TSTP Solution File: GEO212+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 03:48:46 EDT 2022
% Result : Theorem 7.30s 2.38s
% Output : Proof 32.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 23:56:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.62/0.64 ____ _
% 0.62/0.64 ___ / __ \_____(_)___ ________ __________
% 0.62/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.64
% 0.62/0.64 A Theorem Prover for First-Order Logic
% 0.62/0.64 (ePrincess v.1.0)
% 0.62/0.64
% 0.62/0.64 (c) Philipp Rümmer, 2009-2015
% 0.62/0.64 (c) Peter Backeman, 2014-2015
% 0.62/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.64 Bug reports to peter@backeman.se
% 0.62/0.64
% 0.62/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.64
% 0.62/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.01 Prover 0: Preprocessing ...
% 2.28/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.28/1.21 Prover 0: Constructing countermodel ...
% 3.98/1.63 Prover 0: gave up
% 3.98/1.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.98/1.66 Prover 1: Preprocessing ...
% 4.66/1.77 Prover 1: Constructing countermodel ...
% 5.01/1.82 Prover 1: gave up
% 5.01/1.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.01/1.85 Prover 2: Preprocessing ...
% 5.80/1.99 Prover 2: Warning: ignoring some quantifiers
% 5.80/2.00 Prover 2: Constructing countermodel ...
% 7.30/2.38 Prover 2: proved (551ms)
% 7.30/2.38
% 7.30/2.38 No countermodel exists, formula is valid
% 7.30/2.38 % SZS status Theorem for theBenchmark
% 7.30/2.38
% 7.30/2.38 Generating proof ... Warning: ignoring some quantifiers
% 31.64/11.62 found it (size 418)
% 31.64/11.62
% 31.64/11.62 % SZS output start Proof for theBenchmark
% 31.64/11.62 Assumed formulas after preprocessing and simplification:
% 31.64/11.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ? [v10] : ((v10 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v6) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v7) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v6) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v5) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : orthogonal_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7)
% 31.96/11.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 31.96/11.70 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1 & ! [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 | ~ (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) = 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] : ( ~ (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] : (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_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(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(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) = 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(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 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [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] : ( ~ (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] : ( ~ (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) & 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] : ( ~ (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] : ( ~ (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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [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
% 31.96/11.73 |
% 31.96/11.73 | Applying alpha-rule on (1) yields:
% 31.96/11.73 | (2) ! [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)))
% 31.96/11.73 | (3) ! [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)))
% 31.96/11.73 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.96/11.73 | (5) ! [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))
% 31.96/11.73 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 31.96/11.73 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 31.96/11.73 | (8) ! [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)))
% 31.96/11.73 | (9) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 31.96/11.73 | (10) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 31.96/11.73 | (11) ! [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)))
% 31.96/11.73 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 31.96/11.73 | (13) ! [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))
% 31.96/11.73 | (14) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 31.96/11.73 | (15) ! [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)))
% 31.96/11.73 | (16) ! [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)))
% 31.96/11.73 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 31.96/11.74 | (18) ! [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)))
% 31.96/11.74 | (19) ! [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)))
% 31.96/11.74 | (20) ! [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)))
% 31.96/11.74 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 31.96/11.74 | (22) ! [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))
% 31.96/11.74 | (23) ! [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)))
% 31.96/11.74 | (24) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 31.96/11.74 | (25) ! [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)))
% 31.96/11.74 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 31.96/11.74 | (27) ! [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)
% 31.96/11.74 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 31.96/11.74 | (29) ! [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)))
% 31.96/11.74 | (30) ! [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)
% 31.96/11.74 | (31) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 31.96/11.74 | (32) ! [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)))
% 31.96/11.74 | (33) ~ (all_0_1_1 = 0)
% 31.96/11.74 | (34) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 31.96/11.74 | (35) ! [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)))
% 31.96/11.74 | (36) ! [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)))
% 31.96/11.74 | (37) ! [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)))
% 31.96/11.74 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 31.96/11.74 | (39) ! [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)))
% 31.96/11.74 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 31.96/11.74 | (41) ! [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))
% 31.96/11.75 | (42) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 31.96/11.75 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 31.96/11.75 | (44) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 31.96/11.75 | (45) ! [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)))
% 31.96/11.75 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 31.96/11.75 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 31.96/11.75 | (48) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 31.96/11.75 | (49) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 31.96/11.75 | (50) ! [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)))
% 31.96/11.75 | (51) ! [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)))
% 31.96/11.75 | (52) ! [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)))
% 31.96/11.75 | (53) ! [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)
% 31.96/11.75 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 31.96/11.75 | (55) ! [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)))
% 31.96/11.75 | (56) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 31.96/11.75 | (57) ! [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)))
% 31.96/11.75 | (58) ! [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)))
% 31.96/11.75 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 31.96/11.75 | (60) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0
% 31.96/11.75 | (61) ! [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)))
% 31.96/11.75 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 31.96/11.75 | (63) ! [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)))
% 31.96/11.75 | (64) ! [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)))
% 31.96/11.75 | (65) ! [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)))
% 31.96/11.75 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 31.96/11.75 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.96/11.75 | (68) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 31.96/11.76 | (69) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 31.96/11.76 | (70) ~ (all_0_0_0 = 0)
% 31.96/11.76 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 31.96/11.76 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 31.96/11.76 | (73) ! [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)))
% 31.96/11.76 | (74) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 31.96/11.76 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 31.96/11.76 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 31.96/11.76 | (77) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 31.96/11.76 | (78) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 31.96/11.76 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 31.96/11.76 | (80) ! [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)))
% 31.96/11.76 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 31.96/11.76 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 31.96/11.76 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 31.96/11.76 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 31.96/11.76 | (85) ! [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)
% 31.96/11.76 | (86) ! [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)))
% 31.96/11.76 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (72) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 31.96/11.76 | (88) all_0_0_0 = 0 | convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (16) with 0, 0, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 31.96/11.76 | (89) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (20) with 0, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 31.96/11.76 | (90) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (3) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 31.96/11.76 | (91) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (41) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.76 | (92) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (8) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.76 | (93) ? [v0] : ((v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 31.96/11.76 |
% 31.96/11.76 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.76 | (94) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 31.96/11.77 |
% 31.96/11.77 | Instantiating formula (51) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.77 | (95) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0))
% 31.96/11.77 |
% 31.96/11.77 | Instantiating formula (25) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.77 | (96) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 31.96/11.77 |
% 31.96/11.77 | Instantiating formula (71) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 31.96/11.77 | (97) all_0_1_1 = 0 | unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (96) with all_26_0_32, all_26_1_33 yields:
% 31.96/11.77 | (98) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (95) with all_27_0_34 yields:
% 31.96/11.77 | (99) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34) | ( ~ (all_27_0_34 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (94) with all_28_0_35 yields:
% 31.96/11.77 | (100) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35) | ( ~ (all_28_0_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (93) with all_29_0_36 yields:
% 31.96/11.77 | (101) (all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36) | ( ~ (all_29_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (90) with all_30_0_37, all_30_1_38 yields:
% 31.96/11.77 | (102) (all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_30_1_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (89) with all_31_0_39 yields:
% 31.96/11.77 | (103) (all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39) | ( ~ (all_31_0_39 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating (91) with all_33_0_41, all_33_1_42 yields:
% 31.96/11.77 | (104) (all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_33_1_42 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42)
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (88), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (105) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (97), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (104), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (107) (all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (107), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (108) all_33_0_41 = 0 & all_33_1_42 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 | Applying alpha-rule on (108) yields:
% 31.96/11.77 | (109) all_33_0_41 = 0
% 31.96/11.77 | (110) all_33_1_42 = 0
% 31.96/11.77 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.77 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (92), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (113) all_0_1_1 = 0
% 31.96/11.77 |
% 31.96/11.77 | Equations (113) can reduce 33 to:
% 31.96/11.77 | (114) $false
% 31.96/11.77 |
% 31.96/11.77 |-The branch is then unsatisfiable
% 31.96/11.77 |-Branch two:
% 31.96/11.77 | (33) ~ (all_0_1_1 = 0)
% 31.96/11.77 | (116) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 31.96/11.77 |
% 31.96/11.77 | Instantiating formula (62) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 31.96/11.77 | (113) all_0_1_1 = 0
% 31.96/11.77 |
% 31.96/11.77 | Equations (113) can reduce 33 to:
% 31.96/11.77 | (114) $false
% 31.96/11.77 |
% 31.96/11.77 |-The branch is then unsatisfiable
% 31.96/11.77 |-Branch two:
% 31.96/11.77 | (119) all_33_1_42 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 | Applying alpha-rule on (119) yields:
% 31.96/11.77 | (110) all_33_1_42 = 0
% 31.96/11.77 | (121) all_0_0_0 = 0
% 31.96/11.77 | (105) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.77 |
% 31.96/11.77 | Equations (121) can reduce 70 to:
% 31.96/11.77 | (114) $false
% 31.96/11.77 |
% 31.96/11.77 |-The branch is then unsatisfiable
% 31.96/11.77 |-Branch two:
% 31.96/11.77 | (124) ~ (all_33_1_42 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42
% 31.96/11.77 |
% 31.96/11.77 | Applying alpha-rule on (124) yields:
% 31.96/11.77 | (125) ~ (all_33_1_42 = 0)
% 31.96/11.77 | (126) convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42
% 31.96/11.77 |
% 31.96/11.77 +-Applying beta-rule and splitting (92), into two cases.
