TSTP Solution File: GEO189+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 03:48:26 EDT 2022
% Result : Theorem 16.05s 4.37s
% Output : Proof 55.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO189+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 03:45:43 EDT 2022
% 0.13/0.35 % 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
% 0.61/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/0.97 Prover 0: Preprocessing ...
% 2.43/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.52/1.22 Prover 0: Constructing countermodel ...
% 13.30/3.77 Prover 0: gave up
% 13.30/3.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 13.51/3.81 Prover 1: Preprocessing ...
% 13.68/3.93 Prover 1: Constructing countermodel ...
% 14.13/3.98 Prover 1: gave up
% 14.13/3.98 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.41/4.01 Prover 2: Preprocessing ...
% 15.11/4.19 Prover 2: Warning: ignoring some quantifiers
% 15.11/4.20 Prover 2: Constructing countermodel ...
% 16.05/4.36 Prover 2: proved (385ms)
% 16.05/4.37
% 16.05/4.37 No countermodel exists, formula is valid
% 16.05/4.37 % SZS status Theorem for theBenchmark
% 16.05/4.37
% 16.05/4.37 Generating proof ... Warning: ignoring some quantifiers
% 54.01/22.51 found it (size 762)
% 54.01/22.51
% 54.01/22.51 % SZS output start Proof for theBenchmark
% 54.01/22.51 Assumed formulas after preprocessing and simplification:
% 54.01/22.51 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v2, v3) = 0 & incident_point_and_line(v1, v4) = v5 & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7)
% 54.42/22.60 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 54.42/22.60 | (1) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_3_3, all_0_2_2) = 0 & incident_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0 & line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & distinct_points(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1
% 54.62/22.63 |
% 54.62/22.63 | Applying alpha-rule on (1) yields:
% 54.62/22.63 | (2) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 54.62/22.63 | (3) ! [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)))
% 54.62/22.63 | (4) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 54.62/22.63 | (5) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 54.62/22.63 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 54.62/22.63 | (7) ! [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)))
% 54.62/22.64 | (8) ! [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)))
% 54.62/22.64 | (9) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 54.62/22.64 | (10) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 54.62/22.64 | (11) distinct_points(all_0_5_5, all_0_3_3) = 0
% 54.62/22.64 | (12) ! [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)))
% 54.62/22.64 | (13) ! [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))
% 54.62/22.64 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 54.62/22.64 | (15) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 54.62/22.64 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 54.62/22.64 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 54.62/22.64 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 54.62/22.64 | (19) ! [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)))
% 54.62/22.64 | (20) ! [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))
% 54.62/22.64 | (21) ! [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)))
% 54.62/22.64 | (22) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 54.62/22.64 | (23) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 54.62/22.64 | (24) ! [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)))
% 54.62/22.64 | (25) ! [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)))
% 54.62/22.64 | (26) ! [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)))
% 54.62/22.64 | (27) ? [v0] : ? [v1] : line(v0) = v1
% 54.62/22.64 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 54.62/22.64 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 54.62/22.64 | (30) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 54.62/22.64 | (31) ! [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)
% 54.62/22.64 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 54.62/22.64 | (33) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 54.62/22.64 | (34) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 54.62/22.64 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 54.62/22.64 | (36) ! [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)))
% 54.62/22.64 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 54.62/22.64 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 54.62/22.64 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 54.62/22.64 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 54.62/22.64 | (41) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 54.62/22.64 | (42) ! [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)))
% 54.62/22.64 | (43) ! [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))
% 54.62/22.64 | (44) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 54.62/22.65 | (45) ! [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)))
% 54.62/22.65 | (46) ! [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)))
% 54.62/22.65 | (47) ! [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)))
% 54.62/22.65 | (48) ! [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)))
% 54.62/22.65 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 54.62/22.65 | (50) ! [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)))
% 54.62/22.65 | (51) ! [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)))
% 54.62/22.65 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 54.62/22.65 | (53) ! [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)))
% 54.62/22.65 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 54.62/22.65 | (55) ~ (all_0_0_0 = 0)
% 54.62/22.65 | (56) incident_point_and_line(all_0_3_3, all_0_2_2) = 0
% 54.62/22.65 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 54.62/22.65 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 54.62/22.65 | (59) ! [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)))
% 54.62/22.65 | (60) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 54.62/22.65 | (61) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 54.62/22.65 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 54.62/22.65 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 54.62/22.65 | (64) distinct_points(all_0_5_5, all_0_4_4) = 0
% 54.62/22.65 | (65) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 54.62/22.65 | (66) ! [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)))
% 54.62/22.65 | (67) ! [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)))
% 54.62/22.65 | (68) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 54.62/22.65 | (69) incident_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0
% 54.62/22.65 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 54.62/22.65 | (71) ! [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)))
% 54.62/22.65 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 54.62/22.65 | (73) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 54.62/22.65 | (74) ! [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)))
% 54.62/22.65 | (75) ! [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)
% 54.62/22.65 | (76) ! [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)))
% 54.62/22.65 | (77) ! [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)))
% 54.62/22.66 | (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)))
% 54.62/22.66 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 54.62/22.66 | (80) ! [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)))
% 54.62/22.66 | (81) ! [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)))
% 54.62/22.66 | (82) ! [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)
% 54.62/22.66 | (83) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 54.62/22.66 | (84) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 54.62/22.66 | (85) ! [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)))
% 54.62/22.66 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 54.62/22.66 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 54.62/22.66 | (88) ! [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)))
% 54.62/22.66 | (89) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 54.62/22.66 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 54.62/22.66 | (91) ! [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))
% 54.62/22.66 | (92) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 54.62/22.66 | (93) ! [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))
% 54.62/22.66 | (94) ? [v0] : ? [v1] : point(v0) = v1
% 54.62/22.66 | (95) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 54.62/22.66 | (96) ! [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)))
% 54.62/22.66 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 54.62/22.66 | (98) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 54.62/22.66 | (99) ! [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)))
% 54.62/22.66 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 54.62/22.66 | (101) ! [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)
% 54.62/22.66 | (102) ! [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)))
