & left_apart_point(v1, v2) = v7 & left_apart_point(v0, v10) = v11 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v3) = v8 & reverse_line(v2) = v10 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v9 = 0 | v8 = 0 | v7 = 0)))
% 31.40/7.96 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v8 & distinct_points(v0, v1) = v7 & left_apart_point(v1, v13) = v15 & left_apart_point(v1, v3) = v11 & left_apart_point(v1, v2) = v10 & left_apart_point(v0, v13) = v14 & left_apart_point(v0, v5) = v12 & left_apart_point(v0, v2) = v9 & reverse_line(v3) = v13 & ( ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))
% 31.40/7.96 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 31.40/7.96 | (173) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (distinct_points(v0, v1) = v3 & line_connecting(v0, v1) = v4 & equally_directed_lines(v4, v5) = v6 & reverse_line(v2) = v5 & ( ~ (v3 = 0) | v6 = 0)))
% 31.40/7.96 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v3) = v10 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = v9 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0))))
% 31.40/7.96 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (left_apart_point(v1, v5) = v7) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v4) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v4) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.40/7.97 | (176) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v3 & line(v2) = v5 & line(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 31.40/7.97 | (177) ! [v0] : ! [v1] : ( ~ (line(v1) = 0) | ~ (line(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & point(v5) = v6 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & unequally_directed_lines(v0, v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v6 = 0)))
% 31.40/7.97 | (178) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3))
% 31.40/7.97 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (left_apart_point(v1, v11) = v13 & left_apart_point(v1, v8) = v10 & left_apart_point(v1, v3) = v7 & left_apart_point(v1, v2) = v5 & left_apart_point(v0, v11) = v12 & left_apart_point(v0, v8) = v9 & left_apart_point(v0, v3) = v6 & left_apart_point(v0, v2) = v4 & reverse_line(v3) = v11 & reverse_line(v2) = v8 & (v13 = 0 | v12 = 0 | v10 = 0 | v9 = 0 | v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 31.40/7.97 | (180) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 31.40/7.97 | (181) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 31.40/7.97 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (point(v2) = v8 & line(v1) = v4 & line(v0) = v3 & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v8 = 0)))
% 31.40/7.97 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v0, v3, v2) = v5) | ~ (before_on_line(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : (between_on_line(v0, v1, v2, v3) = v8 & before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v7 & (v8 = 0 | (( ~ (v7 = 0) | ~ (v5 = 0)) & ( ~ (v6 = 0) | ~ (v4 = 0))))))
% 31.40/7.97 | (184) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : (left_apart_point(v0, v1) = v2 & right_apart_point(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 31.40/7.97 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (distinct_lines(v2, v3) = v6 & left_apart_point(v1, v5) = v14 & left_apart_point(v1, v4) = v12 & left_apart_point(v1, v3) = v10 & left_apart_point(v1, v2) = v8 & left_apart_point(v0, v5) = v13 & left_apart_point(v0, v4) = v11 & left_apart_point(v0, v3) = v9 & left_apart_point(v0, v2) = v7 & ( ~ (v6 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0 | v8 = 0 | v7 = 0)))
% 31.40/7.97 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, v3) = v5 & before_on_line(v0, v2, v1) = v7 & before_on_line(v0, v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = 0))))
% 31.40/7.97 | (187) ! [v0] : ! [v1] : ! [v2] : ( ~ (line(v0) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & point(v6) = v7 & line(v1) = v3 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0)))
% 31.40/7.97 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (left_convergent_lines(v0, v1) = v6 & unequally_directed_lines(v0, v2) = v5 & unequally_directed_lines(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))
% 31.40/7.97 | (189) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (distinct_lines(v2, v3) = v9 & distinct_points(v0, v1) = v8 & left_apart_point(v1, v6) = v15 & left_apart_point(v1, v3) = v13 & left_apart_point(v1, v2) = v11 & left_apart_point(v0, v4) = v14 & left_apart_point(v0, v3) = v12 & left_apart_point(v0, v2) = v10 & ( ~ (v9 = 0) | ~ (v8 = 0) | v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0)))
% 31.40/7.97 | (190) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (distinct_points(v1, v2) = v4 & before_on_line(v0, v1, v2) = v7 & incident_point_and_line(v2, v0) = v6 & incident_point_and_line(v1, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v7 = 0)))
% 31.40/7.97 | (191) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4))
% 31.40/7.97 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (reverse_line(v2) = v7 & unequally_directed_lines(v1, v7) = v10 & unequally_directed_lines(v1, v2) = v9 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v3) = v6 & unequally_directed_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v4 = 0))))
% 31.40/7.97 | (193) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (incident_point_and_line(v1, v0) = v3) | ~ (line_connecting(v1, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (distinct_points(v1, v2) = v6 & before_on_line(v0, v1, v2) = v5 & incident_point_and_line(v2, v0) = v7 & equally_directed_lines(v0, v4) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v3 = 0))))
% 31.40/7.97 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 31.40/7.97 |
% 31.40/7.97 | Instantiating (21) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields:
% 31.40/7.97 | (195) ~ (all_1_0_0 = 0) & between_on_line(all_1_5_5, all_1_3_3, all_1_2_2, all_1_1_1) = 0 & incident_point_and_line(all_1_2_2, all_1_4_4) = 0 & divides_points(all_1_4_4, all_1_3_3, all_1_1_1) = all_1_0_0 & convergent_lines(all_1_5_5, all_1_4_4) = 0
% 31.40/7.97 |
% 31.40/7.97 | Applying alpha-rule on (195) yields:
% 31.40/7.97 | (196) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 31.40/7.97 | (197) between_on_line(all_1_5_5, all_1_3_3, all_1_2_2, all_1_1_1) = 0
% 31.40/7.97 | (198) incident_point_and_line(all_1_2_2, all_1_4_4) = 0
% 31.40/7.97 | (199) divides_points(all_1_4_4, all_1_3_3, all_1_1_1) = all_1_0_0
% 31.40/7.97 | (200) ~ (all_1_0_0 = 0)
% 31.40/7.97 |
% 31.40/7.97 | Instantiating formula (166) with all_1_0_0, all_1_4_4, all_1_1_1, all_1_3_3 and discharging atoms divides_points(all_1_4_4, all_1_3_3, all_1_1_1) = all_1_0_0, yields:
% 31.40/7.97 | (201) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, all_1_4_4) = v0 & right_apart_point(all_1_1_1, all_1_4_4) = v1 & right_apart_point(all_1_3_3, all_1_4_4) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.40/7.97 |
% 31.40/7.97 | Instantiating formula (64) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.97 | (202) unequally_directed_lines(all_1_5_5, all_1_4_4) = 0 & unequally_directed_opposite_lines(all_1_5_5, all_1_4_4) = 0
% 31.40/7.97 |
% 31.40/7.97 | Applying alpha-rule on (202) yields:
% 31.40/7.97 | (203) unequally_directed_lines(all_1_5_5, all_1_4_4) = 0
% 31.40/7.97 | (204) unequally_directed_opposite_lines(all_1_5_5, all_1_4_4) = 0
% 31.40/7.97 |
% 31.40/7.97 +-Applying beta-rule and splitting (201), into two cases.
