TSTP Solution File: GEO225+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:57 EDT 2022
% Result : Theorem 13.31s 3.85s
% Output : Proof 15.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jun 18 10:58:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.60 ____ _
% 0.53/0.60 ___ / __ \_____(_)___ ________ __________
% 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.60
% 0.53/0.60 A Theorem Prover for First-Order Logic
% 0.53/0.60 (ePrincess v.1.0)
% 0.53/0.60
% 0.53/0.60 (c) Philipp Rümmer, 2009-2015
% 0.53/0.60 (c) Peter Backeman, 2014-2015
% 0.53/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.61 Bug reports to peter@backeman.se
% 0.53/0.61
% 0.53/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.61
% 0.53/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.78/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.98 Prover 0: Preprocessing ...
% 2.29/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.47/1.24 Prover 0: Constructing countermodel ...
% 11.37/3.39 Prover 0: gave up
% 11.37/3.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 11.65/3.43 Prover 1: Preprocessing ...
% 11.93/3.54 Prover 1: Constructing countermodel ...
% 12.38/3.56 Prover 1: gave up
% 12.38/3.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 12.53/3.59 Prover 2: Preprocessing ...
% 13.06/3.76 Prover 2: Warning: ignoring some quantifiers
% 13.31/3.77 Prover 2: Constructing countermodel ...
% 13.31/3.85 Prover 2: proved (285ms)
% 13.31/3.85
% 13.31/3.85 No countermodel exists, formula is valid
% 13.31/3.85 % SZS status Theorem for theBenchmark
% 13.31/3.85
% 13.31/3.85 Generating proof ... Warning: ignoring some quantifiers
% 15.21/4.19 found it (size 52)
% 15.21/4.19
% 15.21/4.19 % SZS output start Proof for theBenchmark
% 15.21/4.19 Assumed formulas after preprocessing and simplification:
% 15.21/4.19 | (0) ? [v0] : ? [v1] : (point(v1) = 0 & point(v0) = 0 & distinct_points(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = 0) | ? [v8] : ((v8 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v3) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v4, v5) = v7) | ~ (apart_point_and_line(v2, v3) = v6) | ? [v8] : ((v8 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v3, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ? [v8] : ((v8 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unorthogonal_lines(v3, v5) = v7) | ~ (apart_point_and_line(v2, v3) = v6) | ~ (distinct_lines(v3, v4) = 0) | ? [v8] : ((v8 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v3, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v2, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v2, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (unorthogonal_lines(v2, v4) = v6) | ~ (unorthogonal_lines(v2, v3) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v4, v3) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v4) = v6) | ~ (apart_point_and_line(v2, v3) = v5) | ? [v7] : ((v7 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v4) = v5) | ~ (convergent_lines(v3, v4) = v6) | ? [v7] : ((v7 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v3) = v5) | ~ (convergent_lines(v3, v4) = v6) | ? [v7] : ((v7 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v3, v4) = v6) | ~ (convergent_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v3, v4) = v6) | ~ (distinct_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) | ~ (unorthogonal_lines(v2, v4) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) | ~ (convergent_lines(v2, v4) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v6) | ~ (unorthogonal_lines(v2, v3) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v6) | ~ (convergent_lines(v2, v3) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v5) | ~ (convergent_lines(v3, v4) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unorthogonal_lines(v2, v3) = v5) | ~ (convergent_lines(v2, v4) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v3, v4) = v6) | ~ (convergent_lines(v2, v4) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (convergent_lines(v2, v4) = v6) | ~ (convergent_lines(v2, v3) = v5) | ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unorthogonal_lines(v2, v4) = v5) | ~ (convergent_lines(v3, v4) = 0) | unorthogonal_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (convergent_lines(v3, v4) = 0) | unorthogonal_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v4, v3) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v4) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v4) = v5) | ~ (distinct_lines(v3, v4) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v2, v3) = 0) | (v6 = 0 & convergent_lines(v3, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = v5) | ~ (distinct_lines(v3, v4) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v2, v4) = 0) | (v6 = 0 & convergent_lines(v3, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v2, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v3, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (orthogonal_lines(v5, v4) = v3) | ~ (orthogonal_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (incident_point_and_line(v5, v4) = v3) | ~ (incident_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_lines(v5, v4) = v3) | ~ (parallel_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equal_lines(v5, v4) = v3) | ~ (equal_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equal_points(v5, v4) = v3) | ~ (equal_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (orthogonal_through_point(v5, v4) = v3) | ~ (orthogonal_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unorthogonal_lines(v5, v4) = v3) | ~ (unorthogonal_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_through_point(v5, v4) = v3) | ~ (parallel_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection_point(v5, v4) = v3) | ~ (intersection_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (line_connecting(v5, v4) = v3) | ~ (line_connecting(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apart_point_and_line(v5, v4) = v3) | ~ (apart_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (convergent_lines(v5, v4) = v3) | ~ (convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_lines(v5, v4) = v3) | ~ (distinct_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_points(v5, v4) = v3) | ~ (distinct_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = v5) | ~ (unorthogonal_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (unorthogonal_lines(v2, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (unorthogonal_lines(v2, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (convergent_lines(v2, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) | ~ (convergent_lines(v2, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) | ~ (unorthogonal_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) | ~ (convergent_lines(v3, v4) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = v5) | ~ (convergent_lines(v3, v4) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = 0) | ~ (convergent_lines(v3, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = 0) | ~ (convergent_lines(v2, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (convergent_lines(v3, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (convergent_lines(v3, v4) = 0) | ~ (convergent_lines(v2, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (convergent_lines(v3, v4) = 0) | ~ (convergent_lines(v2, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (distinct_points(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v5) = 0) | (v6 = 0 & apart_point_and_line(v3, v4) = 0) | (v6 = 0 & apart_point_and_line(v2, v5) = 0) | (v6 = 0 & apart_point_and_line(v2, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (orthogonal_lines(v2, v3) = v4) | unorthogonal_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (incident_point_and_line(v2, v3) = v4) | apart_point_and_line(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (parallel_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_lines(v2, v3) = v4) | distinct_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equal_points(v2, v3) = v4) | distinct_points(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v4) | orthogonal_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (apart_point_and_line(v2, v3) = v4) | incident_point_and_line(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v2, v3) = v4) | parallel_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v2, v3) = v4) | unorthogonal_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (distinct_lines(v2, v3) = v4) | equal_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (distinct_points(v2, v3) = v4) | equal_points(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (point(v4) = v3) | ~ (point(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (line(v4) = v3) | ~ (line(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & unorthogonal_lines(v4, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v4, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & point(v4) = 0) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v3) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & point(v2) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (line(v2) = v3)) & ! [v2] : ! [v3] : ( ~ (orthogonal_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & unorthogonal_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (incident_point_and_line(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & apart_point_and_line(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (parallel_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & convergent_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (equal_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & distinct_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (equal_points(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & distinct_points(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & orthogonal_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & incident_point_and_line(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v3) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v2) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & point(v4) = 0 & intersection_point(v2, v3) = v4) | ( ~ (v4 = 0) & line(v3) = v4) | ( ~ (v4 = 0) & line(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & parallel_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & equal_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v3, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & line(v4) = 0 & line_connecting(v2, v3) = v4) | ( ~ (v4 = 0) & point(v3) = v4) | ( ~ (v4 = 0) & point(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & equal_points(v2, v3) = v4)) & ! [v2] : ( ~ (incident_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v0, v2) = v3)) & ! [v2] : ( ~ (incident_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v1, v2) = v3)) & ! [v2] : ~ (convergent_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_points(v2, v2) = 0) & ? [v2] : ? [v3] : ? [v4] : orthogonal_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : incident_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : parallel_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : equal_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : equal_points(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : orthogonal_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : unorthogonal_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : parallel_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : intersection_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : line_connecting(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : apart_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_points(v3, v2) = v4 & ? [v2] : ? [v3] : point(v2) = v3 & ? [v2] : ? [v3] : line(v2) = v3)
% 15.53/4.25 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 15.53/4.25 | (1) point(all_0_0_0) = 0 & point(all_0_1_1) = 0 & distinct_points(all_0_1_1, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (line(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ( ~ (incident_point_and_line(all_0_0_0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(all_0_1_1, v0) = v1)) & ! [v0] : ( ~ (incident_point_and_line(all_0_1_1, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(all_0_0_0, v0) = v1)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1
% 15.53/4.28 |
% 15.53/4.28 | Applying alpha-rule on (1) yields:
