TSTP Solution File: GEO177+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:13 EDT 2022
% Result : Theorem 17.01s 4.63s
% Output : Proof 34.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 03:48:19 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.61/0.59 ____ _
% 0.61/0.59 ___ / __ \_____(_)___ ________ __________
% 0.61/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.59
% 0.61/0.59 A Theorem Prover for First-Order Logic
% 0.61/0.59 (ePrincess v.1.0)
% 0.61/0.59
% 0.61/0.59 (c) Philipp Rümmer, 2009-2015
% 0.61/0.59 (c) Peter Backeman, 2014-2015
% 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.59 Bug reports to peter@backeman.se
% 0.61/0.59
% 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.59
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.93/1.02 Prover 0: Preprocessing ...
% 2.54/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.54/1.27 Prover 0: Constructing countermodel ...
% 14.27/4.05 Prover 0: gave up
% 14.27/4.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.62/4.09 Prover 1: Preprocessing ...
% 15.21/4.22 Prover 1: Constructing countermodel ...
% 15.31/4.26 Prover 1: gave up
% 15.31/4.26 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.31/4.29 Prover 2: Preprocessing ...
% 16.06/4.45 Prover 2: Warning: ignoring some quantifiers
% 16.06/4.46 Prover 2: Constructing countermodel ...
% 17.01/4.63 Prover 2: proved (374ms)
% 17.01/4.63
% 17.01/4.63 No countermodel exists, formula is valid
% 17.01/4.63 % SZS status Theorem for theBenchmark
% 17.01/4.63
% 17.01/4.63 Generating proof ... Warning: ignoring some quantifiers
% 33.35/9.05 found it (size 1025)
% 33.35/9.05
% 33.35/9.05 % SZS output start Proof for theBenchmark
% 33.35/9.05 Assumed formulas after preprocessing and simplification:
% 33.35/9.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (unorthogonal_lines(v12, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = 0) | ? [v16] : ((v16 = 0 & unorthogonal_lines(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v11) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (unorthogonal_lines(v12, v13) = v15) | ~ (apart_point_and_line(v10, v11) = v14) | ? [v16] : ((v16 = 0 & unorthogonal_lines(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v11, v12) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (unorthogonal_lines(v11, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ? [v16] : ((v16 = 0 & unorthogonal_lines(v12, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v11) = 0) | ( ~ (v16 = 0) & distinct_lines(v11, v12) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (unorthogonal_lines(v11, v13) = v15) | ~ (apart_point_and_line(v10, v11) = v14) | ~ (distinct_lines(v11, v12) = 0) | ? [v16] : ((v16 = 0 & unorthogonal_lines(v12, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v11, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v10, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v13) = v14) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v11, v12) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v12, v13) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v14 = 0 | ~ (apart_point_and_line(v10, v13) = v15) | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_points(v10, v11) = 0) | ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v11, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (unorthogonal_lines(v10, v12) = v14) | ~ (unorthogonal_lines(v10, v11) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v11, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v12, v11) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v14) | ~ (apart_point_and_line(v10, v11) = v13) | ? [v15] : ((v15 = 0 & convergent_lines(v11, v12) = 0) | ( ~ (v15 = 0) & distinct_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (convergent_lines(v11, v12) = v14) | ? [v15] : ((v15 = 0 & apart_point_and_line(v10, v11) = 0) | ( ~ (v15 = 0) & distinct_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (apart_point_and_line(v10, v11) = v13) | ~ (convergent_lines(v11, v12) = v14) | ? [v15] : ((v15 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v15 = 0) & distinct_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (convergent_lines(v10, v12) = v14) | ~ (distinct_lines(v11, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_lines(v11, v12) = v14) | ~ (distinct_lines(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_lines(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = 0 | ~ (distinct_points(v11, v12) = v14) | ~ (distinct_points(v10, v12) = v13) | ? [v15] : ( ~ (v15 = 0) & distinct_points(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v11, v12) = v14) | ~ (unorthogonal_lines(v10, v12) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & convergent_lines(v11, v12) = 0) | (v15 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v10, v11) = v15) | ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & convergent_lines(v11, v12) = 0) | (v15 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v10, v11) = v15) | ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v10, v12) = v14) | ~ (unorthogonal_lines(v10, v11) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & convergent_lines(v10, v12) = 0) | (v15 = 0 & v13 = 0 & convergent_lines(v10, v11) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v11, v12) = v15) | ( ~ (v15 = 0) & convergent_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v10, v12) = v14) | ~ (convergent_lines(v10, v11) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & convergent_lines(v10, v12) = 0) | (v15 = 0 & v13 = 0 & unorthogonal_lines(v10, v11) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v11, v12) = v15) | ( ~ (v15 = 0) & convergent_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v10, v12) = v13) | ~ (convergent_lines(v11, v12) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0) | (v15 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v10, v11) = v15) | ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unorthogonal_lines(v10, v11) = v13) | ~ (convergent_lines(v10, v12) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0) | (v15 = 0 & v13 = 0 & convergent_lines(v10, v11) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v11, v12) = v15) | ( ~ (v15 = 0) & convergent_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (convergent_lines(v11, v12) = v14) | ~ (convergent_lines(v10, v12) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0) | (v15 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v10, v11) = v15) | ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (convergent_lines(v10, v12) = v14) | ~ (convergent_lines(v10, v11) = v13) | ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0) | (v15 = 0 & v13 = 0 & unorthogonal_lines(v10, v11) = 0) | ( ~ (v15 = 0) & unorthogonal_lines(v11, v12) = v15) | ( ~ (v15 = 0) & convergent_lines(v11, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unorthogonal_lines(v10, v12) = v13) | ~ (convergent_lines(v11, v12) = 0) | unorthogonal_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unorthogonal_lines(v10, v11) = v13) | ~ (convergent_lines(v11, v12) = 0) | unorthogonal_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v12, v11) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (apart_point_and_line(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v12) = v13) | ~ (distinct_lines(v11, v12) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v10, v11) = 0) | (v14 = 0 & convergent_lines(v11, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = v13) | ~ (distinct_lines(v11, v12) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v10, v12) = 0) | (v14 = 0 & convergent_lines(v11, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | apart_point_and_line(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (apart_point_and_line(v10, v11) = 0) | ~ (distinct_points(v10, v12) = v13) | apart_point_and_line(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (convergent_lines(v10, v11) = 0) | ~ (distinct_lines(v11, v12) = v13) | convergent_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v11, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_lines(v10, v12) = v13) | ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v11, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (distinct_points(v10, v12) = v13) | ~ (distinct_points(v10, v11) = 0) | distinct_points(v11, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (orthogonal_lines(v13, v12) = v11) | ~ (orthogonal_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (incident_point_and_line(v13, v12) = v11) | ~ (incident_point_and_line(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (parallel_lines(v13, v12) = v11) | ~ (parallel_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (equal_lines(v13, v12) = v11) | ~ (equal_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (equal_points(v13, v12) = v11) | ~ (equal_points(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (orthogonal_through_point(v13, v12) = v11) | ~ (orthogonal_through_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unorthogonal_lines(v13, v12) = v11) | ~ (unorthogonal_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (parallel_through_point(v13, v12) = v11) | ~ (parallel_through_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection_point(v13, v12) = v11) | ~ (intersection_point(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (line_connecting(v13, v12) = v11) | ~ (line_connecting(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (apart_point_and_line(v13, v12) = v11) | ~ (apart_point_and_line(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (convergent_lines(v13, v12) = v11) | ~ (convergent_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_lines(v13, v12) = v11) | ~ (distinct_lines(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (distinct_points(v13, v12) = v11) | ~ (distinct_points(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = v13) | ~ (unorthogonal_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v11, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v11, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = 0) | ~ (unorthogonal_lines(v10, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v11) = 0 & convergent_lines(v10, v11) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = 0) | ~ (unorthogonal_lines(v10, v11) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v11) = 0) | ( ~ (v14 = 0) & convergent_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = 0) | ~ (convergent_lines(v10, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v11) = 0 & convergent_lines(v10, v11) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v11, v12) = 0) | ~ (convergent_lines(v10, v11) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v11) = 0) | ( ~ (v14 = 0) & convergent_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v12) = v13) | ~ (unorthogonal_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0 & convergent_lines(v11, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v12) = v13) | ~ (convergent_lines(v11, v12) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v11) = 0 & convergent_lines(v10, v11) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0 & convergent_lines(v11, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v11) = v13) | ~ (convergent_lines(v11, v12) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & convergent_lines(v10, v11) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v11) = 0) | ~ (convergent_lines(v11, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v11, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unorthogonal_lines(v10, v11) = 0) | ~ (convergent_lines(v10, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0 & convergent_lines(v11, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v14 = 0) & convergent_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (convergent_lines(v11, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v11, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (convergent_lines(v11, v12) = 0) | ~ (convergent_lines(v10, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v11) = 0 & convergent_lines(v10, v11) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (convergent_lines(v11, v12) = 0) | ~ (convergent_lines(v10, v11) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v10, v12) = 0 & convergent_lines(v10, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v11) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v11, v12) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (convergent_lines(v10, v12) = v13) | ~ (convergent_lines(v10, v11) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & unorthogonal_lines(v11, v12) = 0 & convergent_lines(v11, v12) = 0) | (v14 = 0 & v13 = 0 & unorthogonal_lines(v10, v12) = 0) | ( ~ (v14 = 0) & unorthogonal_lines(v10, v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (distinct_lines(v12, v13) = 0) | ~ (distinct_points(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v11, v13) = 0) | (v14 = 0 & apart_point_and_line(v11, v12) = 0) | (v14 = 0 & apart_point_and_line(v10, v13) = 0) | (v14 = 0 & apart_point_and_line(v10, v12) = 0))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (orthogonal_lines(v10, v11) = v12) | unorthogonal_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (incident_point_and_line(v10, v11) = v12) | apart_point_and_line(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (parallel_lines(v10, v11) = v12) | convergent_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (equal_lines(v10, v11) = v12) | distinct_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (equal_points(v10, v11) = v12) | distinct_points(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unorthogonal_lines(v10, v11) = v12) | orthogonal_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unorthogonal_lines(v10, v11) = v12) | convergent_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (apart_point_and_line(v10, v11) = v12) | incident_point_and_line(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (convergent_lines(v10, v11) = v12) | parallel_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (convergent_lines(v10, v11) = v12) | unorthogonal_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (convergent_lines(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & distinct_lines(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (distinct_lines(v10, v11) = v12) | equal_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (distinct_points(v10, v11) = v12) | equal_points(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (point(v12) = v11) | ~ (point(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (line(v12) = v11) | ~ (line(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (orthogonal_through_point(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & unorthogonal_lines(v12, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (orthogonal_through_point(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (orthogonal_through_point(v10, v11) = v12) | ? [v13] : ((v13 = 0 & line(v12) = 0) | ( ~ (v13 = 0) & point(v11) = v13) | ( ~ (v13 = 0) & line(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (parallel_through_point(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (parallel_through_point(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v12, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (parallel_through_point(v10, v11) = v12) | ? [v13] : ((v13 = 0 & line(v12) = 0) | ( ~ (v13 = 0) & point(v11) = v13) | ( ~ (v13 = 0) & line(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : ((v13 = 0 & point(v12) = 0) | ( ~ (v13 = 0) & line(v11) = v13) | ( ~ (v13 = 0) & line(v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v11) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection_point(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : ((v13 = 0 & line(v12) = 0) | ( ~ (v13 = 0) & point(v11) = v13) | ( ~ (v13 = 0) & point(v10) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v11, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (line_connecting(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) & ! [v10] : ! [v11] : ( ~ (orthogonal_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & unorthogonal_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (incident_point_and_line(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (parallel_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (equal_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & distinct_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (equal_points(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & distinct_points(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & orthogonal_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (apart_point_and_line(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & incident_point_and_line(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v11) = v13)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v10) = v13)) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & point(v12) = 0 & intersection_point(v10, v11) = v12) | ( ~ (v12 = 0) & line(v11) = v12) | ( ~ (v12 = 0) & line(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & parallel_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | convergent_lines(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & equal_lines(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v11, v12) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v10, v12) = v13)) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & line(v12) = 0 & line_connecting(v10, v11) = v12) | ( ~ (v12 = 0) & point(v11) = v12) | ( ~ (v12 = 0) & point(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (distinct_points(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & equal_points(v10, v11) = v12)) & ! [v10] : ~ (convergent_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_lines(v10, v10) = 0) & ! [v10] : ~ (distinct_points(v10, v10) = 0) & ? [v10] : ? [v11] : ? [v12] : orthogonal_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : incident_point_and_line(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : parallel_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : equal_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : equal_points(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : orthogonal_through_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unorthogonal_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : parallel_through_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : intersection_point(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : line_connecting(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : apart_point_and_line(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : convergent_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_lines(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : distinct_points(v11, v10) = v12 & ? [v10] : ? [v11] : point(v10) = v11 & ? [v10] : ? [v11] : line(v10) = v11 & ((v6 = 0 & apart_point_and_line(v1, v4) = 0) | (v5 = 0 & apart_point_and_line(v0, v4) = 0)))
% 33.76/9.14 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 33.76/9.14 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5 & line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2 & apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0 & apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(all_0_9_9, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & ((all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0))
% 33.76/9.18 |
% 33.76/9.18 | Applying alpha-rule on (1) yields:
% 33.76/9.18 | (2) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 33.76/9.18 | (3) line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5
% 33.76/9.18 | (4) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 33.76/9.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 33.76/9.18 | (6) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 33.76/9.18 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 33.76/9.18 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 33.76/9.19 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 33.76/9.19 | (10) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 33.76/9.19 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 33.76/9.19 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 33.76/9.19 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 33.76/9.19 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 34.13/9.19 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 34.13/9.19 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.13/9.19 | (17) ~ (all_0_1_1 = 0)
% 34.13/9.19 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 34.13/9.19 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 34.13/9.19 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 34.13/9.19 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 34.13/9.19 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 34.13/9.19 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 34.13/9.19 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 34.13/9.19 | (25) distinct_points(all_0_9_9, all_0_8_8) = 0
% 34.13/9.19 | (26) apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1
% 34.13/9.19 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.13/9.19 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.13/9.19 | (29) ! [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))
% 34.13/9.19 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 34.13/9.19 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 34.13/9.19 | (32) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 34.13/9.19 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 34.13/9.19 | (34) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 34.13/9.19 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.13/9.20 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.13/9.20 | (37) distinct_points(all_0_7_7, all_0_6_6) = 0
% 34.13/9.20 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 34.13/9.20 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 34.13/9.20 | (40) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 34.13/9.20 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 34.13/9.20 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 34.13/9.20 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 34.13/9.20 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 34.13/9.20 | (45) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 34.13/9.20 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 34.13/9.20 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 34.13/9.20 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 34.13/9.20 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 34.13/9.20 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 34.13/9.20 | (51) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 34.13/9.20 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 34.13/9.20 | (53) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 34.13/9.20 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 34.13/9.20 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 34.13/9.20 | (56) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 34.13/9.20 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 34.13/9.20 | (58) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 34.13/9.21 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.13/9.21 | (60) line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2
% 34.13/9.21 | (61) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 34.13/9.21 | (62) ? [v0] : ? [v1] : point(v0) = v1
% 34.13/9.21 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 34.13/9.21 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 34.13/9.21 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 34.13/9.21 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 34.13/9.21 | (67) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 34.13/9.21 | (68) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 34.13/9.21 | (69) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 34.13/9.21 | (70) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 34.13/9.21 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 34.13/9.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 34.13/9.21 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 34.13/9.21 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 34.13/9.21 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 34.13/9.21 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 34.13/9.21 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 34.13/9.21 | (78) ! [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)))
% 34.13/9.21 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 34.13/9.21 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 34.13/9.21 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 34.13/9.21 | (82) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 34.13/9.21 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 34.13/9.21 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 34.13/9.21 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 34.13/9.21 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 34.13/9.21 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 34.13/9.21 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 34.13/9.21 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 34.13/9.21 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 34.13/9.22 | (91) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 34.13/9.22 | (92) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 34.13/9.22 | (93) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 34.13/9.22 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 34.13/9.22 | (95) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 34.13/9.22 | (96) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 34.13/9.22 | (97) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 34.13/9.22 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 34.13/9.22 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 34.13/9.22 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 34.13/9.22 | (101) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 34.13/9.22 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 34.13/9.22 | (103) ! [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)))
% 34.13/9.22 | (104) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 34.13/9.22 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 34.13/9.22 | (106) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 34.13/9.22 | (107) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 34.13/9.22 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 34.13/9.22 | (109) ! [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))
% 34.13/9.22 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 34.13/9.22 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.13/9.22 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 34.13/9.22 | (113) ! [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)))
% 34.13/9.22 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 34.13/9.22 | (115) (all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | (all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0)
% 34.13/9.22 | (116) apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0
% 34.13/9.22 | (117) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 34.13/9.22 | (118) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 34.13/9.22 | (119) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 34.13/9.22 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 34.13/9.22 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 34.13/9.22 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.13/9.22 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 34.13/9.22 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 34.13/9.22 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 34.13/9.22 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 34.13/9.22 | (127) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 34.13/9.22 | (128) ? [v0] : ? [v1] : line(v0) = v1