% 31.96/11.77 |-Branch one:
% 31.96/11.77 | (113) all_0_1_1 = 0
% 31.96/11.78 |
% 31.96/11.78 | Equations (113) can reduce 33 to:
% 31.96/11.78 | (114) $false
% 31.96/11.78 |
% 31.96/11.78 |-The branch is then unsatisfiable
% 31.96/11.78 |-Branch two:
% 31.96/11.78 | (33) ~ (all_0_1_1 = 0)
% 31.96/11.78 | (116) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)
% 31.96/11.78 |
% 31.96/11.78 | Instantiating (116) with all_47_0_44 yields:
% 31.96/11.78 | (131) ~ (all_47_0_44 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44
% 31.96/11.78 |
% 31.96/11.78 | Applying alpha-rule on (131) yields:
% 31.96/11.78 | (132) ~ (all_47_0_44 = 0)
% 31.96/11.78 | (133) convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44
% 31.96/11.78 |
% 31.96/11.78 +-Applying beta-rule and splitting (98), into two cases.
% 31.96/11.78 |-Branch one:
% 31.96/11.78 | (134) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 31.96/11.78 |
% 31.96/11.78 +-Applying beta-rule and splitting (134), into two cases.
% 31.96/11.78 |-Branch one:
% 31.96/11.78 | (135) all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.78 |
% 31.96/11.78 | Applying alpha-rule on (135) yields:
% 31.96/11.78 | (136) all_26_0_32 = 0
% 31.96/11.78 | (137) all_26_1_33 = 0
% 31.96/11.78 | (138) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.78 | (105) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 31.96/11.78 |
% 31.96/11.78 | Instantiating formula (79) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 31.96/11.78 | (121) all_0_0_0 = 0
% 31.96/11.78 |
% 31.96/11.78 | Equations (121) can reduce 70 to:
% 31.96/11.78 | (114) $false
% 31.96/11.78 |
% 31.96/11.78 |-The branch is then unsatisfiable
% 31.96/11.78 |-Branch two:
% 31.96/11.78 | (142) all_26_1_33 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.78 |
% 31.96/11.78 | Applying alpha-rule on (142) yields:
% 31.96/11.78 | (137) all_26_1_33 = 0
% 31.96/11.78 | (113) all_0_1_1 = 0
% 31.96/11.78 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 31.96/11.78 |
% 31.96/11.78 | Equations (113) can reduce 33 to:
% 31.96/11.78 | (114) $false
% 31.96/11.78 |
% 31.96/11.78 |-The branch is then unsatisfiable
% 31.96/11.78 |-Branch two:
% 31.96/11.78 | (147) ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 31.96/11.78 |
% 31.96/11.78 | Applying alpha-rule on (147) yields:
% 31.96/11.78 | (148) ~ (all_26_1_33 = 0)
% 31.96/11.78 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 31.96/11.78 |
% 31.96/11.78 +-Applying beta-rule and splitting (100), into two cases.
% 31.96/11.78 |-Branch one:
% 31.96/11.78 | (150) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35)
% 31.96/11.78 |
% 32.42/11.78 +-Applying beta-rule and splitting (150), into two cases.
% 32.42/11.78 |-Branch one:
% 32.42/11.78 | (151) (all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 32.42/11.78 |
% 32.42/11.78 +-Applying beta-rule and splitting (151), into two cases.