% 15.53/4.28 | (2) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 15.53/4.28 | (3) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 15.53/4.28 | (4) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 15.53/4.28 | (5) ! [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)))
% 15.53/4.28 | (6) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 15.53/4.28 | (7) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 15.53/4.28 | (8) ! [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)))
% 15.53/4.28 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 15.53/4.28 | (10) ! [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)))
% 15.53/4.28 | (11) ! [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)))
% 15.53/4.28 | (12) ! [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))
% 15.53/4.28 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 15.53/4.28 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 15.53/4.28 | (15) ! [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)))
% 15.53/4.28 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 15.53/4.28 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 15.53/4.28 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 15.53/4.28 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 15.53/4.28 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 15.53/4.28 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 15.53/4.28 | (22) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 15.53/4.28 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 15.53/4.28 | (24) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 15.53/4.28 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 15.53/4.28 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 15.53/4.28 | (27) ! [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)))
% 15.53/4.28 | (28) ! [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)))
% 15.53/4.28 | (29) ! [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)))
% 15.53/4.28 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 15.53/4.28 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 15.53/4.28 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (line(v0) = v1))
% 15.53/4.28 | (33) ! [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)))
% 15.53/4.28 | (34) ! [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)))
% 15.53/4.29 | (35) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 15.53/4.29 | (36) ! [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)))
% 15.53/4.29 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 15.53/4.29 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 15.53/4.29 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 15.53/4.29 | (40) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 15.53/4.29 | (41) ! [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)))
% 15.53/4.29 | (42) ! [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)))
% 15.53/4.29 | (43) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 15.53/4.29 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 15.53/4.29 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 15.53/4.29 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 15.53/4.29 | (47) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 15.53/4.29 | (48) distinct_points(all_0_1_1, all_0_0_0) = 0
% 15.53/4.29 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 15.53/4.29 | (50) ! [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)))
% 15.53/4.29 | (51) ! [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))
% 15.53/4.29 | (52) ! [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)))
% 15.53/4.29 | (53) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 15.53/4.29 | (54) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 15.53/4.29 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 15.53/4.29 | (56) ! [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)))
% 15.53/4.29 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 15.53/4.29 | (58) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 15.53/4.29 | (59) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 15.53/4.29 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 15.53/4.29 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 15.53/4.29 | (62) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 15.53/4.29 | (63) ! [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)
% 15.53/4.29 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 15.53/4.29 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 15.53/4.29 | (66) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 15.53/4.29 | (67) ? [v0] : ? [v1] : point(v0) = v1
% 15.53/4.29 | (68) ! [v0] : ( ~ (incident_point_and_line(all_0_1_1, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(all_0_0_0, v0) = v1))
% 15.53/4.29 | (69) ! [v0] : ( ~ (incident_point_and_line(all_0_0_0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(all_0_1_1, v0) = v1))
% 15.53/4.29 | (70) ! [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)))
% 15.53/4.29 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 15.53/4.29 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 15.53/4.29 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 15.53/4.29 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 15.53/4.29 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 15.53/4.29 | (76) ! [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))
% 15.53/4.30 | (77) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 15.53/4.30 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 15.53/4.30 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 15.53/4.30 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 15.53/4.30 | (81) ! [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)))
% 15.53/4.30 | (82) ! [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)))
% 15.53/4.30 | (83) ! [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)))
% 15.53/4.30 | (84) ! [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))
% 15.53/4.30 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 15.53/4.30 | (86) ! [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)
% 15.53/4.30 | (87) ! [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)