% 34.13/9.22 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 34.13/9.22 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 34.13/9.22 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 34.13/9.22 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 34.13/9.22 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 34.13/9.22 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 34.13/9.22 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 34.13/9.23 | (136) ~ (all_0_0_0 = 0)
% 34.13/9.23 | (137) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 34.13/9.23 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 34.13/9.23 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 34.13/9.23 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 34.13/9.23 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 34.13/9.23 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 34.13/9.23 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 34.13/9.23 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 34.13/9.23 | (145) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 34.13/9.23 | (146) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 34.13/9.23 | (147) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 34.13/9.23 | (148) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (75) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 34.13/9.23 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (98) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 34.13/9.23 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (75) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 34.13/9.23 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (98) with all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 34.13/9.23 | (152) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_8_8) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (73) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, yields:
% 34.13/9.23 | (153) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (84) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, yields:
% 34.13/9.23 | (154) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (84) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.23 | (155) all_0_0_0 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (73) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.23 | (156) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (84) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.23 | (157) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (63) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.23 | (158) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (6) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.23 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_6_6, v0) = v1)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (137) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.23 | (160) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_7_7, v0) = v1)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (6) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 34.13/9.23 | (161) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_8_8, v0) = v1)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating formula (137) with all_0_8_8, all_0_9_9 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 34.13/9.23 | (162) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(all_0_9_9, v0) = v1)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (152) with all_42_0_57 yields:
% 34.13/9.23 | (163) ( ~ (all_42_0_57 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57) | ( ~ (all_42_0_57 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_42_0_57)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (151) with all_43_0_58 yields:
% 34.13/9.23 | (164) ( ~ (all_43_0_58 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58) | ( ~ (all_43_0_58 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_43_0_58)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (150) with all_45_0_60 yields:
% 34.13/9.23 | (165) ( ~ (all_45_0_60 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60) | ( ~ (all_45_0_60 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_45_0_60)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (149) with all_47_0_62 yields:
% 34.13/9.23 | (166) ( ~ (all_47_0_62 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62) | ( ~ (all_47_0_62 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_47_0_62)
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (162) with all_49_0_65, all_49_1_66 yields:
% 34.13/9.23 | (167) ~ (all_49_0_65 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_49_1_66 & apart_point_and_line(all_0_9_9, all_49_1_66) = all_49_0_65
% 34.13/9.23 |
% 34.13/9.23 | Applying alpha-rule on (167) yields:
% 34.13/9.23 | (168) ~ (all_49_0_65 = 0)
% 34.13/9.23 | (169) line_connecting(all_0_9_9, all_0_8_8) = all_49_1_66
% 34.13/9.23 | (170) apart_point_and_line(all_0_9_9, all_49_1_66) = all_49_0_65
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (159) with all_52_0_69, all_52_1_70 yields:
% 34.13/9.23 | (171) ~ (all_52_0_69 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_52_1_70 & apart_point_and_line(all_0_6_6, all_52_1_70) = all_52_0_69
% 34.13/9.23 |
% 34.13/9.23 | Applying alpha-rule on (171) yields:
% 34.13/9.23 | (172) ~ (all_52_0_69 = 0)
% 34.13/9.23 | (173) line_connecting(all_0_7_7, all_0_6_6) = all_52_1_70
% 34.13/9.23 | (174) apart_point_and_line(all_0_6_6, all_52_1_70) = all_52_0_69
% 34.13/9.23 |
% 34.13/9.23 | Instantiating (160) with all_54_0_71, all_54_1_72 yields:
% 34.13/9.23 | (175) ~ (all_54_0_71 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_54_1_72 & apart_point_and_line(all_0_7_7, all_54_1_72) = all_54_0_71
% 34.13/9.23 |
% 34.13/9.23 | Applying alpha-rule on (175) yields:
% 34.13/9.23 | (176) ~ (all_54_0_71 = 0)
% 34.13/9.23 | (177) line_connecting(all_0_7_7, all_0_6_6) = all_54_1_72
% 34.13/9.23 | (178) apart_point_and_line(all_0_7_7, all_54_1_72) = all_54_0_71
% 34.13/9.23 |
% 34.13/9.24 | Instantiating (161) with all_56_0_73, all_56_1_74 yields:
% 34.13/9.24 | (179) ~ (all_56_0_73 = 0) & line_connecting(all_0_9_9, all_0_8_8) = all_56_1_74 & apart_point_and_line(all_0_8_8, all_56_1_74) = all_56_0_73
% 34.13/9.24 |
% 34.13/9.24 | Applying alpha-rule on (179) yields:
% 34.13/9.24 | (180) ~ (all_56_0_73 = 0)
% 34.13/9.24 | (181) line_connecting(all_0_9_9, all_0_8_8) = all_56_1_74
% 34.13/9.24 | (182) apart_point_and_line(all_0_8_8, all_56_1_74) = all_56_0_73
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (165), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (183) ~ (all_45_0_60 = 0) & apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60
% 34.13/9.24 |
% 34.13/9.24 | Applying alpha-rule on (183) yields:
% 34.13/9.24 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.24 | (185) apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (153), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (186) all_0_0_0 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (186) can reduce 136 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (136) ~ (all_0_0_0 = 0)
% 34.13/9.24 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (164), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (190) ~ (all_43_0_58 = 0) & apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58
% 34.13/9.24 |
% 34.13/9.24 | Applying alpha-rule on (190) yields:
% 34.13/9.24 | (191) ~ (all_43_0_58 = 0)
% 34.13/9.24 | (192) apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (158), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (193) all_0_1_1 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (193) can reduce 17 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (17) ~ (all_0_1_1 = 0)
% 34.13/9.24 | (196) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (156), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (193) all_0_1_1 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (193) can reduce 17 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (17) ~ (all_0_1_1 = 0)
% 34.13/9.24 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (154), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (186) all_0_0_0 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (186) can reduce 136 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (136) ~ (all_0_0_0 = 0)
% 34.13/9.24 | (204) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (157), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (193) all_0_1_1 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (193) can reduce 17 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (17) ~ (all_0_1_1 = 0)
% 34.13/9.24 | (208) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (163), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (209) ~ (all_42_0_57 = 0) & apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57
% 34.13/9.24 |
% 34.13/9.24 | Applying alpha-rule on (209) yields:
% 34.13/9.24 | (210) ~ (all_42_0_57 = 0)
% 34.13/9.24 | (211) apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (166), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (212) ~ (all_47_0_62 = 0) & apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62
% 34.13/9.24 |
% 34.13/9.24 | Applying alpha-rule on (212) yields:
% 34.13/9.24 | (213) ~ (all_47_0_62 = 0)
% 34.13/9.24 | (214) apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (155), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (186) all_0_0_0 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (186) can reduce 136 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (136) ~ (all_0_0_0 = 0)
% 34.13/9.24 | (218) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.24 |
% 34.13/9.24 +-Applying beta-rule and splitting (218), into two cases.
% 34.13/9.24 |-Branch one:
% 34.13/9.24 | (193) all_0_1_1 = 0
% 34.13/9.24 |
% 34.13/9.24 | Equations (193) can reduce 17 to:
% 34.13/9.24 | (187) $false
% 34.13/9.24 |
% 34.13/9.24 |-The branch is then unsatisfiable
% 34.13/9.24 |-Branch two:
% 34.13/9.24 | (17) ~ (all_0_1_1 = 0)
% 34.13/9.24 | (222) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (11) with all_0_7_7, all_0_6_6, all_54_1_72, all_0_5_5 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_54_1_72, line_connecting(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 34.13/9.24 | (223) all_54_1_72 = all_0_5_5
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (11) with all_0_7_7, all_0_6_6, all_52_1_70, all_54_1_72 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_54_1_72, line_connecting(all_0_7_7, all_0_6_6) = all_52_1_70, yields:
% 34.13/9.24 | (224) all_54_1_72 = all_52_1_70
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (11) with all_0_9_9, all_0_8_8, all_56_1_74, all_0_2_2 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_56_1_74, line_connecting(all_0_9_9, all_0_8_8) = all_0_2_2, yields:
% 34.13/9.24 | (225) all_56_1_74 = all_0_2_2
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (11) with all_0_9_9, all_0_8_8, all_49_1_66, all_56_1_74 and discharging atoms line_connecting(all_0_9_9, all_0_8_8) = all_56_1_74, line_connecting(all_0_9_9, all_0_8_8) = all_49_1_66, yields:
% 34.13/9.24 | (226) all_56_1_74 = all_49_1_66
% 34.13/9.24 |
% 34.13/9.24 | Combining equations (225,226) yields a new equation:
% 34.13/9.24 | (227) all_49_1_66 = all_0_2_2
% 34.13/9.24 |
% 34.13/9.24 | Combining equations (224,223) yields a new equation:
% 34.13/9.24 | (228) all_52_1_70 = all_0_5_5
% 34.13/9.24 |
% 34.13/9.24 | Simplifying 228 yields:
% 34.13/9.24 | (229) all_52_1_70 = all_0_5_5
% 34.13/9.24 |
% 34.13/9.24 | Combining equations (227,226) yields a new equation:
% 34.13/9.24 | (225) all_56_1_74 = all_0_2_2
% 34.13/9.24 |
% 34.13/9.24 | From (229) and (174) follows:
% 34.13/9.24 | (231) apart_point_and_line(all_0_6_6, all_0_5_5) = all_52_0_69
% 34.13/9.24 |
% 34.13/9.24 | From (223) and (178) follows:
% 34.13/9.24 | (232) apart_point_and_line(all_0_7_7, all_0_5_5) = all_54_0_71
% 34.13/9.24 |
% 34.13/9.24 | From (225) and (182) follows:
% 34.13/9.24 | (233) apart_point_and_line(all_0_8_8, all_0_2_2) = all_56_0_73
% 34.13/9.24 |
% 34.13/9.24 | From (227) and (170) follows:
% 34.13/9.24 | (234) apart_point_and_line(all_0_9_9, all_0_2_2) = all_49_0_65
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (19) with all_0_6_6, all_0_5_5, all_52_0_69, all_47_0_62 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_52_0_69, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.24 | (235) all_52_0_69 = all_47_0_62
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (19) with all_0_7_7, all_0_5_5, all_54_0_71, all_45_0_60 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_54_0_71, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.24 | (236) all_54_0_71 = all_45_0_60
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (19) with all_0_8_8, all_0_2_2, all_56_0_73, all_43_0_58 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_56_0_73, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.24 | (237) all_56_0_73 = all_43_0_58
% 34.13/9.24 |
% 34.13/9.24 | Instantiating formula (19) with all_0_9_9, all_0_2_2, all_49_0_65, all_42_0_57 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_49_0_65, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.24 | (238) all_49_0_65 = all_42_0_57
% 34.13/9.24 |
% 34.13/9.24 | Equations (237) can reduce 180 to:
% 34.13/9.24 | (191) ~ (all_43_0_58 = 0)
% 34.13/9.24 |
% 34.13/9.24 | Equations (236) can reduce 176 to:
% 34.13/9.24 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.24 |
% 34.13/9.25 | Equations (235) can reduce 172 to:
% 34.13/9.25 | (213) ~ (all_47_0_62 = 0)
% 34.13/9.25 |
% 34.13/9.25 | Equations (238) can reduce 168 to:
% 34.13/9.25 | (210) ~ (all_42_0_57 = 0)
% 34.13/9.25 |
% 34.13/9.25 | From (235) and (231) follows:
% 34.13/9.25 | (214) apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62
% 34.13/9.25 |