% 31.40/7.97 |-Branch one:
% 31.40/7.97 | (205) all_1_0_0 = 0
% 31.40/7.97 |
% 31.40/7.98 | Equations (205) can reduce 200 to:
% 31.40/7.98 | (206) $false
% 31.40/7.98 |
% 31.40/7.98 |-The branch is then unsatisfiable
% 31.40/7.98 |-Branch two:
% 31.40/7.98 | (200) ~ (all_1_0_0 = 0)
% 31.40/7.98 | (208) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, all_1_4_4) = v0 & right_apart_point(all_1_1_1, all_1_4_4) = v1 & right_apart_point(all_1_3_3, all_1_4_4) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating (208) with all_19_0_18, all_19_1_19, all_19_2_20, all_19_3_21 yields:
% 31.40/7.98 | (209) left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18 & left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21 & right_apart_point(all_1_1_1, all_1_4_4) = all_19_2_20 & right_apart_point(all_1_3_3, all_1_4_4) = all_19_1_19 & ( ~ (all_19_0_18 = 0) | ~ (all_19_1_19 = 0)) & ( ~ (all_19_2_20 = 0) | ~ (all_19_3_21 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Applying alpha-rule on (209) yields:
% 31.40/7.98 | (210) ~ (all_19_0_18 = 0) | ~ (all_19_1_19 = 0)
% 31.40/7.98 | (211) right_apart_point(all_1_1_1, all_1_4_4) = all_19_2_20
% 31.40/7.98 | (212) left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18
% 31.40/7.98 | (213) left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21
% 31.40/7.98 | (214) right_apart_point(all_1_3_3, all_1_4_4) = all_19_1_19
% 31.40/7.98 | (215) ~ (all_19_2_20 = 0) | ~ (all_19_3_21 = 0)
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (114) with all_1_4_4, all_1_1_1 yields:
% 31.40/7.98 | (216) ~ (left_apart_point(all_1_1_1, all_1_4_4) = 0)
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (114) with all_1_4_4, all_1_3_3 yields:
% 31.40/7.98 | (217) ~ (left_apart_point(all_1_3_3, all_1_4_4) = 0)
% 31.40/7.98 |
% 31.40/7.98 | Using (212) and (216) yields:
% 31.40/7.98 | (218) ~ (all_19_0_18 = 0)
% 31.40/7.98 |
% 31.40/7.98 | Using (213) and (217) yields:
% 31.40/7.98 | (219) ~ (all_19_3_21 = 0)
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (145) with all_19_0_18, all_19_0_18, all_1_4_4, all_1_4_4, all_1_1_1, all_1_1_1 and discharging atoms left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18, yields:
% 31.40/7.98 | (220) all_19_0_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (145) with all_19_3_21, all_19_0_18, all_1_4_4, all_1_4_4, all_1_3_3, all_1_1_1 and discharging atoms left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18, left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21, yields:
% 31.40/7.98 | (221) all_19_0_18 = 0 | all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_3_3) = v0 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (145) with all_19_0_18, all_19_3_21, all_1_4_4, all_1_4_4, all_1_1_1, all_1_3_3 and discharging atoms left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18, left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21, yields:
% 31.40/7.98 | (222) all_19_0_18 = 0 | all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (167) with all_19_0_18, all_19_3_21, all_1_4_4, all_1_4_4, all_1_3_3, all_1_1_1 and discharging atoms left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18, left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21, yields:
% 31.40/7.98 | (223) all_19_0_18 = 0 | all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_3_3) = v0 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (167) with all_19_3_21, all_19_0_18, all_1_4_4, all_1_4_4, all_1_1_1, all_1_3_3 and discharging atoms left_apart_point(all_1_1_1, all_1_4_4) = all_19_0_18, left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21, yields:
% 31.40/7.98 | (224) all_19_0_18 = 0 | all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (145) with all_19_3_21, all_19_3_21, all_1_4_4, all_1_4_4, all_1_3_3, all_1_3_3 and discharging atoms left_apart_point(all_1_3_3, all_1_4_4) = all_19_3_21, yields:
% 31.40/7.98 | (225) all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (150) with 0, 0, all_1_4_4, all_1_5_5, all_1_5_5 and discharging atoms unequally_directed_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (226) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (reverse_line(all_1_4_4) = v3 & reverse_line(all_1_5_5) = v1 & unequally_directed_lines(all_1_5_5, v3) = v5 & unequally_directed_lines(all_1_5_5, v3) = v4 & unequally_directed_lines(all_1_5_5, v1) = v2 & unequally_directed_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = 0 | v4 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (35) with 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms unequally_directed_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (227) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (reverse_line(all_1_4_4) = v2 & reverse_line(all_1_4_4) = v0 & unequally_directed_lines(all_1_4_4, v2) = v5 & unequally_directed_lines(all_1_4_4, all_1_4_4) = v4 & unequally_directed_lines(all_1_5_5, v2) = v3 & unequally_directed_lines(all_1_5_5, v0) = v1 & ( ~ (v1 = 0) | v3 = 0 | (v5 = 0 & v4 = 0)))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (160) with all_1_4_4, all_1_5_5 and discharging atoms unequally_directed_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (228) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(all_1_5_5, all_1_4_4) = v4 & point(v4) = v5 & line(all_1_4_4) = v1 & line(all_1_5_5) = v0 & reverse_line(all_1_4_4) = v2 & unequally_directed_lines(all_1_5_5, v2) = v3 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (82) with all_1_4_4, all_1_5_5 and discharging atoms unequally_directed_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (229) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection_point(all_1_5_5, all_1_4_4) = v2 & apart_point_and_line(v2, all_1_4_4) = v4 & apart_point_and_line(v2, all_1_5_5) = v3 & reverse_line(all_1_4_4) = v0 & unequally_directed_lines(all_1_5_5, v0) = v1 & ( ~ (v1 = 0) | ( ~ (v4 = 0) & ~ (v3 = 0))))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (113) with all_1_4_4, all_1_5_5 and discharging atoms unequally_directed_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (230) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (left_convergent_lines(all_1_5_5, v0) = v3 & left_convergent_lines(all_1_5_5, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v0 & unequally_directed_lines(all_1_5_5, v0) = v1 & ( ~ (v1 = 0) | v3 = 0 | v2 = 0))
% 31.40/7.98 |
% 31.40/7.98 | Instantiating formula (180) with all_1_4_4, all_1_5_5 and discharging atoms unequally_directed_opposite_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 31.40/7.98 | (231) ? [v0] : (reverse_line(all_1_4_4) = v0 & unequally_directed_lines(all_1_5_5, v0) = 0)
% 31.40/7.98 |
% 31.40/7.98 | Instantiating (231) with all_42_0_22 yields:
% 31.40/7.98 | (232) reverse_line(all_1_4_4) = all_42_0_22 & unequally_directed_lines(all_1_5_5, all_42_0_22) = 0
% 31.40/7.98 |
% 31.40/7.98 | Applying alpha-rule on (232) yields:
% 31.40/7.98 | (233) reverse_line(all_1_4_4) = all_42_0_22
% 31.40/7.98 | (234) unequally_directed_lines(all_1_5_5, all_42_0_22) = 0
% 31.40/7.98 |
% 31.40/7.98 | Instantiating (229) with all_86_0_86, all_86_1_87, all_86_2_88, all_86_3_89, all_86_4_90 yields:
% 31.40/7.98 | (235) intersection_point(all_1_5_5, all_1_4_4) = all_86_2_88 & apart_point_and_line(all_86_2_88, all_1_4_4) = all_86_0_86 & apart_point_and_line(all_86_2_88, all_1_5_5) = all_86_1_87 & reverse_line(all_1_4_4) = all_86_4_90 & unequally_directed_lines(all_1_5_5, all_86_4_90) = all_86_3_89 & ( ~ (all_86_3_89 = 0) | ( ~ (all_86_0_86 = 0) & ~ (all_86_1_87 = 0)))
% 31.40/7.98 |
% 31.40/7.98 | Applying alpha-rule on (235) yields:
% 31.40/7.98 | (236) apart_point_and_line(all_86_2_88, all_1_4_4) = all_86_0_86
% 31.40/7.98 | (237) intersection_point(all_1_5_5, all_1_4_4) = all_86_2_88
% 31.40/7.98 | (238) reverse_line(all_1_4_4) = all_86_4_90
% 31.40/7.98 | (239) ~ (all_86_3_89 = 0) | ( ~ (all_86_0_86 = 0) & ~ (all_86_1_87 = 0))
% 31.40/7.99 | (240) unequally_directed_lines(all_1_5_5, all_86_4_90) = all_86_3_89
% 31.40/7.99 | (241) apart_point_and_line(all_86_2_88, all_1_5_5) = all_86_1_87
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (227) with all_88_0_91, all_88_1_92, all_88_2_93, all_88_3_94, all_88_4_95, all_88_5_96 yields:
% 31.40/7.99 | (242) reverse_line(all_1_4_4) = all_88_3_94 & reverse_line(all_1_4_4) = all_88_5_96 & unequally_directed_lines(all_1_4_4, all_88_3_94) = all_88_0_91 & unequally_directed_lines(all_1_4_4, all_1_4_4) = all_88_1_92 & unequally_directed_lines(all_1_5_5, all_88_3_94) = all_88_2_93 & unequally_directed_lines(all_1_5_5, all_88_5_96) = all_88_4_95 & ( ~ (all_88_4_95 = 0) | all_88_2_93 = 0 | (all_88_0_91 = 0 & all_88_1_92 = 0))
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (242) yields:
% 31.40/7.99 | (243) ~ (all_88_4_95 = 0) | all_88_2_93 = 0 | (all_88_0_91 = 0 & all_88_1_92 = 0)
% 31.40/7.99 | (244) reverse_line(all_1_4_4) = all_88_5_96
% 31.40/7.99 | (245) unequally_directed_lines(all_1_5_5, all_88_3_94) = all_88_2_93
% 31.40/7.99 | (246) unequally_directed_lines(all_1_4_4, all_88_3_94) = all_88_0_91
% 31.40/7.99 | (247) unequally_directed_lines(all_1_4_4, all_1_4_4) = all_88_1_92
% 31.40/7.99 | (248) unequally_directed_lines(all_1_5_5, all_88_5_96) = all_88_4_95
% 31.40/7.99 | (249) reverse_line(all_1_4_4) = all_88_3_94
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (228) with all_92_0_100, all_92_1_101, all_92_2_102, all_92_3_103, all_92_4_104, all_92_5_105 yields:
% 31.40/7.99 | (250) intersection_point(all_1_5_5, all_1_4_4) = all_92_1_101 & point(all_92_1_101) = all_92_0_100 & line(all_1_4_4) = all_92_4_104 & line(all_1_5_5) = all_92_5_105 & reverse_line(all_1_4_4) = all_92_3_103 & unequally_directed_lines(all_1_5_5, all_92_3_103) = all_92_2_102 & ( ~ (all_92_2_102 = 0) | ~ (all_92_4_104 = 0) | ~ (all_92_5_105 = 0) | all_92_0_100 = 0)
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (250) yields:
% 31.40/7.99 | (251) line(all_1_5_5) = all_92_5_105
% 31.40/7.99 | (252) point(all_92_1_101) = all_92_0_100