% 54.62/22.66 | (103) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 54.62/22.66 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 54.62/22.66 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 54.62/22.66 | (106) ! [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)))
% 54.62/22.66 | (107) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 54.62/22.66 | (108) ! [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)))
% 54.62/22.66 | (109) ! [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))
% 54.62/22.66 | (110) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 54.62/22.66 | (111) ! [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)))
% 54.62/22.66 | (112) ! [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)))
% 54.62/22.67 | (113) ! [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)))
% 54.62/22.67 | (114) ! [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)))
% 54.62/22.67 | (115) line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1
% 54.62/22.67 | (116) ! [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))
% 54.62/22.67 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 54.62/22.67 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 54.62/22.67 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 54.62/22.67 | (120) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 54.62/22.67 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 54.62/22.67 | (122) ! [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)))
% 54.62/22.67 | (123) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 54.62/22.67 | (124) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 54.62/22.67 | (125) ! [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)))
% 54.62/22.67 | (126) ! [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)))
% 54.62/22.67 | (127) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 54.62/22.67 | (128) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 54.62/22.67 | (129) ! [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)))
% 54.62/22.67 | (130) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 54.62/22.67 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 54.62/22.67 | (132) ! [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)))
% 54.62/22.67 | (133) ! [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)))
% 54.62/22.67 | (134) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 54.62/22.67 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 54.62/22.67 | (136) ! [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)))
% 54.62/22.67 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 54.62/22.67 | (138) ! [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)))
% 54.62/22.67 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 54.62/22.67 | (140) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 54.62/22.67 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 54.62/22.68 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 54.62/22.68 | (143) ! [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)))
% 54.62/22.68 | (144) ! [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)))
% 54.62/22.68 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 54.62/22.68 | (146) distinct_points(all_0_4_4, all_0_3_3) = 0
% 54.62/22.68 | (147) ! [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)))
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (128) with all_0_2_2, all_0_3_3 and discharging atoms incident_point_and_line(all_0_3_3, all_0_2_2) = 0, yields:
% 54.62/22.68 | (148) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = v0)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (17) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms incident_point_and_line(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 54.62/22.68 | (149) all_0_0_0 = 0 | apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (114) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 54.62/22.68 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (46) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 54.62/22.68 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (114) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 54.62/22.68 | (152) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (46) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 54.62/22.68 | (153) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (23) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.68 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (5) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.68 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (23) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.68 | (156) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (5) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.68 | (157) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (23) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 54.62/22.68 | (158) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating formula (5) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 54.62/22.68 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (159) with all_43_0_55, all_43_1_56 yields:
% 54.62/22.68 | (160) ~ (all_43_0_55 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56 & apart_point_and_line(all_0_5_5, all_43_1_56) = all_43_0_55
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (160) yields:
% 54.62/22.68 | (161) ~ (all_43_0_55 = 0)
% 54.62/22.68 | (162) line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56
% 54.62/22.68 | (163) apart_point_and_line(all_0_5_5, all_43_1_56) = all_43_0_55
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (158) with all_45_0_57, all_45_1_58 yields:
% 54.62/22.68 | (164) ~ (all_45_0_57 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_45_1_58 & apart_point_and_line(all_0_4_4, all_45_1_58) = all_45_0_57
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (164) yields:
% 54.62/22.68 | (165) ~ (all_45_0_57 = 0)
% 54.62/22.68 | (166) line_connecting(all_0_5_5, all_0_4_4) = all_45_1_58
% 54.62/22.68 | (167) apart_point_and_line(all_0_4_4, all_45_1_58) = all_45_0_57
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (157) with all_50_0_62, all_50_1_63 yields:
% 54.62/22.68 | (168) ~ (all_50_0_62 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_50_1_63 & apart_point_and_line(all_0_5_5, all_50_1_63) = all_50_0_62
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (168) yields:
% 54.62/22.68 | (169) ~ (all_50_0_62 = 0)
% 54.62/22.68 | (170) line_connecting(all_0_5_5, all_0_3_3) = all_50_1_63
% 54.62/22.68 | (171) apart_point_and_line(all_0_5_5, all_50_1_63) = all_50_0_62
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (153) with all_52_0_64 yields:
% 54.62/22.68 | (172) ( ~ (all_52_0_64 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_52_0_64) | ( ~ (all_52_0_64 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_52_0_64)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (152) with all_53_0_65 yields:
% 54.62/22.68 | (173) ( ~ (all_53_0_65 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_53_0_65) | ( ~ (all_53_0_65 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_53_0_65)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (156) with all_54_0_66, all_54_1_67 yields:
% 54.62/22.68 | (174) ~ (all_54_0_66 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_54_1_67 & apart_point_and_line(all_0_3_3, all_54_1_67) = all_54_0_66
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (174) yields:
% 54.62/22.68 | (175) ~ (all_54_0_66 = 0)
% 54.62/22.68 | (176) line_connecting(all_0_5_5, all_0_3_3) = all_54_1_67
% 54.62/22.68 | (177) apart_point_and_line(all_0_3_3, all_54_1_67) = all_54_0_66
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (155) with all_58_0_69, all_58_1_70 yields:
% 54.62/22.68 | (178) ~ (all_58_0_69 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_58_1_70 & apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (178) yields:
% 54.62/22.68 | (179) ~ (all_58_0_69 = 0)
% 54.62/22.68 | (180) line_connecting(all_0_4_4, all_0_3_3) = all_58_1_70
% 54.62/22.68 | (181) apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (154) with all_60_0_71, all_60_1_72 yields:
% 54.62/22.68 | (182) ~ (all_60_0_71 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_60_1_72 & apart_point_and_line(all_0_3_3, all_60_1_72) = all_60_0_71
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (182) yields:
% 54.62/22.68 | (183) ~ (all_60_0_71 = 0)
% 54.62/22.68 | (184) line_connecting(all_0_4_4, all_0_3_3) = all_60_1_72
% 54.62/22.68 | (185) apart_point_and_line(all_0_3_3, all_60_1_72) = all_60_0_71
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (150) with all_63_0_75 yields:
% 54.62/22.68 | (186) ( ~ (all_63_0_75 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_63_0_75) | ( ~ (all_63_0_75 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_63_0_75)
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (148) with all_66_0_78 yields:
% 54.62/22.68 | (187) ~ (all_66_0_78 = 0) & apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78
% 54.62/22.68 |
% 54.62/22.68 | Applying alpha-rule on (187) yields:
% 54.62/22.68 | (188) ~ (all_66_0_78 = 0)
% 54.62/22.68 | (189) apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78
% 54.62/22.68 |
% 54.62/22.68 | Instantiating (151) with all_68_0_79 yields:
% 54.62/22.68 | (190) ( ~ (all_68_0_79 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_68_0_79) | ( ~ (all_68_0_79 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_68_0_79)
% 54.62/22.68 |
% 54.62/22.68 +-Applying beta-rule and splitting (149), into two cases.