% 34.13/9.25 | From (236) and (232) follows:
% 34.13/9.25 | (185) apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60
% 34.13/9.25 |
% 34.13/9.25 | From (237) and (233) follows:
% 34.13/9.25 | (192) apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58
% 34.13/9.25 |
% 34.13/9.25 | From (238) and (234) follows:
% 34.13/9.25 | (211) apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (71) with all_0_0_0, all_47_0_62, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.25 | (247) all_47_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (73) with all_47_0_62, all_0_0_0, all_0_5_5, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (248) all_47_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (73) with all_0_0_0, all_47_0_62, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (249) all_47_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_47_0_62, all_0_0_0, all_0_5_5, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (250) all_47_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_0_0_0, all_47_0_62, all_0_2_2, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (251) all_47_0_62 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_0_1_1, all_47_0_62, all_0_2_2, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.25 | (252) all_47_0_62 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (14) with all_47_0_62, all_0_1_1, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.25 | (253) all_47_0_62 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (14) with all_0_1_1, all_47_0_62, all_0_5_5, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, yields:
% 34.13/9.25 | (254) all_47_0_62 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (71) with all_47_0_62, all_47_0_62, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.25 | (255) all_47_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (73) with all_47_0_62, all_47_0_62, all_0_5_5, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (256) all_47_0_62 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_47_0_62, all_47_0_62, all_0_5_5, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, yields:
% 34.13/9.25 | (257) all_47_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_45_0_60, all_0_0_0, all_0_5_5, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (258) all_45_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_0_0_0, all_45_0_60, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (259) all_45_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (14) with all_45_0_60, all_0_0_0, all_0_2_2, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (260) all_45_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (14) with all_0_0_0, all_45_0_60, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (261) all_45_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (63) with all_45_0_60, all_0_1_1, all_0_5_5, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.25 | (262) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (63) with all_0_1_1, all_45_0_60, all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.25 | (263) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (73) with all_45_0_60, all_0_1_1, all_0_5_5, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (264) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (73) with all_0_1_1, all_45_0_60, all_0_2_2, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (265) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_45_0_60, all_0_1_1, all_0_5_5, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (266) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_0_1_1, all_45_0_60, all_0_2_2, all_0_5_5, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (267) all_45_0_60 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_45_0_60, all_47_0_62, all_0_5_5, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (268) all_47_0_62 = 0 | all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (84) with all_47_0_62, all_45_0_60, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.25 | (269) all_47_0_62 = 0 | all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.25 |
% 34.13/9.25 | Instantiating formula (63) with all_45_0_60, all_45_0_60, all_0_5_5, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.13/9.25 | (270) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.13/9.25 |
% 34.13/9.26 | Instantiating formula (73) with all_45_0_60, all_45_0_60, all_0_5_5, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.26 | (271) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_45_0_60, all_45_0_60, all_0_5_5, all_0_5_5, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, yields:
% 34.13/9.26 | (272) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_43_0_58, all_0_0_0, all_0_2_2, all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (273) all_43_0_58 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_0_0_0, all_43_0_58, all_0_2_2, all_0_2_2, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (274) all_43_0_58 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_43_0_58, all_0_1_1, all_0_2_2, all_0_2_2, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (275) all_43_0_58 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_0_1_1, all_43_0_58, all_0_2_2, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (276) all_43_0_58 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_43_0_58, all_47_0_62, all_0_2_2, all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (277) all_47_0_62 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_47_0_62, all_43_0_58, all_0_5_5, all_0_2_2, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (278) all_47_0_62 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_43_0_58, all_47_0_62, all_0_5_5, all_0_2_2, all_0_8_8, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (279) all_47_0_62 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_47_0_62, all_43_0_58, all_0_2_2, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (280) all_47_0_62 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_43_0_58, all_45_0_60, all_0_2_2, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (281) all_45_0_60 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_45_0_60, all_43_0_58, all_0_5_5, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (282) all_45_0_60 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_43_0_58, all_45_0_60, all_0_5_5, all_0_2_2, all_0_8_8, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (283) all_45_0_60 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_45_0_60, all_43_0_58, all_0_2_2, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (284) all_45_0_60 = 0 | all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (73) with all_43_0_58, all_43_0_58, all_0_2_2, all_0_2_2, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (285) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_43_0_58, all_43_0_58, all_0_2_2, all_0_2_2, all_0_8_8, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, yields:
% 34.13/9.26 | (286) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_42_0_57, all_0_0_0, all_0_2_2, all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (287) all_42_0_57 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_0_0_0, all_42_0_57, all_0_2_2, all_0_2_2, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (288) all_42_0_57 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_42_0_57, all_0_1_1, all_0_2_2, all_0_2_2, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (289) all_42_0_57 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_0_1_1, all_42_0_57, all_0_2_2, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (290) all_42_0_57 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_42_0_57, all_47_0_62, all_0_2_2, all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (291) all_47_0_62 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_47_0_62, all_42_0_57, all_0_5_5, all_0_2_2, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (292) all_47_0_62 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_42_0_57, all_47_0_62, all_0_5_5, all_0_2_2, all_0_9_9, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (293) all_47_0_62 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_47_0_62, all_42_0_57, all_0_2_2, all_0_5_5, all_0_6_6, all_0_9_9 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (294) all_47_0_62 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_42_0_57, all_45_0_60, all_0_2_2, all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (295) all_45_0_60 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (84) with all_45_0_60, all_42_0_57, all_0_5_5, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (296) all_45_0_60 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.13/9.26 |
% 34.13/9.26 | Instantiating formula (14) with all_42_0_57, all_45_0_60, all_0_5_5, all_0_2_2, all_0_9_9, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.26 | (297) all_45_0_60 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.13/9.27 |
% 34.13/9.27 | Instantiating formula (14) with all_45_0_60, all_42_0_57, all_0_2_2, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.27 | (298) all_45_0_60 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.13/9.27 |
% 34.13/9.27 | Instantiating formula (84) with all_42_0_57, all_43_0_58, all_0_2_2, all_0_2_2, all_0_9_9, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.27 | (299) all_43_0_58 = 0 | all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 34.13/9.27 |
% 34.13/9.27 | Instantiating formula (73) with all_42_0_57, all_42_0_57, all_0_2_2, all_0_2_2, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.27 | (300) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.27 |
% 34.13/9.27 | Instantiating formula (84) with all_42_0_57, all_42_0_57, all_0_2_2, all_0_2_2, all_0_9_9, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, yields:
% 34.13/9.27 | (301) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (115), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (302) all_0_3_3 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 34.13/9.27 |
% 34.13/9.27 | Applying alpha-rule on (302) yields:
% 34.13/9.27 | (303) all_0_3_3 = 0
% 34.13/9.27 | (304) apart_point_and_line(all_0_8_8, all_0_5_5) = 0
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (271), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (308) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (285), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (309) all_43_0_58 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (309) can reduce 191 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (191) ~ (all_43_0_58 = 0)
% 34.13/9.27 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (264), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (316) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (265), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (320) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (266), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (324) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (268), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (325) all_47_0_62 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (325) can reduce 213 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (213) ~ (all_47_0_62 = 0)
% 34.13/9.27 | (328) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (260), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (332) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (262), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (336) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (267), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.13/9.27 | (340) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (269), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (325) all_47_0_62 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (325) can reduce 213 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (213) ~ (all_47_0_62 = 0)
% 34.13/9.27 | (344) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.13/9.27 |
% 34.13/9.27 +-Applying beta-rule and splitting (263), into two cases.
% 34.13/9.27 |-Branch one:
% 34.13/9.27 | (305) all_45_0_60 = 0
% 34.13/9.27 |
% 34.13/9.27 | Equations (305) can reduce 184 to:
% 34.13/9.27 | (187) $false
% 34.13/9.27 |
% 34.13/9.27 |-The branch is then unsatisfiable
% 34.13/9.27 |-Branch two:
% 34.13/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.27 | (348) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (275), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (309) all_43_0_58 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (309) can reduce 191 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (191) ~ (all_43_0_58 = 0)
% 34.53/9.27 | (352) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (276), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (309) all_43_0_58 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (309) can reduce 191 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (191) ~ (all_43_0_58 = 0)
% 34.53/9.27 | (356) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (277), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (325) all_47_0_62 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (325) can reduce 213 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (213) ~ (all_47_0_62 = 0)
% 34.53/9.27 | (360) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (278), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (325) all_47_0_62 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (325) can reduce 213 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (213) ~ (all_47_0_62 = 0)
% 34.53/9.27 | (364) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (281), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (305) all_45_0_60 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (305) can reduce 184 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.27 | (368) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.53/9.27 |
% 34.53/9.27 +-Applying beta-rule and splitting (261), into two cases.
