TSTP Solution File: GEO204+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO204+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 03:48:40 EDT 2022
% Result : Theorem 13.64s 3.83s
% Output : Proof 15.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO204+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 14:13:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.58 ____ _
% 0.49/0.58 ___ / __ \_____(_)___ ________ __________
% 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.58
% 0.49/0.58 A Theorem Prover for First-Order Logic
% 0.49/0.58 (ePrincess v.1.0)
% 0.49/0.58
% 0.49/0.58 (c) Philipp Rümmer, 2009-2015
% 0.49/0.58 (c) Peter Backeman, 2014-2015
% 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.58 Bug reports to peter@backeman.se
% 0.49/0.58
% 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.58
% 0.49/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/0.97 Prover 0: Preprocessing ...
% 2.31/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.31/1.20 Prover 0: Constructing countermodel ...
% 12.38/3.62 Prover 0: gave up
% 12.38/3.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.90/3.66 Prover 1: Preprocessing ...
% 13.27/3.77 Prover 1: Constructing countermodel ...
% 13.64/3.83 Prover 1: proved (208ms)
% 13.64/3.83
% 13.64/3.83 No countermodel exists, formula is valid
% 13.64/3.83 % SZS status Theorem for theBenchmark
% 13.64/3.83
% 13.64/3.83 Generating proof ... found it (size 94)
% 15.42/4.17
% 15.42/4.17 % SZS output start Proof for theBenchmark
% 15.42/4.17 Assumed formulas after preprocessing and simplification:
% 15.42/4.17 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (equal_lines(v4, v5) = v6 & equal_points(v1, v2) = 0 & line_connecting(v0, v2) = v5 & line_connecting(v0, v1) = v4 & distinct_points(v0, v2) = v3 & distinct_points(v0, v1) = 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) & ( ~ (v6 = 0) | ~ (v3 = 0)))
% 15.46/4.22 | 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:
% 15.46/4.22 | (1) equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & equal_points(all_0_5_5, all_0_4_4) = 0 & line_connecting(all_0_6_6, all_0_4_4) = all_0_1_1 & line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2 & distinct_points(all_0_6_6, all_0_4_4) = all_0_3_3 & distinct_points(all_0_6_6, all_0_5_5) = 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) & ( ~ (all_0_0_0 = 0) | ~ (all_0_3_3 = 0))
% 15.66/4.23 |
% 15.66/4.23 | Applying alpha-rule on (1) yields:
% 15.66/4.23 | (2) ! [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))
% 15.66/4.23 | (3) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 15.66/4.23 | (4) ! [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)))
% 15.66/4.23 | (5) equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 15.66/4.23 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 15.66/4.24 | (7) line_connecting(all_0_6_6, all_0_4_4) = all_0_1_1
% 15.66/4.24 | (8) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 15.66/4.24 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 15.66/4.24 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 15.66/4.24 | (11) ! [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)))
% 15.66/4.24 | (12) ! [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)))
% 15.66/4.24 | (13) ! [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)))
% 15.66/4.24 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 15.66/4.24 | (15) ! [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))))
% 15.73/4.24 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 15.73/4.24 | (17) distinct_points(all_0_6_6, all_0_5_5) = 0
% 15.73/4.24 | (18) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 15.73/4.24 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 15.73/4.24 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 15.73/4.24 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 15.73/4.24 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 15.73/4.24 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 15.73/4.24 | (24) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 15.73/4.24 | (25) ! [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)))
% 15.73/4.24 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 15.73/4.24 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 15.73/4.24 | (28) ! [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)))