% 31.40/7.99 | (253) line(all_1_4_4) = all_92_4_104
% 31.40/7.99 | (254) intersection_point(all_1_5_5, all_1_4_4) = all_92_1_101
% 31.40/7.99 | (255) reverse_line(all_1_4_4) = all_92_3_103
% 31.40/7.99 | (256) unequally_directed_lines(all_1_5_5, all_92_3_103) = all_92_2_102
% 31.40/7.99 | (257) ~ (all_92_2_102 = 0) | ~ (all_92_4_104 = 0) | ~ (all_92_5_105 = 0) | all_92_0_100 = 0
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (230) with all_96_0_107, all_96_1_108, all_96_2_109, all_96_3_110 yields:
% 31.40/7.99 | (258) left_convergent_lines(all_1_5_5, all_96_3_110) = all_96_0_107 & left_convergent_lines(all_1_5_5, all_1_4_4) = all_96_1_108 & reverse_line(all_1_4_4) = all_96_3_110 & unequally_directed_lines(all_1_5_5, all_96_3_110) = all_96_2_109 & ( ~ (all_96_2_109 = 0) | all_96_0_107 = 0 | all_96_1_108 = 0)
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (258) yields:
% 31.40/7.99 | (259) reverse_line(all_1_4_4) = all_96_3_110
% 31.40/7.99 | (260) unequally_directed_lines(all_1_5_5, all_96_3_110) = all_96_2_109
% 31.40/7.99 | (261) left_convergent_lines(all_1_5_5, all_96_3_110) = all_96_0_107
% 31.40/7.99 | (262) left_convergent_lines(all_1_5_5, all_1_4_4) = all_96_1_108
% 31.40/7.99 | (263) ~ (all_96_2_109 = 0) | all_96_0_107 = 0 | all_96_1_108 = 0
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (226) with all_116_0_138, all_116_1_139, all_116_2_140, all_116_3_141, all_116_4_142, all_116_5_143 yields:
% 31.40/7.99 | (264) reverse_line(all_1_4_4) = all_116_2_140 & reverse_line(all_1_5_5) = all_116_4_142 & unequally_directed_lines(all_1_5_5, all_116_2_140) = all_116_0_138 & unequally_directed_lines(all_1_5_5, all_116_2_140) = all_116_1_139 & unequally_directed_lines(all_1_5_5, all_116_4_142) = all_116_3_141 & unequally_directed_lines(all_1_5_5, all_1_5_5) = all_116_5_143 & ( ~ (all_116_3_141 = 0) | ~ (all_116_5_143 = 0) | all_116_0_138 = 0 | all_116_1_139 = 0)
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (264) yields:
% 31.40/7.99 | (265) unequally_directed_lines(all_1_5_5, all_116_2_140) = all_116_0_138
% 31.40/7.99 | (266) unequally_directed_lines(all_1_5_5, all_116_4_142) = all_116_3_141
% 31.40/7.99 | (267) ~ (all_116_3_141 = 0) | ~ (all_116_5_143 = 0) | all_116_0_138 = 0 | all_116_1_139 = 0
% 31.40/7.99 | (268) reverse_line(all_1_4_4) = all_116_2_140
% 31.40/7.99 | (269) reverse_line(all_1_5_5) = all_116_4_142
% 31.40/7.99 | (270) unequally_directed_lines(all_1_5_5, all_1_5_5) = all_116_5_143
% 31.40/7.99 | (271) unequally_directed_lines(all_1_5_5, all_116_2_140) = all_116_1_139
% 31.40/7.99 |
% 31.40/7.99 +-Applying beta-rule and splitting (225), into two cases.
% 31.40/7.99 |-Branch one:
% 31.40/7.99 | (272) all_19_3_21 = 0
% 31.40/7.99 |
% 31.40/7.99 | Equations (272) can reduce 219 to:
% 31.40/7.99 | (206) $false
% 31.40/7.99 |
% 31.40/7.99 |-The branch is then unsatisfiable
% 31.40/7.99 |-Branch two:
% 31.40/7.99 | (219) ~ (all_19_3_21 = 0)
% 31.40/7.99 | (275) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (275) with all_183_0_222, all_183_1_223, all_183_2_224, all_183_3_225, all_183_4_226, all_183_5_227, all_183_6_228, all_183_7_229, all_183_8_230, all_183_9_231 yields:
% 31.40/7.99 | (276) distinct_lines(all_1_4_4, all_1_4_4) = all_183_8_230 & distinct_points(all_1_3_3, all_1_3_3) = all_183_9_231 & left_apart_point(all_1_3_3, all_183_2_224) = all_183_0_222 & left_apart_point(all_1_3_3, all_183_2_224) = all_183_1_223 & left_apart_point(all_1_3_3, all_183_5_227) = all_183_3_225 & left_apart_point(all_1_3_3, all_183_5_227) = all_183_4_226 & left_apart_point(all_1_3_3, all_1_4_4) = all_183_6_228 & left_apart_point(all_1_3_3, all_1_4_4) = all_183_7_229 & reverse_line(all_1_4_4) = all_183_2_224 & reverse_line(all_1_4_4) = all_183_5_227 & ( ~ (all_183_8_230 = 0) | ~ (all_183_9_231 = 0) | all_183_0_222 = 0 | all_183_1_223 = 0 | all_183_3_225 = 0 | all_183_4_226 = 0 | all_183_6_228 = 0 | all_183_7_229 = 0)
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (276) yields:
% 31.40/7.99 | (277) left_apart_point(all_1_3_3, all_183_2_224) = all_183_1_223
% 31.40/7.99 | (278) left_apart_point(all_1_3_3, all_183_5_227) = all_183_4_226
% 31.40/7.99 | (279) reverse_line(all_1_4_4) = all_183_2_224
% 31.40/7.99 | (280) left_apart_point(all_1_3_3, all_183_5_227) = all_183_3_225
% 31.40/7.99 | (281) left_apart_point(all_1_3_3, all_183_2_224) = all_183_0_222
% 31.40/7.99 | (282) distinct_points(all_1_3_3, all_1_3_3) = all_183_9_231
% 31.40/7.99 | (283) left_apart_point(all_1_3_3, all_1_4_4) = all_183_7_229
% 31.40/7.99 | (284) left_apart_point(all_1_3_3, all_1_4_4) = all_183_6_228
% 31.40/7.99 | (285) reverse_line(all_1_4_4) = all_183_5_227
% 31.40/7.99 | (286) ~ (all_183_8_230 = 0) | ~ (all_183_9_231 = 0) | all_183_0_222 = 0 | all_183_1_223 = 0 | all_183_3_225 = 0 | all_183_4_226 = 0 | all_183_6_228 = 0 | all_183_7_229 = 0
% 31.40/7.99 | (287) distinct_lines(all_1_4_4, all_1_4_4) = all_183_8_230
% 31.40/7.99 |
% 31.40/7.99 +-Applying beta-rule and splitting (220), into two cases.
