TSTP Solution File: GEO203+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO203+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 03:48:39 EDT 2022
% Result : Theorem 21.14s 6.29s
% Output : Proof 23.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO203+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 17 18:46:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.63/0.64 ____ _
% 0.63/0.64 ___ / __ \_____(_)___ ________ __________
% 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.64
% 0.63/0.64 A Theorem Prover for First-Order Logic
% 0.63/0.64 (ePrincess v.1.0)
% 0.63/0.64
% 0.63/0.64 (c) Philipp Rümmer, 2009-2015
% 0.63/0.64 (c) Peter Backeman, 2014-2015
% 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.64 Bug reports to peter@backeman.se
% 0.63/0.64
% 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.64
% 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.84/1.03 Prover 0: Preprocessing ...
% 2.57/1.25 Prover 0: Warning: ignoring some quantifiers
% 2.68/1.28 Prover 0: Constructing countermodel ...
% 19.72/5.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.01/6.05 Prover 1: Preprocessing ...
% 20.64/6.22 Prover 1: Constructing countermodel ...
% 21.14/6.29 Prover 1: proved (305ms)
% 21.14/6.29 Prover 0: stopped
% 21.14/6.29
% 21.14/6.29 No countermodel exists, formula is valid
% 21.14/6.29 % SZS status Theorem for theBenchmark
% 21.14/6.29
% 21.14/6.29 Generating proof ... found it (size 67)
% 22.53/6.59
% 22.53/6.59 % SZS output start Proof for theBenchmark
% 22.53/6.59 Assumed formulas after preprocessing and simplification:
% 22.53/6.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & equal_lines(v5, v0) = v6 & intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_points(v3, v4) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (apart_point_and_line(v7, v8) = v11) | ~ (distinct_lines(v8, v9) = 0) | ? [v13] : ? [v14] : (unorthogonal_lines(v9, v10) = v14 & apart_point_and_line(v7, v9) = v13 & (v14 = 0 | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) | ~ (unorthogonal_lines(v7, v8) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (unorthogonal_lines(v8, v9) = v15 & convergent_lines(v8, v9) = v14 & convergent_lines(v7, v9) = v13 & convergent_lines(v7, v8) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | (v13 = 0 & v11 = 0) | (v12 = 0 & v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v11] : ? [v12] : (apart_point_and_line(v7, v9) = v11 & convergent_lines(v8, v9) = v12 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v7, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v7, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_lines(v10, v9) = v8) | ~ (orthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (incident_point_and_line(v10, v9) = v8) | ~ (incident_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_lines(v10, v9) = v8) | ~ (parallel_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_lines(v10, v9) = v8) | ~ (equal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_points(v10, v9) = v8) | ~ (equal_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (orthogonal_through_point(v10, v9) = v8) | ~ (orthogonal_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unorthogonal_lines(v10, v9) = v8) | ~ (unorthogonal_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (parallel_through_point(v10, v9) = v8) | ~ (parallel_through_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection_point(v10, v9) = v8) | ~ (intersection_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (line_connecting(v10, v9) = v8) | ~ (line_connecting(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apart_point_and_line(v10, v9) = v8) | ~ (apart_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (convergent_lines(v10, v9) = v8) | ~ (convergent_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_lines(v10, v9) = v8) | ~ (distinct_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_points(v10, v9) = v8) | ~ (distinct_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) | ~ (unorthogonal_lines(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (unorthogonal_lines(v8, v9) = v14 & convergent_lines(v8, v9) = v13 & convergent_lines(v7, v9) = v12 & convergent_lines(v7, v8) = v11 & ( ~ (v11 = 0) | (v14 = 0 & v13 = 0) | (v12 = 0 & v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) | ~ (distinct_points(v7, v8) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apart_point_and_line(v8, v10) = v14 & apart_point_and_line(v8, v9) = v13 & apart_point_and_line(v7, v10) = v12 & apart_point_and_line(v7, v9) = v11 & (v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (orthogonal_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (incident_point_and_line(v7, v8) = v9) | apart_point_and_line(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (parallel_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_lines(v7, v8) = v9) | distinct_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_points(v7, v8) = v9) | distinct_points(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (point(v9) = v8) | ~ (point(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (line(v9) = v8) | ~ (line(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ~ (unorthogonal_lines(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) | ~ (apart_point_and_line(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (orthogonal_through_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (point(v8) = v11 & line(v9) = v12 & line(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ~ (apart_point_and_line(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) | ~ (convergent_lines(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (point(v8) = v11 & line(v9) = v12 & line(v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ (apart_point_and_line(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ~ (apart_point_and_line(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (point(v9) = v13 & line(v8) = v11 & line(v7) = v10 & convergent_lines(v7, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ (apart_point_and_line(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ~ (apart_point_and_line(v7, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (point(v8) = v11 & point(v7) = v10 & line(v9) = v13 & distinct_points(v7, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ( ~ (orthogonal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (incident_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (parallel_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_lines(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (equal_points(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | convergent_lines(v7, v8) = 0) & ! [v7] : ~ (convergent_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_points(v7, v7) = 0))
% 22.53/6.63 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 22.53/6.64 | (1) ~ (all_0_0_0 = 0) & equal_lines(all_0_1_1, all_0_6_6) = all_0_0_0 & intersection_point(all_0_6_6, all_0_4_4) = all_0_2_2 & intersection_point(all_0_6_6, all_0_5_5) = all_0_3_3 & line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1 & convergent_lines(all_0_6_6, all_0_4_4) = 0 & convergent_lines(all_0_6_6, all_0_5_5) = 0 & distinct_points(all_0_3_3, all_0_2_2) = 0 & ! [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] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) & ! [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] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 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(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_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(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, 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(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 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) | convergent_lines(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) | ~ (unorthogonal_lines(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))) & ! [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] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 22.87/6.65 |
% 22.87/6.65 | Applying alpha-rule on (1) yields:
% 22.87/6.65 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 22.87/6.65 | (3) convergent_lines(all_0_6_6, all_0_5_5) = 0
% 22.87/6.65 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.87/6.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 22.87/6.65 | (6) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 22.87/6.65 | (7) distinct_points(all_0_3_3, all_0_2_2) = 0
% 22.87/6.65 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 22.87/6.65 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 22.87/6.65 | (10) ! [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)
% 22.87/6.65 | (11) convergent_lines(all_0_6_6, all_0_4_4) = 0
% 22.87/6.65 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 22.87/6.65 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 22.87/6.65 | (14) equal_lines(all_0_1_1, all_0_6_6) = all_0_0_0
% 22.87/6.65 | (15) ! [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)
% 22.87/6.65 | (16) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 22.87/6.65 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 22.87/6.65 | (18) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 22.87/6.65 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.87/6.66 | (20) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 22.87/6.66 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 22.87/6.66 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 22.87/6.66 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 22.87/6.66 | (24) line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1
% 22.87/6.66 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.87/6.66 | (26) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 22.87/6.66 | (27) ~ (all_0_0_0 = 0)