% 54.62/22.68 |-Branch one:
% 54.62/22.68 | (191) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 54.62/22.68 |
% 54.62/22.68 +-Applying beta-rule and splitting (173), into two cases.
% 54.62/22.68 |-Branch one:
% 54.62/22.68 | (192) ~ (all_53_0_65 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_53_0_65
% 54.62/22.69 |
% 54.62/22.69 | Applying alpha-rule on (192) yields:
% 54.62/22.69 | (193) ~ (all_53_0_65 = 0)
% 54.62/22.69 | (194) apart_point_and_line(all_0_4_4, all_0_2_2) = all_53_0_65
% 54.62/22.69 |
% 54.62/22.69 +-Applying beta-rule and splitting (172), into two cases.
% 54.62/22.69 |-Branch one:
% 54.62/22.69 | (195) ~ (all_52_0_64 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_52_0_64
% 54.62/22.69 |
% 54.62/22.69 | Applying alpha-rule on (195) yields:
% 54.62/22.69 | (196) ~ (all_52_0_64 = 0)
% 54.62/22.69 | (197) apart_point_and_line(all_0_5_5, all_0_2_2) = all_52_0_64
% 54.62/22.69 |
% 54.62/22.69 +-Applying beta-rule and splitting (190), into two cases.
% 54.62/22.69 |-Branch one:
% 54.62/22.69 | (198) ~ (all_68_0_79 = 0) & apart_point_and_line(all_0_5_5, all_0_1_1) = all_68_0_79
% 54.62/22.69 |
% 54.62/22.69 | Applying alpha-rule on (198) yields:
% 54.62/22.69 | (199) ~ (all_68_0_79 = 0)
% 54.62/22.69 | (200) apart_point_and_line(all_0_5_5, all_0_1_1) = all_68_0_79
% 54.62/22.69 |
% 54.62/22.69 +-Applying beta-rule and splitting (186), into two cases.
% 54.62/22.69 |-Branch one:
% 54.62/22.69 | (201) ~ (all_63_0_75 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_63_0_75
% 54.62/22.69 |
% 54.62/22.69 | Applying alpha-rule on (201) yields:
% 54.62/22.69 | (202) ~ (all_63_0_75 = 0)
% 54.62/22.69 | (203) apart_point_and_line(all_0_3_3, all_0_1_1) = all_63_0_75
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (57) with all_0_4_4, all_0_3_3, all_58_1_70, all_60_1_72 and discharging atoms line_connecting(all_0_4_4, all_0_3_3) = all_60_1_72, line_connecting(all_0_4_4, all_0_3_3) = all_58_1_70, yields:
% 54.62/22.69 | (204) all_60_1_72 = all_58_1_70
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (57) with all_0_5_5, all_0_3_3, all_54_1_67, all_0_1_1 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_54_1_67, line_connecting(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 54.62/22.69 | (205) all_54_1_67 = all_0_1_1
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (57) with all_0_5_5, all_0_3_3, all_50_1_63, all_54_1_67 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_54_1_67, line_connecting(all_0_5_5, all_0_3_3) = all_50_1_63, yields:
% 54.62/22.69 | (206) all_54_1_67 = all_50_1_63
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (57) with all_0_5_5, all_0_4_4, all_45_1_58, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_45_1_58, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 54.62/22.69 | (207) all_45_1_58 = all_0_2_2
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (57) with all_0_5_5, all_0_4_4, all_43_1_56, all_45_1_58 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_45_1_58, line_connecting(all_0_5_5, all_0_4_4) = all_43_1_56, yields:
% 54.62/22.69 | (208) all_45_1_58 = all_43_1_56
% 54.62/22.69 |
% 54.62/22.69 | Combining equations (206,205) yields a new equation:
% 54.62/22.69 | (209) all_50_1_63 = all_0_1_1
% 54.62/22.69 |
% 54.62/22.69 | Simplifying 209 yields:
% 54.62/22.69 | (210) all_50_1_63 = all_0_1_1
% 54.62/22.69 |
% 54.62/22.69 | Combining equations (207,208) yields a new equation:
% 54.62/22.69 | (211) all_43_1_56 = all_0_2_2
% 54.62/22.69 |
% 54.62/22.69 | Combining equations (211,208) yields a new equation:
% 54.62/22.69 | (207) all_45_1_58 = all_0_2_2
% 54.62/22.69 |
% 54.62/22.69 | From (204) and (185) follows:
% 54.62/22.69 | (213) apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71
% 54.62/22.69 |
% 54.62/22.69 | From (205) and (177) follows:
% 54.62/22.69 | (214) apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66
% 54.62/22.69 |
% 54.62/22.69 | From (207) and (167) follows:
% 54.62/22.69 | (215) apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57
% 54.62/22.69 |
% 54.62/22.69 | From (210) and (171) follows:
% 54.62/22.69 | (216) apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62
% 54.62/22.69 |
% 54.62/22.69 | From (211) and (163) follows:
% 54.62/22.69 | (217) apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (79) with all_0_3_3, all_0_1_1, all_54_0_66, all_63_0_75 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_63_0_75, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.69 | (218) all_63_0_75 = all_54_0_66
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (79) with all_0_4_4, all_0_2_2, all_45_0_57, all_53_0_65 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_53_0_65, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.69 | (219) all_53_0_65 = all_45_0_57
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (79) with all_0_5_5, all_0_1_1, all_50_0_62, all_68_0_79 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_68_0_79, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 54.62/22.69 | (220) all_68_0_79 = all_50_0_62
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (79) with all_0_5_5, all_0_2_2, all_43_0_55, all_52_0_64 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_52_0_64, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 54.62/22.69 | (221) all_52_0_64 = all_43_0_55
% 54.62/22.69 |
% 54.62/22.69 | Equations (220) can reduce 199 to:
% 54.62/22.69 | (169) ~ (all_50_0_62 = 0)
% 54.62/22.69 |
% 54.62/22.69 | Equations (218) can reduce 202 to:
% 54.62/22.69 | (175) ~ (all_54_0_66 = 0)
% 54.62/22.69 |
% 54.62/22.69 | Equations (219) can reduce 193 to:
% 54.62/22.69 | (165) ~ (all_45_0_57 = 0)
% 54.62/22.69 |
% 54.62/22.69 | Equations (221) can reduce 196 to:
% 54.62/22.69 | (161) ~ (all_43_0_55 = 0)
% 54.62/22.69 |
% 54.62/22.69 | From (218) and (203) follows:
% 54.62/22.69 | (214) apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66
% 54.62/22.69 |
% 54.62/22.69 | From (219) and (194) follows:
% 54.62/22.69 | (215) apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57
% 54.62/22.69 |
% 54.62/22.69 | From (220) and (200) follows:
% 54.62/22.69 | (216) apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62
% 54.62/22.69 |
% 54.62/22.69 | From (221) and (197) follows:
% 54.62/22.69 | (217) apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (26) with all_60_0_71, all_60_0_71, all_58_1_70, all_58_1_70, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.69 | (230) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (51) with all_60_0_71, all_60_0_71, all_58_1_70, all_58_1_70, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, yields:
% 54.62/22.69 | (231) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (111) with all_60_0_71, all_60_0_71, all_58_1_70, all_58_1_70, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, yields:
% 54.62/22.69 | (232) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (26) with all_54_0_66, all_60_0_71, all_0_1_1, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.69 | (233) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 54.62/22.69 |
% 54.62/22.69 | Instantiating formula (26) with all_54_0_66, all_60_0_71, all_0_1_1, all_58_1_70, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.69 | (234) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_60_0_71, all_54_0_66, all_58_1_70, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (235) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_54_0_66, all_60_0_71, all_0_1_1, all_58_1_70, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.70 | (236) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_60_0_71, all_54_0_66, all_58_1_70, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.70 | (237) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_54_0_66, all_60_0_71, all_0_1_1, all_58_1_70, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.70 | (238) all_60_0_71 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_54_0_66, all_54_0_66, all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.70 | (239) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_54_0_66, all_54_0_66, all_0_1_1, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (240) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_54_0_66, all_54_0_66, all_0_1_1, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.70 | (241) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_54_0_66, all_54_0_66, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, yields:
% 54.62/22.70 | (242) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_66_0_78, all_60_0_71, all_0_2_2, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.70 | (243) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_66_0_78, all_60_0_71, all_0_2_2, all_58_1_70, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (244) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_60_0_71, all_66_0_78, all_58_1_70, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (245) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_66_0_78, all_60_0_71, all_0_2_2, all_58_1_70, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (246) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_60_0_71, all_66_0_78, all_58_1_70, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (247) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_66_0_78, all_60_0_71, all_0_2_2, all_58_1_70, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (248) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_60_0_71, all_66_0_78, all_58_1_70, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (249) all_66_0_78 = 0 | all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_54_0_66, all_66_0_78, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.70 | (250) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_66_0_78, all_54_0_66, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (251) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_54_0_66, all_66_0_78, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (252) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_66_0_78, all_54_0_66, all_0_2_2, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (253) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_54_0_66, all_66_0_78, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (254) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_66_0_78, all_54_0_66, all_0_2_2, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (255) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_54_0_66, all_66_0_78, all_0_1_1, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (256) all_66_0_78 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_66_0_78, all_66_0_78, all_0_2_2, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.70 | (257) all_66_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (26) with all_66_0_78, all_66_0_78, all_0_2_2, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 54.62/22.70 | (258) all_66_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (51) with all_66_0_78, all_66_0_78, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (259) all_66_0_78 = 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))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_66_0_78, all_66_0_78, all_0_2_2, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, yields:
% 54.62/22.70 | (260) all_66_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_58_0_69, all_60_0_71, all_58_1_70, all_58_1_70, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.70 | (261) all_60_0_71 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_60_0_71, all_58_0_69, all_58_1_70, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.70 | (262) all_60_0_71 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_58_0_69, all_54_0_66, all_58_1_70, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.70 | (263) all_58_0_69 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.70 |
% 54.62/22.70 | Instantiating formula (111) with all_54_0_66, all_58_0_69, all_0_1_1, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (264) all_58_0_69 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_58_0_69, all_54_0_66, all_0_1_1, all_58_1_70, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (265) all_58_0_69 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_54_0_66, all_58_0_69, all_58_1_70, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (266) all_58_0_69 = 0 | all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_58_0_69, all_66_0_78, all_58_1_70, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (267) all_66_0_78 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_66_0_78, all_58_0_69, all_0_2_2, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (268) all_66_0_78 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_58_0_69, all_66_0_78, all_0_2_2, all_58_1_70, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (269) all_66_0_78 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_66_0_78, all_58_0_69, all_58_1_70, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (270) all_66_0_78 = 0 | all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (143) with all_58_0_69, all_58_0_69, all_58_1_70, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.71 | (271) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (26) with all_58_0_69, all_58_0_69, all_58_1_70, all_58_1_70, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 54.62/22.71 | (272) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (51) with all_58_0_69, all_58_0_69, all_58_1_70, all_58_1_70, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (273) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_58_0_69, all_58_0_69, all_58_1_70, all_58_1_70, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, yields:
% 54.62/22.71 | (274) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_45_0_57, all_60_0_71, all_0_2_2, all_58_1_70, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (275) all_60_0_71 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_60_0_71, all_45_0_57, all_58_1_70, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (276) all_60_0_71 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_45_0_57, all_60_0_71, all_58_1_70, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (277) all_60_0_71 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_60_0_71, all_45_0_57, all_0_2_2, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (278) all_60_0_71 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_45_0_57, all_54_0_66, all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (279) all_54_0_66 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_54_0_66, all_45_0_57, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (280) all_54_0_66 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (136) with all_45_0_57, all_54_0_66, all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (281) all_54_0_66 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_45_0_57, all_66_0_78, all_0_2_2, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (282) all_66_0_78 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (143) with all_45_0_57, all_58_0_69, all_0_2_2, all_58_1_70, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 54.62/22.71 | (283) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (26) with all_45_0_57, all_58_0_69, all_0_2_2, all_58_1_70, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 54.62/22.71 | (284) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (26) with all_58_0_69, all_45_0_57, all_58_1_70, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 54.62/22.71 | (285) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (51) with all_45_0_57, all_58_0_69, all_0_2_2, all_58_1_70, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (286) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (51) with all_58_0_69, all_45_0_57, all_58_1_70, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (287) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_45_0_57, all_58_0_69, all_0_2_2, all_58_1_70, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (288) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 54.62/22.71 |
% 54.62/22.71 | Instantiating formula (111) with all_58_0_69, all_45_0_57, all_58_1_70, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 54.62/22.71 | (289) all_58_0_69 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (101) with all_45_0_57, all_0_2_2, all_0_1_1, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_1_1) = 0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 55.08/22.71 | (290) all_45_0_57 = 0 | distinct_lines(all_0_1_1, all_0_2_2) = 0
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (143) with all_45_0_57, all_45_0_57, all_0_2_2, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 55.08/22.71 | (291) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (26) with all_45_0_57, all_45_0_57, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.08/22.71 | (292) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (51) with all_45_0_57, all_45_0_57, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 55.08/22.71 | (293) all_45_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))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (111) with all_45_0_57, all_45_0_57, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, yields:
% 55.08/22.71 | (294) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (111) with all_50_0_62, all_60_0_71, all_0_1_1, all_58_1_70, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.71 | (295) all_60_0_71 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.71 |
% 55.08/22.71 | Instantiating formula (136) with all_50_0_62, all_60_0_71, all_58_1_70, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.71 | (296) all_60_0_71 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_60_0_71, all_50_0_62, all_0_1_1, all_58_1_70, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (297) all_60_0_71 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_50_0_62, all_54_0_66, all_0_1_1, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (298) all_54_0_66 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_54_0_66, all_50_0_62, all_0_1_1, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (299) all_54_0_66 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_50_0_62, all_66_0_78, all_0_1_1, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (300) all_66_0_78 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_50_0_62, all_66_0_78, all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (301) all_66_0_78 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_66_0_78, all_50_0_62, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (302) all_66_0_78 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_50_0_62, all_58_0_69, all_0_1_1, all_58_1_70, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (303) all_58_0_69 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_58_0_69, all_50_0_62, all_0_1_1, all_58_1_70, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (304) all_58_0_69 = 0 | all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_50_0_62, all_45_0_57, all_0_1_1, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (305) all_50_0_62 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_45_0_57, all_50_0_62, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (306) all_50_0_62 = 0 | all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (143) with all_50_0_62, all_50_0_62, all_0_1_1, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.08/22.72 | (307) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (51) with all_50_0_62, all_50_0_62, all_0_1_1, all_0_1_1, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (308) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_50_0_62, all_50_0_62, all_0_1_1, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, yields:
% 55.08/22.72 | (309) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_60_0_71, all_0_2_2, all_58_1_70, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (310) all_60_0_71 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_60_0_71, all_43_0_55, all_58_1_70, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (311) all_60_0_71 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_43_0_55, all_60_0_71, all_58_1_70, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (312) all_60_0_71 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_60_0_71, all_43_0_55, all_0_2_2, all_58_1_70, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_58_1_70) = all_60_0_71, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (313) all_60_0_71 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_54_0_66, all_0_2_2, all_0_1_1, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (314) all_54_0_66 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_54_0_66, all_43_0_55, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (315) all_54_0_66 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_43_0_55, all_54_0_66, all_0_1_1, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (316) all_54_0_66 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_54_0_66, all_43_0_55, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_54_0_66, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (317) all_54_0_66 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_66_0_78, all_0_2_2, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (318) all_66_0_78 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_66_0_78, all_43_0_55, all_0_2_2, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_66_0_78, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (319) all_66_0_78 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_58_0_69, all_0_2_2, all_58_1_70, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (320) all_58_0_69 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_58_0_69, all_43_0_55, all_58_1_70, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (321) all_58_0_69 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_43_0_55, all_58_0_69, all_58_1_70, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (322) all_58_0_69 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (136) with all_58_0_69, all_43_0_55, all_0_2_2, all_58_1_70, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_58_1_70) = all_58_0_69, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (323) all_58_0_69 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_45_0_57, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (324) all_45_0_57 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_45_0_57, all_43_0_55, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_45_0_57, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (325) all_45_0_57 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (143) with all_50_0_62, all_43_0_55, all_0_1_1, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 55.08/22.72 | (326) all_50_0_62 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (143) with all_50_0_62, all_43_0_55, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.08/22.72 | (327) all_50_0_62 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (51) with all_50_0_62, all_43_0_55, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.72 | (328) all_50_0_62 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.72 |
% 55.08/22.72 | Instantiating formula (111) with all_43_0_55, all_50_0_62, all_0_2_2, all_0_1_1, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.73 | (329) all_50_0_62 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.73 |
% 55.08/22.73 | Instantiating formula (111) with all_50_0_62, all_43_0_55, all_0_1_1, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.73 | (330) all_50_0_62 = 0 | all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.73 |
% 55.08/22.73 | Instantiating formula (143) with all_43_0_55, all_43_0_55, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.08/22.73 | (331) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.73 |
% 55.08/22.73 | Instantiating formula (51) with all_43_0_55, all_43_0_55, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.73 | (332) all_43_0_55 = 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))
% 55.08/22.73 |
% 55.08/22.73 | Instantiating formula (111) with all_43_0_55, all_43_0_55, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, yields:
% 55.08/22.73 | (333) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (332), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (334) all_43_0_55 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (334) can reduce 161 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.73 | (337) ? [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))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (290), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (338) distinct_lines(all_0_1_1, all_0_2_2) = 0
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (231), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (339) all_60_0_71 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (339) can reduce 183 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.73 | (342) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (293), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (343) all_45_0_57 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (343) can reduce 165 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.73 | (337) ? [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))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (308), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (347) all_50_0_62 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (347) can reduce 169 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.73 | (350) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (230), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (339) all_60_0_71 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (339) can reduce 183 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.73 | (354) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (253), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (355) all_66_0_78 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (355) can reduce 188 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.73 | (358) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (259), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (355) all_66_0_78 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (355) can reduce 188 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.73 | (337) ? [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))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (273), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (342) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (260), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (355) all_66_0_78 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (355) can reduce 188 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.73 | (370) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (271), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (374) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (333), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (334) all_43_0_55 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (334) can reduce 161 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.73 | (378) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (261), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (339) all_60_0_71 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (339) can reduce 183 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.73 | (382) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (262), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (339) all_60_0_71 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (339) can reduce 183 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.73 | (386) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (263), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (390) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (264), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (394) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (269), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (355) all_66_0_78 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (355) can reduce 188 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.73 | (398) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (265), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (402) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (268), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (355) all_66_0_78 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (355) can reduce 188 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.73 | (406) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.73 |
% 55.08/22.73 +-Applying beta-rule and splitting (266), into two cases.
