TSTP Solution File: GEO268+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 03:49:21 EDT 2022
% Result : Theorem 58.44s 26.36s
% Output : Proof 159.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.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 12:17:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/0.61 ____ _
% 0.44/0.61 ___ / __ \_____(_)___ ________ __________
% 0.44/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.44/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.44/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.44/0.61
% 0.44/0.61 A Theorem Prover for First-Order Logic
% 0.44/0.61 (ePrincess v.1.0)
% 0.44/0.61
% 0.44/0.61 (c) Philipp Rümmer, 2009-2015
% 0.44/0.61 (c) Peter Backeman, 2014-2015
% 0.44/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.44/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.44/0.61 Bug reports to peter@backeman.se
% 0.44/0.61
% 0.44/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.44/0.61
% 0.44/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.99 Prover 0: Preprocessing ...
% 2.59/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.81/1.30 Prover 0: Constructing countermodel ...
% 14.39/4.01 Prover 0: gave up
% 14.39/4.01 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.42/4.05 Prover 1: Preprocessing ...
% 14.85/4.18 Prover 1: Constructing countermodel ...
% 15.27/4.21 Prover 1: gave up
% 15.27/4.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.27/4.24 Prover 2: Preprocessing ...
% 16.27/4.44 Prover 2: Warning: ignoring some quantifiers
% 16.27/4.45 Prover 2: Constructing countermodel ...
% 23.18/6.10 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 23.33/6.16 Prover 3: Preprocessing ...
% 23.72/6.21 Prover 3: Warning: ignoring some quantifiers
% 23.72/6.22 Prover 3: Constructing countermodel ...
% 29.41/7.83 Prover 3: gave up
% 29.41/7.83 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 29.41/7.86 Prover 4: Preprocessing ...
% 29.95/7.97 Prover 4: Warning: ignoring some quantifiers
% 29.95/7.98 Prover 4: Constructing countermodel ...
% 33.25/8.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 33.25/8.76 Prover 5: Preprocessing ...
% 33.84/8.90 Prover 5: Constructing countermodel ...
% 52.98/22.97 Prover 5: stopped
% 53.35/23.17 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 53.61/23.21 Prover 6: Preprocessing ...
% 54.14/23.39 Prover 6: Warning: ignoring some quantifiers
% 54.14/23.40 Prover 6: Constructing countermodel ...
% 58.44/26.35 Prover 6: proved (3185ms)
% 58.44/26.35 Prover 4: stopped
% 58.44/26.35 Prover 2: stopped
% 58.44/26.36
% 58.44/26.36 No countermodel exists, formula is valid
% 58.44/26.36 % SZS status Theorem for theBenchmark
% 58.44/26.36
% 58.44/26.36 Generating proof ... Warning: ignoring some quantifiers
% 157.80/107.88 found it (size 1247)
% 157.80/107.88
% 157.80/107.88 % SZS output start Proof for theBenchmark
% 157.80/107.88 Assumed formulas after preprocessing and simplification:
% 157.80/107.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v1) = v2 & unequally_directed_opposite_lines(v0, v3) = v4 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v6, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v11) = v12) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (left_apart_point(v6, v9) = v10) | ~ (left_apart_point(v5, v11) = v12) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v9) = v11) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v9) = v11) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v8) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v6, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v6, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v8) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v5, v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v7) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v6, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v8) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v11] : (( ~ (v11 = 0) & left_apart_point(v5, v6) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (between_on_line(v10, v9, v8, v7) = v6) | ~ (between_on_line(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v5, v9) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v5, v9) = v10) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v8 = 0 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v8) = v10) | ~ (unequally_directed_lines(v5, v8) = v9) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v7) = v10) | ~ (unequally_directed_lines(v5, v8) = v9) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (left_apart_point(v6, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (left_convergent_lines(v5, v7) = v9) | ~ (unequally_directed_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & left_convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (between_on_line(v5, v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v8, v7) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v7, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (between_on_line(v5, v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v7, v8) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (line_connecting(v5, v6) = v8) | ~ (left_convergent_lines(v8, v7) = v9) | ? [v10] : ((v10 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v5, v6) = v10) | ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_apart_point(v5, v8) = v9) | ~ (left_apart_point(v5, v6) = 0) | ~ (reverse_line(v7) = v8) | ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & left_apart_point(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (before_on_line(v9, v8, v7) = v6) | ~ (before_on_line(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (divides_points(v9, v8, v7) = v6) | ~ (divides_points(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v8) | ~ (equally_directed_lines(v5, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v8) = v9) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v8) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v5, v8) = v9) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v10 = 0 & reverse_line(v7) = v11 & unequally_directed_lines(v5, v11) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v5, v8) = 0) | ~ (unequally_directed_lines(v5, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | (v11 = 0 & v8 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (left_apart_point(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (before_on_line(v5, v6, v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & line_connecting(v6, v7) = v9 & equally_directed_lines(v5, v9) = v10) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (left_apart_point(v5, v7) = 0) | left_apart_point(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (divides_points(v7, v5, v6) = v8) | ? [v9] : (( ~ (v9 = 0) & left_apart_point(v6, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v5, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (divides_points(v7, v5, v6) = v8) | ? [v9] : (( ~ (v9 = 0) & left_apart_point(v5, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (left_convergent_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ( ~ (v9 = 0) & right_convergent_lines(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v6) = 0) | ~ (unequally_directed_lines(v6, v7) = v8) | left_convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v6, v7) = v8) | ~ (left_apart_point(v5, v7) = 0) | distinct_points(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ( ~ (v9 = 0) & right_apart_point(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v8) | unequally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & unequally_directed_opposite_lines(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unequally_directed_lines(v6, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unequally_directed_lines(v5, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (incident_point_and_line(v8, v7) = v6) | ~ (incident_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equally_directed_opposite_lines(v8, v7) = v6) | ~ (equally_directed_opposite_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equally_directed_lines(v8, v7) = v6) | ~ (equally_directed_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (left_convergent_lines(v8, v7) = v6) | ~ (left_convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (right_convergent_lines(v8, v7) = v6) | ~ (right_convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (left_apart_point(v8, v7) = v6) | ~ (left_apart_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (right_apart_point(v8, v7) = v6) | ~ (right_apart_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unequally_directed_lines(v8, v7) = v6) | ~ (unequally_directed_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unequally_directed_opposite_lines(v8, v7) = v6) | ~ (unequally_directed_opposite_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v7) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | (v9 = 0 & left_apart_point(v6, v8) = 0) | (v9 = 0 & left_apart_point(v6, v7) = 0) | (v9 = 0 & left_apart_point(v5, v8) = 0) | (v9 = 0 & left_apart_point(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (between_on_line(v5, v6, v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & before_on_line(v5, v8, v7) = 0 & before_on_line(v5, v7, v6) = 0) | (v10 = 0 & v9 = 0 & before_on_line(v5, v7, v8) = 0 & before_on_line(v5, v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (equally_directed_lines(v5, v8) = 0) | ? [v9] : ((v9 = 0 & before_on_line(v5, v6, v7) = 0) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v5, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8) | ( ~ (v8 = 0) & unequally_directed_opposite_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & left_apart_point(v5, v6) = v8 & right_apart_point(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equally_directed_opposite_lines(v5, v6) = v7) | unequally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equally_directed_lines(v5, v6) = v7) | unequally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v8) = 0 & reverse_line(v6) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_convergent_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & left_convergent_lines(v5, v8) = v9 & reverse_line(v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & right_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & left_apart_point(v5, v8) = v9 & reverse_line(v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & left_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v7) | equally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v7) | ? [v8] : (reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_opposite_lines(v5, v6) = v7) | equally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_opposite_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (point(v7) = v6) | ~ (point(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (line(v7) = v6) | ~ (line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (reverse_line(v7) = v6) | ~ (reverse_line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | equally_directed_lines(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ? [v9] : ((v8 = 0 & point(v7) = 0) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & line_connecting(v5, v6) = v8 & equally_directed_lines(v8, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & line_connecting(v6, v5) = v8 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & point(v5) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (before_on_line(v5, v6, v7) = 0) | ? [v8] : (line_connecting(v6, v7) = v8 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0 & equally_directed_lines(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (divides_points(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & left_apart_point(v6, v7) = 0 & right_apart_point(v5, v7) = 0) | (v9 = 0 & v8 = 0 & left_apart_point(v5, v7) = 0 & right_apart_point(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) | ~ (reverse_line(v6) = v7) | right_convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) | ~ (reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) | ~ (reverse_line(v6) = v7) | right_apart_point(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) | ~ (reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) & ~ (v7 = 0) & right_apart_point(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v6) = 0) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v5, v8) = 0 & reverse_line(v7) = v8) | (v8 = 0 & distinct_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) & ~ (v7 = 0) & left_apart_point(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | unequally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & ~ (v9 = 0) & intersection_point(v5, v6) = v8 & apart_point_and_line(v8, v6) = v10 & apart_point_and_line(v8, v5) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & intersection_point(v5, v6) = v8 & point(v8) = 0) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0) | (v8 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_opposite_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_opposite_lines(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_lines(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (line_connecting(v6, v5) = v8 & line_connecting(v5, v6) = v7 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & line(v7) = 0 & line_connecting(v5, v6) = v7) | ( ~ (v7 = 0) & point(v6) = v7) | ( ~ (v7 = 0) & point(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | (unequally_directed_lines(v5, v6) = 0 & unequally_directed_opposite_lines(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (apart_point_and_line(v5, v6) = 0) | ? [v7] : ((v7 = 0 & left_apart_point(v5, v6) = 0) | (v7 = 0 & right_apart_point(v5, v6) = 0))) & ! [v5] : ! [v6] : ( ~ (equally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equally_directed_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ~ (left_convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (right_convergent_lines(v5, v6) = 0) | ? [v7] : (left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ~ (left_apart_point(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (right_apart_point(v5, v6) = 0) | ? [v7] : (left_apart_point(v5, v7) = 0 & reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & line(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & intersection_point(v5, v6) = v7 & point(v7) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8) | ( ~ (v7 = 0) & line(v6) = v7) | ( ~ (v7 = 0) & line(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7) | (v7 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equally_directed_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equally_directed_opposite_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : (reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = 0)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7))) & ! [v5] : ( ~ (line(v5) = 0) | ? [v6] : (line(v6) = 0 & reverse_line(v5) = v6)) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : between_on_line(v8, v7, v6, v5) = v9 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : before_on_line(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : divides_points(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : incident_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equally_directed_opposite_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equally_directed_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : left_convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : right_convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : left_apart_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : right_apart_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unequally_directed_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unequally_directed_opposite_lines(v6, v5) = v7 & ? [v5] : ? [v6] : point(v5) = v6 & ? [v5] : ? [v6] : line(v5) = v6 & ? [v5] : ? [v6] : reverse_line(v5) = v6 & ((v4 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v4 = 0))))
% 158.31/107.99 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 158.31/107.99 | (1) reverse_line(all_0_3_3) = all_0_1_1 & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_0_2_2 & unequally_directed_opposite_lines(all_0_4_4, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6))) & ! [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] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [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] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) & ! [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] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [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] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) & ! [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 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) & ! [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 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4))) & ! [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] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_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(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 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(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 | ~ (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] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3))) & ! [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] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [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] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [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] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [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] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 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] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) & ! [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] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) & ! [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] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (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] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 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] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [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] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))) & ! [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] : between_on_line(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & ? [v0] : ? [v1] : reverse_line(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_2_2 = 0)) | (all_0_2_2 = 0 & ~ (all_0_0_0 = 0)))
% 158.31/108.05 |
% 158.31/108.05 | Applying alpha-rule on (1) yields:
% 158.31/108.05 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 158.31/108.05 | (3) ! [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))
% 158.31/108.05 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 158.31/108.05 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 158.31/108.05 | (6) ! [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))
% 158.31/108.05 | (7) ! [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))
% 158.31/108.05 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 158.31/108.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 158.31/108.05 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0)))
% 158.31/108.05 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 158.31/108.05 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 158.31/108.05 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 158.31/108.05 | (14) ! [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))
% 158.31/108.05 | (15) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2
% 158.31/108.05 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4)))
% 158.31/108.05 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4)))
% 158.31/108.05 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.31/108.05 | (19) ! [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))
% 158.31/108.05 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 158.31/108.05 | (21) ! [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] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 158.31/108.05 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 158.31/108.05 | (23) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 158.31/108.05 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 158.31/108.05 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 158.31/108.05 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 158.31/108.05 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3)))
% 158.31/108.05 | (28) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 158.31/108.05 | (29) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 158.31/108.05 | (30) unequally_directed_opposite_lines(all_0_4_4, all_0_1_1) = all_0_0_0
% 158.31/108.05 | (31) ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 158.31/108.05 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 158.31/108.06 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0)))
% 158.31/108.06 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 158.31/108.06 | (35) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2
% 158.31/108.06 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4)))
% 158.31/108.06 | (37) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2
% 158.31/108.06 | (38) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 158.31/108.06 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 158.31/108.06 | (40) ! [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))
% 158.31/108.06 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 158.31/108.06 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 158.31/108.06 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 158.31/108.06 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 158.31/108.06 | (45) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 158.31/108.06 | (46) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.06 | (47) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2
% 158.31/108.06 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0))
% 158.31/108.06 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 158.31/108.06 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 158.31/108.06 | (51) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 158.31/108.06 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)))
% 158.31/108.06 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 158.31/108.06 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 158.31/108.06 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 158.31/108.06 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 158.31/108.06 | (57) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2
% 158.31/108.06 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 158.31/108.06 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5)))
% 158.31/108.06 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 158.31/108.06 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 158.31/108.06 | (62) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 158.31/108.06 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 158.31/108.06 | (64) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 158.31/108.06 | (65) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 158.31/108.06 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 158.31/108.06 | (67) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.06 | (68) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 158.31/108.06 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4)))
% 158.31/108.07 | (70) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.07 | (71) ! [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] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 158.31/108.07 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.31/108.07 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 158.31/108.07 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 158.31/108.07 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 158.31/108.07 | (76) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.07 | (77) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.07 | (78) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.07 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 158.31/108.07 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3)))
% 158.31/108.07 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3)))
% 158.31/108.07 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 158.31/108.07 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 158.31/108.07 | (84) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2
% 158.31/108.07 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 158.31/108.07 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 158.31/108.07 | (87) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.07 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 158.31/108.07 | (89) ? [v0] : ? [v1] : line(v0) = v1
% 158.31/108.07 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 158.31/108.07 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 158.31/108.07 | (92) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4
% 158.31/108.07 | (93) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 158.31/108.07 | (94) ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 158.31/108.07 | (95) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 158.31/108.07 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5)))
% 158.31/108.07 | (97) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0)))
% 158.31/108.07 | (98) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 158.31/108.07 | (99) ! [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))
% 158.31/108.08 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5)))
% 158.31/108.08 | (101) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 158.31/108.08 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 158.31/108.08 | (103) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 158.31/108.08 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 158.31/108.08 | (105) ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 158.31/108.08 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 158.31/108.08 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.31/108.08 | (108) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 158.31/108.08 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 158.31/108.08 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 158.31/108.08 | (111) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 158.31/108.08 | (112) reverse_line(all_0_3_3) = all_0_1_1
% 158.31/108.08 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 158.31/108.08 | (114) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2)))
% 158.31/108.08 | (115) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 158.31/108.08 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 158.31/108.08 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 158.31/108.08 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 158.31/108.08 | (119) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 158.31/108.08 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 158.31/108.08 | (121) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2
% 158.31/108.08 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 158.31/108.08 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 158.31/108.08 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 158.31/108.08 | (125) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.31/108.08 | (126) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 158.31/108.08 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 158.31/108.08 | (128) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 158.31/108.08 | (129) ! [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))
% 158.31/108.08 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 158.31/108.08 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 158.31/108.08 | (132) ? [v0] : ? [v1] : point(v0) = v1
% 158.76/108.08 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 158.76/108.08 | (134) ! [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))
% 158.76/108.08 | (135) ! [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))
% 158.76/108.08 | (136) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_0_2_2
% 158.76/108.08 | (137) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)))
% 158.76/108.08 | (138) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)))
% 158.76/108.08 | (139) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2
% 158.76/108.08 | (140) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.76/108.08 | (141) ! [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] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 158.76/108.08 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 158.76/108.09 | (143) ! [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))
% 158.76/108.09 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 158.76/108.09 | (145) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 158.76/108.09 | (146) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 158.76/108.09 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 158.76/108.09 | (148) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 158.76/108.09 | (149) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 158.76/108.09 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 158.76/108.09 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 158.76/108.09 | (152) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 158.76/108.09 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.76/108.09 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 158.76/108.09 | (155) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.76/108.09 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 158.76/108.09 | (157) ! [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))
% 158.76/108.09 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 158.76/108.09 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 158.76/108.09 | (160) (all_0_0_0 = 0 & ~ (all_0_2_2 = 0)) | (all_0_2_2 = 0 & ~ (all_0_0_0 = 0))
% 158.76/108.09 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0)))
% 158.76/108.09 | (162) ? [v0] : ? [v1] : reverse_line(v0) = v1
% 158.76/108.09 | (163) ! [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))
% 158.76/108.09 | (164) ! [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))
% 158.76/108.09 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0)))
% 158.76/108.09 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 158.76/108.09 | (167) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 158.76/108.09 | (168) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 158.76/108.09 | (169) ! [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] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6)))
% 158.76/108.09 | (170) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 158.76/108.09 | (171) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3
% 158.79/108.09 | (172) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 158.79/108.09 | (173) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 158.79/108.09 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 158.79/108.09 | (175) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 158.79/108.09 | (176) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 158.79/108.09 | (177) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3
% 158.79/108.09 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 158.79/108.09 | (179) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 158.79/108.09 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 158.79/108.09 | (181) ! [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] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 158.79/108.09 |
% 158.79/108.09 | Instantiating formula (129) with all_0_2_2, all_0_2_2, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 158.79/108.09 | (182) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_4_4) = v0)
% 158.79/108.09 |
% 158.79/108.09 | Instantiating formula (168) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 158.79/108.09 | (183) all_0_2_2 = 0 | ? [v0] : (reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.79/108.09 |
% 158.79/108.09 | Instantiating formula (157) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms unequally_directed_opposite_lines(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 158.79/108.09 | (184) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1)
% 158.79/108.09 |
% 158.79/108.09 +-Applying beta-rule and splitting (160), into two cases.
% 158.79/108.09 |-Branch one:
% 158.79/108.09 | (185) all_0_0_0 = 0 & ~ (all_0_2_2 = 0)
% 158.79/108.09 |
% 158.79/108.09 | Applying alpha-rule on (185) yields:
% 158.79/108.09 | (186) all_0_0_0 = 0
% 158.79/108.09 | (187) ~ (all_0_2_2 = 0)
% 158.79/108.09 |
% 158.79/108.10 | From (186) and (30) follows:
% 158.79/108.10 | (188) unequally_directed_opposite_lines(all_0_4_4, all_0_1_1) = 0
% 158.79/108.10 |
% 158.79/108.10 +-Applying beta-rule and splitting (183), into two cases.
% 158.79/108.10 |-Branch one:
% 158.79/108.10 | (189) all_0_2_2 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (189) can reduce 187 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (187) ~ (all_0_2_2 = 0)
% 158.79/108.10 | (192) ? [v0] : (reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating (192) with all_73_0_78 yields:
% 158.79/108.10 | (193) reverse_line(all_0_3_3) = all_73_0_78 & unequally_directed_lines(all_0_4_4, all_73_0_78) = 0
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (193) yields:
% 158.79/108.10 | (194) reverse_line(all_0_3_3) = all_73_0_78
% 158.79/108.10 | (195) unequally_directed_lines(all_0_4_4, all_73_0_78) = 0
% 158.79/108.10 |
% 158.79/108.10 +-Applying beta-rule and splitting (182), into two cases.
% 158.79/108.10 |-Branch one:
% 158.79/108.10 | (189) all_0_2_2 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (189) can reduce 187 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (187) ~ (all_0_2_2 = 0)
% 158.79/108.10 | (199) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_4_4) = v0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (133) with all_0_3_3, all_73_0_78, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_73_0_78, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.79/108.10 | (200) all_73_0_78 = all_0_1_1
% 158.79/108.10 |
% 158.79/108.10 | From (200) and (194) follows:
% 158.79/108.10 | (112) reverse_line(all_0_3_3) = all_0_1_1
% 158.79/108.10 |
% 158.79/108.10 | From (200) and (195) follows:
% 158.79/108.10 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (118) with 0, all_0_1_1, all_0_3_3, all_0_1_1, all_0_4_4 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 158.79/108.10 | (203) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1))
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (95) with all_0_1_1, all_0_4_4 and discharging atoms unequally_directed_opposite_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 158.79/108.10 | (204) ? [v0] : (reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating (204) with all_119_0_117 yields:
% 158.79/108.10 | (205) reverse_line(all_0_1_1) = all_119_0_117 & unequally_directed_lines(all_0_4_4, all_119_0_117) = 0
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (205) yields:
% 158.79/108.10 | (206) reverse_line(all_0_1_1) = all_119_0_117
% 158.79/108.10 | (207) unequally_directed_lines(all_0_4_4, all_119_0_117) = 0
% 158.79/108.10 |
% 158.79/108.10 | Instantiating (203) with all_126_0_127, all_126_1_128 yields:
% 158.79/108.10 | (208) (all_126_0_127 = 0 & all_126_1_128 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_126_1_128 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_126_0_127 = 0) & reverse_line(all_0_1_1) = all_126_1_128 & unequally_directed_lines(all_0_4_4, all_126_1_128) = all_126_0_127)
% 158.79/108.10 |
% 158.79/108.10 +-Applying beta-rule and splitting (208), into two cases.