% 22.87/6.66 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 22.87/6.66 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 22.87/6.66 | (30) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 22.87/6.66 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 22.87/6.66 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 22.87/6.66 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 22.87/6.66 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 22.87/6.66 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 22.87/6.66 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 22.87/6.66 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 22.87/6.66 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 22.87/6.66 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 22.87/6.66 | (40) ! [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] : ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 22.87/6.66 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 22.87/6.66 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.87/6.66 | (43) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 22.87/6.66 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.87/6.66 | (45) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 22.87/6.66 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 22.87/6.67 | (47) ! [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))
% 22.87/6.67 | (48) intersection_point(all_0_6_6, all_0_5_5) = all_0_3_3
% 22.87/6.67 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 22.87/6.67 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.87/6.67 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 22.87/6.67 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 22.87/6.67 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 22.87/6.67 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 22.87/6.67 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 22.87/6.67 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 22.87/6.67 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 22.87/6.67 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 22.87/6.67 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 22.87/6.67 | (60) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 23.03/6.67 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 23.03/6.67 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 23.03/6.67 | (63) intersection_point(all_0_6_6, all_0_4_4) = all_0_2_2
% 23.03/6.67 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (61) with all_0_0_0, all_0_6_6, all_0_1_1 and discharging atoms equal_lines(all_0_1_1, all_0_6_6) = all_0_0_0, yields:
% 23.03/6.67 | (65) all_0_0_0 = 0 | distinct_lines(all_0_1_1, all_0_6_6) = 0
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (53) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 23.03/6.67 | (66) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_2_2) = v3 & line(all_0_4_4) = v1 & line(all_0_6_6) = v0 & convergent_lines(all_0_6_6, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (53) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 23.03/6.67 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_3_3) = v3 & line(all_0_5_5) = v1 & line(all_0_6_6) = v0 & convergent_lines(all_0_6_6, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (21) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 23.03/6.67 | (68) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_2_2) = v1 & point(all_0_3_3) = v0 & line(all_0_1_1) = v3 & distinct_points(all_0_3_3, all_0_2_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 23.03/6.67 |
% 23.03/6.67 | Instantiating (68) with all_16_0_7, all_16_1_8, all_16_2_9, all_16_3_10 yields:
% 23.03/6.67 | (69) point(all_0_2_2) = all_16_2_9 & point(all_0_3_3) = all_16_3_10 & line(all_0_1_1) = all_16_0_7 & distinct_points(all_0_3_3, all_0_2_2) = all_16_1_8 & ( ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0)
% 23.03/6.67 |
% 23.03/6.67 | Applying alpha-rule on (69) yields:
% 23.03/6.67 | (70) line(all_0_1_1) = all_16_0_7
% 23.03/6.67 | (71) ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0
% 23.03/6.67 | (72) point(all_0_2_2) = all_16_2_9
% 23.03/6.67 | (73) distinct_points(all_0_3_3, all_0_2_2) = all_16_1_8
% 23.03/6.67 | (74) point(all_0_3_3) = all_16_3_10
% 23.03/6.67 |
% 23.03/6.67 | Instantiating (67) with all_18_0_11, all_18_1_12, all_18_2_13, all_18_3_14 yields:
% 23.03/6.67 | (75) point(all_0_3_3) = all_18_0_11 & line(all_0_5_5) = all_18_2_13 & line(all_0_6_6) = all_18_3_14 & convergent_lines(all_0_6_6, all_0_5_5) = all_18_1_12 & ( ~ (all_18_1_12 = 0) | ~ (all_18_2_13 = 0) | ~ (all_18_3_14 = 0) | all_18_0_11 = 0)
% 23.03/6.67 |
% 23.03/6.67 | Applying alpha-rule on (75) yields:
% 23.03/6.67 | (76) ~ (all_18_1_12 = 0) | ~ (all_18_2_13 = 0) | ~ (all_18_3_14 = 0) | all_18_0_11 = 0
% 23.03/6.67 | (77) point(all_0_3_3) = all_18_0_11
% 23.03/6.67 | (78) line(all_0_5_5) = all_18_2_13
% 23.03/6.67 | (79) convergent_lines(all_0_6_6, all_0_5_5) = all_18_1_12
% 23.03/6.67 | (80) line(all_0_6_6) = all_18_3_14
% 23.03/6.67 |
% 23.03/6.67 | Instantiating (66) with all_20_0_15, all_20_1_16, all_20_2_17, all_20_3_18 yields:
% 23.03/6.67 | (81) point(all_0_2_2) = all_20_0_15 & line(all_0_4_4) = all_20_2_17 & line(all_0_6_6) = all_20_3_18 & convergent_lines(all_0_6_6, all_0_4_4) = all_20_1_16 & ( ~ (all_20_1_16 = 0) | ~ (all_20_2_17 = 0) | ~ (all_20_3_18 = 0) | all_20_0_15 = 0)
% 23.03/6.67 |
% 23.03/6.67 | Applying alpha-rule on (81) yields:
% 23.03/6.67 | (82) line(all_0_4_4) = all_20_2_17
% 23.03/6.67 | (83) line(all_0_6_6) = all_20_3_18
% 23.03/6.67 | (84) ~ (all_20_1_16 = 0) | ~ (all_20_2_17 = 0) | ~ (all_20_3_18 = 0) | all_20_0_15 = 0
% 23.03/6.67 | (85) convergent_lines(all_0_6_6, all_0_4_4) = all_20_1_16
% 23.03/6.67 | (86) point(all_0_2_2) = all_20_0_15
% 23.03/6.67 |
% 23.03/6.67 +-Applying beta-rule and splitting (65), into two cases.