% 31.40/7.99 |-Branch one:
% 31.40/7.99 | (288) all_19_0_18 = 0
% 31.40/7.99 |
% 31.40/7.99 | Equations (288) can reduce 218 to:
% 31.40/7.99 | (206) $false
% 31.40/7.99 |
% 31.40/7.99 |-The branch is then unsatisfiable
% 31.40/7.99 |-Branch two:
% 31.40/7.99 | (218) ~ (all_19_0_18 = 0)
% 31.40/7.99 | (291) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.99 |
% 31.40/7.99 | Instantiating (291) with all_188_0_232, all_188_1_233, all_188_2_234, all_188_3_235, all_188_4_236, all_188_5_237, all_188_6_238, all_188_7_239, all_188_8_240, all_188_9_241 yields:
% 31.40/7.99 | (292) distinct_lines(all_1_4_4, all_1_4_4) = all_188_8_240 & distinct_points(all_1_1_1, all_1_1_1) = all_188_9_241 & left_apart_point(all_1_1_1, all_188_2_234) = all_188_0_232 & left_apart_point(all_1_1_1, all_188_2_234) = all_188_1_233 & left_apart_point(all_1_1_1, all_188_5_237) = all_188_3_235 & left_apart_point(all_1_1_1, all_188_5_237) = all_188_4_236 & left_apart_point(all_1_1_1, all_1_4_4) = all_188_6_238 & left_apart_point(all_1_1_1, all_1_4_4) = all_188_7_239 & reverse_line(all_1_4_4) = all_188_2_234 & reverse_line(all_1_4_4) = all_188_5_237 & ( ~ (all_188_8_240 = 0) | ~ (all_188_9_241 = 0) | all_188_0_232 = 0 | all_188_1_233 = 0 | all_188_3_235 = 0 | all_188_4_236 = 0 | all_188_6_238 = 0 | all_188_7_239 = 0)
% 31.40/7.99 |
% 31.40/7.99 | Applying alpha-rule on (292) yields:
% 31.40/7.99 | (293) left_apart_point(all_1_1_1, all_188_2_234) = all_188_1_233
% 31.40/7.99 | (294) distinct_points(all_1_1_1, all_1_1_1) = all_188_9_241
% 31.40/7.99 | (295) reverse_line(all_1_4_4) = all_188_5_237
% 31.40/7.99 | (296) left_apart_point(all_1_1_1, all_1_4_4) = all_188_6_238
% 31.40/7.99 | (297) distinct_lines(all_1_4_4, all_1_4_4) = all_188_8_240
% 31.40/7.99 | (298) left_apart_point(all_1_1_1, all_188_5_237) = all_188_4_236
% 31.40/7.99 | (299) ~ (all_188_8_240 = 0) | ~ (all_188_9_241 = 0) | all_188_0_232 = 0 | all_188_1_233 = 0 | all_188_3_235 = 0 | all_188_4_236 = 0 | all_188_6_238 = 0 | all_188_7_239 = 0
% 31.40/7.99 | (300) reverse_line(all_1_4_4) = all_188_2_234
% 31.40/7.99 | (301) left_apart_point(all_1_1_1, all_188_2_234) = all_188_0_232
% 31.40/7.99 | (302) left_apart_point(all_1_1_1, all_1_4_4) = all_188_7_239
% 31.40/7.99 | (303) left_apart_point(all_1_1_1, all_188_5_237) = all_188_3_235
% 31.40/7.99 |
% 31.40/7.99 +-Applying beta-rule and splitting (221), into two cases.
% 31.40/7.99 |-Branch one:
% 31.40/7.99 | (288) all_19_0_18 = 0
% 31.40/7.99 |
% 31.40/7.99 | Equations (288) can reduce 218 to:
% 31.40/7.99 | (206) $false
% 31.40/7.99 |
% 31.40/7.99 |-The branch is then unsatisfiable
% 31.40/7.99 |-Branch two:
% 31.40/7.99 | (218) ~ (all_19_0_18 = 0)
% 31.40/7.99 | (307) all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_3_3) = v0 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/7.99 |
% 31.40/7.99 +-Applying beta-rule and splitting (224), into two cases.
% 31.40/7.99 |-Branch one:
% 31.40/7.99 | (288) all_19_0_18 = 0
% 31.40/8.00 |
% 31.40/8.00 | Equations (288) can reduce 218 to:
% 31.40/8.00 | (206) $false
% 31.40/8.00 |
% 31.40/8.00 |-The branch is then unsatisfiable
% 31.40/8.00 |-Branch two:
% 31.40/8.00 | (218) ~ (all_19_0_18 = 0)
% 31.40/8.00 | (311) all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, all_1_4_4) = v3 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v2 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/8.00 |
% 31.40/8.00 +-Applying beta-rule and splitting (222), into two cases.
% 31.40/8.00 |-Branch one:
% 31.40/8.00 | (288) all_19_0_18 = 0
% 31.40/8.00 |
% 31.40/8.00 | Equations (288) can reduce 218 to:
% 31.40/8.00 | (206) $false
% 31.40/8.00 |
% 31.40/8.00 |-The branch is then unsatisfiable
% 31.40/8.00 |-Branch two:
% 31.40/8.00 | (218) ~ (all_19_0_18 = 0)
% 31.40/8.00 | (315) all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/8.00 |
% 31.40/8.00 +-Applying beta-rule and splitting (223), into two cases.
% 31.40/8.00 |-Branch one:
% 31.40/8.00 | (288) all_19_0_18 = 0
% 31.40/8.00 |
% 31.40/8.00 | Equations (288) can reduce 218 to:
% 31.40/8.00 | (206) $false
% 31.40/8.00 |
% 31.40/8.00 |-The branch is then unsatisfiable
% 31.40/8.00 |-Branch two:
% 31.40/8.00 | (218) ~ (all_19_0_18 = 0)
% 31.40/8.00 | (319) all_19_3_21 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_3_3) = v0 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/8.00 |
% 31.40/8.00 +-Applying beta-rule and splitting (315), into two cases.