% 15.73/4.24 | (29) ! [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)
% 15.73/4.24 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 15.73/4.24 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 15.73/4.24 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 15.73/4.24 | (33) line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2
% 15.73/4.24 | (34) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 15.73/4.24 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 15.73/4.25 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 15.73/4.25 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0))
% 15.73/4.25 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ~ (convergent_lines(v2, v1) = 0))
% 15.73/4.25 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 15.73/4.25 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0))
% 15.73/4.25 | (41) ~ (all_0_0_0 = 0) | ~ (all_0_3_3 = 0)
% 15.73/4.25 | (42) equal_points(all_0_5_5, all_0_4_4) = 0
% 15.73/4.25 | (43) ! [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)
% 15.73/4.25 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 15.73/4.25 | (45) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 15.73/4.25 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 15.73/4.25 | (47) distinct_points(all_0_6_6, all_0_4_4) = all_0_3_3
% 15.73/4.25 | (48) ! [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)))
% 15.73/4.25 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 15.73/4.25 | (50) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 15.73/4.25 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 15.73/4.25 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 15.73/4.25 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 15.73/4.25 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 15.73/4.25 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 15.73/4.25 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 15.73/4.25 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 15.73/4.25 | (58) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 15.73/4.25 | (59) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 15.73/4.25 | (60) ! [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))))
% 15.73/4.25 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 15.73/4.25 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 15.73/4.25 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (6) with all_0_6_6, all_0_5_5, 0, all_0_3_3 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.25 | (64) all_0_3_3 = 0 | ~ (distinct_points(all_0_6_6, all_0_5_5) = all_0_3_3)
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 15.73/4.25 | (65) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (58) with all_0_4_4, all_0_5_5 and discharging atoms equal_points(all_0_5_5, all_0_4_4) = 0, yields:
% 15.73/4.25 | (66) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (4) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 15.73/4.25 | (67) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_4_4) = v1 & point(all_0_6_6) = v0 & line(all_0_1_1) = v3 & distinct_points(all_0_6_6, all_0_4_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (4) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 15.73/4.25 | (68) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (point(all_0_5_5) = v1 & point(all_0_6_6) = v0 & line(all_0_2_2) = v3 & distinct_points(all_0_6_6, all_0_5_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 15.73/4.25 |
% 15.73/4.25 | Instantiating formula (19) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_0_3_3, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.25 | (69) all_0_3_3 = 0 | distinct_points(all_0_5_5, all_0_4_4) = 0
% 15.73/4.25 |
% 15.73/4.25 | Instantiating (68) with all_16_0_7, all_16_1_8, all_16_2_9, all_16_3_10 yields:
% 15.73/4.25 | (70) point(all_0_5_5) = all_16_2_9 & point(all_0_6_6) = all_16_3_10 & line(all_0_2_2) = all_16_0_7 & distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8 & ( ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0)
% 15.73/4.25 |
% 15.73/4.25 | Applying alpha-rule on (70) yields:
% 15.73/4.25 | (71) line(all_0_2_2) = all_16_0_7
% 15.73/4.25 | (72) distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8
% 15.73/4.25 | (73) point(all_0_5_5) = all_16_2_9
% 15.73/4.25 | (74) ~ (all_16_1_8 = 0) | ~ (all_16_2_9 = 0) | ~ (all_16_3_10 = 0) | all_16_0_7 = 0