% 32.42/11.78 |-Branch one:
% 32.42/11.78 | (152) all_28_0_35 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 32.42/11.78 |
% 32.42/11.78 | Applying alpha-rule on (152) yields:
% 32.42/11.78 | (153) all_28_0_35 = 0
% 32.42/11.78 | (121) all_0_0_0 = 0
% 32.42/11.78 | (105) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 32.42/11.78 |
% 32.42/11.78 | Equations (121) can reduce 70 to:
% 32.42/11.78 | (114) $false
% 32.42/11.78 |
% 32.42/11.78 |-The branch is then unsatisfiable
% 32.42/11.78 |-Branch two:
% 32.42/11.78 | (157) all_28_0_35 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.42/11.78 |
% 32.42/11.78 | Applying alpha-rule on (157) yields:
% 32.42/11.78 | (153) all_28_0_35 = 0
% 32.42/11.78 | (113) all_0_1_1 = 0
% 32.42/11.78 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.42/11.78 |
% 32.42/11.78 | Equations (113) can reduce 33 to:
% 32.42/11.78 | (114) $false
% 32.42/11.78 |
% 32.42/11.78 |-The branch is then unsatisfiable
% 32.42/11.78 |-Branch two:
% 32.42/11.78 | (162) ~ (all_28_0_35 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 32.42/11.78 |
% 32.42/11.78 | Applying alpha-rule on (162) yields:
% 32.42/11.78 | (163) ~ (all_28_0_35 = 0)
% 32.42/11.78 | (164) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 32.42/11.78 |
% 32.42/11.78 | Instantiating formula (79) with all_0_4_4, all_0_3_3, all_28_0_35, 0 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_28_0_35, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 32.42/11.78 | (153) all_28_0_35 = 0
% 32.42/11.78 |
% 32.42/11.78 | Equations (153) can reduce 163 to:
% 32.42/11.78 | (114) $false
% 32.42/11.78 |
% 32.42/11.78 |-The branch is then unsatisfiable
% 32.42/11.78 |-Branch two:
% 32.42/11.78 | (167) ~ (all_28_0_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 32.42/11.78 |
% 32.42/11.78 | Applying alpha-rule on (167) yields:
% 32.42/11.78 | (163) ~ (all_28_0_35 = 0)
% 32.42/11.78 | (169) convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35
% 32.42/11.78 |
% 32.42/11.78 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_28_0_35, all_33_1_42 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42, convergent_lines(all_0_4_4, all_0_3_3) = all_28_0_35, yields:
% 32.42/11.78 | (170) all_33_1_42 = all_28_0_35
% 32.42/11.78 |
% 32.42/11.78 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_26_1_33, all_33_1_42 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_33_1_42, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.42/11.78 | (171) all_33_1_42 = all_26_1_33
% 32.42/11.78 |
% 32.42/11.78 | Combining equations (170,171) yields a new equation:
% 32.42/11.78 | (172) all_28_0_35 = all_26_1_33
% 32.42/11.78 |
% 32.42/11.78 | Simplifying 172 yields:
% 32.42/11.78 | (173) all_28_0_35 = all_26_1_33
% 32.42/11.78 |
% 32.42/11.78 | Equations (173) can reduce 163 to:
% 32.42/11.78 | (148) ~ (all_26_1_33 = 0)
% 32.42/11.78 |
% 32.42/11.78 | From (173) and (169) follows:
% 32.42/11.79 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (16) with 0, 0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.42/11.79 | (176) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (20) with 0, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.42/11.79 | (177) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (18) with 0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.42/11.79 | (178) ? [v0] : ((v0 = 0 & all_0_1_1 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (25) with all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.42/11.79 | (179) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (46) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 32.42/11.79 | (180) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (42) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields:
% 32.42/11.79 | (181) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_2_2) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (8) with all_26_1_33, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.42/11.79 | (182) ? [v0] : ((v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (18) with 0, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.42/11.79 | (183) ? [v0] : ((v0 = 0 & all_26_1_33 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (25) with all_26_1_33, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.42/11.79 | (184) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & all_26_1_33 = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (8) with all_47_0_44, all_47_0_44, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.42/11.79 | (185) ? [v0] : ((v0 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (25) with all_47_0_44, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.42/11.79 | (186) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (25) with all_47_0_44, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.42/11.79 | (187) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0))
% 32.42/11.79 |
% 32.42/11.79 | Instantiating formula (71) with all_47_0_44, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.42/11.79 | (188) all_47_0_44 = 0 | unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.42/11.79 |
% 32.42/11.79 | Instantiating (187) with all_66_0_45, all_66_1_46 yields:
% 32.48/11.79 | (189) (all_66_0_45 = 0 & all_66_1_46 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_66_1_46 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_66_1_46 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_66_1_46)
% 32.48/11.79 |
% 32.48/11.79 | Instantiating (186) with all_67_0_47, all_67_1_48 yields:
% 32.48/11.79 | (190) (all_67_0_47 = 0 & all_67_1_48 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_67_1_48 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_67_1_48 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_67_1_48)
% 32.48/11.79 |
% 32.48/11.79 | Instantiating (185) with all_68_0_49 yields:
% 32.48/11.79 | (191) (all_68_0_49 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_68_0_49 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_68_0_49) | ( ~ (all_68_0_49 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_68_0_49)
% 32.48/11.79 |
% 32.48/11.79 | Instantiating (179) with all_71_0_53, all_71_1_54 yields:
% 32.48/11.79 | (192) (all_71_0_53 = 0 & all_71_1_54 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_71_1_54 = 0 & all_0_1_1 = 0) | ( ~ (all_71_1_54 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (183) with all_74_0_59 yields:
% 32.48/11.80 | (193) (all_74_0_59 = 0 & all_26_1_33 = 0) | (all_74_0_59 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_74_0_59 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_74_0_59) | ( ~ (all_74_0_59 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_74_0_59)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (182) with all_75_0_60 yields:
% 32.48/11.80 | (194) (all_75_0_60 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_75_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_75_0_60) | ( ~ (all_75_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (181) with all_78_0_64, all_78_1_65 yields:
% 32.48/11.80 | (195) ~ (all_78_0_64 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_78_1_65 & apart_point_and_line(all_78_1_65, all_0_3_3) = all_78_0_64
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (195) yields:
% 32.48/11.80 | (196) ~ (all_78_0_64 = 0)
% 32.48/11.80 | (197) intersection_point(all_0_3_3, all_0_2_2) = all_78_1_65
% 32.48/11.80 | (198) apart_point_and_line(all_78_1_65, all_0_3_3) = all_78_0_64
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (180) with all_81_0_67, all_81_1_68 yields:
% 32.48/11.80 | (199) ~ (all_81_0_67 = 0) & intersection_point(all_0_3_3, all_0_2_2) = all_81_1_68 & apart_point_and_line(all_81_1_68, all_0_2_2) = all_81_0_67
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (199) yields:
% 32.48/11.80 | (200) ~ (all_81_0_67 = 0)
% 32.48/11.80 | (201) intersection_point(all_0_3_3, all_0_2_2) = all_81_1_68
% 32.48/11.80 | (202) apart_point_and_line(all_81_1_68, all_0_2_2) = all_81_0_67
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (184) with all_83_0_69, all_83_1_70 yields:
% 32.48/11.80 | (203) (all_83_0_69 = 0 & all_83_1_70 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_83_1_70 = 0 & all_26_1_33 = 0) | ( ~ (all_83_1_70 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_83_1_70)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (178) with all_84_0_71 yields:
% 32.48/11.80 | (204) (all_84_0_71 = 0 & all_0_1_1 = 0) | (all_84_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_84_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_84_0_71) | ( ~ (all_84_0_71 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_84_0_71)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (177) with all_85_0_72, all_85_1_73 yields:
% 32.48/11.80 | (205) (all_85_0_72 = 0 & all_85_1_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_85_1_73 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_85_1_73 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73)
% 32.48/11.80 |
% 32.48/11.80 | Instantiating (176) with all_86_0_74 yields:
% 32.48/11.80 | (206) (all_86_0_74 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_86_0_74 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_86_0_74) | ( ~ (all_86_0_74 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_86_0_74)
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (188), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (207) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (101), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (208) (all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36)
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (208), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (209) all_29_0_36 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (209) yields:
% 32.48/11.80 | (210) all_29_0_36 = 0
% 32.48/11.80 | (113) all_0_1_1 = 0
% 32.48/11.80 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.48/11.80 |
% 32.48/11.80 | Equations (113) can reduce 33 to:
% 32.48/11.80 | (114) $false
% 32.48/11.80 |
% 32.48/11.80 |-The branch is then unsatisfiable
% 32.48/11.80 |-Branch two:
% 32.48/11.80 | (214) ~ (all_29_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (214) yields:
% 32.48/11.80 | (215) ~ (all_29_0_36 = 0)
% 32.48/11.80 | (216) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 32.48/11.80 |
% 32.48/11.80 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_29_0_36 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_29_0_36, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.48/11.80 | (210) all_29_0_36 = 0
% 32.48/11.80 |
% 32.48/11.80 | Equations (210) can reduce 215 to:
% 32.48/11.80 | (114) $false
% 32.48/11.80 |
% 32.48/11.80 |-The branch is then unsatisfiable
% 32.48/11.80 |-Branch two:
% 32.48/11.80 | (219) ~ (all_29_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (219) yields:
% 32.48/11.80 | (215) ~ (all_29_0_36 = 0)
% 32.48/11.80 | (221) convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (194), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (222) (all_75_0_60 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_75_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_75_0_60)
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (222), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (223) all_75_0_60 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (223) yields:
% 32.48/11.80 | (224) all_75_0_60 = 0
% 32.48/11.80 | (137) all_26_1_33 = 0
% 32.48/11.80 | (49) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.80 |
% 32.48/11.80 | Equations (137) can reduce 148 to:
% 32.48/11.80 | (114) $false
% 32.48/11.80 |
% 32.48/11.80 |-The branch is then unsatisfiable
% 32.48/11.80 |-Branch two:
% 32.48/11.80 | (228) ~ (all_75_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_75_0_60
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (228) yields:
% 32.48/11.80 | (229) ~ (all_75_0_60 = 0)
% 32.48/11.80 | (230) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_75_0_60
% 32.48/11.80 |
% 32.48/11.80 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_75_0_60 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_75_0_60, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.48/11.80 | (224) all_75_0_60 = 0
% 32.48/11.80 |
% 32.48/11.80 | Equations (224) can reduce 229 to:
% 32.48/11.80 | (114) $false
% 32.48/11.80 |
% 32.48/11.80 |-The branch is then unsatisfiable
% 32.48/11.80 |-Branch two:
% 32.48/11.80 | (233) ~ (all_75_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60
% 32.48/11.80 |
% 32.48/11.80 | Applying alpha-rule on (233) yields:
% 32.48/11.80 | (229) ~ (all_75_0_60 = 0)
% 32.48/11.80 | (235) convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60
% 32.48/11.80 |
% 32.48/11.80 +-Applying beta-rule and splitting (206), into two cases.