% 15.53/4.30 | (88) ! [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)))
% 15.53/4.30 | (89) ! [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)))
% 15.53/4.30 | (90) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 15.53/4.30 | (91) ! [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)))
% 15.53/4.30 | (92) ! [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))
% 15.53/4.30 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 15.53/4.30 | (94) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 15.53/4.30 | (95) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 15.53/4.30 | (96) ! [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)))
% 15.53/4.30 | (97) ! [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)))
% 15.53/4.30 | (98) ? [v0] : ? [v1] : line(v0) = v1
% 15.53/4.30 | (99) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 15.53/4.30 | (100) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 15.53/4.30 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 15.53/4.30 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 15.53/4.30 | (103) ! [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))
% 15.53/4.30 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 15.53/4.30 | (105) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 15.53/4.30 | (106) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 15.53/4.30 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 15.53/4.30 | (108) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 15.53/4.30 | (109) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 15.53/4.30 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 15.53/4.30 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 15.53/4.30 | (112) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 15.53/4.30 | (113) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 15.53/4.30 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 15.53/4.30 | (115) ! [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)))
% 15.53/4.30 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 15.53/4.30 | (117) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 15.53/4.30 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 15.53/4.30 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 15.53/4.30 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 15.53/4.31 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 15.53/4.31 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 15.53/4.31 | (123) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 15.53/4.31 | (124) point(all_0_1_1) = 0
% 15.53/4.31 | (125) ! [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)))
% 15.53/4.31 | (126) ! [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)))
% 15.53/4.31 | (127) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 15.53/4.31 | (128) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 15.53/4.31 | (129) point(all_0_0_0) = 0
% 15.53/4.31 | (130) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 15.53/4.31 | (131) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 15.53/4.31 | (132) ! [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)))
% 15.53/4.31 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 15.53/4.31 | (134) ! [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)))
% 15.53/4.31 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 15.53/4.31 | (136) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 15.53/4.31 | (137) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 15.53/4.31 | (138) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 15.53/4.31 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 15.53/4.31 | (140) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 15.53/4.31 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 15.53/4.31 | (142) ! [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)
% 15.53/4.31 | (143) ! [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)))
% 15.53/4.31 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 15.53/4.31 | (145) ! [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)))
% 15.53/4.31 |
% 15.53/4.31 | Instantiating formula (54) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 15.53/4.31 | (146) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_0_0, v0) = v1)
% 15.53/4.31 |
% 15.53/4.31 | Instantiating formula (77) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 15.53/4.31 | (147) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(all_0_1_1, v0) = v1)
% 15.53/4.31 |
% 15.53/4.31 | Instantiating formula (66) with all_0_0_0, all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 15.53/4.31 | (148) ? [v0] : ? [v1] : ((v1 = 0 & line(v0) = 0 & line_connecting(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & point(all_0_0_0) = v0) | ( ~ (v0 = 0) & point(all_0_1_1) = v0))
% 15.53/4.31 |
% 15.53/4.31 | Instantiating (147) with all_46_0_49, all_46_1_50 yields:
% 15.53/4.31 | (149) ~ (all_46_0_49 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_46_1_50 & apart_point_and_line(all_0_1_1, all_46_1_50) = all_46_0_49
% 15.53/4.31 |
% 15.53/4.31 | Applying alpha-rule on (149) yields:
% 15.53/4.31 | (150) ~ (all_46_0_49 = 0)
% 15.53/4.31 | (151) line_connecting(all_0_1_1, all_0_0_0) = all_46_1_50
% 15.53/4.31 | (152) apart_point_and_line(all_0_1_1, all_46_1_50) = all_46_0_49
% 15.53/4.31 |
% 15.53/4.31 | Instantiating (146) with all_48_0_51, all_48_1_52 yields:
% 15.53/4.31 | (153) ~ (all_48_0_51 = 0) & line_connecting(all_0_1_1, all_0_0_0) = all_48_1_52 & apart_point_and_line(all_0_0_0, all_48_1_52) = all_48_0_51
% 15.53/4.31 |
% 15.53/4.31 | Applying alpha-rule on (153) yields:
% 15.53/4.31 | (154) ~ (all_48_0_51 = 0)
% 15.53/4.31 | (155) line_connecting(all_0_1_1, all_0_0_0) = all_48_1_52
% 15.53/4.31 | (156) apart_point_and_line(all_0_0_0, all_48_1_52) = all_48_0_51
% 15.53/4.31 |
% 15.53/4.31 | Instantiating (148) with all_50_0_53, all_50_1_54 yields:
% 15.53/4.31 | (157) (all_50_0_53 = 0 & line(all_50_1_54) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54) | ( ~ (all_50_1_54 = 0) & point(all_0_0_0) = all_50_1_54) | ( ~ (all_50_1_54 = 0) & point(all_0_1_1) = all_50_1_54)
% 15.53/4.31 |
% 15.53/4.31 +-Applying beta-rule and splitting (157), into two cases.