% 23.03/6.67 |-Branch one:
% 23.03/6.67 | (87) distinct_lines(all_0_1_1, all_0_6_6) = 0
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (54) with all_0_6_6, all_0_4_4, all_20_1_16, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = all_20_1_16, convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 23.03/6.67 | (88) all_20_1_16 = 0
% 23.03/6.67 |
% 23.03/6.67 | Instantiating formula (54) with all_0_6_6, all_0_5_5, all_18_1_12, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = all_18_1_12, convergent_lines(all_0_6_6, all_0_5_5) = 0, yields:
% 23.03/6.68 | (89) all_18_1_12 = 0
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (5) with all_0_3_3, all_0_2_2, all_16_1_8, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_16_1_8, distinct_points(all_0_3_3, all_0_2_2) = 0, yields:
% 23.03/6.68 | (90) all_16_1_8 = 0
% 23.03/6.68 |
% 23.03/6.68 | From (88) and (85) follows:
% 23.03/6.68 | (11) convergent_lines(all_0_6_6, all_0_4_4) = 0
% 23.03/6.68 |
% 23.03/6.68 | From (89) and (79) follows:
% 23.03/6.68 | (3) convergent_lines(all_0_6_6, all_0_5_5) = 0
% 23.03/6.68 |
% 23.03/6.68 | From (90) and (73) follows:
% 23.03/6.68 | (7) distinct_points(all_0_3_3, all_0_2_2) = 0
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (37) with all_0_6_6, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms distinct_lines(all_0_1_1, all_0_6_6) = 0, distinct_points(all_0_3_3, all_0_2_2) = 0, yields:
% 23.03/6.68 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_2_2, all_0_1_1) = v2 & apart_point_and_line(all_0_2_2, all_0_6_6) = v3 & apart_point_and_line(all_0_3_3, all_0_1_1) = v0 & apart_point_and_line(all_0_3_3, all_0_6_6) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 23.03/6.68 |
% 23.03/6.68 | Instantiating (94) with all_40_0_19, all_40_1_20, all_40_2_21, all_40_3_22 yields:
% 23.03/6.68 | (95) apart_point_and_line(all_0_2_2, all_0_1_1) = all_40_1_20 & apart_point_and_line(all_0_2_2, all_0_6_6) = all_40_0_19 & apart_point_and_line(all_0_3_3, all_0_1_1) = all_40_3_22 & apart_point_and_line(all_0_3_3, all_0_6_6) = all_40_2_21 & (all_40_0_19 = 0 | all_40_1_20 = 0 | all_40_2_21 = 0 | all_40_3_22 = 0)
% 23.03/6.68 |
% 23.03/6.68 | Applying alpha-rule on (95) yields:
% 23.03/6.68 | (96) apart_point_and_line(all_0_2_2, all_0_1_1) = all_40_1_20
% 23.03/6.68 | (97) apart_point_and_line(all_0_2_2, all_0_6_6) = all_40_0_19
% 23.03/6.68 | (98) apart_point_and_line(all_0_3_3, all_0_1_1) = all_40_3_22
% 23.03/6.68 | (99) apart_point_and_line(all_0_3_3, all_0_6_6) = all_40_2_21
% 23.03/6.68 | (100) all_40_0_19 = 0 | all_40_1_20 = 0 | all_40_2_21 = 0 | all_40_3_22 = 0
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (17) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 23.03/6.68 | (101) ~ (apart_point_and_line(all_0_2_2, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_2_2) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (12) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 23.03/6.68 | (102) ~ (apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 23.03/6.68 | (103) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_2_2) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (12) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 23.03/6.68 | (104) ~ (apart_point_and_line(all_0_3_3, all_0_6_6) = 0) | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_5_5) = v0)
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (104), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (105) ~ (apart_point_and_line(all_0_3_3, all_0_6_6) = 0)
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (102), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (106) ~ (apart_point_and_line(all_0_2_2, all_0_6_6) = 0)
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (101), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (107) ~ (apart_point_and_line(all_0_2_2, all_0_1_1) = 0)
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (103), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (108) ~ (apart_point_and_line(all_0_3_3, all_0_1_1) = 0)
% 23.03/6.68 |
% 23.03/6.68 | Using (96) and (107) yields:
% 23.03/6.68 | (109) ~ (all_40_1_20 = 0)
% 23.03/6.68 |
% 23.03/6.68 | Using (97) and (106) yields:
% 23.03/6.68 | (110) ~ (all_40_0_19 = 0)
% 23.03/6.68 |
% 23.03/6.68 | Using (98) and (108) yields:
% 23.03/6.68 | (111) ~ (all_40_3_22 = 0)
% 23.03/6.68 |
% 23.03/6.68 | Using (99) and (105) yields:
% 23.03/6.68 | (112) ~ (all_40_2_21 = 0)
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (100), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (113) all_40_0_19 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (113) can reduce 110 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (110) ~ (all_40_0_19 = 0)
% 23.03/6.68 | (116) all_40_1_20 = 0 | all_40_2_21 = 0 | all_40_3_22 = 0
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (116), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (117) all_40_1_20 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (117) can reduce 109 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (109) ~ (all_40_1_20 = 0)
% 23.03/6.68 | (120) all_40_2_21 = 0 | all_40_3_22 = 0
% 23.03/6.68 |
% 23.03/6.68 +-Applying beta-rule and splitting (120), into two cases.