% 32.48/11.80 |-Branch one:
% 32.48/11.80 | (236) (all_86_0_74 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_86_0_74 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_86_0_74)
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (236), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (237) all_86_0_74 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (237) yields:
% 32.48/11.81 | (238) all_86_0_74 = 0
% 32.48/11.81 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (62) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.48/11.81 | (113) all_0_1_1 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (113) can reduce 33 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (242) ~ (all_86_0_74 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_86_0_74
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (242) yields:
% 32.48/11.81 | (243) ~ (all_86_0_74 = 0)
% 32.48/11.81 | (244) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_86_0_74
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_86_0_74 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_86_0_74, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.48/11.81 | (238) all_86_0_74 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (238) can reduce 243 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (247) ~ (all_86_0_74 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_86_0_74
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (247) yields:
% 32.48/11.81 | (243) ~ (all_86_0_74 = 0)
% 32.48/11.81 | (249) convergent_lines(all_0_4_4, all_0_4_4) = all_86_0_74
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (103), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (250) (all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39)
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (250), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (251) all_31_0_39 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (251) yields:
% 32.48/11.81 | (252) all_31_0_39 = 0
% 32.48/11.81 | (253) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (62) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 32.48/11.81 | (137) all_26_1_33 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (137) can reduce 148 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (256) ~ (all_31_0_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (256) yields:
% 32.48/11.81 | (257) ~ (all_31_0_39 = 0)
% 32.48/11.81 | (258) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_31_0_39 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_31_0_39, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.48/11.81 | (252) all_31_0_39 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (252) can reduce 257 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (261) ~ (all_31_0_39 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (261) yields:
% 32.48/11.81 | (257) ~ (all_31_0_39 = 0)
% 32.48/11.81 | (263) convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (193), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (264) (all_74_0_59 = 0 & all_26_1_33 = 0) | (all_74_0_59 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_74_0_59 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_74_0_59)
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (264), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (265) (all_74_0_59 = 0 & all_26_1_33 = 0) | (all_74_0_59 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 32.48/11.81 |
% 32.48/11.81 +-Applying beta-rule and splitting (265), into two cases.
% 32.48/11.81 |-Branch one:
% 32.48/11.81 | (266) all_74_0_59 = 0 & all_26_1_33 = 0
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (266) yields:
% 32.48/11.81 | (267) all_74_0_59 = 0
% 32.48/11.81 | (137) all_26_1_33 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (137) can reduce 148 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (270) all_74_0_59 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (270) yields:
% 32.48/11.81 | (267) all_74_0_59 = 0
% 32.48/11.81 | (253) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (62) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 32.48/11.81 | (137) all_26_1_33 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (137) can reduce 148 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (275) ~ (all_74_0_59 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_74_0_59
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (275) yields:
% 32.48/11.81 | (276) ~ (all_74_0_59 = 0)
% 32.48/11.81 | (277) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_74_0_59
% 32.48/11.81 |
% 32.48/11.81 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_74_0_59 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_74_0_59, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.48/11.81 | (267) all_74_0_59 = 0
% 32.48/11.81 |
% 32.48/11.81 | Equations (267) can reduce 276 to:
% 32.48/11.81 | (114) $false
% 32.48/11.81 |
% 32.48/11.81 |-The branch is then unsatisfiable
% 32.48/11.81 |-Branch two:
% 32.48/11.81 | (280) ~ (all_74_0_59 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_74_0_59
% 32.48/11.81 |
% 32.48/11.81 | Applying alpha-rule on (280) yields:
% 32.48/11.81 | (276) ~ (all_74_0_59 = 0)
% 32.48/11.81 | (282) convergent_lines(all_0_4_4, all_0_4_4) = all_74_0_59
% 32.48/11.81 |
% 32.58/11.81 +-Applying beta-rule and splitting (204), into two cases.
% 32.58/11.81 |-Branch one:
% 32.58/11.81 | (283) (all_84_0_71 = 0 & all_0_1_1 = 0) | (all_84_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_84_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_84_0_71)
% 32.58/11.81 |
% 32.58/11.81 +-Applying beta-rule and splitting (283), into two cases.
% 32.58/11.81 |-Branch one:
% 32.58/11.81 | (284) (all_84_0_71 = 0 & all_0_1_1 = 0) | (all_84_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0)
% 32.58/11.81 |
% 32.58/11.81 +-Applying beta-rule and splitting (284), into two cases.
% 32.58/11.81 |-Branch one:
% 32.58/11.81 | (285) all_84_0_71 = 0 & all_0_1_1 = 0
% 32.58/11.81 |
% 32.58/11.81 | Applying alpha-rule on (285) yields:
% 32.58/11.81 | (286) all_84_0_71 = 0
% 32.58/11.81 | (113) all_0_1_1 = 0
% 32.58/11.81 |
% 32.58/11.81 | Equations (113) can reduce 33 to:
% 32.58/11.81 | (114) $false
% 32.58/11.81 |
% 32.58/11.81 |-The branch is then unsatisfiable
% 32.58/11.81 |-Branch two:
% 32.58/11.81 | (289) all_84_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.58/11.81 |
% 32.58/11.81 | Applying alpha-rule on (289) yields:
% 32.58/11.81 | (286) all_84_0_71 = 0
% 32.58/11.81 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.58/11.81 |
% 32.58/11.81 | Instantiating formula (62) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.58/11.81 | (113) all_0_1_1 = 0
% 32.58/11.81 |
% 32.58/11.81 | Equations (113) can reduce 33 to:
% 32.58/11.81 | (114) $false
% 32.58/11.81 |
% 32.58/11.81 |-The branch is then unsatisfiable
% 32.58/11.81 |-Branch two:
% 32.58/11.81 | (294) ~ (all_84_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_84_0_71
% 32.58/11.81 |
% 32.58/11.81 | Applying alpha-rule on (294) yields:
% 32.58/11.81 | (295) ~ (all_84_0_71 = 0)
% 32.58/11.81 | (296) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_84_0_71
% 32.58/11.81 |
% 32.58/11.81 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_84_0_71 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_84_0_71, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.58/11.81 | (286) all_84_0_71 = 0
% 32.58/11.81 |
% 32.58/11.81 | Equations (286) can reduce 295 to:
% 32.58/11.81 | (114) $false
% 32.58/11.81 |
% 32.58/11.81 |-The branch is then unsatisfiable
% 32.58/11.81 |-Branch two:
% 32.58/11.81 | (299) ~ (all_84_0_71 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_84_0_71
% 32.58/11.81 |
% 32.58/11.81 | Applying alpha-rule on (299) yields:
% 32.58/11.81 | (295) ~ (all_84_0_71 = 0)
% 32.58/11.81 | (301) convergent_lines(all_0_4_4, all_0_4_4) = all_84_0_71
% 32.58/11.81 |
% 32.58/11.81 +-Applying beta-rule and splitting (191), into two cases.