% 158.79/108.10 |-Branch one:
% 158.79/108.10 | (209) (all_126_0_127 = 0 & all_126_1_128 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_126_1_128 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0)
% 158.79/108.10 |
% 158.79/108.10 +-Applying beta-rule and splitting (209), into two cases.
% 158.79/108.10 |-Branch one:
% 158.79/108.10 | (210) all_126_0_127 = 0 & all_126_1_128 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (210) yields:
% 158.79/108.10 | (211) all_126_0_127 = 0
% 158.79/108.10 | (212) all_126_1_128 = 0
% 158.79/108.10 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 158.79/108.10 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 158.79/108.10 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating (215) with all_235_0_261 yields:
% 158.79/108.10 | (216) ~ (all_235_0_261 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_235_0_261
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (216) yields:
% 158.79/108.10 | (217) ~ (all_235_0_261 = 0)
% 158.79/108.10 | (218) equally_directed_lines(all_0_1_1, all_0_1_1) = all_235_0_261
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (55) with all_235_0_261, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_235_0_261, yields:
% 158.79/108.10 | (219) all_235_0_261 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (219) can reduce 217 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (221) all_126_1_128 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (221) yields:
% 158.79/108.10 | (212) all_126_1_128 = 0
% 158.79/108.10 | (223) unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (8) with all_0_4_4, all_0_3_3, 0, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_0_2_2, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.79/108.10 | (189) all_0_2_2 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (189) can reduce 187 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (226) ~ (all_126_0_127 = 0) & reverse_line(all_0_1_1) = all_126_1_128 & unequally_directed_lines(all_0_4_4, all_126_1_128) = all_126_0_127
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (226) yields:
% 158.79/108.10 | (227) ~ (all_126_0_127 = 0)
% 158.79/108.10 | (228) reverse_line(all_0_1_1) = all_126_1_128
% 158.79/108.10 | (229) unequally_directed_lines(all_0_4_4, all_126_1_128) = all_126_0_127
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (133) with all_0_1_1, all_119_0_117, all_126_1_128 and discharging atoms reverse_line(all_0_1_1) = all_126_1_128, reverse_line(all_0_1_1) = all_119_0_117, yields:
% 158.79/108.10 | (230) all_126_1_128 = all_119_0_117
% 158.79/108.10 |
% 158.79/108.10 | From (230) and (229) follows:
% 158.79/108.10 | (231) unequally_directed_lines(all_0_4_4, all_119_0_117) = all_126_0_127
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (8) with all_0_4_4, all_119_0_117, all_126_0_127, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_119_0_117) = all_126_0_127, unequally_directed_lines(all_0_4_4, all_119_0_117) = 0, yields:
% 158.79/108.10 | (211) all_126_0_127 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (211) can reduce 227 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (234) all_0_2_2 = 0 & ~ (all_0_0_0 = 0)
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (234) yields:
% 158.79/108.10 | (189) all_0_2_2 = 0
% 158.79/108.10 | (236) ~ (all_0_0_0 = 0)
% 158.79/108.10 |
% 158.79/108.10 | From (189) and (136) follows:
% 158.79/108.10 | (223) unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.79/108.10 |
% 158.79/108.10 +-Applying beta-rule and splitting (184), into two cases.
% 158.79/108.10 |-Branch one:
% 158.79/108.10 | (186) all_0_0_0 = 0
% 158.79/108.10 |
% 158.79/108.10 | Equations (186) can reduce 236 to:
% 158.79/108.10 | (190) $false
% 158.79/108.10 |
% 158.79/108.10 |-The branch is then unsatisfiable
% 158.79/108.10 |-Branch two:
% 158.79/108.10 | (236) ~ (all_0_0_0 = 0)
% 158.79/108.10 | (241) ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating (241) with all_76_0_420, all_76_1_421 yields:
% 158.79/108.10 | (242) ~ (all_76_0_420 = 0) & reverse_line(all_0_1_1) = all_76_1_421 & unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420
% 158.79/108.10 |
% 158.79/108.10 | Applying alpha-rule on (242) yields:
% 158.79/108.10 | (243) ~ (all_76_0_420 = 0)
% 158.79/108.10 | (244) reverse_line(all_0_1_1) = all_76_1_421
% 158.79/108.10 | (245) unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (159) with all_76_0_420, all_76_1_421, all_0_1_1, all_0_4_4 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, yields:
% 158.79/108.10 | (246) all_76_0_420 = 0 | unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (129) with all_76_0_420, all_76_0_420, all_76_1_421, all_0_4_4, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, yields:
% 158.79/108.10 | (247) all_76_0_420 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_4_4) = v0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (168) with all_76_0_420, all_76_1_421, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, yields:
% 158.79/108.10 | (248) all_76_0_420 = 0 | ? [v0] : (reverse_line(all_76_1_421) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (118) with all_76_0_420, all_76_1_421, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.79/108.10 | (249) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_3_3, all_76_1_421) = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1))
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (28) with all_0_3_3, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.79/108.10 | (250) ? [v0] : ? [v1] : ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v2 & apart_point_and_line(v0, all_0_4_4) = v1) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1))
% 158.79/108.10 |
% 158.79/108.10 | Instantiating formula (62) with all_0_3_3, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.79/108.10 | (251) ? [v0] : ? [v1] : ((v1 = 0 & left_convergent_lines(all_0_4_4, v0) = 0 & reverse_line(all_0_3_3) = v0) | (v0 = 0 & left_convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1))
% 158.79/108.10 |
% 158.79/108.11 | Instantiating (251) with all_91_0_425, all_91_1_426 yields:
% 158.79/108.11 | (252) (all_91_0_425 = 0 & left_convergent_lines(all_0_4_4, all_91_1_426) = 0 & reverse_line(all_0_3_3) = all_91_1_426) | (all_91_1_426 = 0 & left_convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_91_0_425 = 0) & reverse_line(all_0_3_3) = all_91_1_426 & unequally_directed_lines(all_0_4_4, all_91_1_426) = all_91_0_425)
% 158.86/108.11 |
% 158.86/108.11 | Instantiating (249) with all_92_0_427, all_92_1_428 yields:
% 158.86/108.11 | (253) (all_92_0_427 = 0 & all_92_1_428 = 0 & unequally_directed_lines(all_0_3_3, all_76_1_421) = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | (all_92_1_428 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | ( ~ (all_92_0_427 = 0) & reverse_line(all_0_3_3) = all_92_1_428 & unequally_directed_lines(all_0_4_4, all_92_1_428) = all_92_0_427)
% 158.86/108.11 |
% 158.86/108.11 | Instantiating (250) with all_95_0_432, all_95_1_433, all_95_2_434 yields:
% 158.86/108.11 | (254) ( ~ (all_95_0_432 = 0) & ~ (all_95_1_433 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_95_2_434 & apart_point_and_line(all_95_2_434, all_0_3_3) = all_95_0_432 & apart_point_and_line(all_95_2_434, all_0_4_4) = all_95_1_433) | ( ~ (all_95_1_433 = 0) & reverse_line(all_0_3_3) = all_95_2_434 & unequally_directed_lines(all_0_4_4, all_95_2_434) = all_95_1_433)
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (248), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (255) all_76_0_420 = 0
% 158.86/108.11 |
% 158.86/108.11 | Equations (255) can reduce 243 to:
% 158.86/108.11 | (190) $false
% 158.86/108.11 |
% 158.86/108.11 |-The branch is then unsatisfiable
% 158.86/108.11 |-Branch two:
% 158.86/108.11 | (243) ~ (all_76_0_420 = 0)
% 158.86/108.11 | (258) ? [v0] : (reverse_line(all_76_1_421) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (246), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (254), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (260) ~ (all_95_0_432 = 0) & ~ (all_95_1_433 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_95_2_434 & apart_point_and_line(all_95_2_434, all_0_3_3) = all_95_0_432 & apart_point_and_line(all_95_2_434, all_0_4_4) = all_95_1_433
% 158.86/108.11 |
% 158.86/108.11 | Applying alpha-rule on (260) yields:
% 158.86/108.11 | (261) apart_point_and_line(all_95_2_434, all_0_3_3) = all_95_0_432
% 158.86/108.11 | (262) ~ (all_95_1_433 = 0)
% 158.86/108.11 | (263) intersection_point(all_0_4_4, all_0_3_3) = all_95_2_434
% 158.86/108.11 | (264) ~ (all_95_0_432 = 0)
% 158.86/108.11 | (265) apart_point_and_line(all_95_2_434, all_0_4_4) = all_95_1_433
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (247), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (255) all_76_0_420 = 0
% 158.86/108.11 |
% 158.86/108.11 | Equations (255) can reduce 243 to:
% 158.86/108.11 | (190) $false
% 158.86/108.11 |
% 158.86/108.11 |-The branch is then unsatisfiable
% 158.86/108.11 |-Branch two:
% 158.86/108.11 | (243) ~ (all_76_0_420 = 0)
% 158.86/108.11 | (199) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_4_4) = v0)
% 158.86/108.11 |
% 158.86/108.11 | Instantiating (199) with all_135_0_449 yields:
% 158.86/108.11 | (270) ~ (all_135_0_449 = 0) & unequally_directed_lines(all_0_4_4, all_0_4_4) = all_135_0_449
% 158.86/108.11 |
% 158.86/108.11 | Applying alpha-rule on (270) yields:
% 158.86/108.11 | (271) ~ (all_135_0_449 = 0)
% 158.86/108.11 | (272) unequally_directed_lines(all_0_4_4, all_0_4_4) = all_135_0_449
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (253), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (273) (all_92_0_427 = 0 & all_92_1_428 = 0 & unequally_directed_lines(all_0_3_3, all_76_1_421) = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | (all_92_1_428 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0)
% 158.86/108.11 |
% 158.86/108.11 +-Applying beta-rule and splitting (273), into two cases.
% 158.86/108.11 |-Branch one:
% 158.86/108.11 | (274) all_92_0_427 = 0 & all_92_1_428 = 0 & unequally_directed_lines(all_0_3_3, all_76_1_421) = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.86/108.11 |
% 158.86/108.11 | Applying alpha-rule on (274) yields:
% 158.86/108.11 | (275) all_92_0_427 = 0
% 158.86/108.11 | (276) all_92_1_428 = 0
% 158.86/108.11 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 158.86/108.11 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.86/108.11 |
% 158.86/108.11 | Instantiating formula (163) with all_95_0_432, all_0_3_3, all_95_2_434 and discharging atoms apart_point_and_line(all_95_2_434, all_0_3_3) = all_95_0_432, yields:
% 158.86/108.11 | (279) all_95_0_432 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & left_apart_point(all_95_2_434, all_0_3_3) = v0 & right_apart_point(all_95_2_434, all_0_3_3) = v1)
% 158.86/108.11 |
% 158.86/108.11 | Instantiating formula (41) with all_76_0_420, 0, all_76_1_421, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, yields:
% 158.86/108.11 | (280) ? [v0] : ? [v1] : ((v0 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = v0))
% 158.86/108.11 |
% 158.86/108.11 | Instantiating formula (41) with 0, 0, all_76_1_421, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 158.86/108.11 | (281) ? [v0] : ? [v1] : ((v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.86/108.11 |
% 158.86/108.11 | Instantiating formula (86) with 0, all_76_1_421, 0, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.86/108.11 | (282) ? [v0] : ? [v1] : (v0 = 0 | unequally_directed_lines(all_0_3_3, all_0_3_3) = v0 | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (44) with 0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (283) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | (v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (34) with 0, all_0_1_1, all_76_1_421, all_0_3_3, all_0_1_1, all_0_3_3 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (284) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (34) with 0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (285) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (110) with 0, 0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.11 | (286) ? [v0] : ? [v1] : ((v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (41) with 0, 0, all_0_1_1, all_0_3_3, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (287) ? [v0] : ? [v1] : ((v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (118) with 0, all_0_1_1, all_0_3_3, all_0_1_1, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (288) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (127) with 0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (289) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & reverse_line(all_0_1_1) = v1 & unequally_directed_lines(all_0_3_3, v1) = 0) | (v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (25) with 0, 0, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (290) ? [v0] : ? [v1] : ((v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (109) with 0, all_76_1_421, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms reverse_line(all_0_1_1) = all_76_1_421, reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.11 | (291) ? [v0] : (v0 = 0 | unequally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (41) with 0, 0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 158.88/108.11 | (292) ? [v0] : ? [v1] : ((v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (25) with 0, 0, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 158.88/108.11 | (293) ? [v0] : ? [v1] : ((v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | (v1 = 0 & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (109) with 0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 158.88/108.11 | (294) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = v0))
% 158.88/108.11 |
% 158.88/108.11 | Instantiating formula (44) with 0, all_0_1_1, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.12 | (295) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v1 = 0 & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = v0))
% 158.88/108.12 |
% 158.88/108.12 | Instantiating formula (44) with all_135_0_449, all_0_1_1, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms reverse_line(all_0_3_3) = all_0_1_1, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, unequally_directed_lines(all_0_4_4, all_0_4_4) = all_135_0_449, yields:
% 158.88/108.12 | (296) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (v1 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = v0))
% 158.88/108.12 |
% 158.88/108.12 | Instantiating formula (53) with all_135_0_449, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, unequally_directed_lines(all_0_4_4, all_0_4_4) = all_135_0_449, yields:
% 158.88/108.12 | (297) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (v1 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0) | ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = v1))
% 158.88/108.12 |
% 158.88/108.12 | Instantiating formula (168) with all_135_0_449, all_0_4_4, all_0_4_4 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_4_4) = all_135_0_449, yields:
% 158.88/108.12 | (298) all_135_0_449 = 0 | ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (282) with all_167_0_468, all_167_1_469 yields:
% 158.88/108.12 | (299) all_167_1_469 = 0 | unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469 | ( ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (297) with all_203_0_537, all_203_1_538, all_203_2_539 yields:
% 158.88/108.12 | (300) (all_203_0_537 = 0 & all_203_1_538 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_3_3, all_203_2_539) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_203_1_538 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_4_4, all_203_2_539) = 0) | ( ~ (all_203_1_538 = 0) & reverse_line(all_0_3_3) = all_203_2_539 & unequally_directed_lines(all_0_4_4, all_203_2_539) = all_203_1_538)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (296) with all_205_0_543, all_205_1_544, all_205_2_545 yields:
% 158.88/108.12 | (301) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0) | ( ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (281) with all_212_0_556, all_212_1_557 yields:
% 158.88/108.12 | (302) (all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556) | ( ~ (all_212_1_557 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (280) with all_213_0_558, all_213_1_559 yields:
% 158.88/108.12 | (303) (all_213_1_559 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | (all_213_1_559 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_213_0_558 = 0) & reverse_line(all_0_4_4) = all_213_1_559 & unequally_directed_lines(all_0_3_3, all_213_1_559) = all_213_0_558) | ( ~ (all_213_1_559 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_213_1_559)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (290) with all_228_0_587, all_228_1_588 yields:
% 158.88/108.12 | (304) (all_228_0_587 = 0 & reverse_line(all_0_1_1) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = 0) | ( ~ (all_228_0_587 = 0) & reverse_line(all_0_3_3) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587) | ( ~ (all_228_1_588 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (288) with all_232_0_598, all_232_1_599 yields:
% 158.88/108.12 | (305) (all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_232_0_598 = 0) & reverse_line(all_0_1_1) = all_232_1_599 & unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (287) with all_233_0_600, all_233_1_601 yields:
% 158.88/108.12 | (306) (all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600) | ( ~ (all_233_1_601 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (289) with all_234_0_602, all_234_1_603, all_234_2_604 yields:
% 158.88/108.12 | (307) (all_234_0_602 = 0 & all_234_2_604 = 0 & reverse_line(all_0_1_1) = all_234_1_603 & unequally_directed_lines(all_0_3_3, all_234_1_603) = 0) | (all_234_1_603 = 0 & reverse_line(all_0_1_1) = all_234_2_604 & unequally_directed_lines(all_0_3_3, all_234_2_604) = 0) | ( ~ (all_234_2_604 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (291) with all_237_0_611 yields:
% 158.88/108.12 | (308) all_237_0_611 = 0 | unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (286) with all_241_0_618, all_241_1_619 yields:
% 158.88/108.12 | (309) (all_241_1_619 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_241_1_619 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | ( ~ (all_241_0_618 = 0) & reverse_line(all_0_4_4) = all_241_1_619 & unequally_directed_lines(all_0_3_3, all_241_1_619) = all_241_0_618) | ( ~ (all_241_1_619 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_241_1_619)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (285) with all_253_0_644, all_253_1_645 yields:
% 158.88/108.12 | (310) (all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_253_1_645 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (284) with all_254_0_646, all_254_1_647 yields:
% 158.88/108.12 | (311) (all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_254_1_647 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (283) with all_273_0_686, all_273_1_687, all_273_2_688 yields:
% 158.88/108.12 | (312) (all_273_0_686 = 0 & all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0) | (all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0) | ( ~ (all_273_2_688 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (295) with all_286_0_717, all_286_1_718, all_286_2_719 yields:
% 158.88/108.12 | (313) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0) | ( ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (294) with all_287_0_720, all_287_1_721 yields:
% 158.88/108.12 | (314) (all_287_0_720 = 0 & all_287_1_721 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | (all_287_1_721 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_287_1_721 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (293) with all_291_0_730, all_291_1_731 yields:
% 158.88/108.12 | (315) (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = 0) | (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_4_4, all_291_1_731) = 0) | ( ~ (all_291_0_730 = 0) & reverse_line(all_0_4_4) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = all_291_0_730) | ( ~ (all_291_1_731 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_291_1_731)
% 158.88/108.12 |
% 158.88/108.12 | Instantiating (292) with all_294_0_737, all_294_1_738 yields:
% 158.88/108.12 | (316) (all_294_1_738 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_294_1_738 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_294_0_737 = 0) & reverse_line(all_0_4_4) = all_294_1_738 & unequally_directed_lines(all_0_3_3, all_294_1_738) = all_294_0_737) | ( ~ (all_294_1_738 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_294_1_738)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (300), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (317) (all_203_0_537 = 0 & all_203_1_538 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_3_3, all_203_2_539) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_203_1_538 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_4_4, all_203_2_539) = 0)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (317), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (318) all_203_0_537 = 0 & all_203_1_538 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_3_3, all_203_2_539) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 158.88/108.12 |
% 158.88/108.12 | Applying alpha-rule on (318) yields:
% 158.88/108.12 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 158.88/108.12 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 158.88/108.12 | (321) all_203_1_538 = 0
% 158.88/108.12 | (322) reverse_line(all_0_4_4) = all_203_2_539
% 158.88/108.12 | (323) all_203_0_537 = 0
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (315), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (324) (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = 0) | (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_4_4, all_291_1_731) = 0) | ( ~ (all_291_0_730 = 0) & reverse_line(all_0_4_4) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = all_291_0_730)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (324), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (325) (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = 0) | (all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_4_4, all_291_1_731) = 0)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (325), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (326) all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = 0
% 158.88/108.12 |
% 158.88/108.12 | Applying alpha-rule on (326) yields:
% 158.88/108.12 | (327) all_291_0_730 = 0
% 158.88/108.12 | (328) reverse_line(all_0_1_1) = all_291_1_731
% 158.88/108.12 | (329) unequally_directed_lines(all_0_3_3, all_291_1_731) = 0
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (303), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (330) (all_213_1_559 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | (all_213_1_559 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_213_0_558 = 0) & reverse_line(all_0_4_4) = all_213_1_559 & unequally_directed_lines(all_0_3_3, all_213_1_559) = all_213_0_558)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (330), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (331) (all_213_1_559 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | (all_213_1_559 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (331), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (332) all_213_1_559 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 158.88/108.12 |
% 158.88/108.12 | Applying alpha-rule on (332) yields:
% 158.88/108.12 | (333) all_213_1_559 = 0
% 158.88/108.12 | (255) all_76_0_420 = 0
% 158.88/108.12 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 158.88/108.12 |
% 158.88/108.12 | Equations (255) can reduce 243 to:
% 158.88/108.12 | (190) $false
% 158.88/108.12 |
% 158.88/108.12 |-The branch is then unsatisfiable
% 158.88/108.12 |-Branch two:
% 158.88/108.12 | (337) all_213_1_559 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.12 |
% 158.88/108.12 | Applying alpha-rule on (337) yields:
% 158.88/108.12 | (333) all_213_1_559 = 0
% 158.88/108.12 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (316), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (340) (all_294_1_738 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_294_1_738 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_294_0_737 = 0) & reverse_line(all_0_4_4) = all_294_1_738 & unequally_directed_lines(all_0_3_3, all_294_1_738) = all_294_0_737)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (340), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (341) (all_294_1_738 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_294_1_738 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0)
% 158.88/108.12 |
% 158.88/108.12 +-Applying beta-rule and splitting (341), into two cases.