% 23.03/6.68 |-Branch one:
% 23.03/6.68 | (121) all_40_2_21 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (121) can reduce 112 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (112) ~ (all_40_2_21 = 0)
% 23.03/6.68 | (124) all_40_3_22 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (124) can reduce 111 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (126) apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 23.03/6.68 | (127) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_2_2) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating (127) with all_65_0_23 yields:
% 23.03/6.68 | (128) ~ (all_65_0_23 = 0) & distinct_points(all_0_3_3, all_0_2_2) = all_65_0_23
% 23.03/6.68 |
% 23.03/6.68 | Applying alpha-rule on (128) yields:
% 23.03/6.68 | (129) ~ (all_65_0_23 = 0)
% 23.03/6.68 | (130) distinct_points(all_0_3_3, all_0_2_2) = all_65_0_23
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (5) with all_0_3_3, all_0_2_2, all_65_0_23, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_65_0_23, distinct_points(all_0_3_3, all_0_2_2) = 0, yields:
% 23.03/6.68 | (131) all_65_0_23 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (131) can reduce 129 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (133) apart_point_and_line(all_0_2_2, all_0_1_1) = 0
% 23.03/6.68 | (127) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_2_2) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating (127) with all_61_0_24 yields:
% 23.03/6.68 | (135) ~ (all_61_0_24 = 0) & distinct_points(all_0_3_3, all_0_2_2) = all_61_0_24
% 23.03/6.68 |
% 23.03/6.68 | Applying alpha-rule on (135) yields:
% 23.03/6.68 | (136) ~ (all_61_0_24 = 0)
% 23.03/6.68 | (137) distinct_points(all_0_3_3, all_0_2_2) = all_61_0_24
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (5) with all_0_3_3, all_0_2_2, all_61_0_24, 0 and discharging atoms distinct_points(all_0_3_3, all_0_2_2) = all_61_0_24, distinct_points(all_0_3_3, all_0_2_2) = 0, yields:
% 23.03/6.68 | (138) all_61_0_24 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (138) can reduce 136 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (140) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 23.03/6.68 | (141) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating (141) with all_57_0_25 yields:
% 23.03/6.68 | (142) ~ (all_57_0_25 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_57_0_25
% 23.03/6.68 |
% 23.03/6.68 | Applying alpha-rule on (142) yields:
% 23.03/6.68 | (143) ~ (all_57_0_25 = 0)
% 23.03/6.68 | (144) convergent_lines(all_0_6_6, all_0_4_4) = all_57_0_25
% 23.03/6.68 |
% 23.03/6.68 | Instantiating formula (54) with all_0_6_6, all_0_4_4, all_57_0_25, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = all_57_0_25, convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 23.03/6.68 | (145) all_57_0_25 = 0
% 23.03/6.68 |
% 23.03/6.68 | Equations (145) can reduce 143 to:
% 23.03/6.68 | (114) $false
% 23.03/6.68 |
% 23.03/6.68 |-The branch is then unsatisfiable
% 23.03/6.68 |-Branch two:
% 23.03/6.68 | (147) apart_point_and_line(all_0_3_3, all_0_6_6) = 0
% 23.03/6.68 | (148) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_5_5) = v0)
% 23.03/6.68 |
% 23.03/6.68 | Instantiating (148) with all_53_0_26 yields:
% 23.03/6.68 | (149) ~ (all_53_0_26 = 0) & convergent_lines(all_0_6_6, all_0_5_5) = all_53_0_26
% 23.03/6.68 |
% 23.03/6.68 | Applying alpha-rule on (149) yields:
% 23.03/6.68 | (150) ~ (all_53_0_26 = 0)
% 23.03/6.68 | (151) convergent_lines(all_0_6_6, all_0_5_5) = all_53_0_26
% 23.03/6.69 |
% 23.03/6.69 | Instantiating formula (54) with all_0_6_6, all_0_5_5, all_53_0_26, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = all_53_0_26, convergent_lines(all_0_6_6, all_0_5_5) = 0, yields:
% 23.03/6.69 | (152) all_53_0_26 = 0
% 23.03/6.69 |
% 23.03/6.69 | Equations (152) can reduce 150 to:
% 23.03/6.69 | (114) $false
% 23.03/6.69 |
% 23.03/6.69 |-The branch is then unsatisfiable
% 23.03/6.69 |-Branch two:
% 23.03/6.69 | (154) ~ (distinct_lines(all_0_1_1, all_0_6_6) = 0)
% 23.03/6.69 | (155) all_0_0_0 = 0
% 23.03/6.69 |
% 23.03/6.69 | Equations (155) can reduce 27 to:
% 23.03/6.69 | (114) $false
% 23.03/6.69 |
% 23.03/6.69 |-The branch is then unsatisfiable
% 23.03/6.69 % SZS output end Proof for theBenchmark
% 23.03/6.69
% 23.03/6.69 6034ms
%------------------------------------------------------------------------------