% 32.58/11.81 |-Branch one:
% 32.58/11.81 | (302) (all_68_0_49 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_68_0_49 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_68_0_49)
% 32.58/11.81 |
% 32.58/11.81 +-Applying beta-rule and splitting (302), into two cases.
% 32.58/11.81 |-Branch one:
% 32.58/11.81 | (303) all_68_0_49 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.58/11.81 |
% 32.58/11.81 | Applying alpha-rule on (303) yields:
% 32.58/11.81 | (304) all_68_0_49 = 0
% 32.58/11.81 | (305) all_47_0_44 = 0
% 32.58/11.81 | (207) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.58/11.81 |
% 32.58/11.81 | Equations (305) can reduce 132 to:
% 32.58/11.81 | (114) $false
% 32.58/11.81 |
% 32.58/11.81 |-The branch is then unsatisfiable
% 32.58/11.81 |-Branch two:
% 32.58/11.81 | (308) ~ (all_68_0_49 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_68_0_49
% 32.59/11.81 |
% 32.59/11.81 | Applying alpha-rule on (308) yields:
% 32.59/11.81 | (309) ~ (all_68_0_49 = 0)
% 32.59/11.81 | (310) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_68_0_49
% 32.59/11.81 |
% 32.59/11.81 | Instantiating formula (79) with all_0_4_4, all_0_4_4, 0, all_68_0_49 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_68_0_49, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.81 | (304) all_68_0_49 = 0
% 32.59/11.81 |
% 32.59/11.81 | Equations (304) can reduce 309 to:
% 32.59/11.81 | (114) $false
% 32.59/11.81 |
% 32.59/11.81 |-The branch is then unsatisfiable
% 32.59/11.81 |-Branch two:
% 32.59/11.81 | (313) ~ (all_68_0_49 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_68_0_49
% 32.59/11.81 |
% 32.59/11.82 | Applying alpha-rule on (313) yields:
% 32.59/11.82 | (309) ~ (all_68_0_49 = 0)
% 32.59/11.82 | (315) convergent_lines(all_0_4_4, all_0_4_4) = all_68_0_49
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (21) with all_0_3_3, all_0_2_2, all_78_1_65, all_81_1_68 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_81_1_68, intersection_point(all_0_3_3, all_0_2_2) = all_78_1_65, yields:
% 32.59/11.82 | (316) all_81_1_68 = all_78_1_65
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_86_0_74, all_47_0_44 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_86_0_74, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.59/11.82 | (317) all_86_0_74 = all_47_0_44
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_75_0_60, all_47_0_44 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60, convergent_lines(all_0_4_4, all_0_4_4) = all_47_0_44, yields:
% 32.59/11.82 | (318) all_75_0_60 = all_47_0_44
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_74_0_59, all_84_0_71 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_84_0_71, convergent_lines(all_0_4_4, all_0_4_4) = all_74_0_59, yields:
% 32.59/11.82 | (319) all_84_0_71 = all_74_0_59
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_74_0_59, all_75_0_60 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60, convergent_lines(all_0_4_4, all_0_4_4) = all_74_0_59, yields:
% 32.59/11.82 | (320) all_75_0_60 = all_74_0_59
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_68_0_49, all_75_0_60 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_75_0_60, convergent_lines(all_0_4_4, all_0_4_4) = all_68_0_49, yields:
% 32.59/11.82 | (321) all_75_0_60 = all_68_0_49
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_31_0_39, all_84_0_71 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_84_0_71, convergent_lines(all_0_4_4, all_0_4_4) = all_31_0_39, yields:
% 32.59/11.82 | (322) all_84_0_71 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (62) with all_0_4_4, all_0_4_4, all_29_0_36, all_86_0_74 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_86_0_74, convergent_lines(all_0_4_4, all_0_4_4) = all_29_0_36, yields:
% 32.59/11.82 | (323) all_86_0_74 = all_29_0_36
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (317,323) yields a new equation:
% 32.59/11.82 | (324) all_47_0_44 = all_29_0_36
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 324 yields:
% 32.59/11.82 | (325) all_47_0_44 = all_29_0_36
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (319,322) yields a new equation:
% 32.59/11.82 | (326) all_74_0_59 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 326 yields:
% 32.59/11.82 | (327) all_74_0_59 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (318,321) yields a new equation:
% 32.59/11.82 | (328) all_68_0_49 = all_47_0_44
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (320,321) yields a new equation:
% 32.59/11.82 | (329) all_74_0_59 = all_68_0_49
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 329 yields:
% 32.59/11.82 | (330) all_74_0_59 = all_68_0_49
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (330,327) yields a new equation:
% 32.59/11.82 | (331) all_68_0_49 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 331 yields:
% 32.59/11.82 | (332) all_68_0_49 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (328,332) yields a new equation:
% 32.59/11.82 | (333) all_47_0_44 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 333 yields:
% 32.59/11.82 | (334) all_47_0_44 = all_31_0_39
% 32.59/11.82 |
% 32.59/11.82 | Combining equations (334,325) yields a new equation:
% 32.59/11.82 | (335) all_31_0_39 = all_29_0_36
% 32.59/11.82 |
% 32.59/11.82 | Simplifying 335 yields:
% 32.59/11.82 | (336) all_31_0_39 = all_29_0_36
% 32.59/11.82 |
% 32.59/11.82 | Equations (336) can reduce 257 to:
% 32.59/11.82 | (215) ~ (all_29_0_36 = 0)
% 32.59/11.82 |
% 32.59/11.82 | From (316) and (202) follows:
% 32.59/11.82 | (338) apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (20) with 0, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.82 | (339) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (20) with 0, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.82 | (340) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (11) with all_0_0_0, all_81_0_67, all_0_2_2, all_0_3_3, all_0_2_2, all_78_1_65 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67, yields:
% 32.59/11.82 | (341) all_81_0_67 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_78_1_65, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (6) with all_81_0_67, all_81_0_67, all_0_2_2, all_0_2_2, all_78_1_65 and discharging atoms apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67, yields:
% 32.59/11.82 | (342) all_81_0_67 = 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))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (39) with all_81_0_67, all_81_0_67, all_0_2_2, all_0_2_2, all_78_1_65, all_78_1_65 and discharging atoms apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67, yields:
% 32.59/11.82 | (343) all_81_0_67 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_78_1_65, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_78_1_65, all_78_1_65) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (32) with all_0_1_1, all_81_0_67, all_0_2_2, all_0_4_4, all_78_1_65 and discharging atoms apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.82 | (344) all_81_0_67 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_78_1_65, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_2_2) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (6) with all_81_0_67, all_78_0_64, all_0_2_2, all_0_3_3, all_78_1_65 and discharging atoms apart_point_and_line(all_78_1_65, all_0_2_2) = all_81_0_67, apart_point_and_line(all_78_1_65, all_0_3_3) = all_78_0_64, yields:
% 32.59/11.82 | (345) all_81_0_67 = 0 | all_78_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 32.59/11.82 |
% 32.59/11.82 | Instantiating (340) with all_130_0_77, all_130_1_78 yields:
% 32.59/11.82 | (346) (all_130_0_77 = 0 & all_130_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_130_1_78 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_130_1_78 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_130_1_78)
% 32.59/11.82 |
% 32.59/11.82 | Instantiating (339) with all_131_0_79, all_131_1_80 yields:
% 32.59/11.82 | (347) (all_131_0_79 = 0 & all_131_1_80 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_131_1_80 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_131_1_80 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80)
% 32.59/11.82 |
% 32.59/11.82 +-Applying beta-rule and splitting (99), into two cases.