% 158.88/108.12 |-Branch one:
% 158.88/108.12 | (342) all_294_1_738 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.12 |
% 158.88/108.13 | Applying alpha-rule on (342) yields:
% 158.88/108.13 | (343) all_294_1_738 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (314), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (345) (all_287_0_720 = 0 & all_287_1_721 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | (all_287_1_721 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (345), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (346) all_287_0_720 = 0 & all_287_1_721 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (346) yields:
% 158.88/108.13 | (347) all_287_0_720 = 0
% 158.88/108.13 | (348) all_287_1_721 = 0
% 158.88/108.13 | (223) unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (302), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (350) (all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (350), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (351) all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (351) yields:
% 158.88/108.13 | (352) all_212_1_557 = 0
% 158.88/108.13 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (299), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (354) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (311), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (355) (all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (355), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (356) all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (356) yields:
% 158.88/108.13 | (357) all_254_0_646 = 0
% 158.88/108.13 | (358) all_254_1_647 = 0
% 158.88/108.13 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 158.88/108.13 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 158.88/108.13 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 158.88/108.13 |
% 158.88/108.13 | Instantiating (215) with all_709_0_4027 yields:
% 158.88/108.13 | (362) ~ (all_709_0_4027 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_4027
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (362) yields:
% 158.88/108.13 | (363) ~ (all_709_0_4027 = 0)
% 158.88/108.13 | (364) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_4027
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (55) with all_709_0_4027, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_4027, yields:
% 158.88/108.13 | (365) all_709_0_4027 = 0
% 158.88/108.13 |
% 158.88/108.13 | Equations (365) can reduce 363 to:
% 158.88/108.13 | (190) $false
% 158.88/108.13 |
% 158.88/108.13 |-The branch is then unsatisfiable
% 158.88/108.13 |-Branch two:
% 158.88/108.13 | (367) all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (367) yields:
% 158.88/108.13 | (358) all_254_1_647 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (133) with all_0_1_1, all_291_1_731, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_291_1_731, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.13 | (370) all_291_1_731 = all_76_1_421
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_167_1_469 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.13 | (371) all_167_1_469 = 0
% 158.88/108.13 |
% 158.88/108.13 | From (370) and (328) follows:
% 158.88/108.13 | (244) reverse_line(all_0_1_1) = all_76_1_421
% 158.88/108.13 |
% 158.88/108.13 | From (371) and (354) follows:
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (304), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (374) (all_228_0_587 = 0 & reverse_line(all_0_1_1) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = 0) | ( ~ (all_228_0_587 = 0) & reverse_line(all_0_3_3) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (374), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (375) all_228_0_587 = 0 & reverse_line(all_0_1_1) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (375) yields:
% 158.88/108.13 | (376) all_228_0_587 = 0
% 158.88/108.13 | (377) reverse_line(all_0_1_1) = all_228_1_588
% 158.88/108.13 | (378) unequally_directed_lines(all_0_3_3, all_228_1_588) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (308), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (305), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (380) (all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (380), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (381) all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (381) yields:
% 158.88/108.13 | (382) all_232_0_598 = 0
% 158.88/108.13 | (383) all_232_1_599 = 0
% 158.88/108.13 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 158.88/108.13 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 158.88/108.13 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 158.88/108.13 |
% 158.88/108.13 | Instantiating (215) with all_709_0_11947 yields:
% 158.88/108.13 | (387) ~ (all_709_0_11947 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_11947
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (387) yields:
% 158.88/108.13 | (388) ~ (all_709_0_11947 = 0)
% 158.88/108.13 | (389) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_11947
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (55) with all_709_0_11947, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_11947, yields:
% 158.88/108.13 | (390) all_709_0_11947 = 0
% 158.88/108.13 |
% 158.88/108.13 | Equations (390) can reduce 388 to:
% 158.88/108.13 | (190) $false
% 158.88/108.13 |
% 158.88/108.13 |-The branch is then unsatisfiable
% 158.88/108.13 |-Branch two:
% 158.88/108.13 | (392) all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (392) yields:
% 158.88/108.13 | (383) all_232_1_599 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.13 | (395) all_237_0_611 = 0
% 158.88/108.13 |
% 158.88/108.13 | From (395) and (379) follows:
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (306), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (397) (all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (397), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (398) all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (398) yields:
% 158.88/108.13 | (399) all_233_1_601 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (310), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (401) (all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.13 |
% 158.88/108.13 +-Applying beta-rule and splitting (401), into two cases.
% 158.88/108.13 |-Branch one:
% 158.88/108.13 | (402) all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (402) yields:
% 158.88/108.13 | (403) all_253_0_644 = 0
% 158.88/108.13 | (404) all_253_1_645 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.13 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 158.88/108.13 |
% 158.88/108.13 | Instantiating (406) with all_898_0_13729 yields:
% 158.88/108.13 | (407) ~ (all_898_0_13729 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_13729
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (407) yields:
% 158.88/108.13 | (408) ~ (all_898_0_13729 = 0)
% 158.88/108.13 | (409) equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_13729
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (55) with all_898_0_13729, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_13729, yields:
% 158.88/108.13 | (410) all_898_0_13729 = 0
% 158.88/108.13 |
% 158.88/108.13 | Equations (410) can reduce 408 to:
% 158.88/108.13 | (190) $false
% 158.88/108.13 |
% 158.88/108.13 |-The branch is then unsatisfiable
% 158.88/108.13 |-Branch two:
% 158.88/108.13 | (412) all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (412) yields:
% 158.88/108.13 | (404) all_253_1_645 = 0
% 158.88/108.13 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.13 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 158.88/108.13 |
% 158.88/108.13 | Instantiating (406) with all_898_0_14867 yields:
% 158.88/108.13 | (416) ~ (all_898_0_14867 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_14867
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (416) yields:
% 158.88/108.13 | (417) ~ (all_898_0_14867 = 0)
% 158.88/108.13 | (418) equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_14867
% 158.88/108.13 |
% 158.88/108.13 | Instantiating formula (55) with all_898_0_14867, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_14867, yields:
% 158.88/108.13 | (419) all_898_0_14867 = 0
% 158.88/108.13 |
% 158.88/108.13 | Equations (419) can reduce 417 to:
% 158.88/108.13 | (190) $false
% 158.88/108.13 |
% 158.88/108.13 |-The branch is then unsatisfiable
% 158.88/108.13 |-Branch two:
% 158.88/108.13 | (421) ~ (all_253_1_645 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 158.88/108.13 |
% 158.88/108.13 | Applying alpha-rule on (421) yields:
% 158.88/108.13 | (422) ~ (all_253_1_645 = 0)
% 158.88/108.14 | (423) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_253_1_645, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.14 | (404) all_253_1_645 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (404) can reduce 422 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (426) ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (426) yields:
% 158.88/108.14 | (427) ~ (all_233_0_600 = 0)
% 158.88/108.14 | (428) reverse_line(all_0_3_3) = all_233_1_601
% 158.88/108.14 | (429) unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 158.88/108.14 |
% 158.88/108.14 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.14 |-Branch one:
% 158.88/108.14 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.14 |
% 158.88/108.14 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.14 |-Branch one:
% 158.88/108.14 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (431) yields:
% 158.88/108.14 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.14 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.14 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.14 | (435) all_286_0_717 = 0
% 158.88/108.14 | (436) all_286_1_718 = 0
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.14 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 158.88/108.14 | (438) all_286_2_719 = all_233_1_601
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (437,438) yields a new equation:
% 158.88/108.14 | (439) all_233_1_601 = all_0_1_1
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (439,438) yields a new equation:
% 158.88/108.14 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.14 |
% 158.88/108.14 | From (437) and (432) follows:
% 158.88/108.14 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.14 |
% 158.88/108.14 | From (439) and (429) follows:
% 158.88/108.14 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.14 | (443) all_233_0_600 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (443) can reduce 427 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (445) yields:
% 158.88/108.14 | (436) all_286_1_718 = 0
% 158.88/108.14 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.14 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.14 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 158.88/108.14 | (438) all_286_2_719 = all_233_1_601
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (437,438) yields a new equation:
% 158.88/108.14 | (439) all_233_1_601 = all_0_1_1
% 158.88/108.14 |
% 158.88/108.14 | From (439) and (429) follows:
% 158.88/108.14 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.14 | (443) all_233_0_600 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (443) can reduce 427 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (455) yields:
% 158.88/108.14 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.14 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.14 | (458) all_286_2_719 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (458) can reduce 456 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (460) ~ (all_233_1_601 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (460) yields:
% 158.88/108.14 | (461) ~ (all_233_1_601 = 0)
% 158.88/108.14 | (462) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_233_1_601, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.14 | (399) all_233_1_601 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (399) can reduce 461 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (465) ~ (all_232_0_598 = 0) & reverse_line(all_0_1_1) = all_232_1_599 & unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (465) yields:
% 158.88/108.14 | (466) ~ (all_232_0_598 = 0)
% 158.88/108.14 | (467) reverse_line(all_0_1_1) = all_232_1_599
% 158.88/108.14 | (468) unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 158.88/108.14 |
% 158.88/108.14 +-Applying beta-rule and splitting (307), into two cases.
% 158.88/108.14 |-Branch one:
% 158.88/108.14 | (469) (all_234_0_602 = 0 & all_234_2_604 = 0 & reverse_line(all_0_1_1) = all_234_1_603 & unequally_directed_lines(all_0_3_3, all_234_1_603) = 0) | (all_234_1_603 = 0 & reverse_line(all_0_1_1) = all_234_2_604 & unequally_directed_lines(all_0_3_3, all_234_2_604) = 0)
% 158.88/108.14 |
% 158.88/108.14 +-Applying beta-rule and splitting (469), into two cases.
% 158.88/108.14 |-Branch one:
% 158.88/108.14 | (470) all_234_0_602 = 0 & all_234_2_604 = 0 & reverse_line(all_0_1_1) = all_234_1_603 & unequally_directed_lines(all_0_3_3, all_234_1_603) = 0
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (470) yields:
% 158.88/108.14 | (471) all_234_0_602 = 0
% 158.88/108.14 | (472) all_234_2_604 = 0
% 158.88/108.14 | (473) reverse_line(all_0_1_1) = all_234_1_603
% 158.88/108.14 | (474) unequally_directed_lines(all_0_3_3, all_234_1_603) = 0
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_234_1_603, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_234_1_603, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.14 | (475) all_234_1_603 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_234_1_603 and discharging atoms reverse_line(all_0_1_1) = all_234_1_603, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 158.88/108.14 | (476) all_234_1_603 = all_232_1_599
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_228_1_588, all_232_1_599 and discharging atoms reverse_line(all_0_1_1) = all_232_1_599, reverse_line(all_0_1_1) = all_228_1_588, yields:
% 158.88/108.14 | (477) all_232_1_599 = all_228_1_588
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (476,475) yields a new equation:
% 158.88/108.14 | (478) all_232_1_599 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | Simplifying 478 yields:
% 158.88/108.14 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (479,477) yields a new equation:
% 158.88/108.14 | (480) all_228_1_588 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | Combining equations (480,477) yields a new equation:
% 158.88/108.14 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | From (479) and (468) follows:
% 158.88/108.14 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 158.88/108.14 |
% 158.88/108.14 | From (480) and (378) follows:
% 158.88/108.14 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 158.88/108.14 | (382) all_232_0_598 = 0
% 158.88/108.14 |
% 158.88/108.14 | Equations (382) can reduce 466 to:
% 158.88/108.14 | (190) $false
% 158.88/108.14 |
% 158.88/108.14 |-The branch is then unsatisfiable
% 158.88/108.14 |-Branch two:
% 158.88/108.14 | (486) all_234_1_603 = 0 & reverse_line(all_0_1_1) = all_234_2_604 & unequally_directed_lines(all_0_3_3, all_234_2_604) = 0
% 158.88/108.14 |
% 158.88/108.14 | Applying alpha-rule on (486) yields:
% 158.88/108.14 | (487) all_234_1_603 = 0
% 158.88/108.14 | (488) reverse_line(all_0_1_1) = all_234_2_604
% 158.88/108.14 | (489) unequally_directed_lines(all_0_3_3, all_234_2_604) = 0
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_234_2_604, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_234_2_604, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.14 | (490) all_234_2_604 = all_76_1_421
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_234_2_604 and discharging atoms reverse_line(all_0_1_1) = all_234_2_604, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 158.88/108.14 | (491) all_234_2_604 = all_232_1_599
% 158.88/108.14 |
% 158.88/108.14 | Instantiating formula (133) with all_0_1_1, all_228_1_588, all_232_1_599 and discharging atoms reverse_line(all_0_1_1) = all_232_1_599, reverse_line(all_0_1_1) = all_228_1_588, yields:
% 158.88/108.14 | (477) all_232_1_599 = all_228_1_588
% 158.88/108.14 |
% 158.88/108.15 | Combining equations (491,490) yields a new equation:
% 158.88/108.15 | (478) all_232_1_599 = all_76_1_421
% 158.88/108.15 |
% 158.88/108.15 | Simplifying 478 yields:
% 158.88/108.15 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (479,477) yields a new equation:
% 158.88/108.15 | (480) all_228_1_588 = all_76_1_421
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (480,477) yields a new equation:
% 158.88/108.15 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.15 |
% 158.88/108.15 | From (479) and (468) follows:
% 158.88/108.15 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 158.88/108.15 |
% 158.88/108.15 | From (480) and (378) follows:
% 158.88/108.15 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 158.88/108.15 | (382) all_232_0_598 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (382) can reduce 466 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (501) ~ (all_234_2_604 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (501) yields:
% 158.88/108.15 | (502) ~ (all_234_2_604 = 0)
% 158.88/108.15 | (503) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.15 | (395) all_237_0_611 = 0
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_234_2_604, all_237_0_611 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604, yields:
% 158.88/108.15 | (505) all_237_0_611 = all_234_2_604
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (395,505) yields a new equation:
% 158.88/108.15 | (472) all_234_2_604 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (472) can reduce 502 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 158.88/108.15 | (395) all_237_0_611 = 0
% 158.88/108.15 |
% 158.88/108.15 | From (395) and (508) follows:
% 158.88/108.15 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.15 |
% 158.88/108.15 | Using (344) and (510) yields:
% 158.88/108.15 | (511) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (512) ~ (all_228_0_587 = 0) & reverse_line(all_0_3_3) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (512) yields:
% 158.88/108.15 | (513) ~ (all_228_0_587 = 0)
% 158.88/108.15 | (514) reverse_line(all_0_3_3) = all_228_1_588
% 158.88/108.15 | (515) unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587
% 158.88/108.15 |
% 158.88/108.15 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.15 |-Branch one:
% 158.88/108.15 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.15 |
% 158.88/108.15 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.15 |-Branch one:
% 158.88/108.15 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (431) yields:
% 158.88/108.15 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.15 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.15 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.15 | (435) all_286_0_717 = 0
% 158.88/108.15 | (436) all_286_1_718 = 0
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.15 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (133) with all_0_3_3, all_228_1_588, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_228_1_588, yields:
% 158.88/108.15 | (524) all_286_2_719 = all_228_1_588
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (437,524) yields a new equation:
% 158.88/108.15 | (525) all_228_1_588 = all_0_1_1
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (525,524) yields a new equation:
% 158.88/108.15 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.15 |
% 158.88/108.15 | From (437) and (432) follows:
% 158.88/108.15 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.15 |
% 158.88/108.15 | From (525) and (515) follows:
% 158.88/108.15 | (528) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_228_0_587, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.15 | (376) all_228_0_587 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (376) can reduce 513 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (445) yields:
% 158.88/108.15 | (436) all_286_1_718 = 0
% 158.88/108.15 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.15 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.15 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (133) with all_0_3_3, all_228_1_588, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_228_1_588, yields:
% 158.88/108.15 | (524) all_286_2_719 = all_228_1_588
% 158.88/108.15 |
% 158.88/108.15 | Combining equations (437,524) yields a new equation:
% 158.88/108.15 | (525) all_228_1_588 = all_0_1_1
% 158.88/108.15 |
% 158.88/108.15 | From (525) and (515) follows:
% 158.88/108.15 | (528) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_228_0_587, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.15 | (376) all_228_0_587 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (376) can reduce 513 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (455) yields:
% 158.88/108.15 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.15 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.15 | (458) all_286_2_719 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (458) can reduce 456 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (546) ~ (all_228_1_588 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (546) yields:
% 158.88/108.15 | (547) ~ (all_228_1_588 = 0)
% 158.88/108.15 | (548) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_228_1_588, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.15 | (549) all_228_1_588 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (549) can reduce 547 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (551) ~ (all_254_1_647 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (551) yields:
% 158.88/108.15 | (552) ~ (all_254_1_647 = 0)
% 158.88/108.15 | (553) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 158.88/108.15 |
% 158.88/108.15 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_254_1_647, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.15 | (358) all_254_1_647 = 0
% 158.88/108.15 |
% 158.88/108.15 | Equations (358) can reduce 552 to:
% 158.88/108.15 | (190) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (556) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469)
% 158.88/108.15 | (557) all_167_1_469 = 0 | ( ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468)
% 158.88/108.15 |
% 158.88/108.15 +-Applying beta-rule and splitting (557), into two cases.
% 158.88/108.15 |-Branch one:
% 158.88/108.15 | (371) all_167_1_469 = 0
% 158.88/108.15 |
% 158.88/108.15 | From (371) and (556) follows:
% 158.88/108.15 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.15 |
% 158.88/108.15 | Using (344) and (510) yields:
% 158.88/108.15 | (511) $false
% 158.88/108.15 |
% 158.88/108.15 |-The branch is then unsatisfiable
% 158.88/108.15 |-Branch two:
% 158.88/108.15 | (561) ~ (all_167_1_469 = 0)
% 158.88/108.15 | (562) ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 158.88/108.15 |
% 158.88/108.15 | Applying alpha-rule on (562) yields:
% 158.88/108.16 | (563) ~ (all_167_0_468 = 0)
% 158.88/108.16 | (564) reverse_line(all_0_3_3) = all_167_1_469
% 158.88/108.16 | (565) unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 158.88/108.16 |
% 158.88/108.16 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.16 |-Branch one:
% 158.88/108.16 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.16 |
% 158.88/108.16 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.16 |-Branch one:
% 158.88/108.16 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (431) yields:
% 158.88/108.16 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.16 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.16 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.16 | (435) all_286_0_717 = 0
% 158.88/108.16 | (436) all_286_1_718 = 0
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.16 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 158.88/108.16 | (574) all_286_2_719 = all_167_1_469
% 158.88/108.16 |
% 158.88/108.16 | Combining equations (437,574) yields a new equation:
% 158.88/108.16 | (575) all_167_1_469 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Combining equations (575,574) yields a new equation:
% 158.88/108.16 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | From (437) and (432) follows:
% 158.88/108.16 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.16 |
% 158.88/108.16 | From (575) and (565) follows:
% 158.88/108.16 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.16 | (579) all_167_0_468 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (579) can reduce 563 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (445) yields:
% 158.88/108.16 | (436) all_286_1_718 = 0
% 158.88/108.16 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.16 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.16 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 158.88/108.16 | (574) all_286_2_719 = all_167_1_469
% 158.88/108.16 |
% 158.88/108.16 | Combining equations (574,437) yields a new equation:
% 158.88/108.16 | (587) all_167_1_469 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Simplifying 587 yields:
% 158.88/108.16 | (575) all_167_1_469 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | From (575) and (565) follows:
% 158.88/108.16 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.16 | (579) all_167_0_468 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (579) can reduce 563 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (455) yields:
% 158.88/108.16 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.16 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.16 | (458) all_286_2_719 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (458) can reduce 456 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (597) ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (597) yields:
% 158.88/108.16 | (598) ~ (all_212_0_556 = 0)
% 158.88/108.16 | (599) reverse_line(all_0_3_3) = all_212_1_557
% 158.88/108.16 | (600) unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 158.88/108.16 |
% 158.88/108.16 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.16 |-Branch one:
% 158.88/108.16 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.16 |
% 158.88/108.16 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.16 |-Branch one:
% 158.88/108.16 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (431) yields:
% 158.88/108.16 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.16 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.16 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.16 | (435) all_286_0_717 = 0
% 158.88/108.16 | (436) all_286_1_718 = 0
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.16 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 158.88/108.16 | (609) all_286_2_719 = all_212_1_557
% 158.88/108.16 |
% 158.88/108.16 | Combining equations (609,437) yields a new equation:
% 158.88/108.16 | (610) all_212_1_557 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Simplifying 610 yields:
% 158.88/108.16 | (611) all_212_1_557 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | From (437) and (432) follows:
% 158.88/108.16 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.16 |
% 158.88/108.16 | From (611) and (600) follows:
% 158.88/108.16 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.16 | (614) all_212_0_556 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (614) can reduce 598 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (445) yields:
% 158.88/108.16 | (436) all_286_1_718 = 0
% 158.88/108.16 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.16 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.16 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 158.88/108.16 | (609) all_286_2_719 = all_212_1_557
% 158.88/108.16 |
% 158.88/108.16 | Combining equations (609,437) yields a new equation:
% 158.88/108.16 | (610) all_212_1_557 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | Simplifying 610 yields:
% 158.88/108.16 | (611) all_212_1_557 = all_0_1_1
% 158.88/108.16 |
% 158.88/108.16 | From (611) and (600) follows:
% 158.88/108.16 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.16 | (614) all_212_0_556 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (614) can reduce 598 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (455) yields:
% 158.88/108.16 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.16 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.16 |
% 158.88/108.16 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.16 | (458) all_286_2_719 = 0
% 158.88/108.16 |
% 158.88/108.16 | Equations (458) can reduce 456 to:
% 158.88/108.16 | (190) $false
% 158.88/108.16 |
% 158.88/108.16 |-The branch is then unsatisfiable
% 158.88/108.16 |-Branch two:
% 158.88/108.16 | (632) ~ (all_212_1_557 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 158.88/108.16 |
% 158.88/108.16 | Applying alpha-rule on (632) yields:
% 158.88/108.17 | (633) ~ (all_212_1_557 = 0)
% 158.88/108.17 | (634) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_212_1_557 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (352) all_212_1_557 = 0
% 158.88/108.17 |
% 158.88/108.17 | Equations (352) can reduce 633 to:
% 158.88/108.17 | (190) $false
% 158.88/108.17 |
% 158.88/108.17 |-The branch is then unsatisfiable
% 158.88/108.17 |-Branch two:
% 158.88/108.17 | (637) all_287_1_721 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (637) yields:
% 158.88/108.17 | (348) all_287_1_721 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (302), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (350) (all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (350), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (351) all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (351) yields:
% 158.88/108.17 | (352) all_212_1_557 = 0
% 158.88/108.17 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (299), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (354) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (311), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (355) (all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (355), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (356) all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (356) yields:
% 158.88/108.17 | (357) all_254_0_646 = 0
% 158.88/108.17 | (358) all_254_1_647 = 0
% 158.88/108.17 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 158.88/108.17 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 158.88/108.17 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 158.88/108.17 |
% 158.88/108.17 | Instantiating (215) with all_709_0_18408 yields:
% 158.88/108.17 | (652) ~ (all_709_0_18408 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_18408
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (652) yields:
% 158.88/108.17 | (653) ~ (all_709_0_18408 = 0)
% 158.88/108.17 | (654) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_18408
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (55) with all_709_0_18408, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_18408, yields:
% 158.88/108.17 | (655) all_709_0_18408 = 0
% 158.88/108.17 |
% 158.88/108.17 | Equations (655) can reduce 653 to:
% 158.88/108.17 | (190) $false
% 158.88/108.17 |
% 158.88/108.17 |-The branch is then unsatisfiable
% 158.88/108.17 |-Branch two:
% 158.88/108.17 | (367) all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (367) yields:
% 158.88/108.17 | (358) all_254_1_647 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (133) with all_0_1_1, all_291_1_731, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_291_1_731, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.17 | (370) all_291_1_731 = all_76_1_421
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_167_1_469 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (371) all_167_1_469 = 0
% 158.88/108.17 |
% 158.88/108.17 | From (370) and (328) follows:
% 158.88/108.17 | (244) reverse_line(all_0_1_1) = all_76_1_421
% 158.88/108.17 |
% 158.88/108.17 | From (371) and (354) follows:
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (304), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (374) (all_228_0_587 = 0 & reverse_line(all_0_1_1) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = 0) | ( ~ (all_228_0_587 = 0) & reverse_line(all_0_3_3) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (374), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (375) all_228_0_587 = 0 & reverse_line(all_0_1_1) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (375) yields:
% 158.88/108.17 | (376) all_228_0_587 = 0
% 158.88/108.17 | (377) reverse_line(all_0_1_1) = all_228_1_588
% 158.88/108.17 | (378) unequally_directed_lines(all_0_3_3, all_228_1_588) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (308), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (305), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (380) (all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (380), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (381) all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (381) yields:
% 158.88/108.17 | (382) all_232_0_598 = 0
% 158.88/108.17 | (383) all_232_1_599 = 0
% 158.88/108.17 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 158.88/108.17 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 158.88/108.17 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 158.88/108.17 |
% 158.88/108.17 | Instantiating (215) with all_709_0_26328 yields:
% 158.88/108.17 | (677) ~ (all_709_0_26328 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_26328
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (677) yields:
% 158.88/108.17 | (678) ~ (all_709_0_26328 = 0)
% 158.88/108.17 | (679) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_26328
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (55) with all_709_0_26328, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_26328, yields:
% 158.88/108.17 | (680) all_709_0_26328 = 0
% 158.88/108.17 |
% 158.88/108.17 | Equations (680) can reduce 678 to:
% 158.88/108.17 | (190) $false
% 158.88/108.17 |
% 158.88/108.17 |-The branch is then unsatisfiable
% 158.88/108.17 |-Branch two:
% 158.88/108.17 | (392) all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (392) yields:
% 158.88/108.17 | (383) all_232_1_599 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (395) all_237_0_611 = 0
% 158.88/108.17 |
% 158.88/108.17 | From (395) and (379) follows:
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (306), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (397) (all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (397), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (398) all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (398) yields:
% 158.88/108.17 | (399) all_233_1_601 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (310), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (401) (all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.17 |
% 158.88/108.17 +-Applying beta-rule and splitting (401), into two cases.