% 31.40/8.00 |-Branch one:
% 31.40/8.00 | (272) all_19_3_21 = 0
% 31.40/8.00 |
% 31.40/8.00 | Equations (272) can reduce 219 to:
% 31.40/8.00 | (206) $false
% 31.40/8.00 |
% 31.40/8.00 |-The branch is then unsatisfiable
% 31.40/8.00 |-Branch two:
% 31.40/8.00 | (219) ~ (all_19_3_21 = 0)
% 31.40/8.00 | (323) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_3_3, all_1_1_1) = v0 & left_apart_point(all_1_1_1, v7) = v9 & left_apart_point(all_1_1_1, v4) = v6 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v8 & left_apart_point(all_1_3_3, v4) = v5 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.40/8.00 |
% 31.40/8.00 | Instantiating (323) with all_209_0_242, all_209_1_243, all_209_2_244, all_209_3_245, all_209_4_246, all_209_5_247, all_209_6_248, all_209_7_249, all_209_8_250, all_209_9_251 yields:
% 31.40/8.00 | (324) distinct_lines(all_1_4_4, all_1_4_4) = all_209_8_250 & distinct_points(all_1_3_3, all_1_1_1) = all_209_9_251 & left_apart_point(all_1_1_1, all_209_2_244) = all_209_0_242 & left_apart_point(all_1_1_1, all_209_5_247) = all_209_3_245 & left_apart_point(all_1_1_1, all_1_4_4) = all_209_7_249 & left_apart_point(all_1_3_3, all_209_2_244) = all_209_1_243 & left_apart_point(all_1_3_3, all_209_5_247) = all_209_4_246 & left_apart_point(all_1_3_3, all_1_4_4) = all_209_6_248 & reverse_line(all_1_4_4) = all_209_2_244 & reverse_line(all_1_4_4) = all_209_5_247 & ( ~ (all_209_8_250 = 0) | ~ (all_209_9_251 = 0) | all_209_0_242 = 0 | all_209_1_243 = 0 | all_209_3_245 = 0 | all_209_4_246 = 0 | all_209_6_248 = 0 | all_209_7_249 = 0)
% 31.40/8.00 |
% 31.40/8.00 | Applying alpha-rule on (324) yields:
% 31.40/8.00 | (325) reverse_line(all_1_4_4) = all_209_5_247
% 31.40/8.00 | (326) reverse_line(all_1_4_4) = all_209_2_244
% 31.40/8.00 | (327) distinct_lines(all_1_4_4, all_1_4_4) = all_209_8_250
% 31.57/8.00 | (328) left_apart_point(all_1_3_3, all_209_5_247) = all_209_4_246
% 31.57/8.00 | (329) distinct_points(all_1_3_3, all_1_1_1) = all_209_9_251
% 31.57/8.00 | (330) left_apart_point(all_1_3_3, all_1_4_4) = all_209_6_248
% 31.57/8.00 | (331) left_apart_point(all_1_1_1, all_209_2_244) = all_209_0_242
% 31.57/8.00 | (332) ~ (all_209_8_250 = 0) | ~ (all_209_9_251 = 0) | all_209_0_242 = 0 | all_209_1_243 = 0 | all_209_3_245 = 0 | all_209_4_246 = 0 | all_209_6_248 = 0 | all_209_7_249 = 0
% 31.57/8.00 | (333) left_apart_point(all_1_1_1, all_1_4_4) = all_209_7_249
% 31.57/8.00 | (334) left_apart_point(all_1_3_3, all_209_2_244) = all_209_1_243
% 31.57/8.00 | (335) left_apart_point(all_1_1_1, all_209_5_247) = all_209_3_245
% 31.57/8.00 |
% 31.57/8.00 +-Applying beta-rule and splitting (319), into two cases.
% 31.57/8.00 |-Branch one:
% 31.57/8.00 | (272) all_19_3_21 = 0
% 31.57/8.00 |
% 31.57/8.00 | Equations (272) can reduce 219 to:
% 31.57/8.00 | (206) $false
% 31.57/8.00 |
% 31.57/8.00 |-The branch is then unsatisfiable
% 31.57/8.00 |-Branch two:
% 31.57/8.00 | (219) ~ (all_19_3_21 = 0)
% 31.57/8.00 | (339) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_3_3) = v0 & left_apart_point(all_1_1_1, v7) = v8 & left_apart_point(all_1_1_1, v4) = v5 & left_apart_point(all_1_1_1, all_1_4_4) = v2 & left_apart_point(all_1_3_3, v7) = v9 & left_apart_point(all_1_3_3, v4) = v6 & left_apart_point(all_1_3_3, all_1_4_4) = v3 & reverse_line(all_1_4_4) = v7 & reverse_line(all_1_4_4) = v4 & ( ~ (v1 = 0) | ~ (v0 = 0) | v9 = 0 | v8 = 0 | v6 = 0 | v5 = 0 | v3 = 0 | v2 = 0))
% 31.57/8.00 |
% 31.57/8.00 | Instantiating (339) with all_214_0_252, all_214_1_253, all_214_2_254, all_214_3_255, all_214_4_256, all_214_5_257, all_214_6_258, all_214_7_259, all_214_8_260, all_214_9_261 yields:
% 31.57/8.00 | (340) distinct_lines(all_1_4_4, all_1_4_4) = all_214_8_260 & distinct_points(all_1_1_1, all_1_3_3) = all_214_9_261 & left_apart_point(all_1_1_1, all_214_2_254) = all_214_1_253 & left_apart_point(all_1_1_1, all_214_5_257) = all_214_4_256 & left_apart_point(all_1_1_1, all_1_4_4) = all_214_7_259 & left_apart_point(all_1_3_3, all_214_2_254) = all_214_0_252 & left_apart_point(all_1_3_3, all_214_5_257) = all_214_3_255 & left_apart_point(all_1_3_3, all_1_4_4) = all_214_6_258 & reverse_line(all_1_4_4) = all_214_2_254 & reverse_line(all_1_4_4) = all_214_5_257 & ( ~ (all_214_8_260 = 0) | ~ (all_214_9_261 = 0) | all_214_0_252 = 0 | all_214_1_253 = 0 | all_214_3_255 = 0 | all_214_4_256 = 0 | all_214_6_258 = 0 | all_214_7_259 = 0)
% 31.57/8.00 |
% 31.57/8.00 | Applying alpha-rule on (340) yields:
% 31.57/8.00 | (341) left_apart_point(all_1_1_1, all_214_2_254) = all_214_1_253
% 31.57/8.00 | (342) left_apart_point(all_1_3_3, all_214_2_254) = all_214_0_252
% 31.57/8.00 | (343) reverse_line(all_1_4_4) = all_214_5_257
% 31.57/8.00 | (344) left_apart_point(all_1_1_1, all_214_5_257) = all_214_4_256
% 31.57/8.00 | (345) left_apart_point(all_1_3_3, all_214_5_257) = all_214_3_255
% 31.57/8.00 | (346) left_apart_point(all_1_3_3, all_1_4_4) = all_214_6_258
% 31.57/8.00 | (347) ~ (all_214_8_260 = 0) | ~ (all_214_9_261 = 0) | all_214_0_252 = 0 | all_214_1_253 = 0 | all_214_3_255 = 0 | all_214_4_256 = 0 | all_214_6_258 = 0 | all_214_7_259 = 0
% 31.57/8.00 | (348) distinct_points(all_1_1_1, all_1_3_3) = all_214_9_261
% 31.57/8.00 | (349) distinct_lines(all_1_4_4, all_1_4_4) = all_214_8_260
% 31.57/8.00 | (350) reverse_line(all_1_4_4) = all_214_2_254
% 31.57/8.00 | (351) left_apart_point(all_1_1_1, all_1_4_4) = all_214_7_259
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (107) with all_1_4_4, all_1_5_5 yields:
% 31.57/8.00 | (352) ~ (left_convergent_lines(all_1_5_5, all_1_4_4) = 0)
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_209_2_244, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_209_2_244, yields:
% 31.57/8.00 | (353) all_214_5_257 = all_209_2_244
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_209_5_247, all_214_2_254 and discharging atoms reverse_line(all_1_4_4) = all_214_2_254, reverse_line(all_1_4_4) = all_209_5_247, yields:
% 31.57/8.00 | (354) all_214_2_254 = all_209_5_247
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_188_2_234, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_188_2_234, yields:
% 31.57/8.00 | (355) all_214_5_257 = all_188_2_234
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_188_5_237, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_188_5_237, yields:
% 31.57/8.00 | (356) all_214_5_257 = all_188_5_237
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_183_2_224, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_183_2_224, yields:
% 31.57/8.00 | (357) all_214_5_257 = all_183_2_224
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_183_2_224, all_209_5_247 and discharging atoms reverse_line(all_1_4_4) = all_209_5_247, reverse_line(all_1_4_4) = all_183_2_224, yields:
% 31.57/8.00 | (358) all_209_5_247 = all_183_2_224
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_183_5_227, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_183_5_227, yields:
% 31.57/8.00 | (359) all_214_5_257 = all_183_5_227
% 31.57/8.00 |
% 31.57/8.00 | Instantiating formula (138) with all_1_4_4, all_116_2_140, all_214_2_254 and discharging atoms reverse_line(all_1_4_4) = all_214_2_254, reverse_line(all_1_4_4) = all_116_2_140, yields:
% 31.57/8.01 | (360) all_214_2_254 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_96_3_110, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_96_3_110, yields:
% 31.57/8.01 | (361) all_214_5_257 = all_96_3_110
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (112) with all_96_3_110, all_1_4_4, all_1_5_5 and discharging atoms reverse_line(all_1_4_4) = all_96_3_110, yields:
% 31.57/8.01 | (362) ~ (left_convergent_lines(all_1_5_5, all_96_3_110) = 0)
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_92_3_103, all_96_3_110 and discharging atoms reverse_line(all_1_4_4) = all_96_3_110, reverse_line(all_1_4_4) = all_92_3_103, yields:
% 31.57/8.01 | (363) all_96_3_110 = all_92_3_103
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_88_3_94, all_188_2_234 and discharging atoms reverse_line(all_1_4_4) = all_188_2_234, reverse_line(all_1_4_4) = all_88_3_94, yields:
% 31.57/8.01 | (364) all_188_2_234 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_88_5_96, all_96_3_110 and discharging atoms reverse_line(all_1_4_4) = all_96_3_110, reverse_line(all_1_4_4) = all_88_5_96, yields:
% 31.57/8.01 | (365) all_96_3_110 = all_88_5_96
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_86_4_90, all_214_5_257 and discharging atoms reverse_line(all_1_4_4) = all_214_5_257, reverse_line(all_1_4_4) = all_86_4_90, yields:
% 31.57/8.01 | (366) all_214_5_257 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (138) with all_1_4_4, all_42_0_22, all_96_3_110 and discharging atoms reverse_line(all_1_4_4) = all_96_3_110, reverse_line(all_1_4_4) = all_42_0_22, yields:
% 31.57/8.01 | (367) all_96_3_110 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (50) with all_1_5_5, all_88_3_94, all_88_2_93, all_96_2_109 and discharging atoms unequally_directed_lines(all_1_5_5, all_88_3_94) = all_88_2_93, yields:
% 31.57/8.01 | (368) all_96_2_109 = all_88_2_93 | ~ (unequally_directed_lines(all_1_5_5, all_88_3_94) = all_96_2_109)
% 31.57/8.01 |
% 31.57/8.01 | Instantiating formula (50) with all_1_5_5, all_42_0_22, 0, all_88_2_93 and discharging atoms unequally_directed_lines(all_1_5_5, all_42_0_22) = 0, yields:
% 31.57/8.01 | (369) all_88_2_93 = 0 | ~ (unequally_directed_lines(all_1_5_5, all_42_0_22) = all_88_2_93)
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (354,360) yields a new equation:
% 31.57/8.01 | (370) all_209_5_247 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 370 yields:
% 31.57/8.01 | (371) all_209_5_247 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (359,353) yields a new equation:
% 31.57/8.01 | (372) all_209_2_244 = all_183_5_227
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (366,353) yields a new equation:
% 31.57/8.01 | (373) all_209_2_244 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (355,353) yields a new equation:
% 31.57/8.01 | (374) all_209_2_244 = all_188_2_234
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (357,353) yields a new equation:
% 31.57/8.01 | (375) all_209_2_244 = all_183_2_224
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (361,353) yields a new equation:
% 31.57/8.01 | (376) all_209_2_244 = all_96_3_110
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (356,353) yields a new equation:
% 31.57/8.01 | (377) all_209_2_244 = all_188_5_237
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (372,377) yields a new equation:
% 31.57/8.01 | (378) all_188_5_237 = all_183_5_227
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (373,377) yields a new equation:
% 31.57/8.01 | (379) all_188_5_237 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (374,377) yields a new equation:
% 31.57/8.01 | (380) all_188_2_234 = all_188_5_237
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 380 yields:
% 31.57/8.01 | (381) all_188_2_234 = all_188_5_237
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (375,377) yields a new equation:
% 31.57/8.01 | (382) all_188_5_237 = all_183_2_224
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (376,377) yields a new equation:
% 31.57/8.01 | (383) all_188_5_237 = all_96_3_110
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (358,371) yields a new equation:
% 31.57/8.01 | (384) all_183_2_224 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 384 yields:
% 31.57/8.01 | (385) all_183_2_224 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (381,364) yields a new equation:
% 31.57/8.01 | (386) all_188_5_237 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 386 yields:
% 31.57/8.01 | (387) all_188_5_237 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (383,378) yields a new equation:
% 31.57/8.01 | (388) all_183_5_227 = all_96_3_110
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (379,378) yields a new equation:
% 31.57/8.01 | (389) all_183_5_227 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (387,378) yields a new equation:
% 31.57/8.01 | (390) all_183_5_227 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (382,378) yields a new equation:
% 31.57/8.01 | (391) all_183_2_224 = all_183_5_227
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 391 yields:
% 31.57/8.01 | (392) all_183_2_224 = all_183_5_227
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (392,385) yields a new equation:
% 31.57/8.01 | (393) all_183_5_227 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 393 yields:
% 31.57/8.01 | (394) all_183_5_227 = all_116_2_140
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (388,394) yields a new equation:
% 31.57/8.01 | (395) all_116_2_140 = all_96_3_110
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (389,394) yields a new equation:
% 31.57/8.01 | (396) all_116_2_140 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (390,394) yields a new equation:
% 31.57/8.01 | (397) all_116_2_140 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (396,397) yields a new equation:
% 31.57/8.01 | (398) all_88_3_94 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (395,397) yields a new equation:
% 31.57/8.01 | (399) all_96_3_110 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 399 yields:
% 31.57/8.01 | (400) all_96_3_110 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (365,363) yields a new equation:
% 31.57/8.01 | (401) all_92_3_103 = all_88_5_96
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (367,363) yields a new equation:
% 31.57/8.01 | (402) all_92_3_103 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (400,363) yields a new equation:
% 31.57/8.01 | (403) all_92_3_103 = all_88_3_94
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (402,401) yields a new equation:
% 31.57/8.01 | (404) all_88_5_96 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (403,401) yields a new equation:
% 31.57/8.01 | (405) all_88_3_94 = all_88_5_96
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 405 yields:
% 31.57/8.01 | (406) all_88_3_94 = all_88_5_96
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (406,398) yields a new equation:
% 31.57/8.01 | (407) all_88_5_96 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 407 yields:
% 31.57/8.01 | (408) all_88_5_96 = all_86_4_90
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (408,404) yields a new equation:
% 31.57/8.01 | (409) all_86_4_90 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Simplifying 409 yields:
% 31.57/8.01 | (410) all_86_4_90 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (410,398) yields a new equation:
% 31.57/8.01 | (411) all_88_3_94 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (404,401) yields a new equation:
% 31.57/8.01 | (402) all_92_3_103 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | Combining equations (402,363) yields a new equation:
% 31.57/8.01 | (367) all_96_3_110 = all_42_0_22
% 31.57/8.01 |
% 31.57/8.01 | From (367) and (261) follows:
% 31.57/8.01 | (414) left_convergent_lines(all_1_5_5, all_42_0_22) = all_96_0_107
% 31.57/8.01 |
% 31.57/8.01 | From (367) and (260) follows:
% 31.57/8.01 | (415) unequally_directed_lines(all_1_5_5, all_42_0_22) = all_96_2_109
% 31.57/8.01 |
% 31.57/8.01 | From (411) and (245) follows:
% 31.57/8.01 | (416) unequally_directed_lines(all_1_5_5, all_42_0_22) = all_88_2_93
% 31.57/8.01 |
% 31.57/8.01 | From (367) and (362) follows:
% 31.57/8.01 | (417) ~ (left_convergent_lines(all_1_5_5, all_42_0_22) = 0)
% 31.57/8.01 |
% 31.57/8.01 +-Applying beta-rule and splitting (369), into two cases.
% 31.57/8.01 |-Branch one:
% 31.57/8.01 | (418) ~ (unequally_directed_lines(all_1_5_5, all_42_0_22) = all_88_2_93)
% 31.57/8.01 |
% 31.57/8.01 | Using (416) and (418) yields:
% 31.57/8.01 | (419) $false
% 31.57/8.01 |
% 31.57/8.01 |-The branch is then unsatisfiable
% 31.57/8.01 |-Branch two:
% 31.57/8.01 | (416) unequally_directed_lines(all_1_5_5, all_42_0_22) = all_88_2_93
% 31.57/8.01 | (421) all_88_2_93 = 0
% 31.57/8.01 |
% 31.57/8.01 +-Applying beta-rule and splitting (368), into two cases.
% 31.57/8.01 |-Branch one:
% 31.57/8.01 | (422) ~ (unequally_directed_lines(all_1_5_5, all_88_3_94) = all_96_2_109)
% 31.57/8.01 |
% 31.57/8.01 | From (411) and (422) follows:
% 31.57/8.01 | (423) ~ (unequally_directed_lines(all_1_5_5, all_42_0_22) = all_96_2_109)
% 31.57/8.01 |
% 31.57/8.01 | Using (415) and (423) yields:
% 31.57/8.01 | (419) $false
% 31.57/8.01 |
% 31.57/8.01 |-The branch is then unsatisfiable
% 31.57/8.01 |-Branch two:
% 31.57/8.01 | (425) unequally_directed_lines(all_1_5_5, all_88_3_94) = all_96_2_109
% 31.57/8.01 | (426) all_96_2_109 = all_88_2_93
% 31.57/8.01 |
% 31.57/8.02 | Combining equations (421,426) yields a new equation:
% 31.57/8.02 | (427) all_96_2_109 = 0
% 31.57/8.02 |
% 31.57/8.02 | Using (414) and (417) yields:
% 31.57/8.02 | (428) ~ (all_96_0_107 = 0)
% 31.57/8.02 |
% 31.57/8.02 | Using (262) and (352) yields:
% 31.57/8.02 | (429) ~ (all_96_1_108 = 0)
% 31.57/8.02 |
% 31.57/8.02 +-Applying beta-rule and splitting (263), into two cases.
% 31.57/8.02 |-Branch one:
% 31.57/8.02 | (430) ~ (all_96_2_109 = 0)
% 31.57/8.02 |
% 31.57/8.02 | Equations (427) can reduce 430 to:
% 31.57/8.02 | (206) $false
% 31.57/8.02 |
% 31.57/8.02 |-The branch is then unsatisfiable
% 31.57/8.02 |-Branch two:
% 31.57/8.02 | (427) all_96_2_109 = 0
% 31.57/8.02 | (433) all_96_0_107 = 0 | all_96_1_108 = 0
% 31.57/8.02 |
% 31.57/8.02 +-Applying beta-rule and splitting (433), into two cases.
% 31.57/8.02 |-Branch one:
% 31.57/8.02 | (434) all_96_0_107 = 0
% 31.57/8.02 |
% 31.57/8.02 | Equations (434) can reduce 428 to:
% 31.57/8.02 | (206) $false
% 31.57/8.02 |
% 31.57/8.02 |-The branch is then unsatisfiable
% 31.57/8.02 |-Branch two:
% 31.57/8.02 | (428) ~ (all_96_0_107 = 0)
% 31.57/8.02 | (437) all_96_1_108 = 0
% 31.57/8.02 |
% 31.57/8.02 | Equations (437) can reduce 429 to:
% 31.57/8.02 | (206) $false
% 31.57/8.02 |
% 31.57/8.02 |-The branch is then unsatisfiable
% 31.57/8.02 % SZS output end Proof for theBenchmark
% 31.57/8.02
% 31.57/8.02 7425ms
%------------------------------------------------------------------------------