% 32.59/11.82 |-Branch one:
% 32.59/11.82 | (348) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34)
% 32.59/11.82 |
% 32.59/11.82 +-Applying beta-rule and splitting (348), into two cases.
% 32.59/11.82 |-Branch one:
% 32.59/11.82 | (349) (all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 32.59/11.82 |
% 32.59/11.82 +-Applying beta-rule and splitting (349), into two cases.
% 32.59/11.82 |-Branch one:
% 32.59/11.82 | (350) all_27_0_34 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0
% 32.59/11.82 |
% 32.59/11.82 | Applying alpha-rule on (350) yields:
% 32.59/11.82 | (351) all_27_0_34 = 0
% 32.59/11.82 | (121) all_0_0_0 = 0
% 32.59/11.82 | (105) convergent_lines(all_0_3_3, all_0_2_2) = 0
% 32.59/11.82 |
% 32.59/11.82 | Equations (121) can reduce 70 to:
% 32.59/11.82 | (114) $false
% 32.59/11.82 |
% 32.59/11.82 |-The branch is then unsatisfiable
% 32.59/11.82 |-Branch two:
% 32.59/11.82 | (355) all_27_0_34 = 0 & all_0_1_1 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.82 |
% 32.59/11.82 | Applying alpha-rule on (355) yields:
% 32.59/11.82 | (351) all_27_0_34 = 0
% 32.59/11.82 | (113) all_0_1_1 = 0
% 32.59/11.82 | (106) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.82 |
% 32.59/11.82 | Equations (113) can reduce 33 to:
% 32.59/11.82 | (114) $false
% 32.59/11.82 |
% 32.59/11.82 |-The branch is then unsatisfiable
% 32.59/11.82 |-Branch two:
% 32.59/11.82 | (360) ~ (all_27_0_34 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 32.59/11.82 |
% 32.59/11.82 | Applying alpha-rule on (360) yields:
% 32.59/11.82 | (361) ~ (all_27_0_34 = 0)
% 32.59/11.82 | (362) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 32.59/11.82 |
% 32.59/11.82 +-Applying beta-rule and splitting (190), into two cases.
% 32.59/11.82 |-Branch one:
% 32.59/11.82 | (363) (all_67_0_47 = 0 & all_67_1_48 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_67_1_48 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.82 |
% 32.59/11.82 +-Applying beta-rule and splitting (363), into two cases.
% 32.59/11.82 |-Branch one:
% 32.59/11.82 | (364) all_67_0_47 = 0 & all_67_1_48 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.82 |
% 32.59/11.82 | Applying alpha-rule on (364) yields:
% 32.59/11.82 | (365) all_67_0_47 = 0
% 32.59/11.82 | (366) all_67_1_48 = 0
% 32.59/11.82 | (367) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.82 | (368) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.82 |
% 32.59/11.82 | Instantiating formula (79) with all_0_3_3, all_0_4_4, 0, all_27_0_34 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 32.59/11.82 | (351) all_27_0_34 = 0
% 32.59/11.82 |
% 32.59/11.82 | Equations (351) can reduce 361 to:
% 32.59/11.82 | (114) $false
% 32.59/11.82 |
% 32.59/11.82 |-The branch is then unsatisfiable
% 32.59/11.82 |-Branch two:
% 32.59/11.82 | (371) all_67_1_48 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (371) yields:
% 32.59/11.83 | (366) all_67_1_48 = 0
% 32.59/11.83 | (305) all_47_0_44 = 0
% 32.59/11.83 | (207) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Combining equations (325,305) yields a new equation:
% 32.59/11.83 | (375) all_29_0_36 = 0
% 32.59/11.83 |
% 32.59/11.83 | Simplifying 375 yields:
% 32.59/11.83 | (210) all_29_0_36 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (210) can reduce 215 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (378) ~ (all_67_1_48 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_67_1_48
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (378) yields:
% 32.59/11.83 | (379) ~ (all_67_1_48 = 0)
% 32.59/11.83 | (380) convergent_lines(all_0_4_4, all_0_3_3) = all_67_1_48
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (346), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (381) (all_130_0_77 = 0 & all_130_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_130_1_78 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (381), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (382) all_130_0_77 = 0 & all_130_1_78 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (382) yields:
% 32.59/11.83 | (383) all_130_0_77 = 0
% 32.59/11.83 | (384) all_130_1_78 = 0
% 32.59/11.83 | (367) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.83 | (368) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (79) with all_0_3_3, all_0_4_4, 0, all_27_0_34 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 32.59/11.83 | (351) all_27_0_34 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (351) can reduce 361 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (389) all_130_1_78 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (389) yields:
% 32.59/11.83 | (384) all_130_1_78 = 0
% 32.59/11.83 | (391) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (10) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.83 | (392) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (393) ~ (all_130_1_78 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_130_1_78
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (393) yields:
% 32.59/11.83 | (394) ~ (all_130_1_78 = 0)
% 32.59/11.83 | (395) convergent_lines(all_0_4_4, all_0_3_3) = all_130_1_78
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_130_1_78, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_130_1_78, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.59/11.83 | (396) all_130_1_78 = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_67_1_48, all_130_1_78 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_130_1_78, convergent_lines(all_0_4_4, all_0_3_3) = all_67_1_48, yields:
% 32.59/11.83 | (397) all_130_1_78 = all_67_1_48
% 32.59/11.83 |
% 32.59/11.83 | Combining equations (396,397) yields a new equation:
% 32.59/11.83 | (398) all_67_1_48 = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Equations (398) can reduce 379 to:
% 32.59/11.83 | (148) ~ (all_26_1_33 = 0)
% 32.59/11.83 |
% 32.59/11.83 | From (398) and (380) follows:
% 32.59/11.83 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (72) with all_27_0_34, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_27_0_34, yields:
% 32.59/11.83 | (401) all_27_0_34 = 0 | convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (102), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (402) (all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0)
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (402), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (403) all_30_0_37 = 0 & all_30_1_38 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (403) yields:
% 32.59/11.83 | (404) all_30_0_37 = 0
% 32.59/11.83 | (405) all_30_1_38 = 0
% 32.59/11.83 | (406) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 | (407) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (10) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 32.59/11.83 | (392) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (409) all_30_1_38 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (409) yields:
% 32.59/11.83 | (405) all_30_1_38 = 0
% 32.59/11.83 | (253) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (62) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 32.59/11.83 | (137) all_26_1_33 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (137) can reduce 148 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (414) ~ (all_30_1_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (414) yields:
% 32.59/11.83 | (415) ~ (all_30_1_38 = 0)
% 32.59/11.83 | (416) convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (401), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (368) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_30_1_38, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_30_1_38, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.59/11.83 | (418) all_30_1_38 = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Equations (418) can reduce 415 to:
% 32.59/11.83 | (148) ~ (all_26_1_33 = 0)
% 32.59/11.83 |
% 32.59/11.83 | From (418) and (416) follows:
% 32.59/11.83 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (203), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (421) (all_83_0_69 = 0 & all_83_1_70 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_83_1_70 = 0 & all_26_1_33 = 0)
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (421), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (422) all_83_0_69 = 0 & all_83_1_70 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (422) yields:
% 32.59/11.83 | (423) all_83_0_69 = 0
% 32.59/11.83 | (424) all_83_1_70 = 0
% 32.59/11.83 | (406) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 | (407) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (10) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 32.59/11.83 | (392) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (428) all_83_1_70 = 0 & all_26_1_33 = 0
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (428) yields:
% 32.59/11.83 | (424) all_83_1_70 = 0
% 32.59/11.83 | (137) all_26_1_33 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (137) can reduce 148 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (432) ~ (all_83_1_70 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_83_1_70