% 158.88/108.17 |-Branch one:
% 158.88/108.17 | (402) all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (402) yields:
% 158.88/108.17 | (403) all_253_0_644 = 0
% 158.88/108.17 | (404) all_253_1_645 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 158.88/108.17 |
% 158.88/108.17 | Instantiating (406) with all_898_0_28110 yields:
% 158.88/108.17 | (697) ~ (all_898_0_28110 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_28110
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (697) yields:
% 158.88/108.17 | (698) ~ (all_898_0_28110 = 0)
% 158.88/108.17 | (699) equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_28110
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (55) with all_898_0_28110, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_28110, yields:
% 158.88/108.17 | (700) all_898_0_28110 = 0
% 158.88/108.17 |
% 158.88/108.17 | Equations (700) can reduce 698 to:
% 158.88/108.17 | (190) $false
% 158.88/108.17 |
% 158.88/108.17 |-The branch is then unsatisfiable
% 158.88/108.17 |-Branch two:
% 158.88/108.17 | (412) all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (412) yields:
% 158.88/108.17 | (404) all_253_1_645 = 0
% 158.88/108.17 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 158.88/108.17 |
% 158.88/108.17 | Instantiating (406) with all_898_0_29248 yields:
% 158.88/108.17 | (706) ~ (all_898_0_29248 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_29248
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (706) yields:
% 158.88/108.17 | (707) ~ (all_898_0_29248 = 0)
% 158.88/108.17 | (708) equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_29248
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (55) with all_898_0_29248, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_898_0_29248, yields:
% 158.88/108.17 | (709) all_898_0_29248 = 0
% 158.88/108.17 |
% 158.88/108.17 | Equations (709) can reduce 707 to:
% 158.88/108.17 | (190) $false
% 158.88/108.17 |
% 158.88/108.17 |-The branch is then unsatisfiable
% 158.88/108.17 |-Branch two:
% 158.88/108.17 | (421) ~ (all_253_1_645 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 158.88/108.17 |
% 158.88/108.17 | Applying alpha-rule on (421) yields:
% 158.88/108.17 | (422) ~ (all_253_1_645 = 0)
% 158.88/108.17 | (423) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 158.88/108.17 |
% 158.88/108.17 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_253_1_645, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.17 | (404) all_253_1_645 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (404) can reduce 422 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (426) ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (426) yields:
% 158.88/108.18 | (427) ~ (all_233_0_600 = 0)
% 158.88/108.18 | (428) reverse_line(all_0_3_3) = all_233_1_601
% 158.88/108.18 | (429) unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 158.88/108.18 |
% 158.88/108.18 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.18 |-Branch one:
% 158.88/108.18 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.18 |
% 158.88/108.18 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.18 |-Branch one:
% 158.88/108.18 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (431) yields:
% 158.88/108.18 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.18 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.18 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.18 | (435) all_286_0_717 = 0
% 158.88/108.18 | (436) all_286_1_718 = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.18 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 158.88/108.18 | (438) all_286_2_719 = all_233_1_601
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (437,438) yields a new equation:
% 158.88/108.18 | (439) all_233_1_601 = all_0_1_1
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (439,438) yields a new equation:
% 158.88/108.18 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.18 |
% 158.88/108.18 | From (437) and (432) follows:
% 158.88/108.18 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.18 |
% 158.88/108.18 | From (439) and (429) follows:
% 158.88/108.18 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.18 | (443) all_233_0_600 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (443) can reduce 427 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (445) yields:
% 158.88/108.18 | (436) all_286_1_718 = 0
% 158.88/108.18 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.18 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.18 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 158.88/108.18 | (438) all_286_2_719 = all_233_1_601
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (437,438) yields a new equation:
% 158.88/108.18 | (439) all_233_1_601 = all_0_1_1
% 158.88/108.18 |
% 158.88/108.18 | From (439) and (429) follows:
% 158.88/108.18 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.18 | (443) all_233_0_600 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (443) can reduce 427 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (455) yields:
% 158.88/108.18 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.18 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.18 | (458) all_286_2_719 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (458) can reduce 456 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (460) ~ (all_233_1_601 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (460) yields:
% 158.88/108.18 | (461) ~ (all_233_1_601 = 0)
% 158.88/108.18 | (462) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_233_1_601, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.18 | (399) all_233_1_601 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (399) can reduce 461 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (465) ~ (all_232_0_598 = 0) & reverse_line(all_0_1_1) = all_232_1_599 & unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (465) yields:
% 158.88/108.18 | (466) ~ (all_232_0_598 = 0)
% 158.88/108.18 | (467) reverse_line(all_0_1_1) = all_232_1_599
% 158.88/108.18 | (468) unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 158.88/108.18 |
% 158.88/108.18 +-Applying beta-rule and splitting (307), into two cases.
% 158.88/108.18 |-Branch one:
% 158.88/108.18 | (469) (all_234_0_602 = 0 & all_234_2_604 = 0 & reverse_line(all_0_1_1) = all_234_1_603 & unequally_directed_lines(all_0_3_3, all_234_1_603) = 0) | (all_234_1_603 = 0 & reverse_line(all_0_1_1) = all_234_2_604 & unequally_directed_lines(all_0_3_3, all_234_2_604) = 0)
% 158.88/108.18 |
% 158.88/108.18 +-Applying beta-rule and splitting (469), into two cases.
% 158.88/108.18 |-Branch one:
% 158.88/108.18 | (470) all_234_0_602 = 0 & all_234_2_604 = 0 & reverse_line(all_0_1_1) = all_234_1_603 & unequally_directed_lines(all_0_3_3, all_234_1_603) = 0
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (470) yields:
% 158.88/108.18 | (471) all_234_0_602 = 0
% 158.88/108.18 | (472) all_234_2_604 = 0
% 158.88/108.18 | (473) reverse_line(all_0_1_1) = all_234_1_603
% 158.88/108.18 | (474) unequally_directed_lines(all_0_3_3, all_234_1_603) = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_234_1_603, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_234_1_603, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.18 | (475) all_234_1_603 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_234_1_603 and discharging atoms reverse_line(all_0_1_1) = all_234_1_603, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 158.88/108.18 | (476) all_234_1_603 = all_232_1_599
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_228_1_588, all_232_1_599 and discharging atoms reverse_line(all_0_1_1) = all_232_1_599, reverse_line(all_0_1_1) = all_228_1_588, yields:
% 158.88/108.18 | (477) all_232_1_599 = all_228_1_588
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (476,475) yields a new equation:
% 158.88/108.18 | (478) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Simplifying 478 yields:
% 158.88/108.18 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (479,477) yields a new equation:
% 158.88/108.18 | (480) all_228_1_588 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (480,477) yields a new equation:
% 158.88/108.18 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | From (479) and (468) follows:
% 158.88/108.18 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 158.88/108.18 |
% 158.88/108.18 | From (480) and (378) follows:
% 158.88/108.18 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 158.88/108.18 | (382) all_232_0_598 = 0
% 158.88/108.18 |
% 158.88/108.18 | Equations (382) can reduce 466 to:
% 158.88/108.18 | (190) $false
% 158.88/108.18 |
% 158.88/108.18 |-The branch is then unsatisfiable
% 158.88/108.18 |-Branch two:
% 158.88/108.18 | (486) all_234_1_603 = 0 & reverse_line(all_0_1_1) = all_234_2_604 & unequally_directed_lines(all_0_3_3, all_234_2_604) = 0
% 158.88/108.18 |
% 158.88/108.18 | Applying alpha-rule on (486) yields:
% 158.88/108.18 | (487) all_234_1_603 = 0
% 158.88/108.18 | (488) reverse_line(all_0_1_1) = all_234_2_604
% 158.88/108.18 | (489) unequally_directed_lines(all_0_3_3, all_234_2_604) = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_234_2_604, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_234_2_604, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 158.88/108.18 | (490) all_234_2_604 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_234_2_604 and discharging atoms reverse_line(all_0_1_1) = all_234_2_604, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 158.88/108.18 | (491) all_234_2_604 = all_232_1_599
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (133) with all_0_1_1, all_228_1_588, all_232_1_599 and discharging atoms reverse_line(all_0_1_1) = all_232_1_599, reverse_line(all_0_1_1) = all_228_1_588, yields:
% 158.88/108.18 | (477) all_232_1_599 = all_228_1_588
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (491,490) yields a new equation:
% 158.88/108.18 | (478) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Simplifying 478 yields:
% 158.88/108.18 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (479,477) yields a new equation:
% 158.88/108.18 | (480) all_228_1_588 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | Combining equations (480,477) yields a new equation:
% 158.88/108.18 | (479) all_232_1_599 = all_76_1_421
% 158.88/108.18 |
% 158.88/108.18 | From (479) and (468) follows:
% 158.88/108.18 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 158.88/108.18 |
% 158.88/108.18 | From (480) and (378) follows:
% 158.88/108.18 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 158.88/108.18 |
% 158.88/108.18 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 158.88/108.19 | (382) all_232_0_598 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (382) can reduce 466 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (501) ~ (all_234_2_604 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (501) yields:
% 158.88/108.19 | (502) ~ (all_234_2_604 = 0)
% 158.88/108.19 | (503) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.19 | (395) all_237_0_611 = 0
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_234_2_604, all_237_0_611 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_234_2_604, yields:
% 158.88/108.19 | (505) all_237_0_611 = all_234_2_604
% 158.88/108.19 |
% 158.88/108.19 | Combining equations (505,395) yields a new equation:
% 158.88/108.19 | (796) all_234_2_604 = 0
% 158.88/108.19 |
% 158.88/108.19 | Simplifying 796 yields:
% 158.88/108.19 | (472) all_234_2_604 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (472) can reduce 502 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 158.88/108.19 | (395) all_237_0_611 = 0
% 158.88/108.19 |
% 158.88/108.19 | From (395) and (508) follows:
% 158.88/108.19 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.19 |
% 158.88/108.19 | Using (344) and (510) yields:
% 158.88/108.19 | (511) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (512) ~ (all_228_0_587 = 0) & reverse_line(all_0_3_3) = all_228_1_588 & unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (512) yields:
% 158.88/108.19 | (513) ~ (all_228_0_587 = 0)
% 158.88/108.19 | (514) reverse_line(all_0_3_3) = all_228_1_588
% 158.88/108.19 | (515) unequally_directed_lines(all_0_3_3, all_228_1_588) = all_228_0_587
% 158.88/108.19 |
% 158.88/108.19 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.19 |-Branch one:
% 158.88/108.19 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.19 |
% 158.88/108.19 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.19 |-Branch one:
% 158.88/108.19 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (431) yields:
% 158.88/108.19 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.19 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.19 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.19 | (435) all_286_0_717 = 0
% 158.88/108.19 | (436) all_286_1_718 = 0
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.19 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_228_1_588, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_228_1_588, yields:
% 158.88/108.19 | (524) all_286_2_719 = all_228_1_588
% 158.88/108.19 |
% 158.88/108.19 | Combining equations (437,524) yields a new equation:
% 158.88/108.19 | (525) all_228_1_588 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | Combining equations (525,524) yields a new equation:
% 158.88/108.19 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | From (437) and (432) follows:
% 158.88/108.19 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.19 |
% 158.88/108.19 | From (525) and (515) follows:
% 158.88/108.19 | (528) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_228_0_587, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.19 | (376) all_228_0_587 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (376) can reduce 513 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (445) yields:
% 158.88/108.19 | (436) all_286_1_718 = 0
% 158.88/108.19 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.19 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.19 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_228_1_588, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_228_1_588, yields:
% 158.88/108.19 | (524) all_286_2_719 = all_228_1_588
% 158.88/108.19 |
% 158.88/108.19 | Combining equations (437,524) yields a new equation:
% 158.88/108.19 | (525) all_228_1_588 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | From (525) and (515) follows:
% 158.88/108.19 | (528) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_228_0_587, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_228_0_587, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.19 | (376) all_228_0_587 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (376) can reduce 513 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (455) yields:
% 158.88/108.19 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.19 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.19 | (458) all_286_2_719 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (458) can reduce 456 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (546) ~ (all_228_1_588 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (546) yields:
% 158.88/108.19 | (547) ~ (all_228_1_588 = 0)
% 158.88/108.19 | (548) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_228_1_588, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_228_1_588, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.19 | (549) all_228_1_588 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (549) can reduce 547 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (551) ~ (all_254_1_647 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (551) yields:
% 158.88/108.19 | (552) ~ (all_254_1_647 = 0)
% 158.88/108.19 | (553) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_254_1_647, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.19 | (358) all_254_1_647 = 0
% 158.88/108.19 |
% 158.88/108.19 | Equations (358) can reduce 552 to:
% 158.88/108.19 | (190) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (556) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469)
% 158.88/108.19 | (557) all_167_1_469 = 0 | ( ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468)
% 158.88/108.19 |
% 158.88/108.19 +-Applying beta-rule and splitting (557), into two cases.
% 158.88/108.19 |-Branch one:
% 158.88/108.19 | (371) all_167_1_469 = 0
% 158.88/108.19 |
% 158.88/108.19 | From (371) and (556) follows:
% 158.88/108.19 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 158.88/108.19 |
% 158.88/108.19 | Using (344) and (510) yields:
% 158.88/108.19 | (511) $false
% 158.88/108.19 |
% 158.88/108.19 |-The branch is then unsatisfiable
% 158.88/108.19 |-Branch two:
% 158.88/108.19 | (561) ~ (all_167_1_469 = 0)
% 158.88/108.19 | (562) ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (562) yields:
% 158.88/108.19 | (563) ~ (all_167_0_468 = 0)
% 158.88/108.19 | (564) reverse_line(all_0_3_3) = all_167_1_469
% 158.88/108.19 | (565) unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 158.88/108.19 |
% 158.88/108.19 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.19 |-Branch one:
% 158.88/108.19 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.19 |
% 158.88/108.19 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.19 |-Branch one:
% 158.88/108.19 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.19 |
% 158.88/108.19 | Applying alpha-rule on (431) yields:
% 158.88/108.19 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.19 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.19 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.19 | (435) all_286_0_717 = 0
% 158.88/108.19 | (436) all_286_1_718 = 0
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.19 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.19 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 158.88/108.19 | (574) all_286_2_719 = all_167_1_469
% 158.88/108.19 |
% 158.88/108.19 | Combining equations (574,437) yields a new equation:
% 158.88/108.19 | (587) all_167_1_469 = all_0_1_1
% 158.88/108.19 |
% 158.88/108.20 | Simplifying 587 yields:
% 158.88/108.20 | (575) all_167_1_469 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | From (437) and (432) follows:
% 158.88/108.20 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.20 |
% 158.88/108.20 | From (575) and (565) follows:
% 158.88/108.20 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.20 | (579) all_167_0_468 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (579) can reduce 563 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (445) yields:
% 158.88/108.20 | (436) all_286_1_718 = 0
% 158.88/108.20 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.20 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.20 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 158.88/108.20 | (574) all_286_2_719 = all_167_1_469
% 158.88/108.20 |
% 158.88/108.20 | Combining equations (574,437) yields a new equation:
% 158.88/108.20 | (587) all_167_1_469 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | Simplifying 587 yields:
% 158.88/108.20 | (575) all_167_1_469 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | From (575) and (565) follows:
% 158.88/108.20 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.20 | (579) all_167_0_468 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (579) can reduce 563 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (455) yields:
% 158.88/108.20 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.20 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.20 | (458) all_286_2_719 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (458) can reduce 456 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (597) ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (597) yields:
% 158.88/108.20 | (598) ~ (all_212_0_556 = 0)
% 158.88/108.20 | (599) reverse_line(all_0_3_3) = all_212_1_557
% 158.88/108.20 | (600) unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 158.88/108.20 |
% 158.88/108.20 +-Applying beta-rule and splitting (313), into two cases.
% 158.88/108.20 |-Branch one:
% 158.88/108.20 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 158.88/108.20 |
% 158.88/108.20 +-Applying beta-rule and splitting (430), into two cases.