% 15.73/4.25 | (75) point(all_0_6_6) = all_16_3_10
% 15.73/4.25 |
% 15.73/4.25 | Instantiating (67) with all_18_0_11, all_18_1_12, all_18_2_13, all_18_3_14 yields:
% 15.73/4.25 | (76) point(all_0_4_4) = all_18_2_13 & point(all_0_6_6) = all_18_3_14 & line(all_0_1_1) = all_18_0_11 & distinct_points(all_0_6_6, all_0_4_4) = all_18_1_12 & ( ~ (all_18_1_12 = 0) | ~ (all_18_2_13 = 0) | ~ (all_18_3_14 = 0) | all_18_0_11 = 0)
% 15.73/4.26 |
% 15.73/4.26 | Applying alpha-rule on (76) yields:
% 15.73/4.26 | (77) line(all_0_1_1) = all_18_0_11
% 15.73/4.26 | (78) point(all_0_4_4) = all_18_2_13
% 15.73/4.26 | (79) distinct_points(all_0_6_6, all_0_4_4) = all_18_1_12
% 15.73/4.26 | (80) point(all_0_6_6) = all_18_3_14
% 15.73/4.26 | (81) ~ (all_18_1_12 = 0) | ~ (all_18_2_13 = 0) | ~ (all_18_3_14 = 0) | all_18_0_11 = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating (66) with all_20_0_15 yields:
% 15.73/4.26 | (82) ~ (all_20_0_15 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_20_0_15
% 15.73/4.26 |
% 15.73/4.26 | Applying alpha-rule on (82) yields:
% 15.73/4.26 | (83) ~ (all_20_0_15 = 0)
% 15.73/4.26 | (84) distinct_points(all_0_5_5, all_0_4_4) = all_20_0_15
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (69), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (85) distinct_points(all_0_5_5, all_0_4_4) = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (6) with all_0_5_5, all_0_4_4, 0, all_20_0_15 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_20_0_15, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 15.73/4.26 | (86) all_20_0_15 = 0
% 15.73/4.26 |
% 15.73/4.26 | Equations (86) can reduce 83 to:
% 15.73/4.26 | (87) $false
% 15.73/4.26 |
% 15.73/4.26 |-The branch is then unsatisfiable
% 15.73/4.26 |-Branch two:
% 15.73/4.26 | (88) ~ (distinct_points(all_0_5_5, all_0_4_4) = 0)
% 15.73/4.26 | (89) all_0_3_3 = 0
% 15.73/4.26 |
% 15.73/4.26 | From (89) and (47) follows:
% 15.73/4.26 | (90) distinct_points(all_0_6_6, all_0_4_4) = 0
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (41), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (91) ~ (all_0_0_0 = 0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (65), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (92) distinct_lines(all_0_2_2, all_0_1_1) = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (6) with all_0_6_6, all_0_4_4, 0, all_18_1_12 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_18_1_12, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 15.73/4.26 | (93) all_18_1_12 = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (6) with all_0_6_6, all_0_5_5, all_16_1_8, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_16_1_8, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.26 | (94) all_16_1_8 = 0
% 15.73/4.26 |
% 15.73/4.26 | From (93) and (79) follows:
% 15.73/4.26 | (90) distinct_points(all_0_6_6, all_0_4_4) = 0
% 15.73/4.26 |
% 15.73/4.26 | From (94) and (72) follows:
% 15.73/4.26 | (17) distinct_points(all_0_6_6, all_0_5_5) = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (48) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.26 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_5_5, all_0_1_1) = v3 & apart_point_and_line(all_0_5_5, all_0_2_2) = v2 & apart_point_and_line(all_0_6_6, all_0_1_1) = v1 & apart_point_and_line(all_0_6_6, all_0_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (48) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 15.73/4.26 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_4_4, all_0_1_1) = v3 & apart_point_and_line(all_0_4_4, all_0_2_2) = v2 & apart_point_and_line(all_0_6_6, all_0_1_1) = v1 & apart_point_and_line(all_0_6_6, all_0_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 15.73/4.26 |
% 15.73/4.26 | Instantiating (97) with all_48_0_16, all_48_1_17, all_48_2_18, all_48_3_19 yields:
% 15.73/4.26 | (99) apart_point_and_line(all_0_5_5, all_0_1_1) = all_48_0_16 & apart_point_and_line(all_0_5_5, all_0_2_2) = all_48_1_17 & apart_point_and_line(all_0_6_6, all_0_1_1) = all_48_2_18 & apart_point_and_line(all_0_6_6, all_0_2_2) = all_48_3_19 & (all_48_0_16 = 0 | all_48_1_17 = 0 | all_48_2_18 = 0 | all_48_3_19 = 0)
% 15.73/4.26 |
% 15.73/4.26 | Applying alpha-rule on (99) yields:
% 15.73/4.26 | (100) all_48_0_16 = 0 | all_48_1_17 = 0 | all_48_2_18 = 0 | all_48_3_19 = 0
% 15.73/4.26 | (101) apart_point_and_line(all_0_5_5, all_0_2_2) = all_48_1_17