% 34.53/9.27 |-Branch one:
% 34.53/9.27 | (305) all_45_0_60 = 0
% 34.53/9.27 |
% 34.53/9.27 | Equations (305) can reduce 184 to:
% 34.53/9.27 | (187) $false
% 34.53/9.27 |
% 34.53/9.27 |-The branch is then unsatisfiable
% 34.53/9.27 |-Branch two:
% 34.53/9.27 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.27 | (372) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (279), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (325) all_47_0_62 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (325) can reduce 213 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.53/9.28 | (376) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (280), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (325) all_47_0_62 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (325) can reduce 213 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.53/9.28 | (380) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (282), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (305) all_45_0_60 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (305) can reduce 184 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.28 | (384) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (283), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (305) all_45_0_60 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (305) can reduce 184 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.28 | (388) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (284), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (305) all_45_0_60 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (305) can reduce 184 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (184) ~ (all_45_0_60 = 0)
% 34.53/9.28 | (392) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (256), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (325) all_47_0_62 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (325) can reduce 213 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.53/9.28 | (308) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (316), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (400) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (320), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (324), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (408) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (336), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (340), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (416) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (352), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.53/9.28 |
% 34.53/9.28 +-Applying beta-rule and splitting (356), into two cases.
% 34.53/9.28 |-Branch one:
% 34.53/9.28 | (193) all_0_1_1 = 0
% 34.53/9.28 |
% 34.53/9.28 | Equations (193) can reduce 17 to:
% 34.53/9.28 | (187) $false
% 34.53/9.28 |
% 34.53/9.28 |-The branch is then unsatisfiable
% 34.53/9.28 |-Branch two:
% 34.53/9.28 | (17) ~ (all_0_1_1 = 0)
% 34.53/9.28 | (424) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.53/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (364), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (309) all_43_0_58 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (309) can reduce 191 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.28 | (428) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (372), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (186) all_0_0_0 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (186) can reduce 136 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.28 | (432) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (376), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (309) all_43_0_58 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (309) can reduce 191 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.28 | (436) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (255), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (325) all_47_0_62 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (325) can reduce 213 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.28 | (440) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (257), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (325) all_47_0_62 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (325) can reduce 213 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.28 | (444) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (380), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (309) all_43_0_58 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (309) can reduce 191 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.28 | (448) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (384), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (309) all_43_0_58 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (309) can reduce 191 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.28 | (452) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (248), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (325) all_47_0_62 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (325) can reduce 213 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.28 | (456) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (249), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (325) all_47_0_62 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (325) can reduce 213 to:
% 34.57/9.28 | (187) $false
% 34.57/9.28 |
% 34.57/9.28 |-The branch is then unsatisfiable
% 34.57/9.28 |-Branch two:
% 34.57/9.28 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.28 | (460) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.57/9.28 |
% 34.57/9.28 +-Applying beta-rule and splitting (253), into two cases.
% 34.57/9.28 |-Branch one:
% 34.57/9.28 | (325) all_47_0_62 = 0
% 34.57/9.28 |
% 34.57/9.28 | Equations (325) can reduce 213 to:
% 34.57/9.28 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (464) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (247), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (325) all_47_0_62 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (325) can reduce 213 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (468) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (254), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (325) all_47_0_62 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (325) can reduce 213 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (472) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (258), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (305) all_45_0_60 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (305) can reduce 184 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.29 | (476) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (259), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (305) all_45_0_60 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (305) can reduce 184 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.29 | (480) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (250), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (325) all_47_0_62 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (325) can reduce 213 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (484) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (251), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (325) all_47_0_62 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (325) can reduce 213 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (488) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (252), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (325) all_47_0_62 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (325) can reduce 213 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.29 | (492) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (332), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (344), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (305) all_45_0_60 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (305) can reduce 184 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.29 | (500) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (388), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (309) all_43_0_58 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (309) can reduce 191 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.29 | (504) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (492), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (193) all_0_1_1 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (193) can reduce 17 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.29 | (508) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (368), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (309) all_43_0_58 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (309) can reduce 191 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (191) ~ (all_43_0_58 = 0)
% 34.57/9.29 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (456), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (400) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (460), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (464), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (193) all_0_1_1 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (193) can reduce 17 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.29 | (524) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 | Instantiating (524) with all_349_0_878 yields:
% 34.57/9.29 | (525) (all_349_0_878 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_878 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_349_0_878 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878) | ( ~ (all_349_0_878 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_349_0_878)
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (468), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (529) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.57/9.29 |
% 34.57/9.29 | Instantiating (529) with all_353_0_879 yields:
% 34.57/9.29 | (530) (all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_353_0_879 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_879)
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (472), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (193) all_0_1_1 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (193) can reduce 17 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.29 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (480), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (538) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 | Instantiating (538) with all_361_0_881 yields:
% 34.57/9.29 | (539) (all_361_0_881 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_881 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_361_0_881 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881) | ( ~ (all_361_0_881 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_361_0_881)
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (484), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (543) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (488), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (186) all_0_0_0 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (186) can reduce 136 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (136) ~ (all_0_0_0 = 0)
% 34.57/9.29 | (547) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (530), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (548) (all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (548), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (549) all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.57/9.29 |
% 34.57/9.29 | Applying alpha-rule on (549) yields:
% 34.57/9.29 | (550) all_353_0_879 = 0
% 34.57/9.29 | (551) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (300), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.29 | (552) all_42_0_57 = 0
% 34.57/9.29 |
% 34.57/9.29 | Equations (552) can reduce 210 to:
% 34.57/9.29 | (187) $false
% 34.57/9.29 |
% 34.57/9.29 |-The branch is then unsatisfiable
% 34.57/9.29 |-Branch two:
% 34.57/9.29 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.29 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.57/9.29 |
% 34.57/9.29 +-Applying beta-rule and splitting (301), into two cases.
% 34.57/9.29 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (288), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (289), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (348), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (193) all_0_1_1 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (193) can reduce 17 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.30 | (571) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (290), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (567), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (193) all_0_1_1 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (193) can reduce 17 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.30 | (579) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (575), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (193) all_0_1_1 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (193) can reduce 17 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (17) ~ (all_0_1_1 = 0)
% 34.57/9.30 | (583) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 34.57/9.30 | (193) all_0_1_1 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (193) can reduce 17 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (586) all_353_0_879 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.57/9.30 |
% 34.57/9.30 | Applying alpha-rule on (586) yields:
% 34.57/9.30 | (550) all_353_0_879 = 0
% 34.57/9.30 | (588) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (270), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (592) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (272), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (297), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (600) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (296), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (604) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (295), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (608) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (298), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (612) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (328), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (184) ~ (all_45_0_60 = 0)
% 34.57/9.30 | (616) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.57/9.30 |
% 34.57/9.30 | Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_45_0_60 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields:
% 34.57/9.30 | (305) all_45_0_60 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (305) can reduce 184 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (619) ~ (all_353_0_879 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_879
% 34.57/9.30 |
% 34.57/9.30 | Applying alpha-rule on (619) yields:
% 34.57/9.30 | (620) ~ (all_353_0_879 = 0)
% 34.57/9.30 | (621) distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_879
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (539), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (622) (all_361_0_881 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_881 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_361_0_881 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881)
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (622), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (623) (all_361_0_881 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_881 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (623), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (624) all_361_0_881 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 34.57/9.30 |
% 34.57/9.30 | Applying alpha-rule on (624) yields:
% 34.57/9.30 | (625) all_361_0_881 = 0
% 34.57/9.30 | (626) apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (291), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (325) all_47_0_62 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (325) can reduce 213 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.30 | (630) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (292), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (325) all_47_0_62 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (325) can reduce 213 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.30 | (634) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (293), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (325) all_47_0_62 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (325) can reduce 213 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.30 | (638) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (294), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (325) all_47_0_62 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (325) can reduce 213 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (213) ~ (all_47_0_62 = 0)
% 34.57/9.30 | (642) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.57/9.30 |
% 34.57/9.30 | Instantiating formula (19) with all_0_6_6, all_0_5_5, 0, all_47_0_62 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_6_6, all_0_5_5) = 0, yields:
% 34.57/9.30 | (325) all_47_0_62 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (325) can reduce 213 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (645) all_361_0_881 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.57/9.30 |
% 34.57/9.30 | Applying alpha-rule on (645) yields:
% 34.57/9.30 | (625) all_361_0_881 = 0
% 34.57/9.30 | (551) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (300), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (301), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (288), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.57/9.30 |
% 34.57/9.30 +-Applying beta-rule and splitting (289), into two cases.
% 34.57/9.30 |-Branch one:
% 34.57/9.30 | (552) all_42_0_57 = 0
% 34.57/9.30 |
% 34.57/9.30 | Equations (552) can reduce 210 to:
% 34.57/9.30 | (187) $false
% 34.57/9.30 |
% 34.57/9.30 |-The branch is then unsatisfiable
% 34.57/9.30 |-Branch two:
% 34.57/9.30 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.30 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.57/9.31 |
% 34.57/9.31 +-Applying beta-rule and splitting (290), into two cases.
% 34.57/9.31 |-Branch one:
% 34.57/9.31 | (552) all_42_0_57 = 0
% 34.57/9.31 |
% 34.57/9.31 | Equations (552) can reduce 210 to:
% 34.57/9.31 | (187) $false
% 34.57/9.31 |
% 34.57/9.31 |-The branch is then unsatisfiable
% 34.57/9.31 |-Branch two:
% 34.57/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.57/9.31 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.57/9.31 |
% 34.57/9.31 +-Applying beta-rule and splitting (348), into two cases.