% 158.88/108.20 |-Branch one:
% 158.88/108.20 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (431) yields:
% 158.88/108.20 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 158.88/108.20 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.20 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 158.88/108.20 | (435) all_286_0_717 = 0
% 158.88/108.20 | (436) all_286_1_718 = 0
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.20 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 158.88/108.20 | (609) all_286_2_719 = all_212_1_557
% 158.88/108.20 |
% 158.88/108.20 | Combining equations (609,437) yields a new equation:
% 158.88/108.20 | (610) all_212_1_557 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | Simplifying 610 yields:
% 158.88/108.20 | (611) all_212_1_557 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | From (437) and (432) follows:
% 158.88/108.20 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 158.88/108.20 |
% 158.88/108.20 | From (611) and (600) follows:
% 158.88/108.20 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.20 | (614) all_212_0_556 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (614) can reduce 598 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (445) yields:
% 158.88/108.20 | (436) all_286_1_718 = 0
% 158.88/108.20 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 158.88/108.20 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 158.88/108.20 | (437) all_286_2_719 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 158.88/108.20 | (609) all_286_2_719 = all_212_1_557
% 158.88/108.20 |
% 158.88/108.20 | Combining equations (437,609) yields a new equation:
% 158.88/108.20 | (611) all_212_1_557 = all_0_1_1
% 158.88/108.20 |
% 158.88/108.20 | From (611) and (600) follows:
% 158.88/108.20 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 158.88/108.20 | (614) all_212_0_556 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (614) can reduce 598 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (455) yields:
% 158.88/108.20 | (456) ~ (all_286_2_719 = 0)
% 158.88/108.20 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.20 | (458) all_286_2_719 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (458) can reduce 456 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (632) ~ (all_212_1_557 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (632) yields:
% 158.88/108.20 | (633) ~ (all_212_1_557 = 0)
% 158.88/108.20 | (634) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_212_1_557 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 158.88/108.20 | (352) all_212_1_557 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (352) can reduce 633 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (927) ~ (all_287_1_721 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (927) yields:
% 158.88/108.20 | (928) ~ (all_287_1_721 = 0)
% 158.88/108.20 | (929) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721
% 158.88/108.20 |
% 158.88/108.20 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_287_1_721, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 158.88/108.20 | (348) all_287_1_721 = 0
% 158.88/108.20 |
% 158.88/108.20 | Equations (348) can reduce 928 to:
% 158.88/108.20 | (190) $false
% 158.88/108.20 |
% 158.88/108.20 |-The branch is then unsatisfiable
% 158.88/108.20 |-Branch two:
% 158.88/108.20 | (932) all_294_1_738 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 158.88/108.20 |
% 158.88/108.20 | Applying alpha-rule on (932) yields:
% 158.88/108.20 | (343) all_294_1_738 = 0
% 158.88/108.20 | (223) unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (279), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (935) all_95_0_432 = 0
% 159.27/108.20 |
% 159.27/108.20 | Equations (935) can reduce 264 to:
% 159.27/108.20 | (190) $false
% 159.27/108.20 |
% 159.27/108.20 |-The branch is then unsatisfiable
% 159.27/108.20 |-Branch two:
% 159.27/108.20 | (264) ~ (all_95_0_432 = 0)
% 159.27/108.20 | (938) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & left_apart_point(all_95_2_434, all_0_3_3) = v0 & right_apart_point(all_95_2_434, all_0_3_3) = v1)
% 159.27/108.20 |
% 159.27/108.20 | Instantiating (938) with all_350_0_29520, all_350_1_29521 yields:
% 159.27/108.20 | (939) ~ (all_350_0_29520 = 0) & ~ (all_350_1_29521 = 0) & left_apart_point(all_95_2_434, all_0_3_3) = all_350_1_29521 & right_apart_point(all_95_2_434, all_0_3_3) = all_350_0_29520
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (939) yields:
% 159.27/108.20 | (940) ~ (all_350_0_29520 = 0)
% 159.27/108.20 | (941) ~ (all_350_1_29521 = 0)
% 159.27/108.20 | (942) left_apart_point(all_95_2_434, all_0_3_3) = all_350_1_29521
% 159.27/108.20 | (943) right_apart_point(all_95_2_434, all_0_3_3) = all_350_0_29520
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (309), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (944) (all_241_1_619 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_241_1_619 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0) | ( ~ (all_241_0_618 = 0) & reverse_line(all_0_4_4) = all_241_1_619 & unequally_directed_lines(all_0_3_3, all_241_1_619) = all_241_0_618)
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (944), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (945) (all_241_1_619 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_241_1_619 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0)
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (945), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (946) all_241_1_619 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (946) yields:
% 159.27/108.20 | (947) all_241_1_619 = 0
% 159.27/108.20 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (314), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (345) (all_287_0_720 = 0 & all_287_1_721 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0) | (all_287_1_721 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (345), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (346) all_287_0_720 = 0 & all_287_1_721 = 0 & unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (346) yields:
% 159.27/108.20 | (347) all_287_0_720 = 0
% 159.27/108.20 | (348) all_287_1_721 = 0
% 159.27/108.20 | (223) unequally_directed_lines(all_0_4_4, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (302), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (350) (all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556)
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (350), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (351) all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (351) yields:
% 159.27/108.20 | (352) all_212_1_557 = 0
% 159.27/108.20 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (311), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (355) (all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.20 |
% 159.27/108.20 +-Applying beta-rule and splitting (355), into two cases.
% 159.27/108.20 |-Branch one:
% 159.27/108.20 | (356) all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (356) yields:
% 159.27/108.20 | (357) all_254_0_646 = 0
% 159.27/108.20 | (358) all_254_1_647 = 0
% 159.27/108.20 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 159.27/108.20 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.20 |
% 159.27/108.20 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 159.27/108.20 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 159.27/108.20 |
% 159.27/108.20 | Instantiating (215) with all_709_0_32792 yields:
% 159.27/108.20 | (965) ~ (all_709_0_32792 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_32792
% 159.27/108.20 |
% 159.27/108.20 | Applying alpha-rule on (965) yields:
% 159.27/108.20 | (966) ~ (all_709_0_32792 = 0)
% 159.27/108.20 | (967) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_32792
% 159.27/108.20 |
% 159.27/108.20 | Instantiating formula (55) with all_709_0_32792, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_32792, yields:
% 159.27/108.20 | (968) all_709_0_32792 = 0
% 159.27/108.20 |
% 159.27/108.20 | Equations (968) can reduce 966 to:
% 159.27/108.20 | (190) $false
% 159.27/108.20 |
% 159.27/108.20 |-The branch is then unsatisfiable
% 159.27/108.20 |-Branch two:
% 159.27/108.20 | (367) all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (367) yields:
% 159.27/108.21 | (358) all_254_1_647 = 0
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (299), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (354) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (133) with all_0_1_1, all_291_1_731, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_291_1_731, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.21 | (370) all_291_1_731 = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_167_1_469 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.21 | (371) all_167_1_469 = 0
% 159.27/108.21 |
% 159.27/108.21 | From (370) and (328) follows:
% 159.27/108.21 | (244) reverse_line(all_0_1_1) = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | From (371) and (354) follows:
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (306), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (397) (all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600)
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (397), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (398) all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (398) yields:
% 159.27/108.21 | (399) all_233_1_601 = 0
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (305), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (380) (all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (380), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (381) all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (381) yields:
% 159.27/108.21 | (382) all_232_0_598 = 0
% 159.27/108.21 | (383) all_232_1_599 = 0
% 159.27/108.21 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 159.27/108.21 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 159.27/108.21 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 159.27/108.21 |
% 159.27/108.21 | Instantiating (215) with all_709_0_35614 yields:
% 159.27/108.21 | (989) ~ (all_709_0_35614 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_35614
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (989) yields:
% 159.27/108.21 | (990) ~ (all_709_0_35614 = 0)
% 159.27/108.21 | (991) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_35614
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (55) with all_709_0_35614, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_35614, yields:
% 159.27/108.21 | (992) all_709_0_35614 = 0
% 159.27/108.21 |
% 159.27/108.21 | Equations (992) can reduce 990 to:
% 159.27/108.21 | (190) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (392) all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (392) yields:
% 159.27/108.21 | (383) all_232_1_599 = 0
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (308), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.21 | (395) all_237_0_611 = 0
% 159.27/108.21 |
% 159.27/108.21 | From (395) and (379) follows:
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (310), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (401) (all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (401), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (402) all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (402) yields:
% 159.27/108.21 | (403) all_253_0_644 = 0
% 159.27/108.21 | (404) all_253_1_645 = 0
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.21 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 159.27/108.21 |
% 159.27/108.21 | Instantiating (406) with all_910_0_37426 yields:
% 159.27/108.21 | (1006) ~ (all_910_0_37426 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_37426
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (1006) yields:
% 159.27/108.21 | (1007) ~ (all_910_0_37426 = 0)
% 159.27/108.21 | (1008) equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_37426
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (55) with all_910_0_37426, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_37426, yields:
% 159.27/108.21 | (1009) all_910_0_37426 = 0
% 159.27/108.21 |
% 159.27/108.21 | Equations (1009) can reduce 1007 to:
% 159.27/108.21 | (190) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (412) all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (412) yields:
% 159.27/108.21 | (404) all_253_1_645 = 0
% 159.27/108.21 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.21 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 159.27/108.21 |
% 159.27/108.21 | Instantiating (406) with all_910_0_38564 yields:
% 159.27/108.21 | (1015) ~ (all_910_0_38564 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_38564
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (1015) yields:
% 159.27/108.21 | (1016) ~ (all_910_0_38564 = 0)
% 159.27/108.21 | (1017) equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_38564
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (55) with all_910_0_38564, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_38564, yields:
% 159.27/108.21 | (1018) all_910_0_38564 = 0
% 159.27/108.21 |
% 159.27/108.21 | Equations (1018) can reduce 1016 to:
% 159.27/108.21 | (190) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (421) ~ (all_253_1_645 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (421) yields:
% 159.27/108.21 | (422) ~ (all_253_1_645 = 0)
% 159.27/108.21 | (423) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_253_1_645, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.21 | (404) all_253_1_645 = 0
% 159.27/108.21 |
% 159.27/108.21 | Equations (404) can reduce 422 to:
% 159.27/108.21 | (190) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 159.27/108.21 | (395) all_237_0_611 = 0
% 159.27/108.21 |
% 159.27/108.21 | From (395) and (508) follows:
% 159.27/108.21 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.21 |
% 159.27/108.21 | Using (344) and (510) yields:
% 159.27/108.21 | (511) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (465) ~ (all_232_0_598 = 0) & reverse_line(all_0_1_1) = all_232_1_599 & unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (465) yields:
% 159.27/108.21 | (466) ~ (all_232_0_598 = 0)
% 159.27/108.21 | (467) reverse_line(all_0_1_1) = all_232_1_599
% 159.27/108.21 | (468) unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (308), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (312), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (1034) (all_273_0_686 = 0 & all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0) | (all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0)
% 159.27/108.21 |
% 159.27/108.21 +-Applying beta-rule and splitting (1034), into two cases.
% 159.27/108.21 |-Branch one:
% 159.27/108.21 | (1035) all_273_0_686 = 0 & all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (1035) yields:
% 159.27/108.21 | (1036) all_273_0_686 = 0
% 159.27/108.21 | (1037) all_273_1_687 = 0
% 159.27/108.21 | (1038) reverse_line(all_0_1_1) = all_273_2_688
% 159.27/108.21 | (1039) unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (133) with all_0_1_1, all_273_2_688, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.21 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_273_2_688 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 159.27/108.21 | (1041) all_273_2_688 = all_232_1_599
% 159.27/108.21 |
% 159.27/108.21 | Combining equations (1040,1041) yields a new equation:
% 159.27/108.21 | (479) all_232_1_599 = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | Combining equations (479,1041) yields a new equation:
% 159.27/108.21 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | From (1040) and (1039) follows:
% 159.27/108.21 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 159.27/108.21 |
% 159.27/108.21 | From (479) and (468) follows:
% 159.27/108.21 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 159.27/108.21 | (382) all_232_0_598 = 0
% 159.27/108.21 |
% 159.27/108.21 | Equations (382) can reduce 466 to:
% 159.27/108.21 | (190) $false
% 159.27/108.21 |
% 159.27/108.21 |-The branch is then unsatisfiable
% 159.27/108.21 |-Branch two:
% 159.27/108.21 | (1048) all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.21 |
% 159.27/108.21 | Applying alpha-rule on (1048) yields:
% 159.27/108.21 | (1037) all_273_1_687 = 0
% 159.27/108.21 | (1038) reverse_line(all_0_1_1) = all_273_2_688
% 159.27/108.21 | (1039) unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (133) with all_0_1_1, all_273_2_688, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.21 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.21 |
% 159.27/108.21 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_273_2_688 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 159.27/108.22 | (1041) all_273_2_688 = all_232_1_599
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (1040,1041) yields a new equation:
% 159.27/108.22 | (479) all_232_1_599 = all_76_1_421
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (479,1041) yields a new equation:
% 159.27/108.22 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.22 |
% 159.27/108.22 | From (1040) and (1039) follows:
% 159.27/108.22 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 159.27/108.22 |
% 159.27/108.22 | From (479) and (468) follows:
% 159.27/108.22 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 159.27/108.22 | (382) all_232_0_598 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (382) can reduce 466 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (1060) ~ (all_273_2_688 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (1060) yields:
% 159.27/108.22 | (1061) ~ (all_273_2_688 = 0)
% 159.27/108.22 | (1062) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_273_2_688, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.22 | (1063) all_273_2_688 = 0
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, all_273_2_688 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, yields:
% 159.27/108.22 | (1064) all_273_2_688 = all_237_0_611
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (1063,1064) yields a new equation:
% 159.27/108.22 | (395) all_237_0_611 = 0
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (395,1064) yields a new equation:
% 159.27/108.22 | (1063) all_273_2_688 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (1063) can reduce 1061 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 159.27/108.22 | (395) all_237_0_611 = 0
% 159.27/108.22 |
% 159.27/108.22 | From (395) and (508) follows:
% 159.27/108.22 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.22 |
% 159.27/108.22 | Using (344) and (510) yields:
% 159.27/108.22 | (511) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (426) ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (426) yields:
% 159.27/108.22 | (427) ~ (all_233_0_600 = 0)
% 159.27/108.22 | (428) reverse_line(all_0_3_3) = all_233_1_601
% 159.27/108.22 | (429) unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 159.27/108.22 |
% 159.27/108.22 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.22 |-Branch one:
% 159.27/108.22 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.22 |
% 159.27/108.22 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.22 |-Branch one:
% 159.27/108.22 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (431) yields:
% 159.27/108.22 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.22 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.22 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.22 | (435) all_286_0_717 = 0
% 159.27/108.22 | (436) all_286_1_718 = 0
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.22 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 159.27/108.22 | (438) all_286_2_719 = all_233_1_601
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (438,437) yields a new equation:
% 159.27/108.22 | (1085) all_233_1_601 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Simplifying 1085 yields:
% 159.27/108.22 | (439) all_233_1_601 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | From (437) and (432) follows:
% 159.27/108.22 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.22 |
% 159.27/108.22 | From (439) and (429) follows:
% 159.27/108.22 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.22 | (443) all_233_0_600 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (443) can reduce 427 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (445) yields:
% 159.27/108.22 | (436) all_286_1_718 = 0
% 159.27/108.22 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.22 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.22 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 159.27/108.22 | (438) all_286_2_719 = all_233_1_601
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (438,437) yields a new equation:
% 159.27/108.22 | (1085) all_233_1_601 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Simplifying 1085 yields:
% 159.27/108.22 | (439) all_233_1_601 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | From (439) and (429) follows:
% 159.27/108.22 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.22 | (443) all_233_0_600 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (443) can reduce 427 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (455) yields:
% 159.27/108.22 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.22 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.22 | (458) all_286_2_719 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (458) can reduce 456 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (460) ~ (all_233_1_601 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (460) yields:
% 159.27/108.22 | (461) ~ (all_233_1_601 = 0)
% 159.27/108.22 | (462) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_233_1_601, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.22 | (399) all_233_1_601 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (399) can reduce 461 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (556) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469)
% 159.27/108.22 | (557) all_167_1_469 = 0 | ( ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468)
% 159.27/108.22 |
% 159.27/108.22 +-Applying beta-rule and splitting (557), into two cases.
% 159.27/108.22 |-Branch one:
% 159.27/108.22 | (371) all_167_1_469 = 0
% 159.27/108.22 |
% 159.27/108.22 | From (371) and (556) follows:
% 159.27/108.22 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.22 |
% 159.27/108.22 | Using (344) and (510) yields:
% 159.27/108.22 | (511) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (561) ~ (all_167_1_469 = 0)
% 159.27/108.22 | (562) ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (562) yields:
% 159.27/108.22 | (563) ~ (all_167_0_468 = 0)
% 159.27/108.22 | (564) reverse_line(all_0_3_3) = all_167_1_469
% 159.27/108.22 | (565) unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 159.27/108.22 |
% 159.27/108.22 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.22 |-Branch one:
% 159.27/108.22 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.22 |
% 159.27/108.22 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.22 |-Branch one:
% 159.27/108.22 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (431) yields:
% 159.27/108.22 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.22 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.22 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.22 | (435) all_286_0_717 = 0
% 159.27/108.22 | (436) all_286_1_718 = 0
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.22 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 159.27/108.22 | (574) all_286_2_719 = all_167_1_469
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (437,574) yields a new equation:
% 159.27/108.22 | (575) all_167_1_469 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (575,574) yields a new equation:
% 159.27/108.22 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | From (437) and (432) follows:
% 159.27/108.22 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.22 |
% 159.27/108.22 | From (575) and (565) follows:
% 159.27/108.22 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.22 | (579) all_167_0_468 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (579) can reduce 563 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (445) yields:
% 159.27/108.22 | (436) all_286_1_718 = 0
% 159.27/108.22 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.22 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.22 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 159.27/108.22 | (574) all_286_2_719 = all_167_1_469
% 159.27/108.22 |
% 159.27/108.22 | Combining equations (437,574) yields a new equation:
% 159.27/108.22 | (575) all_167_1_469 = all_0_1_1
% 159.27/108.22 |
% 159.27/108.22 | From (575) and (565) follows:
% 159.27/108.22 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.22 | (579) all_167_0_468 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (579) can reduce 563 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (455) yields:
% 159.27/108.22 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.22 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.22 | (458) all_286_2_719 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (458) can reduce 456 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (551) ~ (all_254_1_647 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (551) yields:
% 159.27/108.22 | (552) ~ (all_254_1_647 = 0)
% 159.27/108.22 | (553) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 159.27/108.22 |
% 159.27/108.22 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_254_1_647, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.22 | (358) all_254_1_647 = 0
% 159.27/108.22 |
% 159.27/108.22 | Equations (358) can reduce 552 to:
% 159.27/108.22 | (190) $false
% 159.27/108.22 |
% 159.27/108.22 |-The branch is then unsatisfiable
% 159.27/108.22 |-Branch two:
% 159.27/108.22 | (597) ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 159.27/108.22 |
% 159.27/108.22 | Applying alpha-rule on (597) yields:
% 159.27/108.22 | (598) ~ (all_212_0_556 = 0)
% 159.27/108.22 | (599) reverse_line(all_0_3_3) = all_212_1_557
% 159.27/108.23 | (600) unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (431) yields:
% 159.27/108.23 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.23 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 | (435) all_286_0_717 = 0
% 159.27/108.23 | (436) all_286_1_718 = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.23 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 159.27/108.23 | (609) all_286_2_719 = all_212_1_557
% 159.27/108.23 |
% 159.27/108.23 | Combining equations (609,437) yields a new equation:
% 159.27/108.23 | (610) all_212_1_557 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | Simplifying 610 yields:
% 159.27/108.23 | (611) all_212_1_557 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | From (437) and (432) follows:
% 159.27/108.23 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.23 |
% 159.27/108.23 | From (611) and (600) follows:
% 159.27/108.23 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.23 | (614) all_212_0_556 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (614) can reduce 598 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (445) yields:
% 159.27/108.23 | (436) all_286_1_718 = 0
% 159.27/108.23 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.23 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.23 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 159.27/108.23 | (609) all_286_2_719 = all_212_1_557
% 159.27/108.23 |
% 159.27/108.23 | Combining equations (609,437) yields a new equation:
% 159.27/108.23 | (610) all_212_1_557 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | Simplifying 610 yields:
% 159.27/108.23 | (611) all_212_1_557 = all_0_1_1
% 159.27/108.23 |
% 159.27/108.23 | From (611) and (600) follows:
% 159.27/108.23 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.23 | (614) all_212_0_556 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (614) can reduce 598 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (455) yields:
% 159.27/108.23 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.23 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.23 | (458) all_286_2_719 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (458) can reduce 456 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (632) ~ (all_212_1_557 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (632) yields:
% 159.27/108.23 | (633) ~ (all_212_1_557 = 0)
% 159.27/108.23 | (634) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_212_1_557 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (352) all_212_1_557 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (352) can reduce 633 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (637) all_287_1_721 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (637) yields:
% 159.27/108.23 | (348) all_287_1_721 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (302), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (350) (all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (350), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (351) all_212_1_557 = 0 & unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (351) yields:
% 159.27/108.23 | (352) all_212_1_557 = 0
% 159.27/108.23 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (311), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (355) (all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (355), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (356) all_254_0_646 = 0 & all_254_1_647 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (356) yields:
% 159.27/108.23 | (357) all_254_0_646 = 0
% 159.27/108.23 | (358) all_254_1_647 = 0
% 159.27/108.23 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 159.27/108.23 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 159.27/108.23 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 159.27/108.23 |
% 159.27/108.23 | Instantiating (215) with all_709_0_42071 yields:
% 159.27/108.23 | (1211) ~ (all_709_0_42071 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_42071
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (1211) yields:
% 159.27/108.23 | (1212) ~ (all_709_0_42071 = 0)
% 159.27/108.23 | (1213) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_42071
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (55) with all_709_0_42071, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_42071, yields:
% 159.27/108.23 | (1214) all_709_0_42071 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (1214) can reduce 1212 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (367) all_254_1_647 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (367) yields:
% 159.27/108.23 | (358) all_254_1_647 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (299), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (354) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (133) with all_0_1_1, all_291_1_731, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_291_1_731, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.23 | (370) all_291_1_731 = all_76_1_421
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_167_1_469 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (371) all_167_1_469 = 0
% 159.27/108.23 |
% 159.27/108.23 | From (370) and (328) follows:
% 159.27/108.23 | (244) reverse_line(all_0_1_1) = all_76_1_421
% 159.27/108.23 |
% 159.27/108.23 | From (371) and (354) follows:
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (306), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (397) (all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (397), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (398) all_233_1_601 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (398) yields:
% 159.27/108.23 | (399) all_233_1_601 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (305), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (380) (all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0) | (all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (380), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (381) all_232_0_598 = 0 & all_232_1_599 = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0 & unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (381) yields:
% 159.27/108.23 | (382) all_232_0_598 = 0
% 159.27/108.23 | (383) all_232_1_599 = 0
% 159.27/108.23 | (213) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 159.27/108.23 | (214) unequally_directed_lines(all_0_1_1, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (148) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 159.27/108.23 | (215) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 159.27/108.23 |
% 159.27/108.23 | Instantiating (215) with all_709_0_44893 yields:
% 159.27/108.23 | (1235) ~ (all_709_0_44893 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_44893
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (1235) yields:
% 159.27/108.23 | (1236) ~ (all_709_0_44893 = 0)
% 159.27/108.23 | (1237) equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_44893
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (55) with all_709_0_44893, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_709_0_44893, yields:
% 159.27/108.23 | (1238) all_709_0_44893 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (1238) can reduce 1236 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (392) all_232_1_599 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (392) yields:
% 159.27/108.23 | (383) all_232_1_599 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (308), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (395) all_237_0_611 = 0
% 159.27/108.23 |
% 159.27/108.23 | From (395) and (379) follows:
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (310), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (401) (all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.23 |
% 159.27/108.23 +-Applying beta-rule and splitting (401), into two cases.