% 15.53/4.31 |-Branch one:
% 15.53/4.31 | (158) (all_50_0_53 = 0 & line(all_50_1_54) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54) | ( ~ (all_50_1_54 = 0) & point(all_0_0_0) = all_50_1_54)
% 15.84/4.31 |
% 15.84/4.31 +-Applying beta-rule and splitting (158), into two cases.
% 15.84/4.31 |-Branch one:
% 15.84/4.31 | (159) all_50_0_53 = 0 & line(all_50_1_54) = 0 & line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54
% 15.84/4.31 |
% 15.84/4.31 | Applying alpha-rule on (159) yields:
% 15.84/4.31 | (160) all_50_0_53 = 0
% 15.84/4.31 | (161) line(all_50_1_54) = 0
% 15.84/4.31 | (162) line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54
% 15.84/4.31 |
% 15.84/4.31 | Instantiating formula (116) with all_0_1_1, all_0_0_0, all_48_1_52, all_50_1_54 and discharging atoms line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54, line_connecting(all_0_1_1, all_0_0_0) = all_48_1_52, yields:
% 15.84/4.31 | (163) all_50_1_54 = all_48_1_52
% 15.84/4.31 |
% 15.84/4.31 | Instantiating formula (116) with all_0_1_1, all_0_0_0, all_46_1_50, all_50_1_54 and discharging atoms line_connecting(all_0_1_1, all_0_0_0) = all_50_1_54, line_connecting(all_0_1_1, all_0_0_0) = all_46_1_50, yields:
% 15.84/4.31 | (164) all_50_1_54 = all_46_1_50
% 15.84/4.31 |
% 15.84/4.31 | Combining equations (163,164) yields a new equation:
% 15.84/4.31 | (165) all_48_1_52 = all_46_1_50
% 15.84/4.31 |
% 15.84/4.31 | Simplifying 165 yields:
% 15.84/4.31 | (166) all_48_1_52 = all_46_1_50
% 15.84/4.32 |
% 15.84/4.32 | From (166) and (156) follows:
% 15.84/4.32 | (167) apart_point_and_line(all_0_0_0, all_46_1_50) = all_48_0_51
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (83) with all_48_0_51, all_48_0_51, all_46_1_50, all_46_1_50, all_0_0_0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_0_0, all_46_1_50) = all_48_0_51, distinct_points(all_0_1_1, all_0_0_0) = 0, yields:
% 15.84/4.32 | (168) all_48_0_51 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (56) with all_48_0_51, all_48_0_51, all_46_1_50, all_46_1_50, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_46_1_50) = all_48_0_51, yields:
% 15.84/4.32 | (169) all_48_0_51 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_46_1_50, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (105) with all_48_0_51, all_46_1_50, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_46_1_50) = all_48_0_51, yields:
% 15.84/4.32 | (170) all_48_0_51 = 0 | incident_point_and_line(all_0_0_0, all_46_1_50) = 0
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (56) with all_46_0_49, all_46_0_49, all_46_1_50, all_46_1_50, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_46_1_50) = all_46_0_49, yields:
% 15.84/4.32 | (171) all_46_0_49 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_46_1_50, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (105) with all_46_0_49, all_46_1_50, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_46_1_50) = all_46_0_49, yields:
% 15.84/4.32 | (172) all_46_0_49 = 0 | incident_point_and_line(all_0_1_1, all_46_1_50) = 0
% 15.84/4.32 |
% 15.84/4.32 +-Applying beta-rule and splitting (171), into two cases.
% 15.84/4.32 |-Branch one:
% 15.84/4.32 | (173) all_46_0_49 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (173) can reduce 150 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (150) ~ (all_46_0_49 = 0)
% 15.84/4.32 | (176) ? [v0] : ((v0 = 0 & convergent_lines(all_46_1_50, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 +-Applying beta-rule and splitting (172), into two cases.
% 15.84/4.32 |-Branch one:
% 15.84/4.32 | (177) incident_point_and_line(all_0_1_1, all_46_1_50) = 0
% 15.84/4.32 |
% 15.84/4.32 +-Applying beta-rule and splitting (169), into two cases.