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (432) yields:
% 32.59/11.83 | (433) ~ (all_83_1_70 = 0)
% 32.59/11.83 | (434) convergent_lines(all_0_4_4, all_0_3_3) = all_83_1_70
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (62) with all_0_4_4, all_0_3_3, all_83_1_70, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_83_1_70, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.59/11.83 | (435) all_83_1_70 = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Equations (435) can reduce 433 to:
% 32.59/11.83 | (148) ~ (all_26_1_33 = 0)
% 32.59/11.83 |
% 32.59/11.83 | From (435) and (434) follows:
% 32.59/11.83 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (40) with all_26_1_33, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields:
% 32.59/11.83 | (438) all_26_1_33 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (438), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (407) convergent_lines(all_0_3_3, all_0_3_3) = 0
% 32.59/11.83 |
% 32.59/11.83 | Instantiating formula (10) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields:
% 32.59/11.83 | (392) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (441) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0)
% 32.59/11.83 | (137) all_26_1_33 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (137) can reduce 148 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (444) ~ (convergent_lines(all_0_3_3, all_0_4_4) = 0)
% 32.59/11.83 | (351) all_27_0_34 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (351) can reduce 361 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (447) ~ (all_27_0_34 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 32.59/11.83 |
% 32.59/11.83 | Applying alpha-rule on (447) yields:
% 32.59/11.83 | (361) ~ (all_27_0_34 = 0)
% 32.59/11.83 | (449) convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34
% 32.59/11.83 |
% 32.59/11.83 +-Applying beta-rule and splitting (343), into two cases.
% 32.59/11.83 |-Branch one:
% 32.59/11.83 | (450) all_81_0_67 = 0
% 32.59/11.83 |
% 32.59/11.83 | Equations (450) can reduce 200 to:
% 32.59/11.83 | (114) $false
% 32.59/11.83 |
% 32.59/11.83 |-The branch is then unsatisfiable
% 32.59/11.83 |-Branch two:
% 32.59/11.83 | (200) ~ (all_81_0_67 = 0)
% 32.59/11.83 | (453) ? [v0] : ((v0 = 0 & apart_point_and_line(all_78_1_65, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_78_1_65, all_78_1_65) = v0))
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (342), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (450) all_81_0_67 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (450) can reduce 200 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (200) ~ (all_81_0_67 = 0)
% 32.59/11.84 | (457) ? [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))
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (341), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (450) all_81_0_67 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (450) can reduce 200 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (200) ~ (all_81_0_67 = 0)
% 32.59/11.84 | (461) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_78_1_65, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (345), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (450) all_81_0_67 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (450) can reduce 200 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (200) ~ (all_81_0_67 = 0)
% 32.59/11.84 | (465) all_78_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (344), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (450) all_81_0_67 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (450) can reduce 200 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (200) ~ (all_81_0_67 = 0)
% 32.59/11.84 | (469) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_78_1_65, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_2_2) = v0))
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (469), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (113) all_0_1_1 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (113) can reduce 33 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.84 | (473) ? [v0] : ((v0 = 0 & apart_point_and_line(all_78_1_65, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_2_2) = v0))
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (81) with all_27_0_34, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_3_3, all_0_4_4) = all_27_0_34, yields:
% 32.59/11.84 | (474) all_27_0_34 = 0 | convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (474), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (475) convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (189), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (476) (all_66_0_45 = 0 & all_66_1_46 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_66_1_46 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (476), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (477) all_66_0_45 = 0 & all_66_1_46 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (477) yields:
% 32.59/11.84 | (478) all_66_0_45 = 0
% 32.59/11.84 | (479) all_66_1_46 = 0
% 32.59/11.84 | (480) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 | (475) convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (192), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (482) (all_71_0_53 = 0 & all_71_1_54 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_71_1_54 = 0 & all_0_1_1 = 0)
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (482), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (483) all_71_0_53 = 0 & all_71_1_54 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (483) yields:
% 32.59/11.84 | (484) all_71_0_53 = 0
% 32.59/11.84 | (485) all_71_1_54 = 0
% 32.59/11.84 | (486) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.84 | (392) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (489) all_71_1_54 = 0 & all_0_1_1 = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (489) yields:
% 32.59/11.84 | (485) all_71_1_54 = 0
% 32.59/11.84 | (113) all_0_1_1 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (113) can reduce 33 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (493) ~ (all_71_1_54 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (493) yields:
% 32.59/11.84 | (494) ~ (all_71_1_54 = 0)
% 32.59/11.84 | (495) convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_71_1_54, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.84 | (496) all_71_1_54 = all_0_1_1
% 32.59/11.84 |
% 32.59/11.84 | Equations (496) can reduce 494 to:
% 32.59/11.84 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.84 |
% 32.59/11.84 | From (496) and (495) follows:
% 32.59/11.84 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (205), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (499) (all_85_0_72 = 0 & all_85_1_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_85_1_73 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0)
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (499), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (500) all_85_0_72 = 0 & all_85_1_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (500) yields:
% 32.59/11.84 | (501) all_85_0_72 = 0
% 32.59/11.84 | (502) all_85_1_73 = 0
% 32.59/11.84 | (486) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.84 | (392) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (506) all_85_1_73 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (506) yields:
% 32.59/11.84 | (502) all_85_1_73 = 0
% 32.59/11.84 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (62) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.59/11.84 | (113) all_0_1_1 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (113) can reduce 33 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (511) ~ (all_85_1_73 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (511) yields:
% 32.59/11.84 | (512) ~ (all_85_1_73 = 0)
% 32.59/11.84 | (513) convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_85_1_73, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.84 | (514) all_85_1_73 = all_0_1_1
% 32.59/11.84 |
% 32.59/11.84 | Equations (514) can reduce 512 to:
% 32.59/11.84 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.84 |
% 32.59/11.84 | From (514) and (513) follows:
% 32.59/11.84 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (347), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (517) (all_131_0_79 = 0 & all_131_1_80 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_131_1_80 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (517), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (518) all_131_0_79 = 0 & all_131_1_80 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (518) yields:
% 32.59/11.84 | (519) all_131_0_79 = 0
% 32.59/11.84 | (520) all_131_1_80 = 0
% 32.59/11.84 | (480) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 | (475) convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.84 | (523) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 +-Applying beta-rule and splitting (523), into two cases.