% 159.27/108.23 |-Branch one:
% 159.27/108.23 | (402) all_253_0_644 = 0 & all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (402) yields:
% 159.27/108.23 | (403) all_253_0_644 = 0
% 159.27/108.23 | (404) all_253_1_645 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 159.27/108.23 |
% 159.27/108.23 | Instantiating (406) with all_910_0_46705 yields:
% 159.27/108.23 | (1252) ~ (all_910_0_46705 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_46705
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (1252) yields:
% 159.27/108.23 | (1253) ~ (all_910_0_46705 = 0)
% 159.27/108.23 | (1254) equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_46705
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (55) with all_910_0_46705, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_46705, yields:
% 159.27/108.23 | (1255) all_910_0_46705 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (1255) can reduce 1253 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (412) all_253_1_645 = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (412) yields:
% 159.27/108.23 | (404) all_253_1_645 = 0
% 159.27/108.23 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (148) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (406) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0)
% 159.27/108.23 |
% 159.27/108.23 | Instantiating (406) with all_910_0_47843 yields:
% 159.27/108.23 | (1261) ~ (all_910_0_47843 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_47843
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (1261) yields:
% 159.27/108.23 | (1262) ~ (all_910_0_47843 = 0)
% 159.27/108.23 | (1263) equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_47843
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (55) with all_910_0_47843, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_910_0_47843, yields:
% 159.27/108.23 | (1264) all_910_0_47843 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (1264) can reduce 1262 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (421) ~ (all_253_1_645 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 159.27/108.23 |
% 159.27/108.23 | Applying alpha-rule on (421) yields:
% 159.27/108.23 | (422) ~ (all_253_1_645 = 0)
% 159.27/108.23 | (423) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645
% 159.27/108.23 |
% 159.27/108.23 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_253_1_645, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_253_1_645, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.23 | (404) all_253_1_645 = 0
% 159.27/108.23 |
% 159.27/108.23 | Equations (404) can reduce 422 to:
% 159.27/108.23 | (190) $false
% 159.27/108.23 |
% 159.27/108.23 |-The branch is then unsatisfiable
% 159.27/108.23 |-Branch two:
% 159.27/108.23 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 159.27/108.23 | (395) all_237_0_611 = 0
% 159.27/108.23 |
% 159.27/108.23 | From (395) and (508) follows:
% 159.27/108.23 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.23 |
% 159.27/108.24 | Using (344) and (510) yields:
% 159.27/108.24 | (511) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (465) ~ (all_232_0_598 = 0) & reverse_line(all_0_1_1) = all_232_1_599 & unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (465) yields:
% 159.27/108.24 | (466) ~ (all_232_0_598 = 0)
% 159.27/108.24 | (467) reverse_line(all_0_1_1) = all_232_1_599
% 159.27/108.24 | (468) unequally_directed_lines(all_0_3_3, all_232_1_599) = all_232_0_598
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (308), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (379) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (312), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (1034) (all_273_0_686 = 0 & all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0) | (all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0)
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (1034), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (1035) all_273_0_686 = 0 & all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (1035) yields:
% 159.27/108.24 | (1036) all_273_0_686 = 0
% 159.27/108.24 | (1037) all_273_1_687 = 0
% 159.27/108.24 | (1038) reverse_line(all_0_1_1) = all_273_2_688
% 159.27/108.24 | (1039) unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_1_1, all_273_2_688, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.24 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_273_2_688 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 159.27/108.24 | (1041) all_273_2_688 = all_232_1_599
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (1040,1041) yields a new equation:
% 159.27/108.24 | (479) all_232_1_599 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (479,1041) yields a new equation:
% 159.27/108.24 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | From (1040) and (1039) follows:
% 159.27/108.24 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 159.27/108.24 |
% 159.27/108.24 | From (479) and (468) follows:
% 159.27/108.24 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 159.27/108.24 | (382) all_232_0_598 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (382) can reduce 466 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (1048) all_273_1_687 = 0 & reverse_line(all_0_1_1) = all_273_2_688 & unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (1048) yields:
% 159.27/108.24 | (1037) all_273_1_687 = 0
% 159.27/108.24 | (1038) reverse_line(all_0_1_1) = all_273_2_688
% 159.27/108.24 | (1039) unequally_directed_lines(all_0_3_3, all_273_2_688) = 0
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_1_1, all_273_2_688, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.27/108.24 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_1_1, all_232_1_599, all_273_2_688 and discharging atoms reverse_line(all_0_1_1) = all_273_2_688, reverse_line(all_0_1_1) = all_232_1_599, yields:
% 159.27/108.24 | (1041) all_273_2_688 = all_232_1_599
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (1040,1041) yields a new equation:
% 159.27/108.24 | (479) all_232_1_599 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (479,1041) yields a new equation:
% 159.27/108.24 | (1040) all_273_2_688 = all_76_1_421
% 159.27/108.24 |
% 159.27/108.24 | From (1040) and (1039) follows:
% 159.27/108.24 | (277) unequally_directed_lines(all_0_3_3, all_76_1_421) = 0
% 159.27/108.24 |
% 159.27/108.24 | From (479) and (468) follows:
% 159.27/108.24 | (482) unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_76_1_421, all_232_0_598, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_76_1_421) = all_232_0_598, unequally_directed_lines(all_0_3_3, all_76_1_421) = 0, yields:
% 159.27/108.24 | (382) all_232_0_598 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (382) can reduce 466 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (1060) ~ (all_273_2_688 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (1060) yields:
% 159.27/108.24 | (1061) ~ (all_273_2_688 = 0)
% 159.27/108.24 | (1062) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_273_2_688, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.24 | (1063) all_273_2_688 = 0
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_237_0_611, all_273_2_688 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_273_2_688, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611, yields:
% 159.27/108.24 | (1064) all_273_2_688 = all_237_0_611
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (1063,1064) yields a new equation:
% 159.27/108.24 | (395) all_237_0_611 = 0
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (395,1064) yields a new equation:
% 159.27/108.24 | (1063) all_273_2_688 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (1063) can reduce 1061 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (508) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_237_0_611)
% 159.27/108.24 | (395) all_237_0_611 = 0
% 159.27/108.24 |
% 159.27/108.24 | From (395) and (508) follows:
% 159.27/108.24 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.24 |
% 159.27/108.24 | Using (344) and (510) yields:
% 159.27/108.24 | (511) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (426) ~ (all_233_0_600 = 0) & reverse_line(all_0_3_3) = all_233_1_601 & unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (426) yields:
% 159.27/108.24 | (427) ~ (all_233_0_600 = 0)
% 159.27/108.24 | (428) reverse_line(all_0_3_3) = all_233_1_601
% 159.27/108.24 | (429) unequally_directed_lines(all_0_3_3, all_233_1_601) = all_233_0_600
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (431) yields:
% 159.27/108.24 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.24 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.24 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.24 | (435) all_286_0_717 = 0
% 159.27/108.24 | (436) all_286_1_718 = 0
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.24 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 159.27/108.24 | (438) all_286_2_719 = all_233_1_601
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (438,437) yields a new equation:
% 159.27/108.24 | (1085) all_233_1_601 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | Simplifying 1085 yields:
% 159.27/108.24 | (439) all_233_1_601 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | From (437) and (432) follows:
% 159.27/108.24 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.24 |
% 159.27/108.24 | From (439) and (429) follows:
% 159.27/108.24 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.24 | (443) all_233_0_600 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (443) can reduce 427 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (445) yields:
% 159.27/108.24 | (436) all_286_1_718 = 0
% 159.27/108.24 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.24 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.24 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (133) with all_0_3_3, all_233_1_601, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_233_1_601, yields:
% 159.27/108.24 | (438) all_286_2_719 = all_233_1_601
% 159.27/108.24 |
% 159.27/108.24 | Combining equations (438,437) yields a new equation:
% 159.27/108.24 | (1085) all_233_1_601 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | Simplifying 1085 yields:
% 159.27/108.24 | (439) all_233_1_601 = all_0_1_1
% 159.27/108.24 |
% 159.27/108.24 | From (439) and (429) follows:
% 159.27/108.24 | (442) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_233_0_600, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_233_0_600, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.24 | (443) all_233_0_600 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (443) can reduce 427 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (455) yields:
% 159.27/108.24 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.24 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.24 | (458) all_286_2_719 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (458) can reduce 456 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (460) ~ (all_233_1_601 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (460) yields:
% 159.27/108.24 | (461) ~ (all_233_1_601 = 0)
% 159.27/108.24 | (462) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601
% 159.27/108.24 |
% 159.27/108.24 | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_233_1_601, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_233_1_601, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.24 | (399) all_233_1_601 = 0
% 159.27/108.24 |
% 159.27/108.24 | Equations (399) can reduce 461 to:
% 159.27/108.24 | (190) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (556) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = all_167_1_469)
% 159.27/108.24 | (557) all_167_1_469 = 0 | ( ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468)
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (557), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (371) all_167_1_469 = 0
% 159.27/108.24 |
% 159.27/108.24 | From (371) and (556) follows:
% 159.27/108.24 | (510) ~ (unequally_directed_lines(all_0_3_3, all_0_3_3) = 0)
% 159.27/108.24 |
% 159.27/108.24 | Using (344) and (510) yields:
% 159.27/108.24 | (511) $false
% 159.27/108.24 |
% 159.27/108.24 |-The branch is then unsatisfiable
% 159.27/108.24 |-Branch two:
% 159.27/108.24 | (561) ~ (all_167_1_469 = 0)
% 159.27/108.24 | (562) ~ (all_167_0_468 = 0) & reverse_line(all_0_3_3) = all_167_1_469 & unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (562) yields:
% 159.27/108.24 | (563) ~ (all_167_0_468 = 0)
% 159.27/108.24 | (564) reverse_line(all_0_3_3) = all_167_1_469
% 159.27/108.24 | (565) unequally_directed_lines(all_0_3_3, all_167_1_469) = all_167_0_468
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.24 |
% 159.27/108.24 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.24 |-Branch one:
% 159.27/108.24 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.24 |
% 159.27/108.24 | Applying alpha-rule on (431) yields:
% 159.27/108.24 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.24 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.24 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.25 | (435) all_286_0_717 = 0
% 159.27/108.25 | (436) all_286_1_718 = 0
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.25 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 159.27/108.25 | (574) all_286_2_719 = all_167_1_469
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (437,574) yields a new equation:
% 159.27/108.25 | (575) all_167_1_469 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (575,574) yields a new equation:
% 159.27/108.25 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | From (437) and (432) follows:
% 159.27/108.25 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.25 |
% 159.27/108.25 | From (575) and (565) follows:
% 159.27/108.25 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.25 | (579) all_167_0_468 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (579) can reduce 563 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (445) yields:
% 159.27/108.25 | (436) all_286_1_718 = 0
% 159.27/108.25 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.25 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.25 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_167_1_469, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_167_1_469, yields:
% 159.27/108.25 | (574) all_286_2_719 = all_167_1_469
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (437,574) yields a new equation:
% 159.27/108.25 | (575) all_167_1_469 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | From (575) and (565) follows:
% 159.27/108.25 | (578) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_167_0_468, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_167_0_468, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.25 | (579) all_167_0_468 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (579) can reduce 563 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (455) yields:
% 159.27/108.25 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.25 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.25 | (458) all_286_2_719 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (458) can reduce 456 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (551) ~ (all_254_1_647 = 0) & unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (551) yields:
% 159.27/108.25 | (552) ~ (all_254_1_647 = 0)
% 159.27/108.25 | (553) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_254_1_647, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_254_1_647, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.25 | (358) all_254_1_647 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (358) can reduce 552 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (597) ~ (all_212_0_556 = 0) & reverse_line(all_0_3_3) = all_212_1_557 & unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (597) yields:
% 159.27/108.25 | (598) ~ (all_212_0_556 = 0)
% 159.27/108.25 | (599) reverse_line(all_0_3_3) = all_212_1_557
% 159.27/108.25 | (600) unequally_directed_lines(all_0_3_3, all_212_1_557) = all_212_0_556
% 159.27/108.25 |
% 159.27/108.25 +-Applying beta-rule and splitting (313), into two cases.
% 159.27/108.25 |-Branch one:
% 159.27/108.25 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.27/108.25 |
% 159.27/108.25 +-Applying beta-rule and splitting (430), into two cases.
% 159.27/108.25 |-Branch one:
% 159.27/108.25 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (431) yields:
% 159.27/108.25 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.27/108.25 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.25 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.25 | (435) all_286_0_717 = 0
% 159.27/108.25 | (436) all_286_1_718 = 0
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.25 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 159.27/108.25 | (609) all_286_2_719 = all_212_1_557
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (609,437) yields a new equation:
% 159.27/108.25 | (610) all_212_1_557 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Simplifying 610 yields:
% 159.27/108.25 | (611) all_212_1_557 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | From (437) and (432) follows:
% 159.27/108.25 | (278) unequally_directed_lines(all_0_3_3, all_0_1_1) = 0
% 159.27/108.25 |
% 159.27/108.25 | From (611) and (600) follows:
% 159.27/108.25 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.25 | (614) all_212_0_556 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (614) can reduce 598 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (445) yields:
% 159.27/108.25 | (436) all_286_1_718 = 0
% 159.27/108.25 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.27/108.25 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.25 | (437) all_286_2_719 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_3_3, all_212_1_557, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_212_1_557, yields:
% 159.27/108.25 | (609) all_286_2_719 = all_212_1_557
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (609,437) yields a new equation:
% 159.27/108.25 | (610) all_212_1_557 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | Simplifying 610 yields:
% 159.27/108.25 | (611) all_212_1_557 = all_0_1_1
% 159.27/108.25 |
% 159.27/108.25 | From (611) and (600) follows:
% 159.27/108.25 | (613) unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_1_1, all_212_0_556, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_1_1) = all_212_0_556, unequally_directed_lines(all_0_3_3, all_0_1_1) = 0, yields:
% 159.27/108.25 | (614) all_212_0_556 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (614) can reduce 598 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (455) yields:
% 159.27/108.25 | (456) ~ (all_286_2_719 = 0)
% 159.27/108.25 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.25 | (458) all_286_2_719 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (458) can reduce 456 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (632) ~ (all_212_1_557 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (632) yields:
% 159.27/108.25 | (633) ~ (all_212_1_557 = 0)
% 159.27/108.25 | (634) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_3_3, all_0_3_3, 0, all_212_1_557 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_212_1_557, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 159.27/108.25 | (352) all_212_1_557 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (352) can reduce 633 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (927) ~ (all_287_1_721 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (927) yields:
% 159.27/108.25 | (928) ~ (all_287_1_721 = 0)
% 159.27/108.25 | (929) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_287_1_721, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_287_1_721, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.25 | (348) all_287_1_721 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (348) can reduce 928 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (1448) all_241_1_619 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (1448) yields:
% 159.27/108.25 | (947) all_241_1_619 = 0
% 159.27/108.25 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.27/108.25 |
% 159.27/108.25 +-Applying beta-rule and splitting (298), into two cases.