% 15.73/4.26 | (102) apart_point_and_line(all_0_6_6, all_0_1_1) = all_48_2_18
% 15.73/4.26 | (103) apart_point_and_line(all_0_5_5, all_0_1_1) = all_48_0_16
% 15.73/4.26 | (104) apart_point_and_line(all_0_6_6, all_0_2_2) = all_48_3_19
% 15.73/4.26 |
% 15.73/4.26 | Instantiating (98) with all_50_0_20, all_50_1_21, all_50_2_22, all_50_3_23 yields:
% 15.73/4.26 | (105) apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_20 & apart_point_and_line(all_0_4_4, all_0_2_2) = all_50_1_21 & apart_point_and_line(all_0_6_6, all_0_1_1) = all_50_2_22 & apart_point_and_line(all_0_6_6, all_0_2_2) = all_50_3_23 & (all_50_0_20 = 0 | all_50_1_21 = 0 | all_50_2_22 = 0 | all_50_3_23 = 0)
% 15.73/4.26 |
% 15.73/4.26 | Applying alpha-rule on (105) yields:
% 15.73/4.26 | (106) apart_point_and_line(all_0_4_4, all_0_2_2) = all_50_1_21
% 15.73/4.26 | (107) apart_point_and_line(all_0_6_6, all_0_1_1) = all_50_2_22
% 15.73/4.26 | (108) all_50_0_20 = 0 | all_50_1_21 = 0 | all_50_2_22 = 0 | all_50_3_23 = 0
% 15.73/4.26 | (109) apart_point_and_line(all_0_4_4, all_0_1_1) = all_50_0_20
% 15.73/4.26 | (110) apart_point_and_line(all_0_6_6, all_0_2_2) = all_50_3_23
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (23) with all_0_6_6, all_0_1_1, all_48_2_18, all_50_2_22 and discharging atoms apart_point_and_line(all_0_6_6, all_0_1_1) = all_50_2_22, apart_point_and_line(all_0_6_6, all_0_1_1) = all_48_2_18, yields:
% 15.73/4.26 | (111) all_50_2_22 = all_48_2_18
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (23) with all_0_6_6, all_0_2_2, all_48_3_19, all_50_3_23 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_50_3_23, apart_point_and_line(all_0_6_6, all_0_2_2) = all_48_3_19, yields:
% 15.73/4.26 | (112) all_50_3_23 = all_48_3_19
% 15.73/4.26 |
% 15.73/4.26 | From (111) and (107) follows:
% 15.73/4.26 | (102) apart_point_and_line(all_0_6_6, all_0_1_1) = all_48_2_18
% 15.73/4.26 |
% 15.73/4.26 | From (112) and (110) follows:
% 15.73/4.26 | (104) apart_point_and_line(all_0_6_6, all_0_2_2) = all_48_3_19
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (55) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 15.73/4.26 | (115) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0)
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (29) with all_20_0_15, all_0_4_4, all_0_1_1, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_20_0_15, yields:
% 15.73/4.26 | (116) all_20_0_15 = 0 | ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (55) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 15.73/4.26 | (117) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0)
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (35) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 15.73/4.26 | (118) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0)
% 15.73/4.26 |
% 15.73/4.26 | Instantiating formula (35) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms line_connecting(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 15.73/4.26 | (119) ~ (apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (64), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (120) ~ (distinct_points(all_0_6_6, all_0_5_5) = all_0_3_3)
% 15.73/4.26 |
% 15.73/4.26 | From (89) and (120) follows:
% 15.73/4.26 | (121) ~ (distinct_points(all_0_6_6, all_0_5_5) = 0)
% 15.73/4.26 |
% 15.73/4.26 | Using (17) and (121) yields:
% 15.73/4.26 | (122) $false
% 15.73/4.26 |
% 15.73/4.26 |-The branch is then unsatisfiable
% 15.73/4.26 |-Branch two:
% 15.73/4.26 | (123) distinct_points(all_0_6_6, all_0_5_5) = all_0_3_3
% 15.73/4.26 | (89) all_0_3_3 = 0
% 15.73/4.26 |
% 15.73/4.26 | From (89) and (123) follows:
% 15.73/4.26 | (17) distinct_points(all_0_6_6, all_0_5_5) = 0
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (119), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (126) ~ (apart_point_and_line(all_0_6_6, all_0_2_2) = 0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (118), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (127) ~ (apart_point_and_line(all_0_6_6, all_0_1_1) = 0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (117), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (128) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (115), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (129) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0)
% 15.73/4.26 |
% 15.73/4.26 +-Applying beta-rule and splitting (116), into two cases.