% 32.59/11.84 |-Branch one:
% 32.59/11.84 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.84 | (392) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (526) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 32.59/11.84 | (113) all_0_1_1 = 0
% 32.59/11.84 |
% 32.59/11.84 | Equations (113) can reduce 33 to:
% 32.59/11.84 | (114) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (529) all_131_1_80 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 | Applying alpha-rule on (529) yields:
% 32.59/11.84 | (520) all_131_1_80 = 0
% 32.59/11.84 | (391) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.84 |
% 32.59/11.84 | Instantiating formula (10) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.84 | (392) $false
% 32.59/11.84 |
% 32.59/11.84 |-The branch is then unsatisfiable
% 32.59/11.84 |-Branch two:
% 32.59/11.84 | (533) ~ (all_131_1_80 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (533) yields:
% 32.59/11.85 | (534) ~ (all_131_1_80 = 0)
% 32.59/11.85 | (535) convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_131_1_80, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (536) all_131_1_80 = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Equations (536) can reduce 534 to:
% 32.59/11.85 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 | From (536) and (535) follows:
% 32.59/11.85 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (523) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (523), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (526) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 32.59/11.85 | (113) all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (113) can reduce 33 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (545) all_66_1_46 = 0 & all_47_0_44 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (545) yields:
% 32.59/11.85 | (479) all_66_1_46 = 0
% 32.59/11.85 | (305) all_47_0_44 = 0
% 32.59/11.85 | (207) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Combining equations (325,305) yields a new equation:
% 32.59/11.85 | (375) all_29_0_36 = 0
% 32.59/11.85 |
% 32.59/11.85 | Simplifying 375 yields:
% 32.59/11.85 | (210) all_29_0_36 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (210) can reduce 215 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (552) ~ (all_66_1_46 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_66_1_46
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (552) yields:
% 32.59/11.85 | (553) ~ (all_66_1_46 = 0)
% 32.59/11.85 | (554) convergent_lines(all_0_4_4, all_0_2_2) = all_66_1_46
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_66_1_46, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_66_1_46, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (555) all_66_1_46 = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Equations (555) can reduce 553 to:
% 32.59/11.85 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 | From (555) and (554) follows:
% 32.59/11.85 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (192), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (482) (all_71_0_53 = 0 & all_71_1_54 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_71_1_54 = 0 & all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (482), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (483) all_71_0_53 = 0 & all_71_1_54 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (483) yields:
% 32.59/11.85 | (484) all_71_0_53 = 0
% 32.59/11.85 | (485) all_71_1_54 = 0
% 32.59/11.85 | (486) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (489) all_71_1_54 = 0 & all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (489) yields:
% 32.59/11.85 | (485) all_71_1_54 = 0
% 32.59/11.85 | (113) all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (113) can reduce 33 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (493) ~ (all_71_1_54 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (493) yields:
% 32.59/11.85 | (494) ~ (all_71_1_54 = 0)
% 32.59/11.85 | (495) convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_71_1_54, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_71_1_54, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (496) all_71_1_54 = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Equations (496) can reduce 494 to:
% 32.59/11.85 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 | From (496) and (495) follows:
% 32.59/11.85 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (205), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (499) (all_85_0_72 = 0 & all_85_1_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_85_1_73 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0)
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (499), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (500) all_85_0_72 = 0 & all_85_1_73 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (500) yields:
% 32.59/11.85 | (501) all_85_0_72 = 0
% 32.59/11.85 | (502) all_85_1_73 = 0
% 32.59/11.85 | (486) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (506) all_85_1_73 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (506) yields:
% 32.59/11.85 | (502) all_85_1_73 = 0
% 32.59/11.85 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields:
% 32.59/11.85 | (113) all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (113) can reduce 33 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (511) ~ (all_85_1_73 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (511) yields:
% 32.59/11.85 | (512) ~ (all_85_1_73 = 0)
% 32.59/11.85 | (513) convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_85_1_73, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_85_1_73, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (514) all_85_1_73 = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Equations (514) can reduce 512 to:
% 32.59/11.85 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 | From (514) and (513) follows:
% 32.59/11.85 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (347), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (517) (all_131_0_79 = 0 & all_131_1_80 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_131_1_80 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (517), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (518) all_131_0_79 = 0 & all_131_1_80 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (518) yields:
% 32.59/11.85 | (519) all_131_0_79 = 0
% 32.59/11.85 | (520) all_131_1_80 = 0
% 32.59/11.85 | (480) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.85 | (475) convergent_lines(all_0_2_2, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (523) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (523), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (526) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 32.59/11.85 | (113) all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (113) can reduce 33 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (529) all_131_1_80 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (529) yields:
% 32.59/11.85 | (520) all_131_1_80 = 0
% 32.59/11.85 | (391) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (533) ~ (all_131_1_80 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80
% 32.59/11.85 |
% 32.59/11.85 | Applying alpha-rule on (533) yields:
% 32.59/11.85 | (534) ~ (all_131_1_80 = 0)
% 32.59/11.85 | (535) convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (62) with all_0_4_4, all_0_2_2, all_131_1_80, all_0_1_1 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_131_1_80, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (536) all_131_1_80 = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Equations (536) can reduce 534 to:
% 32.59/11.85 | (33) ~ (all_0_1_1 = 0)
% 32.59/11.85 |
% 32.59/11.85 | From (536) and (535) follows:
% 32.59/11.85 | (38) convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 32.59/11.85 | (523) all_0_1_1 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 +-Applying beta-rule and splitting (523), into two cases.
% 32.59/11.85 |-Branch one:
% 32.59/11.85 | (487) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 32.59/11.85 |
% 32.59/11.85 | Instantiating formula (10) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 32.59/11.85 | (392) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (526) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 32.59/11.85 | (113) all_0_1_1 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (113) can reduce 33 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (621) ~ (convergent_lines(all_0_2_2, all_0_4_4) = 0)
% 32.59/11.85 | (351) all_27_0_34 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (351) can reduce 361 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (624) ~ (unorthogonal_lines(all_0_4_4, all_0_4_4) = 0)
% 32.59/11.85 | (305) all_47_0_44 = 0
% 32.59/11.85 |
% 32.59/11.85 | Equations (305) can reduce 132 to:
% 32.59/11.85 | (114) $false
% 32.59/11.85 |
% 32.59/11.85 |-The branch is then unsatisfiable
% 32.59/11.85 |-Branch two:
% 32.59/11.85 | (627) ~ (unorthogonal_lines(all_0_4_4, all_0_2_2) = 0)
% 32.59/11.86 | (113) all_0_1_1 = 0
% 32.59/11.86 |
% 32.59/11.86 | Equations (113) can reduce 33 to:
% 32.59/11.86 | (114) $false
% 32.59/11.86 |
% 32.59/11.86 |-The branch is then unsatisfiable
% 32.59/11.86 |-Branch two:
% 32.59/11.86 | (630) ~ (convergent_lines(all_0_3_3, all_0_2_2) = 0)
% 32.59/11.86 | (121) all_0_0_0 = 0
% 32.59/11.86 |
% 32.59/11.86 | Equations (121) can reduce 70 to:
% 32.59/11.86 | (114) $false
% 32.59/11.86 |
% 32.59/11.86 |-The branch is then unsatisfiable
% 32.59/11.86 % SZS output end Proof for theBenchmark
% 32.59/11.86
% 32.59/11.86 11208ms
%------------------------------------------------------------------------------