% 55.08/22.73 |-Branch one:
% 55.08/22.73 | (363) all_58_0_69 = 0
% 55.08/22.73 |
% 55.08/22.73 | Equations (363) can reduce 179 to:
% 55.08/22.73 | (335) $false
% 55.08/22.73 |
% 55.08/22.73 |-The branch is then unsatisfiable
% 55.08/22.73 |-Branch two:
% 55.08/22.73 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.73 | (410) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (267), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (414) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (270), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (418) all_58_0_69 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (358), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (419) all_54_0_66 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (419) can reduce 175 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.74 | (422) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (402), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (419) all_54_0_66 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (419) can reduce 175 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.74 | (426) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (251), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (430) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (257), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (434) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (258), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (438) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (272), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (363) all_58_0_69 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (363) can reduce 179 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.74 | (354) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (254), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (446) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (247), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (450) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (256), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (454) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (255), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (458) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (274), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (363) all_58_0_69 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (363) can reduce 179 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.74 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (275), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (339) all_60_0_71 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (339) can reduce 183 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.74 | (466) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (248), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (470) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (305), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (347) all_50_0_62 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (347) can reduce 169 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.74 | (474) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (252), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (478) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (249), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (482) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (250), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (486) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (302), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (355) all_66_0_78 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (355) can reduce 188 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.74 | (490) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (303), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (363) all_58_0_69 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (363) can reduce 179 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.74 | (494) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (304), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (363) all_58_0_69 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (363) can reduce 179 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.74 | (498) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (446), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (419) all_54_0_66 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (419) can reduce 175 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.74 | (502) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.74 |
% 55.08/22.74 +-Applying beta-rule and splitting (454), into two cases.
% 55.08/22.74 |-Branch one:
% 55.08/22.74 | (419) all_54_0_66 = 0
% 55.08/22.74 |
% 55.08/22.74 | Equations (419) can reduce 175 to:
% 55.08/22.74 | (335) $false
% 55.08/22.74 |
% 55.08/22.74 |-The branch is then unsatisfiable
% 55.08/22.74 |-Branch two:
% 55.08/22.74 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.74 | (506) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.74 |
% 55.08/22.75 +-Applying beta-rule and splitting (458), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (419) all_54_0_66 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (419) can reduce 175 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.75 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (241), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (419) all_54_0_66 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (419) can reduce 175 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.75 | (350) ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (295), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (339) all_60_0_71 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (339) can reduce 183 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.75 | (518) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (310), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (339) all_60_0_71 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (339) can reduce 183 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.75 | (522) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (474), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (343) all_45_0_57 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (343) can reduce 165 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.75 | (526) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (482), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (339) all_60_0_71 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (339) can reduce 183 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.75 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (486), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (419) all_54_0_66 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (419) can reduce 175 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.75 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (490), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (347) all_50_0_62 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (347) can reduce 169 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.75 | (538) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (494), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (347) all_50_0_62 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (347) can reduce 169 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.75 | (542) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (498), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (347) all_50_0_62 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (347) can reduce 169 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.75 | (546) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (518), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (347) all_50_0_62 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (347) can reduce 169 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.75 | (550) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (522), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (334) all_43_0_55 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (334) can reduce 161 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.75 | (554) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (237), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (339) all_60_0_71 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (339) can reduce 183 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.75 | (558) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (239), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (419) all_54_0_66 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (419) can reduce 175 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.75 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (240), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (419) all_54_0_66 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (419) can reduce 175 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.75 | (566) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (294), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (343) all_45_0_57 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (343) can reduce 165 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.75 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (286), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (363) all_58_0_69 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (363) can reduce 179 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.75 | (574) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (287), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (363) all_58_0_69 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (363) can reduce 179 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.75 | (578) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (236), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (339) all_60_0_71 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (339) can reduce 183 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.75 | (582) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (291), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (343) all_45_0_57 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (343) can reduce 165 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.75 | (586) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (292), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (343) all_45_0_57 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (343) can reduce 165 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.75 | (438) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (282), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (355) all_66_0_78 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (355) can reduce 188 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.75 | (594) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.75 |
% 55.08/22.75 +-Applying beta-rule and splitting (288), into two cases.
% 55.08/22.75 |-Branch one:
% 55.08/22.75 | (363) all_58_0_69 = 0
% 55.08/22.75 |
% 55.08/22.75 | Equations (363) can reduce 179 to:
% 55.08/22.75 | (335) $false
% 55.08/22.75 |
% 55.08/22.75 |-The branch is then unsatisfiable
% 55.08/22.75 |-Branch two:
% 55.08/22.75 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.75 | (598) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (238), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (602) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (289), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (363) all_58_0_69 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (363) can reduce 179 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.76 | (606) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (276), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (610) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (277), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (614) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (278), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (618) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (279), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (419) all_54_0_66 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (419) can reduce 175 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.76 | (622) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (280), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (419) all_54_0_66 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (419) can reduce 175 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.76 | (626) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (281), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (419) all_54_0_66 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (419) can reduce 175 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.76 | (630) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (285), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (363) all_58_0_69 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (363) can reduce 179 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.76 | (634) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (470), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (638) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (232), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (339) all_60_0_71 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (339) can reduce 183 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.76 | (642) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (331), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (334) all_43_0_55 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (334) can reduce 161 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.76 | (434) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (578), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (343) all_45_0_57 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (343) can reduce 165 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.76 | (650) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (610), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (343) all_45_0_57 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (343) can reduce 165 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.76 | (654) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (634), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (343) all_45_0_57 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (343) can reduce 165 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.76 | (658) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (283), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (363) all_58_0_69 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (363) can reduce 179 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.76 | (662) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (284), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (363) all_58_0_69 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (363) can reduce 179 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.76 | (666) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (327), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (347) all_50_0_62 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (347) can reduce 169 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.76 | (670) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (330), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (347) all_50_0_62 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (347) can reduce 169 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.76 | (674) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (662), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (343) all_45_0_57 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (343) can reduce 165 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.76 | (678) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (430), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (419) all_54_0_66 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (419) can reduce 175 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.76 | (682) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 55.08/22.76 |
% 55.08/22.76 | Instantiating (682) with all_483_0_10748 yields:
% 55.08/22.76 | (683) (all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_483_0_10748 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = all_483_0_10748)
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (328), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (347) all_50_0_62 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (347) can reduce 169 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.76 | (687) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (329), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (347) all_50_0_62 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (347) can reduce 169 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.76 | (691) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (670), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (334) all_43_0_55 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (334) can reduce 161 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.76 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (683), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (696) (all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (696), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (697) all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 55.08/22.76 |
% 55.08/22.76 | Applying alpha-rule on (697) yields:
% 55.08/22.76 | (698) all_483_0_10748 = 0
% 55.08/22.76 | (699) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 55.08/22.76 |
% 55.08/22.76 +-Applying beta-rule and splitting (242), into two cases.