% 15.73/4.26 |-Branch one:
% 15.73/4.26 | (130) ~ (apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 15.73/4.26 |
% 15.73/4.26 | Using (103) and (130) yields:
% 15.73/4.26 | (131) ~ (all_48_0_16 = 0)
% 15.73/4.26 |
% 15.73/4.26 | Using (101) and (128) yields:
% 15.73/4.26 | (132) ~ (all_48_1_17 = 0)
% 15.73/4.26 |
% 15.73/4.27 | Using (102) and (127) yields:
% 15.73/4.27 | (133) ~ (all_48_2_18 = 0)
% 15.73/4.27 |
% 15.73/4.27 | Using (104) and (126) yields:
% 15.73/4.27 | (134) ~ (all_48_3_19 = 0)
% 15.73/4.27 |
% 15.73/4.27 +-Applying beta-rule and splitting (100), into two cases.
% 15.73/4.27 |-Branch one:
% 15.73/4.27 | (135) all_48_0_16 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (135) can reduce 131 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (131) ~ (all_48_0_16 = 0)
% 15.73/4.27 | (138) all_48_1_17 = 0 | all_48_2_18 = 0 | all_48_3_19 = 0
% 15.73/4.27 |
% 15.73/4.27 +-Applying beta-rule and splitting (138), into two cases.
% 15.73/4.27 |-Branch one:
% 15.73/4.27 | (139) all_48_1_17 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (139) can reduce 132 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (132) ~ (all_48_1_17 = 0)
% 15.73/4.27 | (142) all_48_2_18 = 0 | all_48_3_19 = 0
% 15.73/4.27 |
% 15.73/4.27 +-Applying beta-rule and splitting (142), into two cases.
% 15.73/4.27 |-Branch one:
% 15.73/4.27 | (143) all_48_2_18 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (143) can reduce 133 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (133) ~ (all_48_2_18 = 0)
% 15.73/4.27 | (146) all_48_3_19 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (146) can reduce 134 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (148) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 15.73/4.27 | (149) all_20_0_15 = 0 | apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 15.73/4.27 |
% 15.73/4.27 +-Applying beta-rule and splitting (149), into two cases.