% 15.84/4.32 |-Branch one:
% 15.84/4.32 | (178) all_48_0_51 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (178) can reduce 154 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (154) ~ (all_48_0_51 = 0)
% 15.84/4.32 | (176) ? [v0] : ((v0 = 0 & convergent_lines(all_46_1_50, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 +-Applying beta-rule and splitting (168), into two cases.
% 15.84/4.32 |-Branch one:
% 15.84/4.32 | (178) all_48_0_51 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (178) can reduce 154 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (154) ~ (all_48_0_51 = 0)
% 15.84/4.32 | (185) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_46_1_50) = 0) | ( ~ (v0 = 0) & distinct_lines(all_46_1_50, all_46_1_50) = v0))
% 15.84/4.32 |
% 15.84/4.32 +-Applying beta-rule and splitting (170), into two cases.
% 15.84/4.32 |-Branch one:
% 15.84/4.32 | (186) incident_point_and_line(all_0_0_0, all_46_1_50) = 0
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (68) with all_46_1_50 and discharging atoms incident_point_and_line(all_0_1_1, all_46_1_50) = 0, yields:
% 15.84/4.32 | (187) ? [v0] : ( ~ (v0 = 0) & incident_point_and_line(all_0_0_0, all_46_1_50) = v0)
% 15.84/4.32 |
% 15.84/4.32 | Instantiating (187) with all_123_0_69 yields:
% 15.84/4.32 | (188) ~ (all_123_0_69 = 0) & incident_point_and_line(all_0_0_0, all_46_1_50) = all_123_0_69
% 15.84/4.32 |
% 15.84/4.32 | Applying alpha-rule on (188) yields:
% 15.84/4.32 | (189) ~ (all_123_0_69 = 0)
% 15.84/4.32 | (190) incident_point_and_line(all_0_0_0, all_46_1_50) = all_123_0_69
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (72) with all_0_0_0, all_46_1_50, all_123_0_69, 0 and discharging atoms incident_point_and_line(all_0_0_0, all_46_1_50) = all_123_0_69, incident_point_and_line(all_0_0_0, all_46_1_50) = 0, yields:
% 15.84/4.32 | (191) all_123_0_69 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (191) can reduce 189 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (193) ~ (incident_point_and_line(all_0_0_0, all_46_1_50) = 0)
% 15.84/4.32 | (178) all_48_0_51 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (178) can reduce 154 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (196) ~ (incident_point_and_line(all_0_1_1, all_46_1_50) = 0)
% 15.84/4.32 | (173) all_46_0_49 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (173) can reduce 150 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (199) ~ (all_50_1_54 = 0) & point(all_0_0_0) = all_50_1_54
% 15.84/4.32 |
% 15.84/4.32 | Applying alpha-rule on (199) yields:
% 15.84/4.32 | (200) ~ (all_50_1_54 = 0)
% 15.84/4.32 | (201) point(all_0_0_0) = all_50_1_54
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (110) with all_0_0_0, all_50_1_54, 0 and discharging atoms point(all_0_0_0) = all_50_1_54, point(all_0_0_0) = 0, yields:
% 15.84/4.32 | (202) all_50_1_54 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (202) can reduce 200 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 |-Branch two:
% 15.84/4.32 | (204) ~ (all_50_1_54 = 0) & point(all_0_1_1) = all_50_1_54
% 15.84/4.32 |
% 15.84/4.32 | Applying alpha-rule on (204) yields:
% 15.84/4.32 | (200) ~ (all_50_1_54 = 0)
% 15.84/4.32 | (206) point(all_0_1_1) = all_50_1_54
% 15.84/4.32 |
% 15.84/4.32 | Instantiating formula (110) with all_0_1_1, all_50_1_54, 0 and discharging atoms point(all_0_1_1) = all_50_1_54, point(all_0_1_1) = 0, yields:
% 15.84/4.32 | (202) all_50_1_54 = 0
% 15.84/4.32 |
% 15.84/4.32 | Equations (202) can reduce 200 to:
% 15.84/4.32 | (174) $false
% 15.84/4.32 |
% 15.84/4.32 |-The branch is then unsatisfiable
% 15.84/4.32 % SZS output end Proof for theBenchmark
% 15.84/4.32
% 15.84/4.32 3701ms
%------------------------------------------------------------------------------