% 55.08/22.76 |-Branch one:
% 55.08/22.76 | (419) all_54_0_66 = 0
% 55.08/22.76 |
% 55.08/22.76 | Equations (419) can reduce 175 to:
% 55.08/22.76 | (335) $false
% 55.08/22.76 |
% 55.08/22.76 |-The branch is then unsatisfiable
% 55.08/22.76 |-Branch two:
% 55.08/22.76 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (703) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (307), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (309), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (711) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (246), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (715) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (326), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (719) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (243), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (723) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (233), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (339) all_60_0_71 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (339) can reduce 183 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.77 | (727) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (306), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (731) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (244), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (735) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (245), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (739) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (234), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (339) all_60_0_71 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (339) can reduce 183 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.77 | (743) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (478), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (419) all_54_0_66 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (419) can reduce 175 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (747) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (582), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (419) all_54_0_66 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (419) can reduce 175 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (751) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (299), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (419) all_54_0_66 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (419) can reduce 175 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (755) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (300), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (759) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (297), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (339) all_60_0_71 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (339) can reduce 183 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.77 | (763) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (296), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (339) all_60_0_71 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (339) can reduce 183 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.77 | (767) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (298), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (419) all_54_0_66 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (419) can reduce 175 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (771) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (318), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (775) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (301), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (355) all_66_0_78 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (355) can reduce 188 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.77 | (779) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (755), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (783) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (763), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (787) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (759), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (791) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (767), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (795) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (771), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (799) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (779), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (803) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.77 |
% 55.08/22.77 | Instantiating formula (79) with all_0_5_5, all_0_1_1, 0, all_50_0_62 and discharging atoms apart_point_and_line(all_0_5_5, all_0_1_1) = all_50_0_62, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (806) all_483_0_10748 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 55.08/22.77 |
% 55.08/22.77 | Applying alpha-rule on (806) yields:
% 55.08/22.77 | (698) all_483_0_10748 = 0
% 55.08/22.77 | (808) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (235), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (339) all_60_0_71 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (339) can reduce 183 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.77 | (812) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (242), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (419) all_54_0_66 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (419) can reduce 175 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.77 | (703) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.77 |
% 55.08/22.77 +-Applying beta-rule and splitting (307), into two cases.
% 55.08/22.77 |-Branch one:
% 55.08/22.77 | (347) all_50_0_62 = 0
% 55.08/22.77 |
% 55.08/22.77 | Equations (347) can reduce 169 to:
% 55.08/22.77 | (335) $false
% 55.08/22.77 |
% 55.08/22.77 |-The branch is then unsatisfiable
% 55.08/22.77 |-Branch two:
% 55.08/22.77 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.77 | (562) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 55.08/22.77 |
% 55.08/22.78 +-Applying beta-rule and splitting (309), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (347) all_50_0_62 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (347) can reduce 169 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.78 | (711) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (246), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (355) all_66_0_78 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (355) can reduce 188 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.78 | (715) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (326), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (347) all_50_0_62 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (347) can reduce 169 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.78 | (719) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (243), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (355) all_66_0_78 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (355) can reduce 188 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.78 | (723) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (233), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (339) all_60_0_71 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (339) can reduce 183 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.78 | (727) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (244), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (355) all_66_0_78 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (355) can reduce 188 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.78 | (735) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (306), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (347) all_50_0_62 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (347) can reduce 169 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (169) ~ (all_50_0_62 = 0)
% 55.08/22.78 | (731) all_45_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (245), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (355) all_66_0_78 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (355) can reduce 188 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.78 | (739) all_60_0_71 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (466), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (856) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (478), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (747) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (582), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (751) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (606), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (868) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (614), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (872) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (630), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (876) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (666), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (880) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (674), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (334) all_43_0_55 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (334) can reduce 161 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.78 | (884) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (812), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (888) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_58_1_70) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (719), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (334) all_43_0_55 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (334) can reduce 161 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.78 | (892) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (723), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (339) all_60_0_71 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (339) can reduce 183 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.78 | (896) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (727), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (900) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (735), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (339) all_60_0_71 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (339) can reduce 183 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.78 | (880) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (731), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (908) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (739), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (339) all_60_0_71 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (339) can reduce 183 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.78 | (658) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (234), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (339) all_60_0_71 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (339) can reduce 183 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.78 | (743) all_54_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (743), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (920) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (574), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (924) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (594), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (928) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (598), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (932) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (602), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (419) all_54_0_66 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (419) can reduce 175 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.78 | (936) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_58_1_70) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (618), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (940) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (622), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.78 |-The branch is then unsatisfiable
% 55.08/22.78 |-Branch two:
% 55.08/22.78 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.78 | (944) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 55.08/22.78 |
% 55.08/22.78 +-Applying beta-rule and splitting (626), into two cases.