% 34.57/9.31 |-Branch one:
% 34.57/9.31 | (193) all_0_1_1 = 0
% 34.57/9.31 |
% 34.57/9.31 | Equations (193) can reduce 17 to:
% 34.57/9.31 | (187) $false
% 34.57/9.31 |
% 34.57/9.31 |-The branch is then unsatisfiable
% 34.57/9.31 |-Branch two:
% 34.57/9.31 | (17) ~ (all_0_1_1 = 0)
% 34.67/9.31 | (571) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (567), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (193) all_0_1_1 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (193) can reduce 17 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (17) ~ (all_0_1_1 = 0)
% 34.67/9.31 | (579) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (575), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (193) all_0_1_1 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (193) can reduce 17 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (17) ~ (all_0_1_1 = 0)
% 34.67/9.31 | (583) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.67/9.31 |
% 34.67/9.31 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 34.67/9.31 | (193) all_0_1_1 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (193) can reduce 17 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (682) ~ (all_361_0_881 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881
% 34.67/9.31 |
% 34.67/9.31 | Applying alpha-rule on (682) yields:
% 34.67/9.31 | (683) ~ (all_361_0_881 = 0)
% 34.67/9.31 | (684) distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (525), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (685) (all_349_0_878 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_878 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_349_0_878 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878)
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (685), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (686) (all_349_0_878 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_878 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (686), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (687) all_349_0_878 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 34.67/9.31 |
% 34.67/9.31 | Applying alpha-rule on (687) yields:
% 34.67/9.31 | (688) all_349_0_878 = 0
% 34.67/9.31 | (689) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (300), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (392), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (309) all_43_0_58 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (309) can reduce 191 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.31 | (697) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (476), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (136) ~ (all_0_0_0 = 0)
% 34.67/9.31 | (701) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (286), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (309) all_43_0_58 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (309) can reduce 191 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.31 | (705) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (301), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (273), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (309) all_43_0_58 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (309) can reduce 191 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.31 | (713) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (288), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (274), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (309) all_43_0_58 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (309) can reduce 191 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.31 | (721) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (289), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (290), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (287), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (552) all_42_0_57 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (552) can reduce 210 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (210) ~ (all_42_0_57 = 0)
% 34.67/9.31 | (733) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (713), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (136) ~ (all_0_0_0 = 0)
% 34.67/9.31 | (737) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (563), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (136) ~ (all_0_0_0 = 0)
% 34.67/9.31 | (741) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (721), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (136) ~ (all_0_0_0 = 0)
% 34.67/9.31 | (745) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (733), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (136) ~ (all_0_0_0 = 0)
% 34.67/9.31 | (749) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 34.67/9.31 | (186) all_0_0_0 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (186) can reduce 136 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (752) all_349_0_878 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.67/9.31 |
% 34.67/9.31 | Applying alpha-rule on (752) yields:
% 34.67/9.31 | (688) all_349_0_878 = 0
% 34.67/9.31 | (588) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (272), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (305) all_45_0_60 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (305) can reduce 184 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.31 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (297), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (305) all_45_0_60 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (305) can reduce 184 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.31 | (600) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.67/9.31 |
% 34.67/9.31 +-Applying beta-rule and splitting (296), into two cases.
% 34.67/9.31 |-Branch one:
% 34.67/9.31 | (305) all_45_0_60 = 0
% 34.67/9.31 |
% 34.67/9.31 | Equations (305) can reduce 184 to:
% 34.67/9.31 | (187) $false
% 34.67/9.31 |
% 34.67/9.31 |-The branch is then unsatisfiable
% 34.67/9.31 |-Branch two:
% 34.67/9.31 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.32 | (604) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (295), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (305) all_45_0_60 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (305) can reduce 184 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.32 | (608) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (298), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (305) all_45_0_60 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (305) can reduce 184 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.32 | (612) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (328), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (305) all_45_0_60 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (305) can reduce 184 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.67/9.32 | (616) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_45_0_60 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields:
% 34.67/9.32 | (305) all_45_0_60 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (305) can reduce 184 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (781) ~ (all_349_0_878 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 | Applying alpha-rule on (781) yields:
% 34.67/9.32 | (782) ~ (all_349_0_878 = 0)
% 34.67/9.32 | (783) distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (392), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (697) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (286), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (705) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (273), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (713) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (274), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (721) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (299), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (803) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (360), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (807) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (43) with all_0_5_5, all_0_2_2, all_353_0_879, all_361_0_881 and discharging atoms distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881, distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_879, yields:
% 34.67/9.32 | (808) all_361_0_881 = all_353_0_879
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (43) with all_0_5_5, all_0_2_2, all_349_0_878, all_361_0_881 and discharging atoms distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_881, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878, yields:
% 34.67/9.32 | (809) all_361_0_881 = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 | Combining equations (808,809) yields a new equation:
% 34.67/9.32 | (810) all_353_0_879 = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 | Simplifying 810 yields:
% 34.67/9.32 | (811) all_353_0_879 = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 | Equations (811) can reduce 620 to:
% 34.67/9.32 | (782) ~ (all_349_0_878 = 0)
% 34.67/9.32 |
% 34.67/9.32 | From (811) and (621) follows:
% 34.67/9.32 | (783) distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (100) with all_43_0_58, all_349_0_878, all_0_2_2, all_0_5_5, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878, yields:
% 34.67/9.32 | (814) all_349_0_878 = 0 | all_43_0_58 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0)
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (139) with all_349_0_878, all_0_2_2, all_0_5_5, all_0_8_8 and discharging atoms apart_point_and_line(all_0_8_8, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_878, yields:
% 34.67/9.32 | (815) all_349_0_878 = 0 | apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (815), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (816) apart_point_and_line(all_0_8_8, all_0_2_2) = 0
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (814), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (688) all_349_0_878 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (688) can reduce 782 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (782) ~ (all_349_0_878 = 0)
% 34.67/9.32 | (820) all_43_0_58 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0)
% 34.67/9.32 |
% 34.67/9.32 +-Applying beta-rule and splitting (820), into two cases.
% 34.67/9.32 |-Branch one:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.67/9.32 | (824) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_8_8, all_0_5_5) = v0)
% 34.67/9.32 |
% 34.67/9.32 | Instantiating formula (19) with all_0_8_8, all_0_2_2, 0, all_43_0_58 and discharging atoms apart_point_and_line(all_0_8_8, all_0_2_2) = all_43_0_58, apart_point_and_line(all_0_8_8, all_0_2_2) = 0, yields:
% 34.67/9.32 | (309) all_43_0_58 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (309) can reduce 191 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.67/9.32 |-Branch two:
% 34.67/9.32 | (827) ~ (apart_point_and_line(all_0_8_8, all_0_2_2) = 0)
% 34.67/9.32 | (688) all_349_0_878 = 0
% 34.67/9.32 |
% 34.67/9.32 | Equations (688) can reduce 782 to:
% 34.67/9.32 | (187) $false
% 34.67/9.32 |
% 34.67/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (830) ~ (all_349_0_878 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_349_0_878
% 34.74/9.32 |
% 34.74/9.32 | Applying alpha-rule on (830) yields:
% 34.74/9.32 | (782) ~ (all_349_0_878 = 0)
% 34.74/9.32 | (832) distinct_points(all_0_7_7, all_0_6_6) = all_349_0_878
% 34.74/9.32 |
% 34.74/9.32 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_349_0_878, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_349_0_878, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.32 | (688) all_349_0_878 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (688) can reduce 782 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (835) ~ (all_361_0_881 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_361_0_881
% 34.74/9.32 |
% 34.74/9.32 | Applying alpha-rule on (835) yields:
% 34.74/9.32 | (683) ~ (all_361_0_881 = 0)
% 34.74/9.32 | (837) distinct_points(all_0_7_7, all_0_6_6) = all_361_0_881
% 34.74/9.32 |
% 34.74/9.32 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_361_0_881, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_361_0_881, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.32 | (625) all_361_0_881 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (625) can reduce 683 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (840) all_0_4_4 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 34.74/9.32 |
% 34.74/9.32 | Applying alpha-rule on (840) yields:
% 34.74/9.32 | (841) all_0_4_4 = 0
% 34.74/9.32 | (842) apart_point_and_line(all_0_9_9, all_0_5_5) = 0
% 34.74/9.32 |
% 34.74/9.32 +-Applying beta-rule and splitting (271), into two cases.
% 34.74/9.32 |-Branch one:
% 34.74/9.32 | (305) all_45_0_60 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (305) can reduce 184 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.32 | (308) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.74/9.32 |
% 34.74/9.32 +-Applying beta-rule and splitting (285), into two cases.
% 34.74/9.32 |-Branch one:
% 34.74/9.32 | (309) all_43_0_58 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (309) can reduce 191 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.32 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.74/9.32 |
% 34.74/9.32 +-Applying beta-rule and splitting (264), into two cases.
% 34.74/9.32 |-Branch one:
% 34.74/9.32 | (305) all_45_0_60 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (305) can reduce 184 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.32 | (316) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.32 |
% 34.74/9.32 +-Applying beta-rule and splitting (265), into two cases.