% 15.73/4.27 |-Branch one:
% 15.73/4.27 | (150) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 15.73/4.27 |
% 15.73/4.27 | Using (150) and (129) yields:
% 15.73/4.27 | (122) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (129) ~ (apart_point_and_line(all_0_4_4, all_0_1_1) = 0)
% 15.73/4.27 | (86) all_20_0_15 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (86) can reduce 83 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (150) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 15.73/4.27 | (156) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0)
% 15.73/4.27 |
% 15.73/4.27 | Instantiating (156) with all_79_0_24 yields:
% 15.73/4.27 | (157) ~ (all_79_0_24 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_79_0_24
% 15.73/4.27 |
% 15.73/4.27 | Applying alpha-rule on (157) yields:
% 15.73/4.27 | (158) ~ (all_79_0_24 = 0)
% 15.73/4.27 | (159) distinct_points(all_0_6_6, all_0_4_4) = all_79_0_24
% 15.73/4.27 |
% 15.73/4.27 | Instantiating formula (6) with all_0_6_6, all_0_4_4, all_79_0_24, 0 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_79_0_24, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 15.73/4.27 | (160) all_79_0_24 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (160) can reduce 158 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (162) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 15.73/4.27 | (163) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0)
% 15.73/4.27 |
% 15.73/4.27 | Instantiating (163) with all_75_0_25 yields:
% 15.73/4.27 | (164) ~ (all_75_0_25 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_75_0_25
% 15.73/4.27 |
% 15.73/4.27 | Applying alpha-rule on (164) yields:
% 15.73/4.27 | (165) ~ (all_75_0_25 = 0)
% 15.73/4.27 | (166) distinct_points(all_0_6_6, all_0_5_5) = all_75_0_25
% 15.73/4.27 |
% 15.73/4.27 | Instantiating formula (6) with all_0_6_6, all_0_5_5, all_75_0_25, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_75_0_25, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.27 | (167) all_75_0_25 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (167) can reduce 165 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (169) apart_point_and_line(all_0_6_6, all_0_1_1) = 0
% 15.73/4.27 | (156) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0)
% 15.73/4.27 |
% 15.73/4.27 | Instantiating (156) with all_71_0_26 yields:
% 15.73/4.27 | (171) ~ (all_71_0_26 = 0) & distinct_points(all_0_6_6, all_0_4_4) = all_71_0_26
% 15.73/4.27 |
% 15.73/4.27 | Applying alpha-rule on (171) yields:
% 15.73/4.27 | (172) ~ (all_71_0_26 = 0)
% 15.73/4.27 | (173) distinct_points(all_0_6_6, all_0_4_4) = all_71_0_26
% 15.73/4.27 |
% 15.73/4.27 | Instantiating formula (6) with all_0_6_6, all_0_4_4, all_71_0_26, 0 and discharging atoms distinct_points(all_0_6_6, all_0_4_4) = all_71_0_26, distinct_points(all_0_6_6, all_0_4_4) = 0, yields:
% 15.73/4.27 | (174) all_71_0_26 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (174) can reduce 172 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (176) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 15.73/4.27 | (163) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0)
% 15.73/4.27 |
% 15.73/4.27 | Instantiating (163) with all_67_0_27 yields:
% 15.73/4.27 | (178) ~ (all_67_0_27 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_67_0_27
% 15.73/4.27 |
% 15.73/4.27 | Applying alpha-rule on (178) yields:
% 15.73/4.27 | (179) ~ (all_67_0_27 = 0)
% 15.73/4.27 | (180) distinct_points(all_0_6_6, all_0_5_5) = all_67_0_27
% 15.73/4.27 |
% 15.73/4.27 | Instantiating formula (6) with all_0_6_6, all_0_5_5, all_67_0_27, 0 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_67_0_27, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 15.73/4.27 | (181) all_67_0_27 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (181) can reduce 179 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (183) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0)
% 15.73/4.27 | (184) all_0_0_0 = 0
% 15.73/4.27 |
% 15.73/4.27 | Equations (184) can reduce 91 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 |-Branch two:
% 15.73/4.27 | (184) all_0_0_0 = 0
% 15.73/4.27 | (187) ~ (all_0_3_3 = 0)
% 15.73/4.27 |
% 15.73/4.27 | Equations (89) can reduce 187 to:
% 15.73/4.27 | (87) $false
% 15.73/4.27 |
% 15.73/4.27 |-The branch is then unsatisfiable
% 15.73/4.27 % SZS output end Proof for theBenchmark
% 15.73/4.27
% 15.73/4.27 3676ms
%------------------------------------------------------------------------------