% 159.27/108.25 |-Branch one:
% 159.27/108.25 | (1451) all_135_0_449 = 0
% 159.27/108.25 |
% 159.27/108.25 | Equations (1451) can reduce 271 to:
% 159.27/108.25 | (190) $false
% 159.27/108.25 |
% 159.27/108.25 |-The branch is then unsatisfiable
% 159.27/108.25 |-Branch two:
% 159.27/108.25 | (271) ~ (all_135_0_449 = 0)
% 159.27/108.25 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.27/108.25 |
% 159.27/108.25 | Instantiating (1454) with all_388_0_48081 yields:
% 159.27/108.25 | (1455) reverse_line(all_0_4_4) = all_388_0_48081 & unequally_directed_lines(all_0_4_4, all_388_0_48081) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (1455) yields:
% 159.27/108.25 | (1456) reverse_line(all_0_4_4) = all_388_0_48081
% 159.27/108.25 | (1457) unequally_directed_lines(all_0_4_4, all_388_0_48081) = 0
% 159.27/108.25 |
% 159.27/108.25 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.25 |-Branch one:
% 159.27/108.25 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.25 |
% 159.27/108.25 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.25 |-Branch one:
% 159.27/108.25 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.25 |
% 159.27/108.25 | Applying alpha-rule on (1459) yields:
% 159.27/108.25 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.25 | (1461) all_205_0_543 = 0
% 159.27/108.25 | (1462) all_205_1_544 = 0
% 159.27/108.25 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.25 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_4_4, all_205_2_545, all_388_0_48081 and discharging atoms reverse_line(all_0_4_4) = all_388_0_48081, reverse_line(all_0_4_4) = all_205_2_545, yields:
% 159.27/108.25 | (1465) all_388_0_48081 = all_205_2_545
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (133) with all_0_4_4, all_203_2_539, all_388_0_48081 and discharging atoms reverse_line(all_0_4_4) = all_388_0_48081, reverse_line(all_0_4_4) = all_203_2_539, yields:
% 159.27/108.25 | (1466) all_388_0_48081 = all_203_2_539
% 159.27/108.25 |
% 159.27/108.25 | Combining equations (1465,1466) yields a new equation:
% 159.27/108.25 | (1467) all_205_2_545 = all_203_2_539
% 159.27/108.25 |
% 159.27/108.25 | Simplifying 1467 yields:
% 159.27/108.25 | (1468) all_205_2_545 = all_203_2_539
% 159.27/108.25 |
% 159.27/108.25 | From (1468) and (1464) follows:
% 159.27/108.25 | (322) reverse_line(all_0_4_4) = all_203_2_539
% 159.27/108.25 |
% 159.27/108.25 | From (1468) and (1463) follows:
% 159.27/108.25 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (6) with all_350_0_29520, all_0_3_3, all_95_2_434 and discharging atoms right_apart_point(all_95_2_434, all_0_3_3) = all_350_0_29520, yields:
% 159.27/108.25 | (1471) all_350_0_29520 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & left_apart_point(all_95_2_434, v0) = v1 & reverse_line(all_0_3_3) = v0)
% 159.27/108.25 |
% 159.27/108.25 | Instantiating formula (127) with 0, all_203_2_539, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms reverse_line(all_0_4_4) = all_203_2_539, unequally_directed_lines(all_0_3_3, all_203_2_539) = 0, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.25 | (1472) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & reverse_line(all_0_3_3) = v1 & unequally_directed_lines(all_0_3_3, v1) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v1 = 0 & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = v0))
% 159.27/108.25 |
% 159.27/108.25 | Instantiating (1472) with all_497_0_48207, all_497_1_48208, all_497_2_48209 yields:
% 159.27/108.25 | (1473) (all_497_0_48207 = 0 & all_497_2_48209 = 0 & reverse_line(all_0_3_3) = all_497_1_48208 & unequally_directed_lines(all_0_3_3, all_497_1_48208) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_497_1_48208 = 0 & reverse_line(all_0_3_3) = all_497_2_48209 & unequally_directed_lines(all_0_4_4, all_497_2_48209) = 0) | ( ~ (all_497_2_48209 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_497_2_48209)
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (1471), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1474) all_350_0_29520 = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1474) can reduce 940 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (940) ~ (all_350_0_29520 = 0)
% 159.27/108.26 | (1477) ? [v0] : ? [v1] : ( ~ (v1 = 0) & left_apart_point(all_95_2_434, v0) = v1 & reverse_line(all_0_3_3) = v0)
% 159.27/108.26 |
% 159.27/108.26 | Instantiating (1477) with all_768_0_48661, all_768_1_48662 yields:
% 159.27/108.26 | (1478) ~ (all_768_0_48661 = 0) & left_apart_point(all_95_2_434, all_768_1_48662) = all_768_0_48661 & reverse_line(all_0_3_3) = all_768_1_48662
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1478) yields:
% 159.27/108.26 | (1479) ~ (all_768_0_48661 = 0)
% 159.27/108.26 | (1480) left_apart_point(all_95_2_434, all_768_1_48662) = all_768_0_48661
% 159.27/108.26 | (1481) reverse_line(all_0_3_3) = all_768_1_48662
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (133) with all_0_3_3, all_768_1_48662, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_768_1_48662, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.26 | (1482) all_768_1_48662 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | From (1482) and (1481) follows:
% 159.27/108.26 | (112) reverse_line(all_0_3_3) = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (252), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1484) (all_91_0_425 = 0 & left_convergent_lines(all_0_4_4, all_91_1_426) = 0 & reverse_line(all_0_3_3) = all_91_1_426) | (all_91_1_426 = 0 & left_convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (1484), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1485) all_91_0_425 = 0 & left_convergent_lines(all_0_4_4, all_91_1_426) = 0 & reverse_line(all_0_3_3) = all_91_1_426
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1485) yields:
% 159.27/108.26 | (1486) all_91_0_425 = 0
% 159.27/108.26 | (1487) left_convergent_lines(all_0_4_4, all_91_1_426) = 0
% 159.27/108.26 | (1488) reverse_line(all_0_3_3) = all_91_1_426
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (170) with all_91_1_426, all_0_3_3, all_0_4_4 and discharging atoms left_convergent_lines(all_0_4_4, all_91_1_426) = 0, reverse_line(all_0_3_3) = all_91_1_426, yields:
% 159.27/108.26 | (511) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1490) all_91_1_426 = 0 & left_convergent_lines(all_0_4_4, all_0_3_3) = 0
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1490) yields:
% 159.27/108.26 | (1491) all_91_1_426 = 0
% 159.27/108.26 | (1492) left_convergent_lines(all_0_4_4, all_0_3_3) = 0
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (98) with all_0_3_3, all_0_4_4 and discharging atoms left_convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.26 | (511) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1494) ~ (all_91_0_425 = 0) & reverse_line(all_0_3_3) = all_91_1_426 & unequally_directed_lines(all_0_4_4, all_91_1_426) = all_91_0_425
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1494) yields:
% 159.27/108.26 | (1495) ~ (all_91_0_425 = 0)
% 159.27/108.26 | (1488) reverse_line(all_0_3_3) = all_91_1_426
% 159.27/108.26 | (1497) unequally_directed_lines(all_0_4_4, all_91_1_426) = all_91_0_425
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (1473), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1498) (all_497_0_48207 = 0 & all_497_2_48209 = 0 & reverse_line(all_0_3_3) = all_497_1_48208 & unequally_directed_lines(all_0_3_3, all_497_1_48208) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_497_1_48208 = 0 & reverse_line(all_0_3_3) = all_497_2_48209 & unequally_directed_lines(all_0_4_4, all_497_2_48209) = 0)
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (1498), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1499) all_497_0_48207 = 0 & all_497_2_48209 = 0 & reverse_line(all_0_3_3) = all_497_1_48208 & unequally_directed_lines(all_0_3_3, all_497_1_48208) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1499) yields:
% 159.27/108.26 | (1500) all_497_0_48207 = 0
% 159.27/108.26 | (1501) unequally_directed_lines(all_0_3_3, all_497_1_48208) = 0
% 159.27/108.26 | (1502) reverse_line(all_0_3_3) = all_497_1_48208
% 159.27/108.26 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.27/108.26 | (1504) all_497_2_48209 = 0
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (133) with all_0_3_3, all_497_1_48208, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_497_1_48208, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.26 | (1505) all_497_1_48208 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (133) with all_0_3_3, all_91_1_426, all_497_1_48208 and discharging atoms reverse_line(all_0_3_3) = all_497_1_48208, reverse_line(all_0_3_3) = all_91_1_426, yields:
% 159.27/108.26 | (1506) all_497_1_48208 = all_91_1_426
% 159.27/108.26 |
% 159.27/108.26 | Combining equations (1505,1506) yields a new equation:
% 159.27/108.26 | (1507) all_91_1_426 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | From (1507) and (1497) follows:
% 159.27/108.26 | (1508) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_91_0_425
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_91_0_425, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_91_0_425, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.27/108.26 | (1486) all_91_0_425 = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1486) can reduce 1495 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1511) all_497_1_48208 = 0 & reverse_line(all_0_3_3) = all_497_2_48209 & unequally_directed_lines(all_0_4_4, all_497_2_48209) = 0
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1511) yields:
% 159.27/108.26 | (1512) all_497_1_48208 = 0
% 159.27/108.26 | (1513) reverse_line(all_0_3_3) = all_497_2_48209
% 159.27/108.26 | (1514) unequally_directed_lines(all_0_4_4, all_497_2_48209) = 0
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (133) with all_0_3_3, all_497_2_48209, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_497_2_48209, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.27/108.26 | (1515) all_497_2_48209 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (133) with all_0_3_3, all_91_1_426, all_497_2_48209 and discharging atoms reverse_line(all_0_3_3) = all_497_2_48209, reverse_line(all_0_3_3) = all_91_1_426, yields:
% 159.27/108.26 | (1516) all_497_2_48209 = all_91_1_426
% 159.27/108.26 |
% 159.27/108.26 | Combining equations (1515,1516) yields a new equation:
% 159.27/108.26 | (1507) all_91_1_426 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | Combining equations (1507,1516) yields a new equation:
% 159.27/108.26 | (1515) all_497_2_48209 = all_0_1_1
% 159.27/108.26 |
% 159.27/108.26 | From (1515) and (1514) follows:
% 159.27/108.26 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.27/108.26 |
% 159.27/108.26 | From (1507) and (1497) follows:
% 159.27/108.26 | (1508) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_91_0_425
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_91_0_425, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_91_0_425, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.27/108.26 | (1486) all_91_0_425 = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1486) can reduce 1495 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1523) ~ (all_497_2_48209 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_497_2_48209
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1523) yields:
% 159.27/108.26 | (1524) ~ (all_497_2_48209 = 0)
% 159.27/108.26 | (1525) unequally_directed_lines(all_0_3_3, all_0_4_4) = all_497_2_48209
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (8) with all_0_3_3, all_0_4_4, all_497_2_48209, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_4_4) = all_497_2_48209, unequally_directed_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 159.27/108.26 | (1504) all_497_2_48209 = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1504) can reduce 1524 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1528) yields:
% 159.27/108.26 | (1462) all_205_1_544 = 0
% 159.27/108.26 | (1451) all_135_0_449 = 0
% 159.27/108.26 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.26 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1451) can reduce 271 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1534) yields:
% 159.27/108.26 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.26 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.26 |
% 159.27/108.26 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.26 | (1537) all_205_2_545 = 0
% 159.27/108.26 |
% 159.27/108.26 | Equations (1537) can reduce 1535 to:
% 159.27/108.26 | (190) $false
% 159.27/108.26 |
% 159.27/108.26 |-The branch is then unsatisfiable
% 159.27/108.26 |-Branch two:
% 159.27/108.26 | (1539) ~ (all_241_0_618 = 0) & reverse_line(all_0_4_4) = all_241_1_619 & unequally_directed_lines(all_0_3_3, all_241_1_619) = all_241_0_618
% 159.27/108.26 |
% 159.27/108.26 | Applying alpha-rule on (1539) yields:
% 159.27/108.26 | (1540) ~ (all_241_0_618 = 0)
% 159.27/108.26 | (1541) reverse_line(all_0_4_4) = all_241_1_619
% 159.27/108.26 | (1542) unequally_directed_lines(all_0_3_3, all_241_1_619) = all_241_0_618
% 159.27/108.26 |
% 159.27/108.26 +-Applying beta-rule and splitting (298), into two cases.
% 159.27/108.26 |-Branch one:
% 159.27/108.26 | (1451) all_135_0_449 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1451) can reduce 271 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (271) ~ (all_135_0_449 = 0)
% 159.27/108.27 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.27/108.27 |
% 159.27/108.27 | Instantiating (1454) with all_388_0_48667 yields:
% 159.27/108.27 | (1547) reverse_line(all_0_4_4) = all_388_0_48667 & unequally_directed_lines(all_0_4_4, all_388_0_48667) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1547) yields:
% 159.27/108.27 | (1548) reverse_line(all_0_4_4) = all_388_0_48667
% 159.27/108.27 | (1549) unequally_directed_lines(all_0_4_4, all_388_0_48667) = 0
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1459) yields:
% 159.27/108.27 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 | (1461) all_205_0_543 = 0
% 159.27/108.27 | (1462) all_205_1_544 = 0
% 159.27/108.27 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.27 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (133) with all_0_4_4, all_241_1_619, all_388_0_48667 and discharging atoms reverse_line(all_0_4_4) = all_388_0_48667, reverse_line(all_0_4_4) = all_241_1_619, yields:
% 159.27/108.27 | (1557) all_388_0_48667 = all_241_1_619
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (133) with all_0_4_4, all_205_2_545, all_241_1_619 and discharging atoms reverse_line(all_0_4_4) = all_241_1_619, reverse_line(all_0_4_4) = all_205_2_545, yields:
% 159.27/108.27 | (1558) all_241_1_619 = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (133) with all_0_4_4, all_203_2_539, all_388_0_48667 and discharging atoms reverse_line(all_0_4_4) = all_388_0_48667, reverse_line(all_0_4_4) = all_203_2_539, yields:
% 159.27/108.27 | (1559) all_388_0_48667 = all_203_2_539
% 159.27/108.27 |
% 159.27/108.27 | Combining equations (1557,1559) yields a new equation:
% 159.27/108.27 | (1560) all_241_1_619 = all_203_2_539
% 159.27/108.27 |
% 159.27/108.27 | Simplifying 1560 yields:
% 159.27/108.27 | (1561) all_241_1_619 = all_203_2_539
% 159.27/108.27 |
% 159.27/108.27 | Combining equations (1561,1558) yields a new equation:
% 159.27/108.27 | (1468) all_205_2_545 = all_203_2_539
% 159.27/108.27 |
% 159.27/108.27 | Combining equations (1468,1558) yields a new equation:
% 159.27/108.27 | (1561) all_241_1_619 = all_203_2_539
% 159.27/108.27 |
% 159.27/108.27 | From (1561) and (1542) follows:
% 159.27/108.27 | (1564) unequally_directed_lines(all_0_3_3, all_203_2_539) = all_241_0_618
% 159.27/108.27 |
% 159.27/108.27 | From (1468) and (1463) follows:
% 159.27/108.27 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (8) with all_0_3_3, all_203_2_539, all_241_0_618, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_203_2_539) = all_241_0_618, unequally_directed_lines(all_0_3_3, all_203_2_539) = 0, yields:
% 159.27/108.27 | (1566) all_241_0_618 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1566) can reduce 1540 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1528) yields:
% 159.27/108.27 | (1462) all_205_1_544 = 0
% 159.27/108.27 | (1451) all_135_0_449 = 0
% 159.27/108.27 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.27 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1451) can reduce 271 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1534) yields:
% 159.27/108.27 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.27 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.27 | (1537) all_205_2_545 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1537) can reduce 1535 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1579) ~ (all_241_1_619 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_241_1_619
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1579) yields:
% 159.27/108.27 | (1580) ~ (all_241_1_619 = 0)
% 159.27/108.27 | (1581) unequally_directed_lines(all_0_3_3, all_0_4_4) = all_241_1_619
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (298), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1451) all_135_0_449 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1451) can reduce 271 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (271) ~ (all_135_0_449 = 0)
% 159.27/108.27 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1459) yields:
% 159.27/108.27 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 | (1461) all_205_0_543 = 0
% 159.27/108.27 | (1462) all_205_1_544 = 0
% 159.27/108.27 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.27 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (8) with all_0_3_3, all_0_4_4, 0, all_241_1_619 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_4_4) = all_241_1_619, unequally_directed_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 159.27/108.27 | (947) all_241_1_619 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (947) can reduce 1580 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1528) yields:
% 159.27/108.27 | (1462) all_205_1_544 = 0
% 159.27/108.27 | (1451) all_135_0_449 = 0
% 159.27/108.27 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.27 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1451) can reduce 271 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1534) yields:
% 159.27/108.27 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.27 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.27 | (1537) all_205_2_545 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1537) can reduce 1535 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (1606) ~ (all_294_0_737 = 0) & reverse_line(all_0_4_4) = all_294_1_738 & unequally_directed_lines(all_0_3_3, all_294_1_738) = all_294_0_737
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1606) yields:
% 159.27/108.27 | (1607) ~ (all_294_0_737 = 0)
% 159.27/108.27 | (1608) reverse_line(all_0_4_4) = all_294_1_738
% 159.27/108.27 | (1609) unequally_directed_lines(all_0_3_3, all_294_1_738) = all_294_0_737
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 |
% 159.27/108.27 | Applying alpha-rule on (1459) yields:
% 159.27/108.27 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.27 | (1461) all_205_0_543 = 0
% 159.27/108.27 | (1462) all_205_1_544 = 0
% 159.27/108.27 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.27 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.27 |
% 159.27/108.27 +-Applying beta-rule and splitting (298), into two cases.
% 159.27/108.27 |-Branch one:
% 159.27/108.27 | (1451) all_135_0_449 = 0
% 159.27/108.27 |
% 159.27/108.27 | Equations (1451) can reduce 271 to:
% 159.27/108.27 | (190) $false
% 159.27/108.27 |
% 159.27/108.27 |-The branch is then unsatisfiable
% 159.27/108.27 |-Branch two:
% 159.27/108.27 | (271) ~ (all_135_0_449 = 0)
% 159.27/108.28 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.27/108.28 |
% 159.27/108.28 | Instantiating (1454) with all_372_0_48671 yields:
% 159.27/108.28 | (1621) reverse_line(all_0_4_4) = all_372_0_48671 & unequally_directed_lines(all_0_4_4, all_372_0_48671) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1621) yields:
% 159.27/108.28 | (1622) reverse_line(all_0_4_4) = all_372_0_48671
% 159.27/108.28 | (1623) unequally_directed_lines(all_0_4_4, all_372_0_48671) = 0
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_294_1_738, all_372_0_48671 and discharging atoms reverse_line(all_0_4_4) = all_372_0_48671, reverse_line(all_0_4_4) = all_294_1_738, yields:
% 159.27/108.28 | (1624) all_372_0_48671 = all_294_1_738
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_205_2_545, all_294_1_738 and discharging atoms reverse_line(all_0_4_4) = all_294_1_738, reverse_line(all_0_4_4) = all_205_2_545, yields:
% 159.27/108.28 | (1625) all_294_1_738 = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_203_2_539, all_372_0_48671 and discharging atoms reverse_line(all_0_4_4) = all_372_0_48671, reverse_line(all_0_4_4) = all_203_2_539, yields:
% 159.27/108.28 | (1626) all_372_0_48671 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.28 | Combining equations (1624,1626) yields a new equation:
% 159.27/108.28 | (1627) all_294_1_738 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.28 | Simplifying 1627 yields:
% 159.27/108.28 | (1628) all_294_1_738 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.28 | Combining equations (1628,1625) yields a new equation:
% 159.27/108.28 | (1468) all_205_2_545 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.28 | Combining equations (1468,1625) yields a new equation:
% 159.27/108.28 | (1628) all_294_1_738 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.28 | From (1628) and (1609) follows:
% 159.27/108.28 | (1631) unequally_directed_lines(all_0_3_3, all_203_2_539) = all_294_0_737
% 159.27/108.28 |
% 159.27/108.28 | From (1468) and (1463) follows:
% 159.27/108.28 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (8) with all_0_3_3, all_203_2_539, all_294_0_737, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_203_2_539) = all_294_0_737, unequally_directed_lines(all_0_3_3, all_203_2_539) = 0, yields:
% 159.27/108.28 | (1633) all_294_0_737 = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1633) can reduce 1607 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1528) yields:
% 159.27/108.28 | (1462) all_205_1_544 = 0
% 159.27/108.28 | (1451) all_135_0_449 = 0
% 159.27/108.28 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.28 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1451) can reduce 271 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1534) yields:
% 159.27/108.28 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.28 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.28 | (1537) all_205_2_545 = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1537) can reduce 1535 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1646) ~ (all_294_1_738 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_294_1_738
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1646) yields:
% 159.27/108.28 | (1647) ~ (all_294_1_738 = 0)
% 159.27/108.28 | (1648) unequally_directed_lines(all_0_3_3, all_0_4_4) = all_294_1_738
% 159.27/108.28 |
% 159.27/108.28 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.28 |-Branch one:
% 159.27/108.28 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.28 |
% 159.27/108.28 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.28 |-Branch one:
% 159.27/108.28 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1459) yields:
% 159.27/108.28 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.28 | (1461) all_205_0_543 = 0
% 159.27/108.28 | (1462) all_205_1_544 = 0
% 159.27/108.28 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.28 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (8) with all_0_3_3, all_0_4_4, 0, all_294_1_738 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_4_4) = all_294_1_738, unequally_directed_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 159.27/108.28 | (343) all_294_1_738 = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (343) can reduce 1647 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1528) yields:
% 159.27/108.28 | (1462) all_205_1_544 = 0
% 159.27/108.28 | (1451) all_135_0_449 = 0
% 159.27/108.28 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.28 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1451) can reduce 271 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1534) yields:
% 159.27/108.28 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.28 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.28 | (1537) all_205_2_545 = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1537) can reduce 1535 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (1669) ~ (all_213_0_558 = 0) & reverse_line(all_0_4_4) = all_213_1_559 & unequally_directed_lines(all_0_3_3, all_213_1_559) = all_213_0_558
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1669) yields:
% 159.27/108.28 | (1670) ~ (all_213_0_558 = 0)
% 159.27/108.28 | (1671) reverse_line(all_0_4_4) = all_213_1_559
% 159.27/108.28 | (1672) unequally_directed_lines(all_0_3_3, all_213_1_559) = all_213_0_558
% 159.27/108.28 |
% 159.27/108.28 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.28 |-Branch one:
% 159.27/108.28 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.27/108.28 |
% 159.27/108.28 +-Applying beta-rule and splitting (1458), into two cases.
% 159.27/108.28 |-Branch one:
% 159.27/108.28 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1459) yields:
% 159.27/108.28 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.27/108.28 | (1461) all_205_0_543 = 0
% 159.27/108.28 | (1462) all_205_1_544 = 0
% 159.27/108.28 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.27/108.28 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 +-Applying beta-rule and splitting (298), into two cases.
% 159.27/108.28 |-Branch one:
% 159.27/108.28 | (1451) all_135_0_449 = 0
% 159.27/108.28 |
% 159.27/108.28 | Equations (1451) can reduce 271 to:
% 159.27/108.28 | (190) $false
% 159.27/108.28 |
% 159.27/108.28 |-The branch is then unsatisfiable
% 159.27/108.28 |-Branch two:
% 159.27/108.28 | (271) ~ (all_135_0_449 = 0)
% 159.27/108.28 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.27/108.28 |
% 159.27/108.28 | Instantiating (1454) with all_380_0_48679 yields:
% 159.27/108.28 | (1684) reverse_line(all_0_4_4) = all_380_0_48679 & unequally_directed_lines(all_0_4_4, all_380_0_48679) = 0
% 159.27/108.28 |
% 159.27/108.28 | Applying alpha-rule on (1684) yields:
% 159.27/108.28 | (1685) reverse_line(all_0_4_4) = all_380_0_48679
% 159.27/108.28 | (1686) unequally_directed_lines(all_0_4_4, all_380_0_48679) = 0
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_213_1_559, all_380_0_48679 and discharging atoms reverse_line(all_0_4_4) = all_380_0_48679, reverse_line(all_0_4_4) = all_213_1_559, yields:
% 159.27/108.28 | (1687) all_380_0_48679 = all_213_1_559
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_205_2_545, all_213_1_559 and discharging atoms reverse_line(all_0_4_4) = all_213_1_559, reverse_line(all_0_4_4) = all_205_2_545, yields:
% 159.27/108.28 | (1688) all_213_1_559 = all_205_2_545
% 159.27/108.28 |
% 159.27/108.28 | Instantiating formula (133) with all_0_4_4, all_203_2_539, all_380_0_48679 and discharging atoms reverse_line(all_0_4_4) = all_380_0_48679, reverse_line(all_0_4_4) = all_203_2_539, yields:
% 159.27/108.28 | (1689) all_380_0_48679 = all_203_2_539
% 159.27/108.28 |
% 159.27/108.29 | Combining equations (1687,1689) yields a new equation:
% 159.27/108.29 | (1690) all_213_1_559 = all_203_2_539
% 159.27/108.29 |
% 159.27/108.29 | Simplifying 1690 yields:
% 159.27/108.29 | (1691) all_213_1_559 = all_203_2_539
% 159.27/108.29 |
% 159.27/108.29 | Combining equations (1688,1691) yields a new equation:
% 159.27/108.29 | (1467) all_205_2_545 = all_203_2_539
% 159.27/108.29 |
% 159.27/108.29 | Simplifying 1467 yields:
% 159.27/108.29 | (1468) all_205_2_545 = all_203_2_539
% 159.27/108.29 |
% 159.27/108.29 | From (1691) and (1672) follows:
% 159.27/108.29 | (1694) unequally_directed_lines(all_0_3_3, all_203_2_539) = all_213_0_558
% 159.27/108.29 |
% 159.27/108.29 | From (1468) and (1463) follows:
% 159.27/108.29 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 159.27/108.29 |
% 159.27/108.29 | Instantiating formula (8) with all_0_3_3, all_203_2_539, all_213_0_558, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_203_2_539) = all_213_0_558, unequally_directed_lines(all_0_3_3, all_203_2_539) = 0, yields:
% 159.27/108.29 | (1696) all_213_0_558 = 0
% 159.27/108.29 |
% 159.27/108.29 | Equations (1696) can reduce 1670 to:
% 159.27/108.29 | (190) $false
% 159.27/108.29 |
% 159.27/108.29 |-The branch is then unsatisfiable
% 159.27/108.29 |-Branch two:
% 159.27/108.29 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.29 |
% 159.27/108.29 | Applying alpha-rule on (1528) yields:
% 159.27/108.29 | (1462) all_205_1_544 = 0
% 159.27/108.29 | (1451) all_135_0_449 = 0
% 159.27/108.29 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.27/108.29 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.27/108.29 |
% 159.27/108.29 | Equations (1451) can reduce 271 to:
% 159.27/108.29 | (190) $false
% 159.27/108.29 |
% 159.27/108.29 |-The branch is then unsatisfiable
% 159.27/108.29 |-Branch two:
% 159.27/108.29 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.29 |
% 159.27/108.29 | Applying alpha-rule on (1534) yields:
% 159.27/108.29 | (1535) ~ (all_205_2_545 = 0)
% 159.27/108.29 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.27/108.29 |
% 159.27/108.29 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.27/108.29 | (1537) all_205_2_545 = 0
% 159.27/108.29 |
% 159.27/108.29 | Equations (1537) can reduce 1535 to:
% 159.27/108.29 | (190) $false
% 159.27/108.29 |
% 159.27/108.29 |-The branch is then unsatisfiable
% 159.27/108.29 |-Branch two:
% 159.27/108.29 | (1709) ~ (all_213_1_559 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_213_1_559
% 159.27/108.29 |
% 159.27/108.29 | Applying alpha-rule on (1709) yields:
% 159.27/108.29 | (1710) ~ (all_213_1_559 = 0)
% 159.27/108.29 | (1711) unequally_directed_lines(all_0_3_3, all_0_4_4) = all_213_1_559
% 159.27/108.29 |
% 159.27/108.29 +-Applying beta-rule and splitting (301), into two cases.