% 34.74/9.32 |-Branch one:
% 34.74/9.32 | (305) all_45_0_60 = 0
% 34.74/9.32 |
% 34.74/9.32 | Equations (305) can reduce 184 to:
% 34.74/9.32 | (187) $false
% 34.74/9.32 |
% 34.74/9.32 |-The branch is then unsatisfiable
% 34.74/9.32 |-Branch two:
% 34.74/9.32 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.32 | (320) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (266), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (324) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (268), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (328) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (260), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (332) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (262), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (336) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (267), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (340) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (269), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (344) all_45_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (263), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (348) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (275), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (309) all_43_0_58 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (309) can reduce 191 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.33 | (352) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (276), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (309) all_43_0_58 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (309) can reduce 191 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.33 | (356) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (277), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (360) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (278), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (364) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (281), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (368) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (261), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (372) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (279), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (376) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (280), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (380) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (282), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (384) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (283), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (388) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (284), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (305) all_45_0_60 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (305) can reduce 184 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.33 | (392) all_43_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (256), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (325) all_47_0_62 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (325) can reduce 213 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.33 | (308) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (316), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (400) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (320), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (324), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (408) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (336), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (412) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (340), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (416) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (352), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (420) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (356), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (193) all_0_1_1 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (193) can reduce 17 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.33 | (424) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (364), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (309) all_43_0_58 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (309) can reduce 191 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.33 | (428) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.33 |
% 34.74/9.33 +-Applying beta-rule and splitting (372), into two cases.
% 34.74/9.33 |-Branch one:
% 34.74/9.33 | (186) all_0_0_0 = 0
% 34.74/9.33 |
% 34.74/9.33 | Equations (186) can reduce 136 to:
% 34.74/9.33 | (187) $false
% 34.74/9.33 |
% 34.74/9.33 |-The branch is then unsatisfiable
% 34.74/9.33 |-Branch two:
% 34.74/9.33 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.33 | (432) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (376), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (309) all_43_0_58 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (309) can reduce 191 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.34 | (436) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (255), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (440) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (257), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (444) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (380), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (309) all_43_0_58 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (309) can reduce 191 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.34 | (448) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (384), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (309) all_43_0_58 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (309) can reduce 191 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.34 | (452) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (248), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (456) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (249), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (460) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (253), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (464) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (247), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (468) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (254), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (472) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (258), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (305) all_45_0_60 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (305) can reduce 184 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.34 | (476) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (259), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (305) all_45_0_60 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (305) can reduce 184 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.34 | (480) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (250), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (484) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (251), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (488) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (252), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (325) all_47_0_62 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (325) can reduce 213 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.34 | (492) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (332), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (344), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (305) all_45_0_60 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (305) can reduce 184 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.34 | (500) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (388), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (309) all_43_0_58 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (309) can reduce 191 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.34 | (504) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (492), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (193) all_0_1_1 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (193) can reduce 17 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.34 | (508) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (368), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (309) all_43_0_58 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (309) can reduce 191 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.34 | (512) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_8_8) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (456), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (400) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (460), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (404) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (464), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (193) all_0_1_1 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (193) can reduce 17 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.34 | (524) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 | Instantiating (524) with all_349_0_1982 yields:
% 34.74/9.34 | (1063) (all_349_0_1982 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_1982 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_349_0_1982 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982) | ( ~ (all_349_0_1982 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_349_0_1982)
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (468), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (529) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0))
% 34.74/9.34 |
% 34.74/9.34 | Instantiating (529) with all_353_0_1983 yields:
% 34.74/9.34 | (1068) (all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_353_0_1983 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_1983)
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (472), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (193) all_0_1_1 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (193) can reduce 17 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.34 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (480), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (538) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 | Instantiating (538) with all_361_0_1985 yields:
% 34.74/9.34 | (1077) (all_361_0_1985 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_1985 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_361_0_1985 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985) | ( ~ (all_361_0_1985 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_361_0_1985)
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (484), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (543) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (488), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (186) all_0_0_0 = 0
% 34.74/9.34 |
% 34.74/9.34 | Equations (186) can reduce 136 to:
% 34.74/9.34 | (187) $false
% 34.74/9.34 |
% 34.74/9.34 |-The branch is then unsatisfiable
% 34.74/9.34 |-Branch two:
% 34.74/9.34 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.34 | (547) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (1063), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (1086) (all_349_0_1982 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_1982 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (all_349_0_1982 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982)
% 34.74/9.34 |
% 34.74/9.34 +-Applying beta-rule and splitting (1086), into two cases.
% 34.74/9.34 |-Branch one:
% 34.74/9.34 | (1087) (all_349_0_1982 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_349_0_1982 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (1087), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (1088) all_349_0_1982 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 34.74/9.35 |
% 34.74/9.35 | Applying alpha-rule on (1088) yields:
% 34.74/9.35 | (1089) all_349_0_1982 = 0
% 34.74/9.35 | (689) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (300), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (552) all_42_0_57 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (552) can reduce 210 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.35 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (392), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (309) all_43_0_58 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (309) can reduce 191 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.35 | (697) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (476), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.35 | (701) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (286), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (309) all_43_0_58 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (309) can reduce 191 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.35 | (705) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (301), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (552) all_42_0_57 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (552) can reduce 210 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.35 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (287), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (552) all_42_0_57 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (552) can reduce 210 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.35 | (733) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (288), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (552) all_42_0_57 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (552) can reduce 210 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.35 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (273), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (309) all_43_0_58 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (309) can reduce 191 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.35 | (713) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (274), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (309) all_43_0_58 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (309) can reduce 191 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.35 | (721) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (733), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.35 | (749) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (563), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.35 | (741) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (713), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.35 | (737) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (721), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (136) ~ (all_0_0_0 = 0)
% 34.74/9.35 | (745) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.35 |
% 34.74/9.35 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 34.74/9.35 | (186) all_0_0_0 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (186) can reduce 136 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (1145) all_349_0_1982 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.74/9.35 |
% 34.74/9.35 | Applying alpha-rule on (1145) yields:
% 34.74/9.35 | (1089) all_349_0_1982 = 0
% 34.74/9.35 | (588) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (270), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (592) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (272), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (297), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (600) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (296), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (604) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (295), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (608) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (298), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (612) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (328), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.35 | (616) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 | Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_45_0_60 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields:
% 34.74/9.35 | (305) all_45_0_60 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (305) can reduce 184 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (1178) ~ (all_349_0_1982 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982
% 34.74/9.35 |
% 34.74/9.35 | Applying alpha-rule on (1178) yields:
% 34.74/9.35 | (1179) ~ (all_349_0_1982 = 0)
% 34.74/9.35 | (1180) distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (300), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (552) all_42_0_57 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (552) can reduce 210 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.35 | (189) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (392), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (309) all_43_0_58 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (309) can reduce 191 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.35 | (697) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_7_7) = v0))
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (1077), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (1189) (all_361_0_1985 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_1985 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_361_0_1985 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985)
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (1189), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (1190) (all_361_0_1985 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (all_361_0_1985 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (1190), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (1191) all_361_0_1985 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 34.74/9.35 |
% 34.74/9.35 | Applying alpha-rule on (1191) yields:
% 34.74/9.35 | (1192) all_361_0_1985 = 0
% 34.74/9.35 | (626) apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 34.74/9.35 |
% 34.74/9.35 +-Applying beta-rule and splitting (291), into two cases.
% 34.74/9.35 |-Branch one:
% 34.74/9.35 | (325) all_47_0_62 = 0
% 34.74/9.35 |
% 34.74/9.35 | Equations (325) can reduce 213 to:
% 34.74/9.35 | (187) $false
% 34.74/9.35 |
% 34.74/9.35 |-The branch is then unsatisfiable
% 34.74/9.35 |-Branch two:
% 34.74/9.35 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.35 | (630) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (292), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (325) all_47_0_62 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (325) can reduce 213 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.36 | (634) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (293), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (325) all_47_0_62 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (325) can reduce 213 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.36 | (638) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (294), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (325) all_47_0_62 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (325) can reduce 213 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.36 | (642) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.36 |
% 34.74/9.36 | Instantiating formula (19) with all_0_6_6, all_0_5_5, 0, all_47_0_62 and discharging atoms apart_point_and_line(all_0_6_6, all_0_5_5) = all_47_0_62, apart_point_and_line(all_0_6_6, all_0_5_5) = 0, yields:
% 34.74/9.36 | (325) all_47_0_62 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (325) can reduce 213 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (1212) all_361_0_1985 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.74/9.36 |
% 34.74/9.36 | Applying alpha-rule on (1212) yields:
% 34.74/9.36 | (1192) all_361_0_1985 = 0
% 34.74/9.36 | (551) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (301), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (288), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (287), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (733) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (289), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (290), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (567), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.36 | (579) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (575), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.36 | (583) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (1245) ~ (all_361_0_1985 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985
% 34.74/9.36 |
% 34.74/9.36 | Applying alpha-rule on (1245) yields:
% 34.74/9.36 | (1246) ~ (all_361_0_1985 = 0)
% 34.74/9.36 | (1247) distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (1068), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (1248) (all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (1248), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (1249) all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.74/9.36 |
% 34.74/9.36 | Applying alpha-rule on (1249) yields:
% 34.74/9.36 | (1250) all_353_0_1983 = 0
% 34.74/9.36 | (551) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (301), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (288), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (289), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (290), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (552) all_42_0_57 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (552) can reduce 210 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.36 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (575), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.36 | (583) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (567), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (17) ~ (all_0_1_1 = 0)
% 34.74/9.36 | (579) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 34.74/9.36 | (193) all_0_1_1 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (193) can reduce 17 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (1278) all_353_0_1983 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.74/9.36 |
% 34.74/9.36 | Applying alpha-rule on (1278) yields:
% 34.74/9.36 | (1250) all_353_0_1983 = 0
% 34.74/9.36 | (588) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (272), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (297), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (600) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (296), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (604) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (295), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (608) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (298), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (612) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 +-Applying beta-rule and splitting (328), into two cases.