% 55.08/22.78 |-Branch one:
% 55.08/22.78 | (343) all_45_0_57 = 0
% 55.08/22.78 |
% 55.08/22.78 | Equations (343) can reduce 165 to:
% 55.08/22.78 | (335) $false
% 55.08/22.78 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.79 | (948) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (715), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (339) all_60_0_71 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (339) can reduce 183 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.79 | (924) ? [v0] : ((v0 = 0 & convergent_lines(all_58_1_70, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (317), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (419) all_54_0_66 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (419) can reduce 175 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.79 | (956) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (315), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (419) all_54_0_66 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (419) can reduce 175 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.79 | (960) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (316), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (419) all_54_0_66 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (419) can reduce 175 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.79 | (964) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (318), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (355) all_66_0_78 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (355) can reduce 188 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.79 | (775) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (323), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (363) all_58_0_69 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (363) can reduce 179 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.79 | (972) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (324), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (343) all_45_0_57 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (343) can reduce 165 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.79 | (976) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (319), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (355) all_66_0_78 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (355) can reduce 188 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (188) ~ (all_66_0_78 = 0)
% 55.08/22.79 | (980) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (320), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (363) all_58_0_69 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (363) can reduce 179 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.79 | (984) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (321), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (363) all_58_0_69 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (363) can reduce 179 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.79 | (988) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (322), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (363) all_58_0_69 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (363) can reduce 179 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (179) ~ (all_58_0_69 = 0)
% 55.08/22.79 | (992) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (325), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (343) all_45_0_57 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (343) can reduce 165 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (165) ~ (all_45_0_57 = 0)
% 55.08/22.79 | (996) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (299), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (419) all_54_0_66 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (419) can reduce 175 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.79 | (755) all_50_0_62 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (313), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (339) all_60_0_71 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (339) can reduce 183 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.79 | (1004) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (311), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (339) all_60_0_71 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (339) can reduce 183 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.79 | (1008) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (312), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (339) all_60_0_71 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (339) can reduce 183 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (183) ~ (all_60_0_71 = 0)
% 55.08/22.79 | (1012) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (314), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (419) all_54_0_66 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (419) can reduce 175 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (175) ~ (all_54_0_66 = 0)
% 55.08/22.79 | (1016) all_43_0_55 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (980), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1020) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (956), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1024) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (964), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1028) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (775), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1032) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (984), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1036) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (1004), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1040) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (1008), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1044) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (1012), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1048) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (1016), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (1052) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (687), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.79 |
% 55.08/22.79 |-The branch is then unsatisfiable
% 55.08/22.79 |-Branch two:
% 55.08/22.79 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.79 | (502) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 55.08/22.79 |
% 55.08/22.79 +-Applying beta-rule and splitting (691), into two cases.
% 55.08/22.79 |-Branch one:
% 55.08/22.79 | (334) all_43_0_55 = 0
% 55.08/22.79 |
% 55.08/22.79 | Equations (334) can reduce 161 to:
% 55.08/22.79 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1060) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (960), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1064) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (972), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1068) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_58_1_70, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (976), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1072) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (988), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1076) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (992), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1080) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_58_1_70) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_58_1_70) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 55.08/22.80 |
% 55.08/22.80 +-Applying beta-rule and splitting (996), into two cases.
% 55.08/22.80 |-Branch one:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (161) ~ (all_43_0_55 = 0)
% 55.08/22.80 | (1084) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 55.08/22.80 |
% 55.08/22.80 | Instantiating formula (79) with all_0_5_5, all_0_2_2, 0, all_43_0_55 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_43_0_55, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 55.08/22.80 | (334) all_43_0_55 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (334) can reduce 161 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.08/22.80 |-Branch two:
% 55.08/22.80 | (1087) ~ (all_483_0_10748 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = all_483_0_10748
% 55.08/22.80 |
% 55.08/22.80 | Applying alpha-rule on (1087) yields:
% 55.08/22.80 | (1088) ~ (all_483_0_10748 = 0)
% 55.08/22.80 | (1089) distinct_lines(all_0_1_1, all_0_2_2) = all_483_0_10748
% 55.08/22.80 |
% 55.08/22.80 | Instantiating formula (97) with all_0_1_1, all_0_2_2, 0, all_483_0_10748 and discharging atoms distinct_lines(all_0_1_1, all_0_2_2) = all_483_0_10748, distinct_lines(all_0_1_1, all_0_2_2) = 0, yields:
% 55.08/22.80 | (698) all_483_0_10748 = 0
% 55.08/22.80 |
% 55.08/22.80 | Equations (698) can reduce 1088 to:
% 55.08/22.80 | (335) $false
% 55.08/22.80 |
% 55.08/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1092) ~ (distinct_lines(all_0_1_1, all_0_2_2) = 0)
% 55.43/22.80 | (343) all_45_0_57 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (343) can reduce 165 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1095) ~ (all_63_0_75 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_63_0_75
% 55.43/22.80 |
% 55.43/22.80 | Applying alpha-rule on (1095) yields:
% 55.43/22.80 | (202) ~ (all_63_0_75 = 0)
% 55.43/22.80 | (1097) distinct_points(all_0_5_5, all_0_3_3) = all_63_0_75
% 55.43/22.80 |
% 55.43/22.80 | Instantiating formula (145) with all_0_5_5, all_0_3_3, all_63_0_75, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_63_0_75, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 55.43/22.80 | (1098) all_63_0_75 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (1098) can reduce 202 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1100) ~ (all_68_0_79 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_68_0_79
% 55.43/22.80 |
% 55.43/22.80 | Applying alpha-rule on (1100) yields:
% 55.43/22.80 | (199) ~ (all_68_0_79 = 0)
% 55.43/22.80 | (1102) distinct_points(all_0_5_5, all_0_3_3) = all_68_0_79
% 55.43/22.80 |
% 55.43/22.80 | Instantiating formula (145) with all_0_5_5, all_0_3_3, all_68_0_79, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_68_0_79, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 55.43/22.80 | (1103) all_68_0_79 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (1103) can reduce 199 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1105) ~ (all_52_0_64 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_52_0_64
% 55.43/22.80 |
% 55.43/22.80 | Applying alpha-rule on (1105) yields:
% 55.43/22.80 | (196) ~ (all_52_0_64 = 0)
% 55.43/22.80 | (1107) distinct_points(all_0_5_5, all_0_4_4) = all_52_0_64
% 55.43/22.80 |
% 55.43/22.80 | Instantiating formula (145) with all_0_5_5, all_0_4_4, all_52_0_64, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_52_0_64, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.43/22.80 | (1108) all_52_0_64 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (1108) can reduce 196 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1110) ~ (all_53_0_65 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_53_0_65
% 55.43/22.80 |
% 55.43/22.80 | Applying alpha-rule on (1110) yields:
% 55.43/22.80 | (193) ~ (all_53_0_65 = 0)
% 55.43/22.80 | (1112) distinct_points(all_0_5_5, all_0_4_4) = all_53_0_65
% 55.43/22.80 |
% 55.43/22.80 | Instantiating formula (145) with all_0_5_5, all_0_4_4, all_53_0_65, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_53_0_65, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 55.43/22.80 | (1113) all_53_0_65 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (1113) can reduce 193 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 |-Branch two:
% 55.43/22.80 | (1115) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0)
% 55.43/22.80 | (1116) all_0_0_0 = 0
% 55.43/22.80 |
% 55.43/22.80 | Equations (1116) can reduce 55 to:
% 55.43/22.80 | (335) $false
% 55.43/22.80 |
% 55.43/22.80 |-The branch is then unsatisfiable
% 55.43/22.80 % SZS output end Proof for theBenchmark
% 55.43/22.80
% 55.43/22.80 22199ms
%------------------------------------------------------------------------------