% 159.27/108.29 |-Branch one:
% 159.27/108.29 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.65/108.29 |
% 159.65/108.29 +-Applying beta-rule and splitting (1458), into two cases.
% 159.65/108.29 |-Branch one:
% 159.65/108.29 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1459) yields:
% 159.65/108.29 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.29 | (1461) all_205_0_543 = 0
% 159.65/108.29 | (1462) all_205_1_544 = 0
% 159.65/108.29 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.65/108.29 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (8) with all_0_3_3, all_0_4_4, 0, all_213_1_559 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_4_4) = all_213_1_559, unequally_directed_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 159.65/108.29 | (333) all_213_1_559 = 0
% 159.65/108.29 |
% 159.65/108.29 | Equations (333) can reduce 1710 to:
% 159.65/108.29 | (190) $false
% 159.65/108.29 |
% 159.65/108.29 |-The branch is then unsatisfiable
% 159.65/108.29 |-Branch two:
% 159.65/108.29 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1528) yields:
% 159.65/108.29 | (1462) all_205_1_544 = 0
% 159.65/108.29 | (1451) all_135_0_449 = 0
% 159.65/108.29 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.29 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.29 |
% 159.65/108.29 | Equations (1451) can reduce 271 to:
% 159.65/108.29 | (190) $false
% 159.65/108.29 |
% 159.65/108.29 |-The branch is then unsatisfiable
% 159.65/108.29 |-Branch two:
% 159.65/108.29 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1534) yields:
% 159.65/108.29 | (1535) ~ (all_205_2_545 = 0)
% 159.65/108.29 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.65/108.29 | (1537) all_205_2_545 = 0
% 159.65/108.29 |
% 159.65/108.29 | Equations (1537) can reduce 1535 to:
% 159.65/108.29 | (190) $false
% 159.65/108.29 |
% 159.65/108.29 |-The branch is then unsatisfiable
% 159.65/108.29 |-Branch two:
% 159.65/108.29 | (1732) all_291_0_730 = 0 & reverse_line(all_0_1_1) = all_291_1_731 & unequally_directed_lines(all_0_4_4, all_291_1_731) = 0
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1732) yields:
% 159.65/108.29 | (327) all_291_0_730 = 0
% 159.65/108.29 | (328) reverse_line(all_0_1_1) = all_291_1_731
% 159.65/108.29 | (1735) unequally_directed_lines(all_0_4_4, all_291_1_731) = 0
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (133) with all_0_1_1, all_291_1_731, all_76_1_421 and discharging atoms reverse_line(all_0_1_1) = all_291_1_731, reverse_line(all_0_1_1) = all_76_1_421, yields:
% 159.65/108.29 | (370) all_291_1_731 = all_76_1_421
% 159.65/108.29 |
% 159.65/108.29 | From (370) and (1735) follows:
% 159.65/108.29 | (1737) unequally_directed_lines(all_0_4_4, all_76_1_421) = 0
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (8) with all_0_4_4, all_76_1_421, 0, all_76_0_420 and discharging atoms unequally_directed_lines(all_0_4_4, all_76_1_421) = all_76_0_420, unequally_directed_lines(all_0_4_4, all_76_1_421) = 0, yields:
% 159.65/108.29 | (255) all_76_0_420 = 0
% 159.65/108.29 |
% 159.65/108.29 | Equations (255) can reduce 243 to:
% 159.65/108.29 | (190) $false
% 159.65/108.29 |
% 159.65/108.29 |-The branch is then unsatisfiable
% 159.65/108.29 |-Branch two:
% 159.65/108.29 | (1740) ~ (all_291_0_730 = 0) & reverse_line(all_0_4_4) = all_291_1_731 & unequally_directed_lines(all_0_3_3, all_291_1_731) = all_291_0_730
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1740) yields:
% 159.65/108.29 | (1741) ~ (all_291_0_730 = 0)
% 159.65/108.29 | (1742) reverse_line(all_0_4_4) = all_291_1_731
% 159.65/108.29 | (1743) unequally_directed_lines(all_0_3_3, all_291_1_731) = all_291_0_730
% 159.65/108.29 |
% 159.65/108.29 +-Applying beta-rule and splitting (298), into two cases.
% 159.65/108.29 |-Branch one:
% 159.65/108.29 | (1451) all_135_0_449 = 0
% 159.65/108.29 |
% 159.65/108.29 | Equations (1451) can reduce 271 to:
% 159.65/108.29 | (190) $false
% 159.65/108.29 |
% 159.65/108.29 |-The branch is then unsatisfiable
% 159.65/108.29 |-Branch two:
% 159.65/108.29 | (271) ~ (all_135_0_449 = 0)
% 159.65/108.29 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.65/108.29 |
% 159.65/108.29 | Instantiating (1454) with all_364_0_48690 yields:
% 159.65/108.29 | (1748) reverse_line(all_0_4_4) = all_364_0_48690 & unequally_directed_lines(all_0_4_4, all_364_0_48690) = 0
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1748) yields:
% 159.65/108.29 | (1749) reverse_line(all_0_4_4) = all_364_0_48690
% 159.65/108.29 | (1750) unequally_directed_lines(all_0_4_4, all_364_0_48690) = 0
% 159.65/108.29 |
% 159.65/108.29 +-Applying beta-rule and splitting (301), into two cases.
% 159.65/108.29 |-Branch one:
% 159.65/108.29 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.65/108.29 |
% 159.65/108.29 +-Applying beta-rule and splitting (1458), into two cases.
% 159.65/108.29 |-Branch one:
% 159.65/108.29 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.29 |
% 159.65/108.29 | Applying alpha-rule on (1459) yields:
% 159.65/108.29 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.29 | (1461) all_205_0_543 = 0
% 159.65/108.29 | (1462) all_205_1_544 = 0
% 159.65/108.29 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.65/108.29 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (133) with all_0_4_4, all_291_1_731, all_364_0_48690 and discharging atoms reverse_line(all_0_4_4) = all_364_0_48690, reverse_line(all_0_4_4) = all_291_1_731, yields:
% 159.65/108.29 | (1758) all_364_0_48690 = all_291_1_731
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (133) with all_0_4_4, all_205_2_545, all_291_1_731 and discharging atoms reverse_line(all_0_4_4) = all_291_1_731, reverse_line(all_0_4_4) = all_205_2_545, yields:
% 159.65/108.29 | (1759) all_291_1_731 = all_205_2_545
% 159.65/108.29 |
% 159.65/108.29 | Instantiating formula (133) with all_0_4_4, all_203_2_539, all_364_0_48690 and discharging atoms reverse_line(all_0_4_4) = all_364_0_48690, reverse_line(all_0_4_4) = all_203_2_539, yields:
% 159.65/108.30 | (1760) all_364_0_48690 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | Combining equations (1758,1760) yields a new equation:
% 159.65/108.30 | (1761) all_291_1_731 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | Simplifying 1761 yields:
% 159.65/108.30 | (1762) all_291_1_731 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | Combining equations (1762,1759) yields a new equation:
% 159.65/108.30 | (1468) all_205_2_545 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | Combining equations (1468,1759) yields a new equation:
% 159.65/108.30 | (1762) all_291_1_731 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | From (1762) and (1743) follows:
% 159.65/108.30 | (1765) unequally_directed_lines(all_0_3_3, all_203_2_539) = all_291_0_730
% 159.65/108.30 |
% 159.65/108.30 | From (1468) and (1463) follows:
% 159.65/108.30 | (320) unequally_directed_lines(all_0_3_3, all_203_2_539) = 0
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (8) with all_0_3_3, all_203_2_539, all_291_0_730, 0 and discharging atoms unequally_directed_lines(all_0_3_3, all_203_2_539) = all_291_0_730, unequally_directed_lines(all_0_3_3, all_203_2_539) = 0, yields:
% 159.65/108.30 | (327) all_291_0_730 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (327) can reduce 1741 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1528) yields:
% 159.65/108.30 | (1462) all_205_1_544 = 0
% 159.65/108.30 | (1451) all_135_0_449 = 0
% 159.65/108.30 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.30 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1451) can reduce 271 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1534) yields:
% 159.65/108.30 | (1535) ~ (all_205_2_545 = 0)
% 159.65/108.30 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.65/108.30 | (1537) all_205_2_545 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1537) can reduce 1535 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1780) ~ (all_291_1_731 = 0) & unequally_directed_lines(all_0_3_3, all_0_4_4) = all_291_1_731
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1780) yields:
% 159.65/108.30 | (1781) ~ (all_291_1_731 = 0)
% 159.65/108.30 | (1782) unequally_directed_lines(all_0_3_3, all_0_4_4) = all_291_1_731
% 159.65/108.30 |
% 159.65/108.30 +-Applying beta-rule and splitting (298), into two cases.
% 159.65/108.30 |-Branch one:
% 159.65/108.30 | (1451) all_135_0_449 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1451) can reduce 271 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (271) ~ (all_135_0_449 = 0)
% 159.65/108.30 | (1454) ? [v0] : (reverse_line(all_0_4_4) = v0 & unequally_directed_lines(all_0_4_4, v0) = 0)
% 159.65/108.30 |
% 159.65/108.30 +-Applying beta-rule and splitting (301), into two cases.
% 159.65/108.30 |-Branch one:
% 159.65/108.30 | (1458) (all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0) | (all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0)
% 159.65/108.30 |
% 159.65/108.30 +-Applying beta-rule and splitting (1458), into two cases.
% 159.65/108.30 |-Branch one:
% 159.65/108.30 | (1459) all_205_0_543 = 0 & all_205_1_544 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_3_3, all_205_2_545) = 0 & unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1459) yields:
% 159.65/108.30 | (319) unequally_directed_lines(all_0_3_3, all_0_4_4) = 0
% 159.65/108.30 | (1461) all_205_0_543 = 0
% 159.65/108.30 | (1462) all_205_1_544 = 0
% 159.65/108.30 | (1463) unequally_directed_lines(all_0_3_3, all_205_2_545) = 0
% 159.65/108.30 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (8) with all_0_3_3, all_0_4_4, 0, all_291_1_731 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_4_4) = all_291_1_731, unequally_directed_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 159.65/108.30 | (1794) all_291_1_731 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1794) can reduce 1781 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1528) all_205_1_544 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_205_2_545 & unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1528) yields:
% 159.65/108.30 | (1462) all_205_1_544 = 0
% 159.65/108.30 | (1451) all_135_0_449 = 0
% 159.65/108.30 | (1464) reverse_line(all_0_4_4) = all_205_2_545
% 159.65/108.30 | (1532) unequally_directed_lines(all_0_4_4, all_205_2_545) = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1451) can reduce 271 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1534) ~ (all_205_2_545 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1534) yields:
% 159.65/108.30 | (1535) ~ (all_205_2_545 = 0)
% 159.65/108.30 | (1536) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_205_2_545, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_205_2_545, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.65/108.30 | (1537) all_205_2_545 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1537) can reduce 1535 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1807) all_203_1_538 = 0 & all_135_0_449 = 0 & reverse_line(all_0_4_4) = all_203_2_539 & unequally_directed_lines(all_0_4_4, all_203_2_539) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1807) yields:
% 159.65/108.30 | (321) all_203_1_538 = 0
% 159.65/108.30 | (1451) all_135_0_449 = 0
% 159.65/108.30 | (322) reverse_line(all_0_4_4) = all_203_2_539
% 159.65/108.30 | (1811) unequally_directed_lines(all_0_4_4, all_203_2_539) = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (1451) can reduce 271 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (1813) ~ (all_203_1_538 = 0) & reverse_line(all_0_3_3) = all_203_2_539 & unequally_directed_lines(all_0_4_4, all_203_2_539) = all_203_1_538
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (1813) yields:
% 159.65/108.30 | (1814) ~ (all_203_1_538 = 0)
% 159.65/108.30 | (1815) reverse_line(all_0_3_3) = all_203_2_539
% 159.65/108.30 | (1816) unequally_directed_lines(all_0_4_4, all_203_2_539) = all_203_1_538
% 159.65/108.30 |
% 159.65/108.30 +-Applying beta-rule and splitting (313), into two cases.
% 159.65/108.30 |-Branch one:
% 159.65/108.30 | (430) (all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0)
% 159.65/108.30 |
% 159.65/108.30 +-Applying beta-rule and splitting (430), into two cases.
% 159.65/108.30 |-Branch one:
% 159.65/108.30 | (431) all_286_0_717 = 0 & all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_3_3, all_286_2_719) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (431) yields:
% 159.65/108.30 | (432) unequally_directed_lines(all_0_3_3, all_286_2_719) = 0
% 159.65/108.30 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.65/108.30 | (344) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0
% 159.65/108.30 | (435) all_286_0_717 = 0
% 159.65/108.30 | (436) all_286_1_718 = 0
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.65/108.30 | (437) all_286_2_719 = all_0_1_1
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (133) with all_0_3_3, all_203_2_539, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_203_2_539, yields:
% 159.65/108.30 | (1825) all_286_2_719 = all_203_2_539
% 159.65/108.30 |
% 159.65/108.30 | Combining equations (437,1825) yields a new equation:
% 159.65/108.30 | (1826) all_203_2_539 = all_0_1_1
% 159.65/108.30 |
% 159.65/108.30 | From (1826) and (1816) follows:
% 159.65/108.30 | (1827) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_203_1_538
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_203_1_538, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_203_1_538, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.65/108.30 | (321) all_203_1_538 = 0
% 159.65/108.30 |
% 159.65/108.30 | Equations (321) can reduce 1814 to:
% 159.65/108.30 | (190) $false
% 159.65/108.30 |
% 159.65/108.30 |-The branch is then unsatisfiable
% 159.65/108.30 |-Branch two:
% 159.65/108.30 | (445) all_286_1_718 = 0 & reverse_line(all_0_3_3) = all_286_2_719 & unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.65/108.30 |
% 159.65/108.30 | Applying alpha-rule on (445) yields:
% 159.65/108.30 | (436) all_286_1_718 = 0
% 159.65/108.30 | (433) reverse_line(all_0_3_3) = all_286_2_719
% 159.65/108.30 | (448) unequally_directed_lines(all_0_4_4, all_286_2_719) = 0
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (133) with all_0_3_3, all_286_2_719, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.65/108.30 | (437) all_286_2_719 = all_0_1_1
% 159.65/108.30 |
% 159.65/108.30 | Instantiating formula (133) with all_0_3_3, all_203_2_539, all_286_2_719 and discharging atoms reverse_line(all_0_3_3) = all_286_2_719, reverse_line(all_0_3_3) = all_203_2_539, yields:
% 159.65/108.31 | (1825) all_286_2_719 = all_203_2_539
% 159.65/108.31 |
% 159.65/108.31 | Combining equations (1825,437) yields a new equation:
% 159.65/108.31 | (1836) all_203_2_539 = all_0_1_1
% 159.65/108.31 |
% 159.65/108.31 | Simplifying 1836 yields:
% 159.65/108.31 | (1826) all_203_2_539 = all_0_1_1
% 159.65/108.31 |
% 159.65/108.31 | From (437) and (448) follows:
% 159.65/108.31 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.65/108.31 |
% 159.65/108.31 | From (1826) and (1816) follows:
% 159.65/108.31 | (1827) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_203_1_538
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_203_1_538, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_203_1_538, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.65/108.31 | (321) all_203_1_538 = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (321) can reduce 1814 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 |-Branch two:
% 159.65/108.31 | (455) ~ (all_286_2_719 = 0) & unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.65/108.31 |
% 159.65/108.31 | Applying alpha-rule on (455) yields:
% 159.65/108.31 | (456) ~ (all_286_2_719 = 0)
% 159.65/108.31 | (457) unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_286_2_719, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_3_3) = all_286_2_719, unequally_directed_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 159.65/108.31 | (458) all_286_2_719 = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (458) can reduce 456 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 |-Branch two:
% 159.65/108.31 | (1847) all_92_1_428 = 0 & all_76_0_420 = 0 & unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.65/108.31 |
% 159.65/108.31 | Applying alpha-rule on (1847) yields:
% 159.65/108.31 | (276) all_92_1_428 = 0
% 159.65/108.31 | (255) all_76_0_420 = 0
% 159.65/108.31 | (202) unequally_directed_lines(all_0_4_4, all_0_1_1) = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (255) can reduce 243 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 |-Branch two:
% 159.65/108.31 | (1852) ~ (all_92_0_427 = 0) & reverse_line(all_0_3_3) = all_92_1_428 & unequally_directed_lines(all_0_4_4, all_92_1_428) = all_92_0_427
% 159.65/108.31 |
% 159.65/108.31 | Applying alpha-rule on (1852) yields:
% 159.65/108.31 | (1853) ~ (all_92_0_427 = 0)
% 159.65/108.31 | (1854) reverse_line(all_0_3_3) = all_92_1_428
% 159.65/108.31 | (1855) unequally_directed_lines(all_0_4_4, all_92_1_428) = all_92_0_427
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (133) with all_0_3_3, all_92_1_428, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_92_1_428, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.65/108.31 | (1856) all_92_1_428 = all_0_1_1
% 159.65/108.31 |
% 159.65/108.31 | From (1856) and (1855) follows:
% 159.65/108.31 | (1857) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_92_0_427
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_92_0_427, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_92_0_427, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.65/108.31 | (275) all_92_0_427 = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (275) can reduce 1853 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 |-Branch two:
% 159.65/108.31 | (1860) ~ (all_95_1_433 = 0) & reverse_line(all_0_3_3) = all_95_2_434 & unequally_directed_lines(all_0_4_4, all_95_2_434) = all_95_1_433
% 159.65/108.31 |
% 159.65/108.31 | Applying alpha-rule on (1860) yields:
% 159.65/108.31 | (262) ~ (all_95_1_433 = 0)
% 159.65/108.31 | (1862) reverse_line(all_0_3_3) = all_95_2_434
% 159.65/108.31 | (1863) unequally_directed_lines(all_0_4_4, all_95_2_434) = all_95_1_433
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (133) with all_0_3_3, all_95_2_434, all_0_1_1 and discharging atoms reverse_line(all_0_3_3) = all_95_2_434, reverse_line(all_0_3_3) = all_0_1_1, yields:
% 159.65/108.31 | (1864) all_95_2_434 = all_0_1_1
% 159.65/108.31 |
% 159.65/108.31 | From (1864) and (1863) follows:
% 159.65/108.31 | (1865) unequally_directed_lines(all_0_4_4, all_0_1_1) = all_95_1_433
% 159.65/108.31 |
% 159.65/108.31 | Instantiating formula (8) with all_0_4_4, all_0_1_1, all_95_1_433, 0 and discharging atoms unequally_directed_lines(all_0_4_4, all_0_1_1) = all_95_1_433, unequally_directed_lines(all_0_4_4, all_0_1_1) = 0, yields:
% 159.65/108.31 | (1866) all_95_1_433 = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (1866) can reduce 262 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 |-Branch two:
% 159.65/108.31 | (1868) ~ (unequally_directed_lines(all_0_4_4, all_0_1_1) = 0)
% 159.65/108.31 | (255) all_76_0_420 = 0
% 159.65/108.31 |
% 159.65/108.31 | Equations (255) can reduce 243 to:
% 159.65/108.31 | (190) $false
% 159.65/108.31 |
% 159.65/108.31 |-The branch is then unsatisfiable
% 159.65/108.31 % SZS output end Proof for theBenchmark
% 159.65/108.31
% 159.65/108.31 107691ms
%------------------------------------------------------------------------------