% 34.74/9.36 |-Branch one:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.36 | (616) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 34.74/9.36 |
% 34.74/9.36 | Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_45_0_60 and discharging atoms apart_point_and_line(all_0_7_7, all_0_5_5) = all_45_0_60, apart_point_and_line(all_0_7_7, all_0_5_5) = 0, yields:
% 34.74/9.36 | (305) all_45_0_60 = 0
% 34.74/9.36 |
% 34.74/9.36 | Equations (305) can reduce 184 to:
% 34.74/9.36 | (187) $false
% 34.74/9.36 |
% 34.74/9.36 |-The branch is then unsatisfiable
% 34.74/9.36 |-Branch two:
% 34.74/9.36 | (1307) ~ (all_353_0_1983 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_1983
% 34.74/9.36 |
% 34.74/9.36 | Applying alpha-rule on (1307) yields:
% 34.74/9.36 | (1308) ~ (all_353_0_1983 = 0)
% 34.74/9.37 | (1309) distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_1983
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (272), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (305) all_45_0_60 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (305) can reduce 184 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.37 | (596) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (286), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (309) all_43_0_58 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (309) can reduce 191 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.37 | (705) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_8_8) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (301), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (559) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (288), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (563) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (273), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (309) all_43_0_58 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (309) can reduce 191 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.37 | (713) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_8_8) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (297), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (305) all_45_0_60 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (305) can reduce 184 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.37 | (600) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (274), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (309) all_43_0_58 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (309) can reduce 191 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.37 | (721) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (289), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (567) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (290), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (575) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (291), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (325) all_47_0_62 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (325) can reduce 213 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.37 | (630) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (287), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (733) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (292), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (325) all_47_0_62 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (325) can reduce 213 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.37 | (634) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (293), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (325) all_47_0_62 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (325) can reduce 213 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.37 | (638) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (296), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (305) all_45_0_60 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (305) can reduce 184 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.37 | (604) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (294), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (325) all_47_0_62 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (325) can reduce 213 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.37 | (642) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (295), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (305) all_45_0_60 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (305) can reduce 184 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.37 | (608) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (298), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (305) all_45_0_60 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (305) can reduce 184 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.37 | (612) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (299), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (309) all_43_0_58 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (309) can reduce 191 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.37 | (803) all_42_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (630), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1385) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (634), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1389) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (638), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1393) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (604), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1397) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (642), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1401) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_6_6) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (608), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1405) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (612), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1409) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_9_9, all_0_7_7) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (803), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.37 |
% 34.74/9.37 | Equations (552) can reduce 210 to:
% 34.74/9.37 | (187) $false
% 34.74/9.37 |
% 34.74/9.37 |-The branch is then unsatisfiable
% 34.74/9.37 |-Branch two:
% 34.74/9.37 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.37 | (1413) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_8_8, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_8_8, all_0_9_9) = v0))
% 34.74/9.37 |
% 34.74/9.37 +-Applying beta-rule and splitting (600), into two cases.
% 34.74/9.37 |-Branch one:
% 34.74/9.37 | (552) all_42_0_57 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (552) can reduce 210 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.38 | (1417) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_9_9, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_9_9) = v0))
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (43) with all_0_5_5, all_0_2_2, all_353_0_1983, all_361_0_1985 and discharging atoms distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985, distinct_lines(all_0_5_5, all_0_2_2) = all_353_0_1983, yields:
% 34.74/9.38 | (1418) all_361_0_1985 = all_353_0_1983
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (43) with all_0_5_5, all_0_2_2, all_349_0_1982, all_361_0_1985 and discharging atoms distinct_lines(all_0_5_5, all_0_2_2) = all_361_0_1985, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982, yields:
% 34.74/9.38 | (1419) all_361_0_1985 = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Combining equations (1418,1419) yields a new equation:
% 34.74/9.38 | (1420) all_353_0_1983 = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Simplifying 1420 yields:
% 34.74/9.38 | (1421) all_353_0_1983 = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Equations (1421) can reduce 1308 to:
% 34.74/9.38 | (1179) ~ (all_349_0_1982 = 0)
% 34.74/9.38 |
% 34.74/9.38 | From (1421) and (1309) follows:
% 34.74/9.38 | (1180) distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (100) with all_42_0_57, all_349_0_1982, all_0_2_2, all_0_5_5, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982, yields:
% 34.74/9.38 | (1424) all_349_0_1982 = 0 | all_42_0_57 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0)
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (139) with all_349_0_1982, all_0_2_2, all_0_5_5, all_0_9_9 and discharging atoms apart_point_and_line(all_0_9_9, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_2_2) = all_349_0_1982, yields:
% 34.74/9.38 | (1425) all_349_0_1982 = 0 | apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 34.74/9.38 |
% 34.74/9.38 +-Applying beta-rule and splitting (1425), into two cases.
% 34.74/9.38 |-Branch one:
% 34.74/9.38 | (1426) apart_point_and_line(all_0_9_9, all_0_2_2) = 0
% 34.74/9.38 |
% 34.74/9.38 +-Applying beta-rule and splitting (1424), into two cases.
% 34.74/9.38 |-Branch one:
% 34.74/9.38 | (1089) all_349_0_1982 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (1089) can reduce 1179 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1179) ~ (all_349_0_1982 = 0)
% 34.74/9.38 | (1430) all_42_0_57 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0)
% 34.74/9.38 |
% 34.74/9.38 +-Applying beta-rule and splitting (1430), into two cases.
% 34.74/9.38 |-Branch one:
% 34.74/9.38 | (552) all_42_0_57 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (552) can reduce 210 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.38 | (1434) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_9_9, all_0_5_5) = v0)
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (19) with all_0_9_9, all_0_2_2, 0, all_42_0_57 and discharging atoms apart_point_and_line(all_0_9_9, all_0_2_2) = all_42_0_57, apart_point_and_line(all_0_9_9, all_0_2_2) = 0, yields:
% 34.74/9.38 | (552) all_42_0_57 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (552) can reduce 210 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1437) ~ (apart_point_and_line(all_0_9_9, all_0_2_2) = 0)
% 34.74/9.38 | (1089) all_349_0_1982 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (1089) can reduce 1179 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1440) ~ (all_361_0_1985 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_361_0_1985
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1440) yields:
% 34.74/9.38 | (1246) ~ (all_361_0_1985 = 0)
% 34.74/9.38 | (1442) distinct_points(all_0_7_7, all_0_6_6) = all_361_0_1985
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_361_0_1985, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_361_0_1985, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.38 | (1192) all_361_0_1985 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (1192) can reduce 1246 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1445) ~ (all_349_0_1982 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1445) yields:
% 34.74/9.38 | (1179) ~ (all_349_0_1982 = 0)
% 34.74/9.38 | (1447) distinct_points(all_0_7_7, all_0_6_6) = all_349_0_1982
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_349_0_1982, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_349_0_1982, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.38 | (1089) all_349_0_1982 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (1089) can reduce 1179 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1450) ~ (all_47_0_62 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_47_0_62
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1450) yields:
% 34.74/9.38 | (213) ~ (all_47_0_62 = 0)
% 34.74/9.38 | (1452) distinct_points(all_0_7_7, all_0_6_6) = all_47_0_62
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_47_0_62, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_47_0_62, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.38 | (325) all_47_0_62 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (325) can reduce 213 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1455) ~ (all_42_0_57 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_42_0_57
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1455) yields:
% 34.74/9.38 | (210) ~ (all_42_0_57 = 0)
% 34.74/9.38 | (1457) distinct_points(all_0_9_9, all_0_8_8) = all_42_0_57
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_9_9, all_0_8_8, all_42_0_57, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_42_0_57, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 34.74/9.38 | (552) all_42_0_57 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (552) can reduce 210 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1460) ~ (all_43_0_58 = 0) & distinct_points(all_0_9_9, all_0_8_8) = all_43_0_58
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1460) yields:
% 34.74/9.38 | (191) ~ (all_43_0_58 = 0)
% 34.74/9.38 | (1462) distinct_points(all_0_9_9, all_0_8_8) = all_43_0_58
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_9_9, all_0_8_8, all_43_0_58, 0 and discharging atoms distinct_points(all_0_9_9, all_0_8_8) = all_43_0_58, distinct_points(all_0_9_9, all_0_8_8) = 0, yields:
% 34.74/9.38 | (309) all_43_0_58 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (309) can reduce 191 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 |-Branch two:
% 34.74/9.38 | (1465) ~ (all_45_0_60 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_45_0_60
% 34.74/9.38 |
% 34.74/9.38 | Applying alpha-rule on (1465) yields:
% 34.74/9.38 | (184) ~ (all_45_0_60 = 0)
% 34.74/9.38 | (1467) distinct_points(all_0_7_7, all_0_6_6) = all_45_0_60
% 34.74/9.38 |
% 34.74/9.38 | Instantiating formula (138) with all_0_7_7, all_0_6_6, all_45_0_60, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_45_0_60, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 34.74/9.38 | (305) all_45_0_60 = 0
% 34.74/9.38 |
% 34.74/9.38 | Equations (305) can reduce 184 to:
% 34.74/9.38 | (187) $false
% 34.74/9.38 |
% 34.74/9.38 |-The branch is then unsatisfiable
% 34.74/9.38 % SZS output end Proof for theBenchmark
% 34.74/9.38
% 34.74/9.38 8772ms
%------------------------------------------------------------------------------